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ADVANCES IN ELECTRONICS

VOLUME I V

This Page Intentionally Left Blank

ADVANCES IN ELECTRONICS Edited by L. MARTON National Bureau of Standards, Washington, D . C.

Editorial Board T. E. Allibone W. B. Nottingham E. R. Piore H. B. G. Casimir L. T. DeVore M. Ponte W. G. Dow A. Rose L. P. Smith A. 0. C. Nier

VOLUME IV

1952

ACADEMIC PRESS INC., PUBLISHERS NEW YORK, N. Y.

COPYRIGHT@

1952 BY ACADEMIC PRESS INC.

ALL RIGHTS RESERVED NO PART OF THIS BOOK MAY BE REPRODUCED I N ANY FORM BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS

ACADEMIC PRESS INC. 111 FIFTHAVENUE NEW YORK,NEW YORK 10003

United Kingdom Edition Published by

ACADEMIC PRESS INC. (LONDON) LTD. BERKELEY SQUARE HOUSE, LONDON W. 1 First Printing, 1952 Second Printing, 1964

PRINTED I N T HE UNITED STATES OF AMERICA

CONTRIBUTORS TO VOLUME IV

J. S . DONAL,JR., Radio Corporation of America, R C A Laboratories Division, Princeton, New Jersey WINFIELDE. FROMM, Airborne Instruments Laboratory, Inc., Mineola, New York

H. S. W. MASSEY,F. R. S., Department of Mathematics, University College, London, England G. A. MORTON, Radio Corporation of America, R C A Laboratories Division, Princeton, New Jersey M. G. PAWLEY, National Bureau of Standards, Corona, California C. V. L. SMITH,Ofice of Naval Research, Washington, D. C.

W. E. TRIEST,International Business Machines Corporation, Poughkeepsie, New York ALDERT VAN DER ZIEL, Department of Electrical Engineering, Institute of Technology, University of Minnesota, Minneapolis, Minnesota

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PREFACE

Another volume of “Advances in Electronics” the fourth in the series, is now presented to the scientific community. It is with deep satisfaction that members of the Editorial Board note the growing recognition of these volumes. I n fact the book reviews of the past years have been on the average so favorable that, more than anything else, the obligation to keep up with the various reviewers’ expectations, has set the level of this and future volumes. It is sincerely hoped that the present volume will find as favorable a reception as its predecessors.

L. MARTON Washington, D.C.

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CONTENTS CONTRIBUTORS TO VOLUME IV . . . . . . . . . . . . . . . . . . . . . .

v

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

Electron Scattering in Solids

BY H . S. W . MASSEY,F.R.S:, Department of Mathematics. University College, London. England

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I1. Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 3 I11. Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . 17 IV. Multiple Scattering . . . . . . . . . . . . . . . . . . . . . . . . 32 V. Energy Loss of Electrons in Passage through Solids . . . . . . . . . . 48 VI . The Mobility of Electrons in Metals, Alloys and Semi-Conductors . . . 58 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 The Scintillation Counter

.

BYG A . MORTON, Radio Corporation of America, RCA Laboratories Division, Princeton, New Jersey

I . Introduction . . . . . . . . . . . . . . . . . I1. The Photomultiplier . . . . . : . . . . . . . I11. Multiplier Performance . . . . . . . . . . . . . IV . Phosphor Crystals . . . . . . . . . . . . . . . V. Scintillation Counter Applications . . . . . . . References . . . . . . . . . . . . . . . . . .

. . . . . . . . . . 69 . . . . . . . . . . . 71 . . . . . . . . . . 78 88 . . . . . . . . . . . . . . . . . . . . . 94 . . . . . . . . . . 106

Fluctuation Phenomena B Y ALDERTVAN DER ZIEL, Department of Electrical Engineering, Institute of Technology. University of Minnesota, Minneapolis, Minnesota

I . Introduction . . . . . . . . . . . . . I1. Fourier Analysis of Fluctuating Quantities I11. Application t o Various Noise Generators . IV. Noise in Receivers . . . . . . . . . . . References . . . . . . . . . . . . . .

. . . . 110 . . . . 112 . . . . 117 . . . . 147 . . . . 153

Electronic Digital Computers

BY C. V . L. SMITH.Ofice of Naval Research. Washington. D . C .

.

I Introduction . . . . . . . . . . . . I1. Input-Output . . . . . . . . . . . . I11. Internal Storage’. . . . . . . . . . . I V . Arithmetic and Control Organs . . . V. Whirlwind . . . . . . . . . . . . . ix

157 . . . . . . . . . . . . . . . 160 . . . . . . . . . . . . . . . 161 . . . . . . . . . . . . . . . . 171 . . . . . . . . . . . . . . . 174

. . . . . . . . . . . . . . .

X

CONTENTS

.

VI SEAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V I I . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .

180 185

Modulation of Continuous-Wave Magnetrons BY J . S. DONAL, JR.,Radio Corporation of America, R C A Laboratories Division. Princeton. N e w Jersey

I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Frequency Modulation or Control by Spiral Electron Beams . . . . . . I11. Frequency Modulation by Electron Clouds . . . . . . . . . . . . . . IV . Voltage Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . V . Amplitude Modulation Using Absorption by a Spiral Electron Beam . . . VI . Amplitude Modulation by Means of the Electron Coupler . . . . . . . VII . Contro! or hfodulation by Injection Phase Locking . . . . . . . . . . VIII . Amplitude Modulation by Plate Modulation of a Magnetron with Simultaneous Frequency Control . . . . . . . . . . . . . . . . . . . . . IX . The Injection Magnetron as the Possible Means of Producing Amplitude or Frequency Modulation . . . . . . . . . . . . . . . . . . . . . . X . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

188 194 201 207 211 219 225

234 247 253 254

The Magnetic Airborne Detector BY WINFIELDE . FROMM, Airborne Znstruments Laboratory, Inc., Mineola, N e w York

I . Introduction . . . . . . . . . . . . . . . . . . . . . . I1. Types of Magnetic Anomaly Detectors . . . . . . . . . . I11. Historical Development of the Magnetic Airborne Detector . IV. The Saturable-Core Magnetometer . . . . . . . . . . . V . Magnetic Stabilization and Orientation . . . . . . . . . . VI . Magnetic Airborne Detector System . . . . . . . . . . . VII . The Noise Problem . . . . . . . . . . . . . . . . . . . VIII Conclusion . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . .

.

. . . . . 258 . . . . . . 263 . . . . . . 267

. . . . . .

268 . . . . . . 279 . . . . . . 292 . . . . . 295 . . . . . 298 . . . . . 298

Multichannel Radio Telemetering BY M . G . PAWLEY A N D W . E . TRIEST, National Bureau of Standards, Corona, California, and International Business Machines Corporation, Poughkeepsie, N e w York I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 I1. Evolution of Radio Telemetering . . . . . . . . . . . . . . . . . . 302 111. Basic Systems of Radio Telemetering . . . . . . . . . . . . . . . . 304 312 IV . Typical Telemetering Systems . . . . . . . . . . . . . . . . . . . . V . Future Trends in Telemetering . . . . . . . . . . . . . . . . . . . 328 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Author Index .

. . . . . . . . . . . . . . . . . . . . . . . . . . Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . .

331

336

Electron Scattering in Solids H. S. W. MASSEY, F. R. S. Department of Mathematics, University College, London, England CONTENTS Page I. Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 11. Elastic Scattering.. . . . . . . .......... 1. Elastic Scattering of F a a. Scattering by Free Atoms.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 b. Relativistic Correction ............ ... 8 c. Validity of Born’s App .......................... 9 d. Comparison of Born’s Approximation with Observation. . . . . . . . . . . . . 10 13 . . . . . . . . 13 . . . . . . . . . . . . . . . . . . 15 ........

b. Effect of Atomic Binding Forces..

........

III. Inelastic Scattering. ...... .......... ................. 1. Inelastic Scattering of s-Born’s Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Angular Distribution of the Totality of Inelastically Scattered Electrons.. .... .. ...... b. Total Cross Sections for Inelastic and Total Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c. Relativistic Modifications. . . . . . . . .......... 2. Experimental Evidence on Inelastic S 3. Influence of the Solid Binding.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a. Dynamical Polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Study of Low Energy-Loss Collisions with a Solid.. . . . . . . . . . . . . . . . IV. Multiple Scattering. ........... ................. 1. The Boltzmann Equation .......................... 2. The Angular Dist ................... a. Momentum Loss Cross Section and Mean Free P a t h . . . . . . . . . . . . . b. Small-Angle Multiple Scattering. ....................... c. Multiple Scattering Distribution in Terms of Projected Angle of Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Mean Values.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e. Allowance for Energy Loss.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f. Experimental Evidence on Multiple Scattering of Fast Electrons in Foils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g . Multiple Scattering of Electrons in Photographic Emulsions. . . . . . . . 3. Space Distribution of Multiply Scattered Electrons-Absorption of Electrons in Plates.. . . . . . . . . . . . . . . ......................... 1

17

18

23 28 28 30 32 33 34 35 36 40 41 41 42 43 43

2

H. S. W . MASSEY

Page 4. The Diffusion Stage.. . . ................... V. Energy Loss of Electrons in hrough Solids. . . . . . . 1. Stopping by Free Atoms ................................. 49 2. Effect of Atomic Interaction in the Solid State.. . . . . . . . . . . . . . . . . . . . 51 3. Attempts to Detect Atomic Interaction Effects.. . . . . . . . . . . . . . . . . . . . . 55 4. The Range of Electrons in M a t t e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 V I . The Mobility of Electrons in Metals, Alloys and Semi-Conductors. . . . . . . . 58 1. Scattering by Lattice Vibrations-Resistance of Pure Metals.. . . . . . . . . 61 2. Scattering by Foreign Atoms-Resistance of Alloys.. . . . . . . . . . . . . . . . . . 63 3. The Resistance of Semi-Conductors.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 a. Non-degenerate Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 b. Degenerate Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 References.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

I. INTRODUCTION Many phenomena associated with the scattering of electrons by solids are of great importance and application in various branches of physics. Electron diffraction provides a valuable supplementary technique t o the diffraction of x-rays and of neutrons for the exploration of the structure of solid materials. The electron microscope, now proving such a n important tool in many fields of research, depends for image formation on small angle scattering by the specimen. I n recent years the photographic plate has become a most useful medium for the investigation of the properties of high-energy particles including, as a result of the latest developments, electrons. For these studies it is essential t o have reliable information on the rate of energy loss of electrons in the solid material of the plate as well as of the probability of multiple scattering. The determination of the range of electrons in a chosen solid material has long been a n important method for measuring the initial energy of the electrons. Secondary electron emission is another phenomenon which has been put t o use in electron multiplier tubes and in any case has always t o be reckoned with in any apparatus in which electrons impinge on a solid. The electrical resistance of conductors and semi-conductors is another property of great practical importance which is determined by the probability of scattering of the conduction electrons within the material. I n addition t o all these specifically solid state phenomena a great number of fundamental investigations on single scattering of electrons have been carried out, using of necessity solid scatterers. Included among these have been the attempts, now partly successful, t o detect the polarization of electrons by double scattering. It is clearly out of the question in the present review t o attempt even a cursory description of all these aspects of the subject. Instead we shall discuss a selection only. Secondary electron emission has already been the subject of a review in this series,' and we shall omit any further dis-

ELECTRON SCATTERING IN SOLIDS

3

cussion of it here, Another major subject we shall exclude is electron diffraction, as many books on this subject2 already exist. The first section will be devoted to a discussion of single elastic scattering of fast electrons which may be treated, apart from superposed coherent diffraction effects, in much the same way as scattering by single atoms of the material. Single inelastic scattering mill form the subject of the second section. Attention will be directed particularly toward obtaining formulas which are likely to be useful in application t o the electron microscope. The rather meager information available about the probability of energy losses due to excitation of the loosely bound electrons in a solid mill also be reviewed. The theory of multiple scattering and diffusion of electrons in a solid scatterer forms the subject of the third section, together with a brief discussion of experimental evidence. Formulas are obtained which allow for energy loss in passing through the material, but a detailed discussion of the determination of the rate of energy loss is reserved for the next section. This section includes a n elementary account of the way in which the dynamic polarization of the medium influences the energy loss. The final section is concerned with the consideration of the relative importance of the different scattering processes which determine the electrical resistance of metals, alloys, and semi-conductors.

11. ELASTIC SCATTERING

If a fast electron enters a solid the chance that it will undergo a n elastic collision in a small distance 6x mag be calculated to a good approximation by regarding the atoms of the solid as free. This is particularly true of collisions in which the electron is scattered through a large angle. Such collisions involve close approach of the electron and a n atomic nucleus so that the modification of the interaction due to the solid binding is quite negligible. On the other hand the probability of distant collisions in which the electron suffers only a very small deviation may be markedly influenced by the solid binding. Thus in a metal in which the atoms are ionized and the valence electrons more or less free, the charge distribution of the latter electrons is very different from t h a t in the free atom, and this will be reflected in the small angle elastic scattering. We shall begin by a discussion of the elastic scattering by isolated atoms and then consider in what way the results are modified by the solid binding. 1 . Elastic Scattering of Fast Electrons a. Scattering by Free Atoms. The scattering of fast electrons by a n atom may be treated by regarding the atom as a static center of force which exerts a force of potential energy V ( r ) on a n electron at distance r

H. S. W. MASSEY

4

from it. Polarization and other distortion effects which are important when the velocity of the electron is comparable with t h a t of the atomic electrons may be neglected. The potential energy V ( r ) of the atomic field can only be calculated accurately for atomic hydrogen but for other atoms approximate methods exist which are accurate enough for many purposes. For atoms which are not too light the most convenient approximation is obtained by treating the atom as a statistical assembly of electrons obeying the Fermi-Dirac statistics. This method, due t o Thomas3 and Fermi4 gives, for a neutral atom,

where Z is the nuclear charge and the length

p

is given by

p = 0.885aoZ-~,

(2)

where a0 is the radius, 0.53 X lo-* cm, of the first Bohr orbit of hydrogen. The function 4, which represents the effect of the atomic electrons in screening the nuclear charge, has been tabulated by Bush and C a l d ~ e l l . ~ Various analytical approximations for exist but for many purposes i t is sufficient t o write

+

+(r/p) =

e-ar/P

(31

where s is a constant of order unity t o be determined empirically [see (30)]. The actual function falls off much more slowly at large distances but a t such distances the statistical theory considerably over-estimates the field so t h a t (3) probably gives as good a n average representation of the field as may be obtained with any simple formula. For light atoms the statistical model is not very accurate. I n such cases the Hartree-Fock self-consistent field method may be used. This has t o be determined separately for each atom. Results exist in tabular form for a number of atoms and ions.6 We first calculate the scattering in the nonrelativistic approximation. The Schrodinger equation for the motion of an electron of kinetic energy E ( = k2h2/2m)is given by V2+

+ ( k 2 - 2mV/h2)+ = 0.

(4)

The electron incident in the direction of the unit vector no is represented by a plane wave A exp (ikno . r). At a great distance from the scattering atom the scattered electrons will be represented by an outgoing spherical wave Ar-1eikrf(0,4). Remembering that the current density of electrons

ELECTRON SCATTERING IN SOLIDS

5

represented by a wave function J. is given b y i€h 2m

j = - (J.* grad # - J. grad #*),

(5)

we have t ha t the number of electrons incident per square centimeter per second is vAA* and th at the number scattered into the solid angle dw about (B,+) is vAA*If(B,+)I2dw. The ratio of these gives the differential elastic scattering cross section

I(%,+>dw= lf(@)I2dw.

(6)

The total elastic cross section Qo is then given by

Thus, if the atom were actually a spherical obstacle of cross section Q o the number of incident electrons colliding with the sphere per second would be vAA*Qo exactly as in the above formulation. To solve the scattering problem it is therefore necessary to obtain a solution of the equation (4) which, while being a well-behaved function throughout space, has the asymptotic form J.

-

eikno.r

+ r-leikrf(8,4).

(8)

Born’s approximation, satisfactory for the discussion of the scattering of fast electrons by most atoms, may be obtained by treating the scattering potential ‘v as a small perturbation and regarding the scattering probability as small. Writing (4)in the form V2#

+ k2# = 2mVJ./h2.

(9)

we then substitute for J. on the right-hand side of (9), simply the part exp (&no . r) representing the incident wave. This gives VY,

+ k2#

2mVeikno’r/h2,

(10) with the right-hand side a known iunction of r. This equation may be solved by Green’s theorem to give as a well-behaved solution’ =

which has the asymptotic form (8) with

where nlis a unit vector in the direction (%,+)measured with respect to the direction of incidence as polar axis.

6

H. S . W. MASSEY

Since Ino - rill

=

2 sin +6,

we have

sin 0’ dr’ do’ d+’, -

-

V(r’) sin (2kr’ sin @)r’ dr’.

h2k sin $3

(14)

The scattered amplitudef(O,+) may be related to the atom form factor F for scattering of x rays by writing

where p ( r l ) is the density of the atomic electrons. (12) and use of the formulas

Ir - rll

dT1

4R

= -

.

’ lim

K2

LT+O

/om

On substitution in

1 e-ar sin Xrdr = xy

(16)

we find

p(r’)

sin (2 kr’ sin + e ) r f dr’,

is the atomic form factor. In this form the term F ( 0 ) represents the shielding effect of the atomic electrons. If it is omitted f(e,+) takes the well-known form for the Rutherford scattering of electrons by a charge ZE. If the form (1) is substituted for V ( r ) in (14) we have

=

(Zp2/ao)G(krsin + O ) ,

where

It follows then that I(e)

= =

lf(o)121

( Z 2 p 4 / u O 2 ) J ( ksin p ae),

where J(Y)

=

(G(?4)12.

(19)

ELECTRON SCATTERING IN SOLIDS

7

Since p is given by (2) we have

I ( 0 ) = 0.613ZMao2J(0.885kaoZ-~~ sin +O).

(22)

Given the function 4(z) in tabular form G(y) and hence J ( y ) may be obtained by numerical integration. From a table of J ( y ) over a sufficient range Z(0) may thus be determined for all angles, electron velocities and scattering atoms. A table of J ( y ) has been given by Bullard and Massey* but does not cover small angle scattering very effectively. In any case the statistical model is not very accurate for these angles and the simple approximation (3) may be used to give useful results. Substituting (3) for 4 in (20) we find

r(e) = 4m2v4(sin2&e + a2)-2 Z2€4

~

where (Y

=

O.%~Z>’S(~T~~/~V).

Once again the cross section is exhibited in a form which shows the close relation to Rutherford scattering which is obtained if a ---f 0. The mean velocity of atomic electrons is of the order 2?rZ”e2/h so that, provided the incident electrons are fast, a is small and the scattering is as given by the Rutherford formula except for angles e < 2a. It follows from (22) that the total elastic cross section can be written in the form Qo = 1.23sao2ZZ6q (0.885kaoZ-%), (26) where q(u) =

Jo”

~ ( sin u

+e) sin e de.

Thus Q02-nis a function of vZ-35 so that a single numerical tabulation of q(u) will give, in principle, Qo for all electron velocities and all atoms. No such table is available at present although Bullard and Massey* have given a diagram illustrating QOZ-SS as a function of vZ->$.However, if the form (3) is used for 4 a good approximation to Qo is obtained by integrating the expression (24)for I ( 0 ) . This gives 7rZ2€4

Qo

= -

YG7 ay1

1

+

a2)

Z+Sh2 1 1.28m2v2s21 a2 2 3.13~Z++/k~s~,

+

for fast electrons, a being then very small compared with unity.

8

H. S. W. MASSEY

This may be compared with the approximation given by Debye.lo We have, from (26) QO

/6' - 'w /oUo

=

-

1.23ra0~Z3~ J(0.885kaoZ-% sin +e) sin

e do,

J ( u ) u du,

where uo = 0.885kaoZ-4s.

The contribution from the upper limit is so small th a t we may take the limit as 00 without appreciable error. This gives

'r/om

Q 0 =.A J ( u ) u du

which is of the same form as (27) except th a t the numerical factor is different. Numerical evaluation of the integral gives 256

Qo = 7 . 1 4 ~ 7 -

k

This agrees with (27) if we take s

= 0.66 as we shall do henceforward. Other approximate forms for I ( @and ) Qo have been given by different authors. l 1 s S 2 It is probable that for applications t o the solid state in which the charge distribution of the valence electrons is not well known the formulas (24) and (27) or (30) are as accurate as the neglect of modifications due t o the solid justifies, except for the lighter atoms. For these the Fermi-Thomas interaction should be replaced by the appropriate HartreeFock field. Some tables of I(0) calculated from the Hartree field of atoms are given in The Theory of Atomic Collisions,12but these do not cover very small angles of scattering. Marton and Schiff13 have given data from which the formulas (24) and (27) may be corrected for light atoms. The correcting factors are.given in Table I.

TABLE I. Factors to replace 2 9 s in formulas (24) and (27) for elastic scattering cross sections. Atom Li C N 0 F Ne Factor replacing Z56 2.7 11 10.5 9.5 13.5 9.8

b . Relativistic Correction. The only correction to the small angle scattering formula arises from the Lorentz contraction which changes the relation between the momentum k and the energy or velocity of the electron. The formula (24) remains unchanged provided k is given by k = mvy/h,

y =

(1 - v2/c2)-%,

(31)

9

ELECTRON SCATTERING IN SOLIDS

instead of by mv/h and the mass m is replaced by my. Thus (22) is replaced by I ( 0 ) = 0.613Z~ao2J(0.8851ca,Z-~ sin +0), (32) and (24) by Z9e4

I(0) = 243 (sin2 +e 4mvy

+

(33)

d/y2)-2.

The angle a t which the effect of the screening produces departure from the relativistic form of the Rutherford formula is thus reduced by a factor y. The total cross section QOis obtained from (27) by interpreting k as mv/h, not as mvy/h. All these corrections ignore spin-orbit coupling effects. These may be included if Dirac’s equations for the electron ape used in place of the Schrodinger equation (4). It is found’l that they introduce an additional factor 1 - p2 sin2 $8 into the expression (32) for I ( @ ) . This factor is negligible a t small angles and has no important influence on Q,,. c. Validity of Born’s Approximation. l6 The approximation will certainly be valid if the part of the approximate wave function representing a plane wave is always large compared with that corresponding to the scattered wave. Referring to (11) it will beseen that this requires

+

for all r. The right-hand expression in (11) is probably a maximum a t If this is so then the approximation will be a good one if T = 0.

el/ V(T’)exp Iikr’(1 + cos 8’))r‘sin 8‘ dr’ do’ d+’ h2

I

<< 1.

(35)

Substituting the form (1) for V(r’) and using (3) we find that the condition becomes 47r2(9)*[(t

log (1 4-4k2p2s-2))24- {arctan2pkck/~)~] << 1. (36)

For high-energy electrons this is satisfied if

27rZe2/hv << 1. (37) This condition is unchanged when relativistic modifications are introduced. It is noteworthy that for the heaviest atoms such as gold 27rZe2/hc is as large as 0.55 so that Born’s approximation must be used with caution for such atoms. In general, however, the failure of the approximation is much less marked a t small than a t large angles and

.

H. S. W . MASSEY

10

even for gold the expressions for the differential cross section given in Sec. II.la will be valid a t these angles as will also be those for the total cross section. d . Comparison of Born's Approximation with Observation. Very few observations of single elastic scattering of fast electrons through small angles provide a test of the formulas we have obtained in Secs. 1I.laand b. Evidence of the general validity of the results has been provided from a study of multiple scattering and will be discussed in Sec. IV.2f. There is a considerable body of evidence in support of the validity of Born's approximation for scattering of electrons of medium energy. Much of this has been obtained from studies of scattering by gases and will not be discussed here. It is described in the Theory of Atomic Collisions16 and Electronic and Ionic Impact Phenomena. l7 The large-angle scattering of fast electrons by atoms has been the subject of many experimental investigations. In most cases the electron energy has been so high that the scattering a t the angles concerned is given by (33) with sin $I> cr/y > and with the spin-orbit correction included so that

I ( e ) = 242

z2c4

4mvy

cosec4+e(l - p2 sin2;e)

Although many of the observations are inconsistent with each other and do not agree with (38) the careful experiments of van der Graaff and his collaborators'* on the scattering of electrons with energy in the range 1.27-2.27 mev by thin foils confirm the formula for scattering by light elements. Thus Table I1 gives the ratio of the observed to predicted scattering [according to (38)] at a number of angles for beryllium and aluminum. For heavy nuclei such as gold, the formula (38) is far from correct and Born's approximation is not valid at any energy for largeangle scattering. TABLE 11. Ratio of observed ,to calculated scattered intensity for fast electrons. Angle of scattering Electron energy (mev)

35"

2.1 2.2 2.3

1.02 0.97 0.98

2.1 2.2 2.3

0.99 1 .oo 1.02

40"

45O

Beryllium Scatterer 0.93 0.98 0.96 0.98 1.01 1 .oo A l u m i n u m Scatterer 0.94 0.94 1.03 1.02 1.05 1.00

50"

55"

60"

1 .oo 0.99 1 .oo

0.97 0.99 0.99

0.93 1.11 1.02

0.93 1.06 0.99

0.95 1.02 1.04

0.91 1.03 1 .oo

ELECTRON SCATTERING IN SOLIDS

11

Even for light nuclei it must be anticipated th a t the large-scale scattering will show deviations from the formula (38) for sufficiently fast electrons. When the wavelength becomes comparable with nuclear dimensions the fact that the nucleus is not a point charge becomes important and modifies the formula. These modifications will first be apparent only at large angles as i t is only the scattering field at very short distances which is changed. We shall now give a brief discussion of these important effects and of the evidence a t present available concerning them.

I

1.5

i

I / //-30'

180"

0

I

I

I

0.1

0.2

0.3

I

0.4 2/137

I

I

0.5

0.6

FIG.1. Ratio R of the scattering of Zmev electrons by nuclei of charge Zt, calcu lated using the exact solutions of Dirac's equations, to that given by the relativistic f) 40. form of the Rutherford scattering formula Z(0) = ( Z z t 4 / 4 m * v ~ cosec4

e. ModiJications to Born's Relativistic Formula at Large Angles. A thoroughgoing treatment of the scattering of electrons by a n atom including relativistic and spin-orbit effects as well as the screening of the Coulomb field of the nucleus and the modification of th a t field by the finite size of the nucleus has not been carried out and would be very tedious. The most complete investigations have been carried out for the gold and mercury atoms. Mottlg in 1932 calculated the scattering by a gold nucleus, treated as a point charge, using exact solutions of Dirac's equations for the problem. Similar calculations were carried out in much greater detail in 1941 by Bartlett' and Welton20 for mercury,

H. 8. W. MASSEY

12

Finally, McKinley and Feshbachzl extended the work to cover all values of 2 and gave data for scattering of 1-,2-, and 4-mev electrons. Figure 1 illustrates their results €or 2-mev electrons. Comparison of these results with the observations of van der Graaff et al.ls shows that the very good agreement obtained for the light nuclei now extends to all the cases investigated-Be, Al, Cu, Ag, Pt, and Au. It follows that, for these energies, the effect of the outer and inner screening of the nuclear field is negligible.

0

30"

60"

90" 120"

150"

180"

Angle of scattering

FIG.2. Effect of nuclear charge distribution on scattering of 20-mev electrons by gold nuclei. R is the ratio of the scattering by the distributed charge to that by a point charge. Curve A, assuming uniform volume distribution; curve B, assuming uniform surface distribution.

The outer screening will become apparent at lower energies. Calculations similar to those of Mott, l9 but in which the Coulomb field of the gold nucleus is replaced by the Hartree field of the gold atom, have been carried out by Massey and Mohr,22and by M ~ h r .These ~ ~ confirm that, for 1-mev electrons the screening effect is negligible at angles > 10". The energy range in which effects due to the finite size of the nucleus become apparent was first investigated by Rosez4using Born's approximation. Roughly speaking it is to be expected that even for the heaviest nuclei the effect will not be appreciable except at very large angles of scattering unless the electron energy is greater than 20 mev. Eltonz5 has carried out detailed calculations for the scattering of 20-mev electrons by gold in which exact solutions of the Dirac equations have been obtained, assuming the field of the gold nucleus to be given by

ELECTRON SCATTERING IN SOLIDS

13

(39) and

The first case corresponds to a nucleus in which the charge is uniformly distributed throughout a sphere of radius ro, the second to one in which the charge is distributed uniformly over the surface of the sphere. The radius ro was taken as 8.2 x cm in accordance with the usual estimates of nuclear radii. Figure 2 illustrates the results obtained in terms of the ratio of the scattering by the extended nucleus to that by a point nucleus. The modifications are quite marked and indicate that the scattering of very energetic electrons by nuclei is likely to yield very useful information about the charge distribution within the nucleus. Preliminary results obtained experimentally by Lyman, Hanson, and Scott26for the scattering of 16.5-mev electrons by gold are comparable with those predicted from Elton's calculations. The comparison is given in Table 111. More extensive calculations have since been carried TABLE111. Comparison of observed ratio of scattering by gold to that expected for a point nucleus, with calculated ratios. Angle of scattering 30' 90" 150" Observed ratio 0.87 0.59 0.43 Calculated ratio 0.99 0.52 0.41 Case A 0.97 0.35 0.32 Case B

out by Achesongsfor electrons of energies between 15 and 35 mev scattered by aluminium, copper, tin, and gold, assuming the same two interactions (39) and (40). Parzen*' has carried out similar calculations for the scattering of 100 mev electrons by lead nuclei and a potential energy of the form (39) with ro = 8.09 x cm. At these energies diffraction maxima and minima appear in the angular distribution as may be seen by reference to Fig. 3. 2. Modifications Introduced b y the Solid Binding a. Effectof Perturbation of Valence Electrons. When atoms are bound to form a solid the valence electrons are strongly perturbed, but the

14

H. S. W . MASSEY

inner electrons remain unaffected. The scattering by the free atom is modified only in so far as the valence electrons contribute to it, i.e., a t very small angles. To estimate at what angle a perturbation of the valence electron is likely to influence the scattering we may proceed as follows. If ro is the radius of the outer electron shell in an atom, the atomic field will be markedly modified by the solid binding only a t distances greater than ro. Referring to (14) we see that the scattering at an angle

Angle of scattering

FIG. 3. Calculated cross section for scattering of 100-mev electrons by lead nuclei. Curve I, treating the nucleus as a point charge; curve 11, assuming the cm. nuclear charge distributed uniformly throughout a sphere of radius 8.09 X

0 comes mainly from the scattering field a t a distance r where

2kr sin 46 N 1.

(41)

Hence a modification of the field for r > ro will become apparent for angles t9 < O0 where eo N l / k r o . (42) Since the radius of the outer shell will be of the order ao, 0 0 will be of the order Z-sa where a is given by (25). For the calculation of total cross sections for fast electrons the perturbation of the valence electrons is therefore negligible (see Table IV). This applies even when the atoms are ionized as in a metal. Although no finite cross section exists for an unscreened Coulomb field, the cross section calculated for the neutral atom will give a good approxi-

15

ELECTRON SCATTERING I N SOLIDS

mation as the free electrons in the metal will provide sufficient screening to reduce the contribution from the net positive charge on the ions to negligible proportions. TABLE IV. Values of the three limiting angles 01, ea, and Or and of the total cross section QOfor elastic scattering of fast electrons by solid carbon and gold. Electron energy (ev) 10,000 50,000 100,000

a

00

(radians) C Au

(radians) Cand Au

0.024 0.011 0.007

0.055 0.025 0.018

ev

0.013 0.006 0.004

(radians) C Au 2 X 4 X 2 X

2 X 4 X 2 X

&o

(in 10-18 em*) C AU

9.24 1.82 0.9

287 56.6 29

b. E$ect of Atomic Binding Forces. A second point concerns the effect of the binding of the atoms within the solid lattice on the transfer of energy from a fast electron to a lattice atom. If the atom were free and of mass M , an electron would lose a fraction of order 2(m/M)02of its energy to an atom in undergoing elastic scattering through a small angle 8. It is important in certain considerations regarding the coherence of the incident and scattered electron waves to know the extent to which this is modified by the binding'of the atom within the lattice. We may obtain an estimate as follows of the minimum angle of scattering for which the binding exerts any restrictive effect on the energy transfer. If v is the frequency of vibration of the atom, the energy transfer t c the vibration will be negligible if the time of collision is so long that the Fourier analysis of the perturbing force due to the colliding electron contains no component of frequency v with appreciable amplitude. If the electron is incident in such a direction as to pass the center of the atom at a distance p (the impact parameter) the time of collision is of order p / v where v is the electron velocity. The restrictive effect will be confined to collisions in which p / v > l/v. (43)

Making use again of (41) we see that the restrictive effect will only be apparent for collisions in which

e < e,

=

=

?iv/mv2, 2b/E

(44)

where E is the kinetic energy of the incident electron. Although this argument is essentially a classical one it is clearly valid, for p is so large that the electron is practically undeviated from the straight path and may be treated as a center of force moving classically.

16

H. S. W. MASSEY

A similar argument will be given in Sec. V.1 in which the transfer of energy from the incident to atomic electrons is discussed. It is instructive to compare the magnitudes of the three limiting angles a , 00, and 0.. Typical values are given in Table IV. It will be seen that the effect of the solid binding on the transfer of energy between the incident electron and the struck atom is confined to angles much less than a so that in all but a very small proportion of collisions the fractional energy transfer is of order 2me2/2M. 3. Elastic Reflection of Electrons from Metal Surfaces

As an illustration of the opposite extreme to the conditions we have been assuming, in which the perturbation of the atoms by their neighbors is very ineffective, we shall briefly discuss the elastic reflection of electrons of much lower energy (< 100 ev) by a metal surface. The metal is now treated as a single entity which exerts a force on an electron approaching its surface. This force is a combination of the so-called image force and the potential drop a t the surface. If the metal is taken to occupy the space on the negative side of the plane, 2 = 0, the potential energy acting on an electron incident normally on the metal may be written

v

= -vo = -€‘/4X01 = -$/4x,

x

> 50.

X

< 20, (45)

+

The potential drop Vo is given by 4 p where 4 is the work function of the metal and p is the maximum Fermi energy of an electron in the metal. 4 may be obtained from experiment and p is given by (3no/?r)” h2/8mwhere no is the number of free electrons per cubic centimeter in the metal. Typical values of Vo are 10.2 ev for silver and 5.7 ev for barium. MacCol128 has calculated the coefficient r for elastic reflections of electrons a t the surface of a metal assuming the surface interaction given by (45). For small electron energies r N h2Vo/8e4rn, and for high energies E r

-

hzVo4/8r4mE3.

Observations of the elastic reflection of slow electrons from copper have been made by Gimpel and Richardsonz9 (electron energy range 0.35-0.85 ev), and by Farnsworth30 (electron energy range 5-10 ev) while Bruining31 has measured r for electrons of energy ranging from 2.5 to 25 ev reflected from Ba, Ag, and BaO. A comparison of Bruining’s results with MacColl’s calculations for silver is given in Fig. 4. Although there is qualitative agreement, the observed values are considerably

ELECTRON SCATTERING IN SOLIDS

17

larger than the calculated and the observed rate of decrease of r with increase of electron energy is smaller than the calculated.

5

10 15 Electron energy in ev.

20

FIO.4. Reflection coefficients for electrons incident normally on a metal surface. Curves I and I1 calculated by MacColl*a for V o = 10 and 20 ev respectively. X observed for silver (V,= 10.2 ev) by Bruining.sl There is clearly scope for more extensive investigations, both experimental and theoretical, in this field. 111. INELASTIC SCATTERING

Just as for elastic scattering it is convenient at first to regard the inelastic collisions of electrons in passing through a solid as if they were taking place with isolated free atoms of the solid. This is clearly a very good approximation for collisions in which ionization of the atoms in the solid occurs from inner shells. These are only very slightly perturbed by the solid binding so that a purely atomic theory of the ionization of the K or L shells of heavy atoms is quite accurate. On the other hand we must expect that when the collisions involve energy losses of the order of the excitation energies of the electrons the free atom approximation is no longer so satisfactory. Nevertheless, in attempting a theoretical estimate of the probability of inelastic scattering it is usually only possible to work to this approximation. We shall first discuss the theory of the inelastic scattering of fast electrons by free atoms with special reference to applications to the solid state. This will be followed by a short account of investigations, both experimental and theoretical, which have been carried out for solids specifically. The effect of inelastic collisions in determining the energy loss and hence the range of electrons in a solid will form the subject of Sec. V.

18

H. 8. W. MASSEY

1. Inelastic Scattering of Fast Electrons by Free Atoms-Born’s

Approximation

To discuss the inelastic scattering of electrons of initial energy k2h2/2mby an atom containing Z electrons we write the Schrodinger wave equation for the system, atom colliding electron, in the form

+

N

-V2 -

Ha(rl,

-

. . , rN)

+ Eo + 2m

s=l

+ 7 )*(r,rl, Z€2

.

. . , r,)

=

0.

(46)

Ha(rl, . . . , rN) is the Hapiltonian of the atom and EOthe energy of the atom in its ground state. 2e2/1r - rs( is the interaction energy between the incident electron and the atomic electrons which gives rise to the finite probability of energy transfer between the atom and the incident electron. Let h 4 - 1 , . . . , rN), &(rl, . * . , rN) be the respective wave functions for the ground state and for the nth excited state of the atom so that (Ha - Eo)4o = 0y ( H a - En)A = 0(47) We may expand the function P in terms of these atomic functions in the form \k = 2&(r1, . * * , rN)Fn(f). (48) Substituting in (46) we have

In the absence of the interaction

P

=

$1 e2/lr

-

ral we have

40(r1, . . . rN)eikao.r, )

(50)

where nois a unit vector in the direction of incidence. If the interaction is treated as a small perturbation, we may substitute this expression for P on the right-hand side of (49) to give

ELECTRON SCATTERING IN SOLIDS

19

Multiplying both sides by +,* and integrating over the configuration space of the atomic electrons gives

where

Provided kn2 > 0 the excitation of the nth state is energetically possible. T o obtain the differential cross section for this excitation it is only necessary to obtain a solution of ( 5 2 ) which has the asymptotic form Fn ,.,

T-l

eiknrfn(e,+)-

(54)

This corresponds t o a spherical outgoing electron wave of wave number k,, leaving the atom in the n th state. The outgoing flux of these electrons may be calculated as for the elastic scattering in Sec. II.la, and we find for the differential cross section I,(O,+) for a n inelastic collision in which the nt h state is excited

Proceeding as with equation (10) we have, from ( l l ) ,

and where Kn

=

kno - k,nl,

nlbeing a unit vector in the direction (e,+).

we have

N

Since

H. S. W. MASSEY

20

In terms of the angle of scattering we have ~2

= k2

+ k,2

- 2kk, cos e.

Also, for fast electrons, for which

we have, for all inelastic collisions of appreciable probability, where

Hence, for 0

> aom2/2k2we have K 2N 4k2sin2

while, for B

=

0

K = k - k,, 2 ao,2/2k.

To a close approximation, over the whole angular range

K 2 N 4k2 sin2 40

+ (aon4/4k2) cos 0.

(67)

It is clear then that fn(O,+) falls off very rapidly as 0 increases so that the major contributions to the integrand come from the first nonvanishing terms in the expansion of eixn'r*in power series. Thus

S

where zll = II

- r..

As the product +o&* will be very small for values of r > rg, the radius of the shell concerned in the excitation, (68) is essentially the first term in an expansion in powers of Kro. It can therefore be used provided Kro < 1 or, in terms of 8, provided 8

< l/kro.

(69)

If Eo is the energy of an electron in its initial state then l / r o 21~ 87r2mlEol/h2,

(70)

ELECTRON SCATTERING I N SOLIDS

21

so the expansion will be valid provided

e < ( I E , I / E )=~ e~1, say,

(71) where E is the energy of the incident electron. The cross section for scattering through angles > 0, will be very small and for many purposes, such as the calculation of the total cross section, may be neglected. The expression (68) will be a good approximation for 8 < O1 unless the integral vanishes, which will be so if the transition to the n th state from the ground state is optically forbidden. For optically disallowed transitions the first nonvanishing terms involve the matrix elements (ZZ,)~,. The cross sections for excitation of such collisions are considerably smaller than for optically allowed ones except possibly when the electron energy is close to the excitation threshold. At much higher energies they become less and less important as the energy increases. We shall ignore them henceforward. We have now

where EH is the binding energy of the ground state of hydrogen, E is the kinetic energy of the incident electron and AEn = En - Eo. We see then th at the angular distribution of the electrons scattered after exciting a particular optically allowed transition falls off steadily with increasing angle. As the electron energy increases the steepness of the distribution increases. Thus

(73) and (74)

for 8

> AEn/El

so that, whereas the zero angle limit increases as the energy, the intensity takes on its asymptotic form a t an angle which decreases as the energy increases. The asymptotic form itself varies inversely as the energy. a. Angular Distribution of the Totality of Inelastically Scattered Electrons. The angular distribution of all inelastically scattered electrons will be given by

H. S. W. MASSEY

22

provided the condition e < (IEo(/E)$$is satisfied for all transitions which contribute appreciably t o the sum. For excitation from a particular shell the only transitions of appreciable probability are those for which AE is of the same order as (Eel. If we introduce a suitable mean value A T for AE we may then write

For e > (E,/E)'* where E, is the ionization energy of the most firmly bound electrons, we may return t o (60) and substitute ( 6 5 ) for K t o give

where

H e i ~ e n b e r ghas ~ ~ shown how S may be calculated if the Thomas-Fermi statistical atom model is used. It takes the form

S

=

I - R ( k sin

+el

where R tends to zero as k sin &O increases. high electron energies,

(79)

Thus, in the limit of very

which is the Rutherford formula for scattering of an electron by N free electrons initially a t rest. For the calculation of total cross sections the contributions from 0 > may be neglectredso t h a t the formula (76) is adequate, If, on the other hand, i t is necessary to calculate the mean energy loss due t o inelastic collisions, contributions from larger angles can no longer be neglected as they involve relatively large energy losses. For such purposes a different procedure is desirable, as sketched in Sec. V.l. I n the present section we shall be concerned only with the angular range for which (76) is valid. A convenient method of calculation is as follows. Using the usual summation rules,

el

Z f l J ( W o n 1= 2 [(2,z,)2100.

(81)

23

ELECTRON SCATTERING IN SOLIDS

If, further, we represent the wave function of the ground state of the atom as an antisymmetrized product of one electron wave functions then

where i and j refer to occupied one-electron states of the atom.

Iin(e,4)= ( B E x / E ){sin240

Thus

+ (aE/4E)2cos el-*.

(83)

where

Formulas closely similar to (83) have been given by Marton and Schiffla and by K ~ p p e . The ~ ~ former authors have calculated B for a number of atoms using Slater wave functions for the individual electrons. They have also estimated the appropriate value of AE as a mean of the binding energy of individual electrons weighted in proportion to their contribution to B. Table V gives the values they obtain. K ~ p p eignored ~ ~ the cross terms Izii12 in B which may then be

2

iPi

related to the atomic diamagnetic susceptibility x which is given by

so that

B

=

18mc2x/e2.

a

Observed values of x may then be used to determine €3. was taken as the ionization energy of the atom concerned. Koppe’s estimates of B and are also included in Table V . b. Total Cross Sections for Inelastic Scattering, Inner Shell Ionization, and Total Ionization. The total cross section Qnfor excitation of the nth state of an atom is given by Q,,

=

%

/o” I,(e) sin e de.

(87)

To evaluate this integral the approximate form (72) for I,,(O) may be used. It is not accurate for large angles of scattering, but the contribution of the integral from such angles is so small that this inaccuracy is unimportant. We find then that Qn

= ( 2 E x / E )I( zzJon I log

(4E/AE,)

(88)

If the excited state is one of the continuous spectrum, a similar formula may be used provided the kinetic energy E, of the ejected electron is not

24

H. S . W. MASSEY

Xoccurring in the formula for the TABLE V. Values of the quantities B and A angular distribution of the totality of inelastically scattered electrons. B (in units lo-'* cm*) Atom or ion Marton and Schiff H Li+ C N

0 FNs+ P S

K+ Ca++ cu+ BrRb+ Ag+ Sb

I-

Cs+

29.7 7.6 78.2 62.6 51.5 58.1 29.1 179 156 96.1 73.7 203 268 197 446 492 402 268

Koppe

AE (in ev)

Marton and Schiff

31

366 240

13.5 98 44 63 83 91 180 63 74 140 180 130 130 170 170 180 150 230

Koppe

11.2

11.1 10.4

much greater than Eo. Thus if Q,dK is the cross section for ionization of a n atom in which a n electron with energy

Ex = ~ ' h ~ / 2 m

(89)

is ejected then

Q ~ K (~EH/E)\(XZ~)O./~ log ( 4 E / A E , ) (90) , being the energy of the state in where AEx = E+ - Eo ~ % ~ / 2 r nE+ which the positive ion is left after the ionization has occurred. I n calculating (zs)Ox the wave function for the ejected electron must of course be appropriately normalized. The sum Qin of all cross sections for inelastic scattering may be evaluated by using the expression (83) to give

+

&in = (2BEx/E) log ( 4 E / n E ) , (91) are as defined in (84)and (76). where B and Another cross section, involving an incomplete sum of individual cross sections for excitation and ionization of an atom, is t h a t which refers t o ionization of the inner shell of an atom, important in the generation of x-rays.

ELECTRON SCATTERING I N SOLIDS

25

I n this case i t is best to proceed as follows. Let the inner shell from which ionization occurs be the nl-shell. If there were no outer atomic electrons the total cross section for removal of a n electron from the shell in a collision would be given by &is

where

=

( ~ B ~ E x /log E )( 4 E / D u ) ,

(92)

is the mean excitation energy from the shell and Bis

= Znl(Z2)nl,ni,

(93)

Zz, being the number of electrons in the shell. Owing, however, t o the excluded transitions, Bi, must be modified to take the form

the sum being over all excluded transitions. should also be somewhat higher than it would be in the absence of outer electrons. We therefore obtmain finally &is

=

(2B’Ex/E) log (4EIZEis)

(95)

where B’ is of order Znz(z2)nl,n~. Finally there is the total cross section for all ionization processes, a knowledge of which is very important in the interpretation of many experimental results. This will be obtained by integrating (90) over all possible energies of the ejected electron. It is true th a t (90) is not accurate for those collisions in which the incident electron loses a considerable fraction of its initial energy, but the probability of such collisions is so low that they may be ignored. This cannot be done in cslculating the rate of energy loss as the low probability is partly offset by the large energy loss involved. Betheg has shown that, with these assumptions, the total cross section for ionization Q takes the form, for electrons of velocity v %re4 jl 2mv2

&i =

where I is a mean ionization energy and f l is a quantity of order unity which varies from atom to atom. jl and I cannot be obtained with any accuracy from theory and are best derived from experiments at one electron energy for each substance. Table VI gives some values of cross sections Qi, for different atoms and various electron energies calculated using values of B and I given by Marton and Schiff.

26

H. S. W. MASSEY

TABLEVI. Calculated cross sections for excitation of all inelastic collisions by imuact of fast electrons. Electron energy (kev) 10 50 100

Atom or ion-Cross section in C

0

1.5

0.89 0.22 0.12

0.36 0.20

Na+ 0.43 0.11 0.06

K+

Ca++

Rb+

1.5 0.38 0.21

1.1 0.29 0.16

3.0 0.76 0.42

cm2 Ag+

Sb

Cs+

7.0 1.7 0.96

7.6 1.9 1.0

3.8 1.0 0.55

c. Relativistic ModiJications. As long as we are not concerned with inelastic scattering through large angles, the only important modification introduced by relativity arises from the change in the relation between the wave number k , the kinetic energy and the mass of the incident electron. I n relativity theory the kinetic energy E is related to the wave number IG by E mc2 = ch(k2 l c o 2 ) ~ P 1 (97) where k o = mc/h, k = ymv/h, y = (1 - v2/c2)-ss

+

+

Equation (53a) must therefore be replaced by

(kn2

+ ko2))6 = ( k 2 + ko2))fr - AE,/ch,

(98)

and (63) becomes

k,

k -CYO,~/~~,

where aOn2

(2ym/h2)(En - Eo)

=

I n place of (72b), (83), (99), (95), and (96) we now have respectively

B[sin2 +O

+ (ae/2F)2 cos el-',

(102) (103)

(L) (e B log (2F/@, 137 v) 2

&in

= 2

+ ')'

2

&in =

2('->137

e(e

+ 2) B' log (2F/L\e,,),

27

ELECTRON SCATTERING I N SOLIDS

where e

=

E/mc2, Ae

=

AE/mc2, F

=

ye(e

+ 2 ) / ( e + 1)2,

E being the kinetic energy of the incident electron. 6. Experimental Evidence on Inelastic Scattering by Atoms Direct experimental evidence in support of the above theoretical considerations is still very meager. It would be out of place in this review t o discuss the evidence available from the study of electron scattering in gases, It is sufficient t o say that from this evidence there is little doubt of the general correctness of the theory.34 I n view of the

1-: No

t

I I

I

1

I

1

I

I

I

Energy of incident electron (in units of ionization energy of shell)

FIG.5. Comparison of observed and calculated cross sections for inner shell I. observed cross sections;3611. calculated cross sections.36

ionization.

difficulty of providing quantitative theoretical cross sections for inelastic scattering by heavy atoms, most of the detailed comparison must be done in experiments on excitation of hydrogen or helium. I n other cases the lack of accurate theoretical knowledge of such quantities as the mean excitation energy hE and the quantity B in (83) precludes any detailed test. There is in fact a serious need for experiments devoted t o a determination of these quantities for different atoms.

28

H . S . W. MASSEY

The only processes involving heavy atoms which are reasonably predictable in detail are those in which inner shell ionization occurs, particularly of a K or L shell. As in these cases very few electrons are involved and their wave functions are very nearly hydrogenic, i t is possible t o calculate Iis(O) and &is more accurately than given by the formula (95). This has been done by B ~ r h o pfor~ ~ ionization of the K and L shells of Nil Ag, and Hg. I n Fig. 5 his results are compared with observed cross sections obtained by various authors.36 On the whole the agreement obtained is very satisfactory in view of the fact that the comparison is between calculated and observed absolule values. Also in Burhop's calculations no relativistic modifications are included. When these are allowed for the calculated value is increased relatively a t the higher incident energies [see (lOS)] by a n amount which very substantially reduces the discrepancies apparent at these energies. I n some ways the agreement is even better than would be expected a t the lower energies because Born's approximation would not be expected t o give good results when the energy loss is comparable with the incident energy. 3. Influence of the Solid Binding

So far we have neglected any consideration of the effect of binding of the atoms in a solid on the inelastic scattering. This will take the form principally of a modification of the excitation energies AE and D . I n general such modifications can only be detected by comparing observations of inelastic scattering by the same atoms in the free and bound states, experiments which are very difficult t o carry out. Some measurements have been made, using mainly electrons of medium velocity, which provide evidence on the relative probabilities of different energy losses being suffered by a n electron in scattering from a solid. Before describing the results of this work and the theoretical interpretation in terms of the quantum theory of the solid state we shall consider the effect of the dynamic polarizability of the medium which is, paradoxically, of great importance when the incident electrons are of very high energy. a. Dynamical Polarization. A detailed discussion of this effect will be deferred until Sec. V.2 when i t is considered in relation t o the energy loss of electrons in passing through a solid, but we shall give here the main resu!ts as far as inelastic scattering is concerned. By following a correspondence principle argument as in Sec. V.2 we would expect the polarization t o change the natural frequencies of the electrons bound in the atoms of the solid from AE,/h t o AE,'/h, where

+

(AE,I/h)' = ( A E n / h ) 2

vo being given by vo2 =

ane2/rm,

VO',

(107) (108)

ELECTRON SCATTERING IN SOLIDS

29

where n is the number of electrons per cubic centimeter and a is a constant of order unity. This follows from the classical electron theory of the refractive index or dielectric constant of a solid medium and is correct under nonrelativistic conditions. The modification introduced by (107) is usually not very important except for scattering by the nearly free conduction electrons in a metal. For these electrons the minimum value of AE,, would be effectively zero were it not for (107) which ensures that the effective value cannot be less than hvo. It follows then, as in (SO), t ha t the contribution of the conduction electrons t o the scattering of incident electrons of energy E may be expressed in terms of a differential cross section

nl being the number of conduction electrons per cubic centimeter. (hvo/E))’” is usually so small that the form of the cross section a t smaller angles is of no practical interest. Thus for metallic lithium hvo ‘v 7.5 ev. As discussed in Sec. V.2 a remarkable effect arises when the incident electron has a velocity comparable with that of light. On account of the possibility of interaction through electromagnetic radiation, the influence of the interaction between the electrons of the material becomes relatively much more important. (107) now takes the form where y = (1 - v2,’c*)+, v being the velocity of the incident electron. Thus, in particular, the total cross section (106) for primary ionization becomes, when y >> 1,

so that the cross section now tends to a finite limit instead of increasing logarithmically as y -+ cc , according to (106). So far no very definite evidence in confirmation of this effect has been found though some support for it is provided by the measurements of Hayward37 on the ionization produced by very energetic cosmic ray electrons. The closely similar effect on the stopping power of very fast electrons is discussed in more detail in Sec. V.2. Observations of the variation of grain density along the tracks of fast particles in a photographic emulsion have not been easy to reconcile with the theory, but Messel and R i t s ~ have n ~ ~recently pointed out that t o be effective in producing photographic action a secondary electron must be absorbed in a grain. High-speed electrons will not be absorbed and when this is allowed for the discrepancy is largely removed.

30

H. S . W. MASSEY

b. Study of Low Energy-Loss Collisions with a Solid. Some progress has been made toward a detailed theory of inelastic scattering of electrons of medium speed by metals. This has become.possible because of the experiments carried out in the first instance by R ~ d b e r g . ~ ~ I n these experiments a homogeneous beam of electrons of a few hundred elecbron volts energy was allowed t o impinge a t a n angle of 45 degrees on a solid target T. Secondary electrons emitted from this target were largely collected on a cylindrical shield C enclosing T so t h a t the primary current could be measured as the sum of the currents t o T and C. Those electrons emitted from T in a particular narrow range

I

I

10

I

20

I

30

Energy loss in ev.

FIG.6. Energy distributions of electrons scattered from a copper surface observed by R ~ d b e r g . ~ Numbers $ refer to the init,ial energy of the electrons in electron volts.

of angles about a direction a t right angles to the primary beam passed through a slit in the shield C into a magnetic analyzer. The velocity distribution of these emitted electrons could therefore be determined. Typical curves obtained for copper targets are illustrated in Fig. 6. It will be seen that the shape of the curves is independent of the electron energy, showing that the maxima correspond t o energy losses determined by the structure of the metal. Similar results were obtained for Au and Ag. I n view of the comparatively low penetrating power of the primary electrons, Rudberg investigated the possibility that the effects arise from collisions of electrons with surface atoms or ions and are not determined by the bulk structure of the metal. He found that even if a layer of CaO, Ba, or BaO several atoms thick is present on the surface of a silver

ELECTRON SCATTERING IN SOLIDS

31

target, the chief features of the velocity distribution curve for silver are still present. This indicates that the effects are not determined solely by the purely surface properties of the metal. Slater and Rudberg40 therefore attempted a theoretical description of the results, based on the quantum theory of the solid state. In a solid the allowed energy levels fall in bands between which there are gaps in which no stationary states exist (see Sec. VI). These bands can be regarded as arising from the broadening of atomic energy levels due to the mutual interaction of the lattice ions. In the normal metal the allowed energy levels are filled up so that each electron occupies the lowest level accessible according to Pauli's principle. In copper the least firmly bound electrons occupy levels in a band arising from the perturbation of the 3d and 4s levels of atomic copper. The band is only partially filled, the occupied levels arising from the 3d state of the atom and the vacant levels partly from 4s as well as 3d. Incident primary electrons are considered to cause transitions from the occupied 3d levels of the band to 4s levels and others above. To calculate the relative probability of different energy losses it is necessary to know the density N ( E ) of the electronic levels in the metal as a function of energy E (such that N ( E ) d E is the number of levels with energies between E and E d E ) . It is also necessary to know the wave functions corresponding to each of these levels. Sufficient information was available about both energies and wave functions from applications of quantum theory t o metallic copper to enable Slater and Rudberg40 to make a theoretical estimate of the shape of velocity distribution curve for the inelastically scattered electrons. These results are compared with the observations in Fig. 7. I t will be seen that there is good general agreement as to the position of the first two maxima although for higher energy losses the theory predicts two further maxima which are not observed. Reasons are given by Slater and Rudberg why their calculations, which are only approximate, are likely to be less satisfactory for these losses. On the whole the agreement is encouraging, but no further theoretical work on these lines has been carried out. Further experimental work has been done by Rudberg, 4 1 Turnbull and Farnsworth, 4 2 and Ruthemann. *3 The work carried out by the last author is of special interest in that he studied the energy distribution of faster electrons (2.8 kev energy) which had been scattered through very small angles (up to 4 O ) in passing through thin films (100-500 A thick) of collodion, A1203, Be, Al, and Ag. I n all cases, with the thinnest foils, a sharp maximum was found for a single energy loss at 21.4, 22.3, 19.0, 14.7, and 22.6 ev for the respective materials studied. As the foil thickness was increased, energy losses closely equal to integral multiples of these respective values were found,

+

32

H. 5. W. MASSEY

showing that multiple inelastic collisions were occurring. No evidence for other discrete energy losses was found. Rudberg’s results for electrons of much lower energy (129-248 ev) scattered by gold do show evidence of a maximum in the neighborhood of 24 ev, which may correspond to the loss observed by Ruthemann. No evidence of the maxima found at lower energies by Rudberg is found by Ruthemann, although his resolving power should have been adequate t o find them. This discrepancy may be due to the different conditions of the two experiments, but

20

10 Energy loss ev.

FIG.7. Comparison of observedJ9and calculated40energy distribution of electrons of 180 electron volts incident energy scattered from copper. Calculated.

- - - _ - - -Observed.

it is clearly desirable that more investigations should be carried out on these lines. The results would be of interest not only for the theory of metals but also for checking estimates of inelastic scattering cross sections for use in electron microscopy and in other cases in which the scattering is due to solids rather than gases.

IV. MULTIPLE SCATTERING It is clear that in passing through a densely packed set of atoms as in a solid the chance of an electron undergoing more than one collision in passing through the solid is likely to be high unless the solid is very thin. Thus, using the cross sections of Table IV, it is seen that the chance of an electron of 100,000 ev energy undergoing an electron collision in gold in traversing a small distance 61 is given by p

=

2.9

x

10-17~61

ELECTRON SCATTERING IN SOLIDS

33

where N is the number of atoms per cubic centimeter. In gold N = 5.9 X so that p is already approaching unity when 61 is ‘v lo-’ cm. The theory of the scattering which can arise when the path length in the solid is sufficient for many collisions to occur is, in its most general aspect, very complicated. As the electron proceeds through the solid its mean angle of scattering increases so that the path length traversed in passing through a foil may be considerably greater than that given by the thickness of the solid. Furthermore, inelastic as well as elastic scattering occurs so that the mean energy of the electron also changes on its way through the solid. Since the differential cross section for both elastic and inelastic scattering depends on the energy, the ultimate angular distribution of electrons emerging from the foil will be influenced by the rate of energy loss. For these reasons it is necessary to consider the problem in stages each of which has a useful range of validity. The simplest case to consider is that in which the electrons are quite fast so that even after making a great number of collisions the mean angle of deviation is small. The thickness of the foil or plate through which the electrons pass is supposed to be large enough for many collisions to occur in passing through so that the problem can be treated statistically. On the other hand the foil must not be too thick, for then the mean scattering is so large that the path length of the electrons is much greater than the foil thickness. I t is also usually supposed that the thickness of the foil is small enough for the energy loss to be ignored although this restriction can be raised, at least in principle. We call this case one of multiple scattering through small angles. A second, rather extreme, case arises when the plate is so thick that all trace of the initial direction of motion is lost and the electrons diffuse through the material over a large part of their path. The intermediate cases between single scattering, small angle multiple scattering, and diffusion are very much more difficult to treat. It is usual to refer to the case in which the probability of an electron making more than one collision in passing through the solid is considerable, but not large enough for statistical considerations to apply accurately, as that of plural scattering. Some progress has been made in dealing with this case, but little has been achieved toward developing a theory of the transition stage between multiple scattering through small angles and true diffusion. 1. The Boltzmann Equation The theory of multiple ~ ~ a t t e r i nmay g ~be~ based * ~ ~on~the ~ Boltz~ ~ ~ ~ mann equation which gives the rate of change of the distribution function of the electrons in coordinate and velocity space as they pass through the scattering medium. In deriving this equation it is assumed that only

34

H. S. W. MASSEY

elastic scattering occurs so that the magnitude v of the velocity v of the electrons remains unchanged. Approximate methods of allowing for energy losses will be described later. Let f(r,e,+,t) sin 6 dB d 4 dr be the probability of finding an electron in an element d7 of volume a t the point r moving in the direction (0,4) at the time t. The local time rate of change off arises partly from convection and partly from scattering. The former contributes an amount -V . grad f. We thus have af =

at

- v . grad f

+ n+ - n-,

(112)

where n+ and n- represent respectively the number of electrons entering and leaving the distribution per second by scattering. If I({,v) sin l d{ d x is the differential cross section for elastic scattering into the solid angle sin l d{ dx then

where N is the number of scattering atoms per unit volume and cos 1

=

cos 8 cos e

+ sin 8 sin e cos (a - 4).

(114)

We thus have

where v3 = v and 6s is the path length traversed by the electron in time St. The initial condition to be satisfied by f if we suppose the electrons incident at the origin in the direction e = 0 is that

We shall not attempt to deal with the full equation (115) but consider simplified forms applicable to special problems.

2. The Angular Distribution of Multiple Scattering The angular distribution function is obtained by integrating the function j over all space to give

F(O,4,s) = lff(r,e,4,s)d7.

(117)

ELECTRON SCATTERING IN SOLIDS

35

F(B,+,s) sin 8 dt9 d+ is the probability of finding the electron moving in the direction (e,+) after traversing a total path length s in the scattering medium. It follows from (115) that

I/

as = N

I([,v)[F(e,a,s)- F(B,+,s)] sin 1 d r d x

the term involving grad f vanishing on integration. The boundary condition (116) becomes q i - cos e) F(e,+,o) = 2*

(118)

(119)

As we are concerned with the scattering of a homogeneous beam of electrons incident a t a point of a plane surface of the scattering material in a direction normal to the surface the function F will not depend on 9 and we may write F = ZFi(S,v)Pl(COS e), ( 120) where aFl

-

as

+ K~FZ= 0,

(121)

with Kl

=

[

2 n ~ ~ ( ~ , v )[ l~ l ( c o [>I s sin

Since

qaz

c dl.

+ i)Pl(cos e) = 26(1 - cos el,

(122) (123)

the boundary condition for F Z is that Fi(0)

=

21 -t

+1

4a

so we have, integrating (121)

z=o

a. Momentum Loss Cross Section and Mean Free Path. The expression ~1 plays a n especially important part in the theory of multiple scattering, diffusion, and energy loss. It may be written in terms of the momentum loss or diffusion cross section &Om which is defined as =

2a

/o" I ( C , ~ ) ( I- cos 1) sin

dy,

(126)

and occurs in the theory of many processes such as gaseous diffusion,

36

H. S. W. MASSEY

ion mobility and electron mobility in gases and in solids (see Sec. VI). 1 'NQom can be regarded as the momentum loss free path X so that K 1 = 1/x. For the scattering of fast electrons we have, using (33) for I(l,v)

where p = v/c. b. Small-Angle Multiple Scattering. If single scattering is mainly confined t o small angles and we consider thicknesses d of scattering medium which are not too large so the average value of cos 0 in the multiple scattering distribution is still close t o unity, then we may replace s by the actual thickness d t o give the formula of Goudsmit and Saunder~on~~ m

i=e

where in terms of the total elastic collision cross section QO

=

v =

I(l,v) sin 1 d l , 2aNd h r I ( { , v ) sin 1 d{ 2a

(129)

and I(e,v)

= ( & 0 / 4 r ) Z ( 2 1 + i)pzpz(cose>.

(130)

v is thus the total number of collisions made by the electron in passing through the material. T o obtain Fl(0,s) in a form which exhibits not only the Gaussian distribution of multiple scattering but also the transition t o single scattering as 8 increases50 we use the approximation Pl(cos e) N Jo(ZB)for small e. Substituting in (122) we find then

where

A = 8rZze4/m2v4yz. Now since JO(Xy) =

* sin (Xg cosh

t)dt,

(133)

ELECTRON SCATTERING IN SOLIDS

37

we have

1

=

cosh t

-,A

cosh t dt

KI(X) is here the Bessel function49 whose series expansion is

where

-c + 2 r

F(r)

=

n-1,

n= 1

C being Euler's constant,

=

0.5772

Hence K

Z

= ~

Nd[Qo

*

...

+ (Ah/4a)K1(2la/-~)l

(137)

as the upper limit in (137) may be taken as co without appreciable error. To the same approximation

=

so that

Ay2/8(r2,

(138)

+ (2Za/~)K1(21a/~)l, + (2la/-Y)K1(2Ea/-Y)l,

(139) (140) v being, as before, the total number of collisions made in passing through the foil. Hence on substitution in (125) and transformation of the sum to an integral we have K Z = ~

NdQ&

= 41

F ( 0 ) = 27r Since

1

zJo(z0) exp [ - v { 1

+ (2az/7)R1(2awc/y)1]dz.

v = NQod = NAY2d/8a2,

(141) (142)

38

H. S. W. MASSEY

we have, on changing the variable of integration to

where

y = (NAd/2)&,

(143)

x

(145)

= (NAd/2)-550.

We are interested now in the case where v is large. we have, from (136))

For small values of

IJ/V>+

(146)

where r = ec. The first term of this series is a good representation provided y < v34. For larger values of y the exponent is already so large that the contributions to the integral are negligible. We may therefore write

where

b

=

log v

+ 1 - 2C.

Finally, provided log v is considerably greater than unity, F ( 6 ) may be expanded in powers of b or more conveniently, in powers of B , where b = B - log B.

(149)

If we change to a new variable u = B54y

then F ( 0 ) ‘v

/n

(B”))’r

1 m d

uJo(xB-’*u) exp

where

and

+*

=

e2/e22,

where

e2 = (NAdB/2)55.

(153)

ELECTRON SCATTERING IN SOLIDS

39

The first term in (151) is the Gaussian distribution of the multiple scattering. It has the standard form

F(e)

=

(1/1re2z)e-~1/8~'

where 0 2 the mean square angle of deflection is given on substitution for A and B from (149), (148), (142), and (132) in (151) by* 0 2 = (8*NdZ2e4/m2v4y2)log { 6 0 3 Z ~ ( N d~)~ / m v c )

(154)

if log B is small compared with B. The remaining terms in (151) represent the correction to the Gaussian distribution and the transition t o single scattering. When 0 > Oz these terms become important and the transition to single scattering is obtained by considering their asymptotic form when e >> ez so $ >> 1. By expanding exp ( -+v2) in the integrand of (152) and integrating term by term we find

--

+

+

+

Fi($) (2/#') (8/#6) (36/#') ..., F ~ ( ~ L )(16/+6)(10g - Q) ~ / # 8 ) ( l o g - A+),

w

-

+

w

(155)

and so on. Hence, for large values of 6/62,

F(e)

NAd/2d4

= 4Z2e4Nd/m2v4y204,

the single scattering law. I n order that the scattering through an angle e should be effectively the result of a single deflection we must therefore have

e >> e2.

The transition from the Gaussian to the Rutherford distribution is a rather gradual one as will be seen by reference to Fig. 8. The functions F1 and F z have been tabulated by M ~ l i B r eand , ~ ~Table VII reproduces his results. The expression (151) for the multiple scattering distribution ignoring higher terms in Fs, F,, etc. is a correct representation of the integral (150) to order B-3. The approximation made of ignoring the effect of the higher terms in the expansion (146) is of order v-l = e-B. Errors * In Molibre's analysis a more accurate expression for Z(0) is used. The h a 1 formula again follows from (153), (149), and (148)but with

Y

now given by

In a recent paper Hanson, Lanzl, Lyman, and Scott*' have found that the observed multiple scattering distribution of electrons of 15.7 mev energy after passing through thin gold foils agrees with Molibre's theory within the experimental accuracy of 2-3 % (see (f)).

H. 8. W. MASSEY

40

arising from both sources will lead to an inaccuracy of less than 1 per cent if B > 4.5, i.e., if the average number v of collisions made in passing

Of 02

FIQ.8. Illustrating the transition from the multiple scattering to the single scattering distribution as the angle of scattering increases. Distribution including multiple scattering.

_ _ - - - - -Single scattering distribution.

8 2 is the mean square angle of scattering and the number of collisions per centimeter path is taken as e1O.

through the scatterer is > 20. On substitution for v we can express the condition that the scattering should be largely multiple in the form

c. Multiple Scattering Distribution i n Terms of Projected Angle of Scattering. In practice it is often convenient to measure a scattering distribution not in terms of the angle 8 but of its projection $I on a particular plane. This applies not only to investigations of the trails of fast particles in cloud chambers but also to the tracks of such particles, including electrons, in photographic emulsions. The multiple scattering distribution in terms of 4 may be obtained without difficulty by resolving e into two perpendicular components $I and w and integrating over w . ~ O If f(+)d+ is the chance of observing a projected deflection between $I and 4 d 4 then

+

41

ELECTRON SCATTERING IN SOLIDS

f(+)d4 =

e2-l(

+

( 2 / ~ r 9 e - + ' / ~ + ~B*- W 1 ( 4 / G 42) B-%t(4/& 42)

where

+

+

*

+

*

1 d4

42 = e 2 / d ,

(157) (158)

is the root mean square projected angle of scattering. The functions 01 and Gz are tabulated in Table VII. TABLE VII. Functions occurring in multiple scattering formula.

* 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3 3.2 3.5 4

Fz(J.)

Fl (*)

0.8456 0.700 0.343 -0.073 -0.396 -0.528 -0.477 -0.318 -0.147

O.OO0

+O .080 0.106 0.101 0.082 0.062 0.045 0.033 0.0206 0.0105

2.49 2.07 1.05 -0.003 -0.606 -0.636 -0.305 0.052 0.243 0.238 0.131 0.020 -0.046 -0.064 -0.055 -0.036 -0.019 ,0052 +.001

+

GI(*)

GI(*)

+0.0206

+O. 416 0.299 0,019 -0.229 -0.292 -0.174 +o. 010 0.138 0.146 0.094 +O. 045 -0.049 -0.071 -0.064 -0.043 -0.024 -0.010 +o. 001

-0.0246 -0.1336 -0,2440 -0.2953 -0.2630 -0.1622 -0.0423 +o. 0609

0.1274

0.147 0.142 0.1225 0.100 0.078 0.059 0.045 0.0316 +O. 0194

0.006

d. Mean Values. Using the distribution functions (151) and (157) mean values of various functions of the angles 0 or 4 may be obtained. I n particular the mean values 8, 4 are given by '

=

(e2/T>s

0.982

--0.117 - - B2

e. Allowance for Energy Loss. It is possible to make some allowance for energy loss as follows. The mean energy will be a function of the distance s traversed in the material so that the quantities KI in (121) which depend, through the cross section I(T,v), on the energy, will be functions of s. The function Ft appearing in (120) will now be given by

H. 6. W. MASSEY

42

where E is the mean energy. Knowing the rate of energy loss dE/ds (see Sec. V.l), Fl may be calculated. The subsequent procedure then follows the same lines as in Sec. IV.28b but is necessarily much more complicated. f. Experimental Evidence o n Multiple Scattering of Fast Electrons in Foils. The most comprehensive and precise investigation of the multiple scattering of fast electrons in metal foils is that of Kulchitsky and T,aty~chev.~~* They obtained a narrow and almost parallel beam of 2.25 mev electrons by analyzing the @-raysemitted from a thin-walled glass tube containing radium emanation. The angular divergence of the beam was less than 0.8 degree and the energy spread less than 1 per cent. The beam was allowed to impinge on a metal foil mounted at the center of a scattering chamber. Scattered electrons were observed by means of two counters in a coincident arrangement which ensured that the electrons observed could only have arisen from a small volume of the target and not from any other part of the apparatus. Table VIII gives the results they obtained for the angle at which the multiple scattering distribution falls to half-value. Included in the TABLEVIII. Comparison of Observed and Calculated Half-widths of Multiple Scattering Distributions. Half-width angle (degrees) Scattering material A1

Fe cu Mo Ag

Sn

Ta Au Pb

Y

Obs.

Calc .

60.2 41.4 46.8 36.6 35.1 34.2 28.7 29.4 26.1

9.50 9.60 10.40 10.25 10.20 10.65 9.85 9.90 9.70

9.40 9.60 10.50 10.35 10.30 10.65 10.95 11.35 10.85

table are the values of this angle calculated according to the theory of Goudsmit and Saunderson48 which, for small angles of scattering, is equivalent to (151). The quantity v of (156) which must be greater than 20 in order that the scattering should be multiple over a large part of the angular range is also included in each case. The agreement between the observed and calculated values is very good except for the heavy elements, where the disagreement is well outside experimental error. The reason for the discrepancy in these cases has been traced by Moli61-e~~ as due t o the form assumed for the angle *See footnote on p. 139.

ELECTRON SCATTERING IN SOLIDS

43

scattering distribution. The calculated values in Table VIII are obtained, using a distribution essentially of the form (24). This is accurate enough for the light elements but not'for heavy elements. For these elements MoliGre found that the function I ( 8 ) obtained by use of the true function 4 in (19) may be represented for small angles of scattering, by

relativistic effects being included, the notation being as in Sec. II.la. When this is used in the multiple scattering formula the discrepancies for the heavy elements are greatly reduced. g . Multiple Scattering of Electrons in Photographic Emulsions. It has recently been showns3that multiple scattering may be used in conjunction with measurements of grain density to determine under certain circumstances the momentum and mass of the fast particle producing a track in a photographic emulsion. The multiple scattering is measured by dividing the track into elements of length and measuring the average angular deviation 4 between successive chords. This will be given by (159) with the appropriate substitutions corresponding to the constitution of the emulsion. Ignoring the changes in the logarithmic term, 4 is simply given by k / p v where p is the momentum and v the velocity of the particle, assumed to be singly charged, and k is a constant depending on the material. The grain density along the track may be determined as a function of the velocity by observing it as a function of the rate of energy loss in the plate, use being made of the formula (197) of Sec. V.l for the latter quantity. It is not within the scope of the present review to discuss these techniques as they are concerned with mesons and heavier particles rather than electrons, but the technique of multiple scattering measurement has rece'ntly been applied by CorsonS4to check the theory for multiple scattering of 115-mev electrons in Ilford G-5 plates. The mean angle 6,considering only angles less than four times the mean and obtained between chords of interval length 100 microns, was found to be 0.17 f 0.02'. This compares very well with the value 0.20" calculated from the theory of Snyder and which is equivalent, apart from small details, to that of Moli6resodescribed in Sec. IV.2c. 3. Space Distribution of Multiply Scattered Electrons-Absorption

of

Electrons in Plates

The difficult problem of determining the distribution in space of multiply scattered electrons arising from a narrow incident beam is one which occurs quite frequently in practice. Thus if a homogeneous beam

44

H. 8. W. MASSEY

of electrons is incident normally on a thick plate, it is of interest to determine the flux and energy distribution of the electrons which penetrate the plate and also of those which are “back-diffused” to pass out again through the surface on which the beam is incident. Even when the energy loss is neglected, the problem is a complicated one. has used the Boltzmann equation (115) to calculate the values of such quantities as zn where z is the distance traversed through the scatterer, and also for angular correlation functions such as z cos 8. Although his formulas provide in principle all the information required, they are not very convenient for use in practice, but it has not proved possible so far to obtain space distribution functions without using the Fokker-Planck approximation t o the Boltzmann equation (I18). This is equivalent to assuming that

instead of merely taking PZ(C0S

as has been done in Sec. IV.2. - = -3.

as

r> = JLm,

It gives in place of (115) grad f

+ (1/X)V2f,

where h is the momentum loss free path defined in Sec. IV.2a and V2 is the Laplace operator in the angular ooordinates 8 and 4-

vz

i a ae (sin

= __ sin 8

06)

1 a2 +s e a(p2-

It has the disadvantage of giving a purely Gaussian distribution for the multiple scattering and does not exhibit the transition to single scattering a t large angles. Bethe, Rose, and Smith44have applied the equation (161) to discuss the penetration of electrons through a thick plate in which there is no energy loss. In this problem, in which there is symmetry about the axis of the incident beam if it is incident normally on the plate, the equation (161) for the steady state takes the form

where z is measured normal to the surfaces of the plate and p = cos 8. By solving this equation it is found that the fraction r of the incident beam transmitted through a plate of thickness d is given by T

= 0.862/(0.719

+ d/h).

ELECTRON SCATTERING I N SOLIDS

45

The distribution function a t any point of the plate is given in terms of an expansion in unfamiliar functions which are solutions of the equation

Furthermore, in many applications it is preferable to work with a distribution in terms of projected angles of scattering. Provided the mean angle of scattering is small, a simple distribution function of this kind may be obtained.55*56 Let W(x,y,41,4~,z)dxdyd~ld~z be the probability that, after penetrating a distance z in the scatterer, the coordinates of the particle in a perpendicular plane are (x,y) and it is moving in a direction whose projections in t&e xz and yz planes make angles and 42 with the axis of z. If 41 and 42 are small, the equation (161) for the steady state takes the form

aw aw + =+ 41%

m)'

42-aw au = -xl r w + a2w

since 82 'V

412

+

( ~ ~ 2 .

This equation is separable so that, writing

W

=

Wl(X,41,Z)W2(M,42,z)

we have

If the incident beam passes through the origin in a direction parallel to the z-axis Wl(X,41,0) = %)6(41). (169) The solution of (168) satisfying (169) was found by FermiK6in the form

W1

=

, e x p 2u2

z

Integration over x gives the Gaussian angular distribution with the mean square angle of scattering = (2z/X)" which agrees fairly closely with the more accurate value (153) obtained without the Fokker-Planck equation. Similarly, integration over 41 gives the lateral distribution in the Gaussian form.

The distribution function (170) is often useful for interpretation of the

H. S. W. MASSEY

46

tracks of charged particles in cloud chambers and photographic emulsions as well as the study of the passage of electrons through foils.

4. The Difusion Stage We now consider the stage in which almost all trace of the original direction of motion is lost and we are concerned with the spatial distribution only. If the distribution is nearly isotropic and axially symmetrical we have f(r,e,s) =fdr,s)

where

j,,

= 2s

+ fl(r,s) cos 8,

(172)

l,”f(r,s,s) sin e de,

fl = 21

cos 0 f(r,e,s) sin 0 do.

(173)

f,, is thus the total electron density p and f is the magnitude of the total electron flux density j. It is convenient now t o work in terms of p and j . Substituting in the equation (161) and integrating over all angles we have

Again, multiplying (161) first by cos 0 and then integrating over all angles gives

For true diffusion to prevail p and j must not vary much in a free path so that aj/as is small compared with 2 j / X and may be neglected in (175). We then have, on elimination of j between (174) and (175), the standard diffusion equation

So far we have taken no account of energy loss. To do this approximately we note that X is uniquely determined by the distance traversed in the plate as this determines the mean energy. We define a new variable r so that r(s)

=

&

lu”

X(s)ds.

This may be rewritten in terms of the electron energy in the convenient form

ELECTRON SCATTERING IN SOLIDS

47

E , being the initial electron energy and E the energy after traversing a path s in the material. This form for r is convenient because explicit formulas are available both for X(E)[see (127)] and dE/ds [see (197)l. Substituting for r we find (176) takes the form

There is no difficulty in obtaining solutions of this equation satisfying definite boundary conditions, but the formulation of these conditions in problems of the type we have been considering is not easy. This is because the diffusion stage is only reached after passage from the stage of low-angle multiple scattering through an intermediate transition stage which is very difficult to deal with. Bethe, Rose, and Smith44 overcame this difficulty in an approximate manner by ignoring the transition stage and laying down a reasonable criterion to determine when the behavior could be regarded as changing abruptly from the first stage to that of diffusion. When a homogeneous beam of electrons enters a plate, the mean angle of deviation from the incident direction due to elastic scattering increases very slowly while energy loss occurs due to inelastic collisions. When the mean value of cos e becomes small enough, the conditions are those of diffusion. Bethe, Rose, and Smith44assume that there is an abrupt change to this stage when cos 8 = Remembering that, in the 'notation of Sec. IV.2, = 47rF1, we have, using (125),

e

a.

a

-

cos 8 = exp (- Jkl ds) = exp ( - Jds/X).

(179) The change to diffusion will then occur when the path s1 traversed in the plate is given by l ' d s / h = $7

(180)

or, in terms of the energy, when the mean energy El is given by

The average penetration in the first, nearly straight, path is then given by (E)1 = ds. (182)

lo" cos)

To follow the process further the diffusion equation (178) is used with the boundary condition that the source of the diffusing electrons is a point source located within the plate a t a depth z =

48

H. 8. W. MASSEY

The fraction of electrons emerging with energy between E and E from the back of the plate is then given by

+ dE

where

The fraction of electrons absorbed by the plate, i.e., the fraction which is brought to rest within the plate is then given by 1- rln(E)dE.

Bethe, Rose, and Smith have applied this approximate theory to the absorption in aluminium of electrons produced by y-rays and the agreement with observed datas7 on the half-value thickness as a function of y-ray quantum energy is very satisfactory. There have been many investigations made of the phenomenon of back diffusion of electrons from plates of different materials. Thus BotheS8has recently measured the energy distribution and “back diffusion coefficient” (the fraction of the electrons which diffuse out through the front face of the plate or foil) for electrons of energies in the range 10-700 kev and a number of materials (C, All Cu, Sn, Pb). B ~ t h e ~ ~ has given a rough theoretical interpretation of these- results but they have not yet been discussed from the viewpoint of the theory of Bethe, Rose, and Smith.44 V. ENERGY Loss

OF

ELECTRONS IN PASSAGE THROUGH SOLIDS

In the preceding section we have discussed the passage of electrons through foils or plates in terms of the rate of energy loss dE/ds per unit of path traversed. To apply the formulas obtained it is necessary to know, either from theory or experiment, or from a combination of both, this rate of energy loss as a function of the material concerned and of the energy of the electrons. I n view of its great importance in the physics of high-energy particles very much attention has been devoted to the theory of the processes by means of which energy is given up by a fast charged particle to the medium through which it passes. I n order to bring out clearly the physical principles involved we shall first give a simplified theory which nevertheless exhibits the main features of the phenomenon.

49

ELECTRON SCATTERING IN SOLIDS

I. Stopping by Free

Atoms69-60

Consider a fast electron passing through matter containing n electrons per cubic centimeter. If these electrons can be regarded as free the number p dB of collisions which the incident electron will make per centimeter path in which it is deviated through a n angle between e and e dB is given by the relativistic form of the Rutherford scattering formula (80) 8 m e 4 d0 p d O = --

+

.

I

y2m2v4

83’

where v is the velocity of the incident electron, y = (1 - v 2 / c z ) - ~ +and the angle 6 is supposed small. In suffering a deflection between 0 and 0 de the energy transferred to the struck electron is approximately h v 2 y 2 t 1 2 . Hence the energy loss per centimeter caused by collisions in which e > eminwill be given b y

+

This formula may be applied to the rate of energy loss in a n actual and Omin. To the material if we make appropriate substitution for , O, accuracy with which we are working Omax can be taken as unity, but the choice of em, requires much more careful consideration. The formula (186) breaks down at sufficiently small angles because the electrons of the stopping material are not free but subject to binding forces which limit their response t o a force which varies with the time. Under classical conditions the response will be small if the time of collision is long compared with the period of oscillation 1/v of a n electron about its equilibrium position under the binding forces. I n a collision in which the incident electron would, if undeviated, pass a bound electron at a minimum distance p , the time of collision is given roughly by p / v y where v is the velocity of the incident electron and the factor y arises from the Lorentz contraction. Hence, if a classical treatment is valid, the effect of the binding is to limit the energy loss t o collisions in which P/VY

< 1/5

(189)

i.e., t o those in which the impact parameter p satisfies

P < YV/V. (190) It has been pointed out in Sec II.2a th a t scattering through an angle < e arises from the interaction between colliding particles at

50

H . S. W. MASSEY

distances > h/mv9. If collisions for which p > yv/v are t o be regarded as ineffective in producing energy loss, Omin in (188) must be taken as hlmvp = hv/ymv2,t o give

- d-E-- ds

my2

log (mv2y/hv),

Provided p >> d where d is of the order of the amplitude of vibration of the bound electrons, the classical determination of the limiting impact parameter p will be valid-the incident electron will be only slightly perturbed and can be regarded as a center of force following a classical trajectory. For a complete translation to the quantum description it is only necessary to interpret the frequency of oscillation. Corresponding to each possible process of excitation of a particular electron involving a transition from the ground state (of energy Eo) to a particular excited state (of energy Em)there will be a frequency and a corresponding oscillator strength f m a such that

1

fm"

=

1.

(193)

m

If x. is the fraction of electrons with this set of possible transitions and oscillator strengths then

1

- dE = %?T4 xafmslog (mv2y/hvm). ds mu2 -

(194)

8-m

This may be put into a more convenient form by introducing a mean excitation energy I so that

- - dE _ ds

-

(195)

with log I

=

Zx,fmalog hv,'.

(196)

A more accurate discussion reproduces this result with a small correction so that61*62 dE = -ds

mu2 (log (mv2y/l)

+

(197)

The calculation of I cannot be carried out with any accuracy except for atomic hydrogen but Bloch,62 who treated the problem as one of the perturbation of a sphere of charge with density corresponding to the Fermi-Thomas atom model, showed that I should be given approxi-

ELECTRON SCATTERING IN SOLIDS

51

mately by 13.52 electron volts, where 2 is the atomic number of the material concerned. I n practice, it is convenient t o determine I once and for all for a particular substance by a n observation for electrons or other particles of a convenient energy. The variation of dE/ds with electron energy according t o (197) is illustrated in Fig. 10 for different materials. It exhibits a minimum a t a n energy of the order of a few mev. for each material after which it increases steadily in the ultra-relativistic region. This minimum arises from the presence of the factor y in the argument of the logarithm in (197). The introduction of this factor can be traced t o the decrease of the collision time for a given impact parameter due t o the Lorentz transformation and is therefore a purely kinematic effect of special relativity. 2. E$ect of Atomic Interaction in the Solid State

I n deriving the formula (195) it was implicitly supposed t h a t the binding forces concerned are those which bind electrons t o individual atoms. For the calculation of the rate of energy loss in a gas at normal pressure this is correct, but in a condensed material other possibilities arise which can lead t o substantial modification of the formula (195), particularly for very high electron energies. I n a solid or liquid medium the displacement of a n electron from its equilibrium position sets up a polarization of the surrounding medium which tends t o oppose the initial displacement. If we are concerned with purely nonrelativistic phenomena, the effect may be represented as a modification of the effective electric force acting on the electron. If in the absence of the polarization a field E would act, then when polarization is allowed for i t becomes E 47raP where a is a constant of order unity and P is the polarization. Since P is given b y -ntr where r is the average displacement of each electron, the polarization gives rise t o an additional restoring force equal t o nt2a times the displacement. The effective frequency of the electron oscillations about equilibrium due t o atomic binding forces is therefore changed from urn to v,’ where

+

vmr2

= v2

+

vo2,

with v02

=

ne2a/rm.

Y,’ will be recognized as the absorption frequency of the medium in the classical theory of dispersion. When a = 1, v 0 is the frequency of oscillation of a free electron gas of concentration n. Under most nonrelativistic circumstances v o is very small compared with ‘,v for all m and s and has little influence. Its effect is only important when v,’ is especially small or zero as for the free

52

H. S. W. MASSEY

electrons in a metal. The contribution of these electrons to the stopping power is obtained by taking their effective binding energy as hvo. It was shown by Kramersa3th at this is indeed the limiting factor and not the resistance of the metal as originally suggested by von W e i ~ z a c k e r . ~ ~ The situation is quite different when the velocity of the incident particle is comparable with th at of light. The reaction of the surrounding electrons on a particular electron of a solid when all are disturbed by the passage of a n ultrarelativistic particle can no longer be treated as a quasi-static polarization effect. Most of the interaction arises from the radiation field and is relatively much stronger than under nonrelativistic conditions. As a result the maximum effective impact parameter p,,, due t o the atomic interaction effects does not increase in the same way as does t ha t due to atomic binding. Thus as v 4 c, p,,,, due to atomic binding, -+ yc/vm8whereas p,.,, due to atomic interaction effects, -+ c/vo no factor y appearing. Hence, at sufficiently high incident energies, for which y > I/hvo the limitation arises from the atomic interaction and not the atomic binding forces. These conclusions may be rendered plausible by the following argument due t o A. Bohr.60 Consider a fast electron following the path A B through the medium which is colliding a t time t with an electron at the point P where P N , the perpendicular from P t o A B , equals p . The electron a t P is also under the action of the fields due to the acceleration of the surrounding electrons. The field a t P due t o an electron at a point Q where PQ = r is given by

E

= (E

sin +/c2r)a(t - T / c ) ,

(200)

where a(t - T / C ) is the acceleration of the electron a t the retarded time and 4 is the angle between the acceleration and the direction PQ. The only electrons effective in influencing the motion of the one a t P will be those which, a t the retarded time, were themselves undergoing collision. The volume in which these electrons are located may be determined as follows. We choose P as origin with the x-axis measured in a direction parallel to A B . An electron a t Q for which x 2 = r2 - p 2 (see Fig. 9) will, a t the retarded time, be in a phase of collision earlier than that of P a t the time t by a n amount r given by r = - r- - . x c v Points for which r is a constant will therefore lie on the hyperboloid

When r

=

0 the hyperboloid degenerates to a cone of angle 2 arcsin (I/y)

ELECTRON SCATTERING I N SOLIDS

53

extending backwards from P , which intersects the path of the particle at a point for which z = ypv/c. Electrons which a t the retarded time were in the same stage of collision as is the one a t P a t time t lie on the surface of this cone. Since the collision time is of order p l v y , the electrons which effectively interact with the one a t P a t the time t will lie within the two hyperboloids for which 7 = + p / 2 y v . Electrons within this volume a t points for which x < y v p / c all lie on the same side of the path of the incident electron as P , and their contributions t o the net force on the electron a t P will be additive. Electrons in the remainder of the volume will give a much smaller contribution as they will be

FIG.9

accelerated in all directions. Hence if v 'v c s o y >> 1the electrons eff cctive in producing acceleration of the one .at P are confined within a volume of the same order as that of the cone PRS of height y p and semi-vertical angle arcsin (l/y), i.e., a volume of order p 3 y . If a is the acceleration of the electron a t P a t time t due t o the field of the incident electron, i t follows from (ZOO), since sin 4 N 1, that the surrounding electrons produce a net force on the electron a t P a t time t of order (202) ? 2 ( E 2 / C 2 ) ( P 3 Y )W P Y ) = (E"P2/c2)a, in a sense opposite t o a. This force is negligible compared with the total force ma acting on the electron, only if p

<< c / v o ,

(203)

where v o is as in (199). The rate of energy loss for very great incident energies thus takes the asymptotic form, in a solid medium,

where k is a constant of order of magnitude unity. The effect of the atomic interaction in the solid state is quite marked for high-energy electrons as may be seen by reference to Fig. 10 in which

54

H. S. W. MASSEY

the rate of energy loss for electrons in different materials calculated with and without allowance for atomic interaction, is illustrated as a function of electron energy. Instead of increasing steadily in the relativistic region ldE/dsI tends t o a constant value a t very high energies. The possibility that atomic interaction might influence the rate of energy loss in condensed materials was first suggested by S v ~ a n in n ~1938 ~ and a detailed theory was first given by Fermi.G6 The most elaborate calculations have been carried out by Halpern and Hall6’ some of whose results

I-

/

/

/

/

Energy in mev.

FIG. 10. Rate of energy loss, due to excitation and ionization, of electrons in lead, carbon and water. -

Calculated allowing for polarization.

- - - - - - - Calculated ignoring polarization.

are illustrated in Fig. 10. Some years earlier, however Cerenkov68had discovered that very fast electrons passing through condensed matter emit a radiation 11hich has properties characteristic of a coherent emission from large regions of the matter. Frank and TammGgpointed out that the radiation may be regarded as electromagnetic shock waves due to the phase velocity of the electromagnetic radiation in the matter being less than the velocity of the incident electrons. Since the reduction of the phase velocity below t h a t of light is due t o the cooperative action of the atoms of the medium, it is clear that there is a close connection betueen the Cerenliov radiation and the reduction of the rate of energy loss in condensed matter. Both arise from the coherent electromagnetic waves radiated from electrons of the medium accelerated by the incident electrons.

ELECTRON SCATTERING IN SOLIDS

55

3. Attempts to Detect Atomic Interaction Effects

The experimental verification of the effect of atomic interaction on stopping power is a difficult task. The effects are negligible for energies less than 1-2 mev while, at energies greater than 10-15 mev, energy loss by radiation is becoming important and masks the sought after modification. The most definite evidence that the atomic interaction effect does exist is probably that obtained by Crane, Olesen, and Chao70 from an investigation of the stopping of 10 mev electrons in carbon. These electrons are so energetic that the condition y v o >',v is certainly satisfied for all frequencies ',v of importance. The observed rate of energy loss was 1.82 & 0.08 mev/g cm-2. The loss due to radiation was 0.13 mev/g cm-2 leaving 1.69 k 0.08 mev/g cm-2 arising from electron collisions. The theory uncorrected for atomic interaction gives 1.93 mev/g cm-* whereas the corrected value gives 1.72 mev/g cm-2 in much closer agreement . Further less definite evidence favoring the modified formula has been obtained by Hereford71and by Paul and R e i ~ h . ~ ~ Evidence obtained from a study of the specific primary ionization produced by fast electrons has been referred to in 111, 4a.

4. The Range of Electrons in Matter The total path traversed through matter by an electron of initial energy E , before it is brought to rest is given by s = rdE/ldE/dsl.

(205)

Owing to scattering, the path will not be straight and an important distinction must be made between the range of electrons in a solid absorber and the total path traversed before coming to rest, The observed range is usually associated with the distance traversed in a direction normal to the absorbing plate whereas the actual path in the material must be much greater. However, in an electron sensitive emulsion the total path may be measured and is defined as the range of electrons of a given initial energy in the emulsion. This is an important quantity for all quantitative research on electron phenomena using these emulsions. It has been measured by Zajac and Ross13for electrons with energies ranging from 30 to 250 kev in Kodak NT4 photographic emulsions. Their results are given in Table IX and have been compared with the ranges calculated by the same authors, using the formula (197) with a mean excitation energy I = 125 ev. The agreement obtained is remarkably good.

56

H. S. W . MASSEY

TABLE IX. Observed and calculated mean ranges of electrons in Kodak NT4 photographic emulsions. Electron energy (kev)

Number of tracks examined

Mean range in microns with standard error

Percentage standard deviation

Calculated range (microns)

30 40 50 60 80 100 147 200 250

25 55 25 51 25 50 25 26 27

7.0 k 0.3 10.8 ? 0 . 4 15.8 f 0 . 5 21.4 ? 0 . 6 32.7 k 1 . 6 46.7 k 1 . 5 95.4 k 1.2 141 5 6 201 8

23 28 16 20 24 21 6 21 20

6.0 9.9 14.6 20.0 32.8 47.8 92.0 149 21 1

*

-

There have been a great number of experimental investigations of the absorption of electrons in solids. Summaries of our present knowledge of the subject have been given recently by Bleuler and Ziintilh and by Glendennin.Is

Absorber thickness

FIQ. 11. Illustrating the distinction between effective range (R,) and actual range (Ro) of electrons in ~b solid absorber.

Provided the initial energy of the electrons is not too low the shape of the absorption curve for electrons of homogeneous energy is as indicated in Fig. 11. There is a considerable “tail” to the curve which renders practical determination of t,he actual range rather arbitrary. It i s

ELECTRON SCATTERING IN SOLIDS

57

customary to overcome this difficulty by defining an effective range by interpolation of the linear part of the absorption curve as shown in Fig. 11. This is not satisfactory when the initial electron energy is less than 10 kev for then no part of the absorption curve is straight enough for unambiguous determination of an effective range. For this reason it is to be expected that results obtained by different observers for electrons of these energies will show discrepancies due to the arbitrariness of definition. Most attention has been devoted to the range of electrons in aluminum. Bleuler and Zunti74give the following semi-empirical expression for the maximum range Ro in this material for electrons with energies below 3 mev:

where E , is the kinetic energy and mc2 the rest mass energy of the electrons measured in mev. The rate of energy loss as a function of energy derived from this expression agrees with that calculated from the formula (197) with I = 125 ev, provided the electron energy is greater than 1 mev, but for lower energies this agreement becomes less satisfactory. This is to be expected because scattering increases as the energy decreases SO that the actual path traversed becomes substantially greater than the thickness of the material. Fowler, Lauritsen, and L a ~ r i t s e nhave ~~ extended the range energy curve to higher energies by evaluating

L6%)

where El is the maximum energy, 3 mev, considered by Bleuler and Ziinti,74the theoretical expression (197) with I = 125 ev being used for IdE/dsl. This gives for Eo > 3 mev

Ro = &Ei(log 316 (Eo

+ m c z ) ) - 0.39 em,

(207)

where Ei denotes the exponential integral. In the same way, for the effective range R,, Bleuler and Zunti74give

R,

=

+ +

EO me2 0.22Eo E~ 2mc2 cm)

which has been extrapolated by Fowler, Lauritsen, and L a u r i t ~ e n ’to ~ give R - ltoEi(log 316(Eo mc2)1 - 0.44 cm. (209)

+

Hereford and Swarm'? have tested the formula (209) by measuring the effective range in aluminum for electrons with energy between

H. 6. W. MASSEY

58

3 and 12 mev. The comparison of their results with those calculated from (209) is shown in Fig. 12. It will be seen that there is a considerable discrepancy which has been traced by Hereford and Swannll t o the effect of multiple scattering.

Energy in mev.

FIG.12. Effective range of electrons in aluminum as a function of electron energy. X

Observed by Hereford and Swan.??

____ For energies less than 3 mev as given by Bleuler and Z t i r ~ t i . ~ ~ - - - - - - - Extrapolated by Fowler, Lauritsen, and Lauritsen.’e VI. THE MOBILITYOF ELECTRONS IN METALS,ALLOYS,A N D SEMI-CONDUCTORS If a swarm of electrons of mass m and charge E is diffusing through a medium under the action of a uniform electric field F , a steady state will be reached in which the swarm drifts with a steady velocity u in the direction of the field. I n this state the energy gained from the field per second is equal t o that lost per second in collisions with the atoms of the medium. The drift velocity u is proportional t o the field strength and the constant of proportionality is known as the mobility p of the charges under the prescribed conditions. Thus u = Fp.

The mobility is determined by the frequency with which the diffusing particles make collisions with the atoms of the medium. If n is the

ELECTRON SCATTERING IN SOLIDS

59

number of scattering centers per unit volume then I.L =

E/nrniiQm,

(210)

where D is the mean velocity of the swarm and Qn is the so-called momentum loss or diffusion cross section (see Sec. IV.2a) for collisions of the particles with an atom of the medium. Qm is given by

Q~

=

2a

/o”

(1

- cos e ) i ( e ) sin e de,

(211)

where I ( B ) d w is the differential scattering cross section as defined in Sec. II.la. If Qm is a function of the velocity of the electrons, then in (210), DQ, must be replaced b y

Jo

* vf (v)Qm(v)dv,

(212)

where f ( v ) d v is the fraction of electrons with velocity between v and v dv. Many experimental and theoretical studies have been devoted to the determination of the mobilities of electrons and of positive ions in gases, but the mobility of an electron in a solid is also of great importance. The electrical conductivity c of a solid metal, alloy, or semi-conductor is essentially determined not only b y the number iV of electrons able t o move through the solid but also by their mobility p. Thus

+

u = hrcp.

(213)

The only feature which does not arise in the gaseous case is the presence of the periodic field of the solid lattice which modulates the otherwise plane waves of the “free” electrons responsible for the conductivity. Electrons move through a perfect lattice without undergoing scattering. It is only deviations from the perfect lattice which are effective in this respect. I n a pure metal lattice distortion arises from the heat motion of the lattice ions, and it is this which gives rise to the resistance. I n an alloy consisting of a pure metal in which a foreign metal is present t o a small extent an otherwise perfect lattice of the pure metal will be distorted in the neighborhood of the foreign ions. Such regions will also act as scattering centers and give rise t o additional resistance. Again a semi-conductor owes its conductivity t o the presence within an otherwise perfect nonconducting crystal of small amounts of impurity which either releases electrons t o wander freely through the crystal or removes electrons t o leave freely movable positive holes. The conductivity due t o the flow of these electrons or positive holes under the action of a n electric field is limited not only by scattering due t o the

60

11. S .

R. MASSEY

vibrations of the crystal lattice but also by scattering a t the centers where the inipurity is located. The ca1cul:ition of the cross section Q m in these cases can often be c a n i d out by a method similar in principle t o that used in Sec. 11. The only essential difference is that the undisturbed motion is represented by planc wa\-rs modulated by the pcrfect crystal lattice field. Thus, provided thc distortion of the perfect lattice is small enough, the differential cross section n hich appcars in (21 1) is given by

U is thc potential energy due t o the distortion of the perfect lattice. and J.,are the wave functions of the initial and final state of the

#%

electron and arc givcn by

#$ = zik(r)evLnoT, #,

=

uA,(r)eZL’nl r.

(215)

The modulating fuiictioiis u k , u j b ’ have the periodicity of the crystal lattice. The actual mass nz is replaced by an effective mass meffwhich is determined by the crystalline field and the electron energy. The integral in (214) is taken over the whole of the crystal but this is not necessary. If the crystal is divided up into regular polyhedra centered round each ion, a good a p p r o ~ i m a t i o nt o~ ~uk(r) ~ ~ ~may be obtaincd by solving the equation

within a polyhedron, V being the potential energy of an electron in the field of the central ion. The function is t o be a proper function within the polyhedron and must satisfy the condition that its normal derivative shall vanish on the surface of the polyhedron. I n order that such a solution should exist, the energy must have ccrtain proper values. For a particular proper value E,, say, there will be a solution The allowed energy states of an electron in the crystal mill then be given approximately hy

with the corresponding wave functions having the form

#

= eikna.r+s(T),

in each polyhedron, r being measured from the center. assured by the boundary conditions satisfied by the I#J8.

(218)

Continuity is

ELECTRON SCATTERING IN SOLIDS

61

The energy level diagram thus consists of a number of bands characterized by the different values of s and of width, depending on k,.,". In a crystal in its normal state the electrons will fill the lowest accessible states. If the number of electrons is such t h a t the uppermost occupied levels only partially fill a band, the crystal will be a conductor. The electrons which take part in the conduction will be those with energies near the minimum. The energy gained from the field is small but, according t o Pauli's principle, i t must be sufficient t o excite an electron t o a n unoccupied level. This will clearly be possible when there are unoccupied levels in the uppermost partly occupied band, but if the number of electrons is such that the uppermost occupied levels completely fill a band, the pure crystal will be a n insulator. The electrons can be accelerated by the field only if they acquire sufficient energy t o jump t o a state in the nearest unoccupied band, across the gap between the bands. This will not be possible with electric fields of ordinary strength. An insulator will be converted t o a semi-conductor if impurities are present which either donate electrons to the crystal or capture electrons from the crystal. I n the former case, that of a n excess semi-conductor, the donated electrons must fill the lowest vacant levels which will be at the bottom of the lowest unoccupied band. These electrons can be accelerated by the field, giving rise t o conduction. If the impurities capture electrons these will come from the uppermost levels of the completely filled band leaving that band only partially filled so that conduction can occur. 111 this case the material is a defect semi-conductor. To apply the theory sketched above i t is necessary t o replace the polyhedra by spheres of radius ro so that

where the integration is taken over a sphere of radius ro surrounding a scattering center. We now consider the contributions t o the scattering from the different kinds of lattice distribution outlined above. 1 . Scattering by Lattice Vibrations-Resistance

of Pure Metalsaosal

The conductivity of a pure metal is limited by the scattering due t o lattice vibrations. Except at very low temperatures this may be calculated by adding the contributions due t o scattering from separate ions. If we assume that the displacement of a n ion from the center of a polyhedron does not affect the field outside the polyhedron, (219) may be applied with U = R * grad V ,

62

H. S. W . MASSEY

where R is the displacement of the ion from the center. differential cross section is then given by

The mean

as the motion of the ions maybe treated classically. R 2 ,the mean square displacement of the ions of mass M , is given by h 2 T / M k 0 2where T is the absolute temperature, 8 the characteristic temperature of the solid, and li Boltzmann's constant. To complete the calculation it is convenient t o transform the volume integral t o one over the surface of the polyhedron. This may be done by using the fact that 4.eikno.*is a solution of the equation

GoGi* grad

1' = grad (V$&*) - l'Ic.o grad $I* - V$,* grad $o, =

[

grad ( V

- E,

- 2m

$o$l*

h2 +[J.oV2 grad 2m

$I*

h2

- 2m - $0v2$1*] - V*+Ograd $I*].

(222)

The first term in brackets vanishes as satisfies (22lj, and the second may be transformed t o a n integral over the surface of the polyhedron t o give

s

$I*

grad Vfi0 d7

= 2m h2

1

($I*

-$grad

- grad

__ a'1d*)r

dS.

(223)

For metals such as the alkali metals &(ro) N 1 and +s'(ro) = 0 so that

Over the surface of a polyhedron

as & satisfies (221) and, for the alkali metals, is spherically symmetrical. Hence

.c

grad V $ od7

=

4rro2 cos x[V(ro) - Es(ro)l (sin Kro - Kro cos KrO)/K2r02, (225)

ELECTRON SCATTERING IN SOLIDS

where K = 2k sin 40 and Thus

63

x is the angle between no - nl and grad V . (sin Kro - Kro cos K r o ) 2 / K 4 r ~ 4(226) .

It remains to determine the value of k appropriate to the conduction electrons. This may be done as follows. The number of energy levels per unit volume between k and k dk is

+

k2dk/8n3,

(227)

so that, if the total number of electrons occupying levels in the s-band is N , per unit volume N , = km3/31r2, (228) where k, is the value of k for the electron in the highest occupied level. Thus k , = (31r2N,)’. (229) Finally, for the alkali metals, of unit valency, there will be one “free” electron per atom, i.e., one per polyhedron so

N . = 3/4?rr03. This gives kro

=

(97r/4)%= 1.92.

On substitution in (226) we find that Qm

4?rm.rr2Tro4(v - E ) 2 1 - cos 0)f(3.84 sin 40) sin 8 de, h2M~e2 0 = 2.2$merr2Tro4(V - E)2/h2M~82, (232)

=

where

f(z)

=

(sin x - x cos z)~z-~.

(233)

The conductivity obtained using this expression is of the correct order of magnitude and exhibits the observed variation with temperature,80s81and there is little doubt that $he principal source of resistance of pure metals arises from scattering by lattice vibrations. 2. Scattering by Foreign Atoms-Resistance of Alloys

A foreign atom introduced within the lattice will produce a disturbance of the lattice field in its immediate neighborhood. This will lead to additional scattering and resistance. If the replacement of an ion within a polyhedron by a foreign ion changes the potential energy by an amount U ( r ) then, provided this perturbation is small, the formula

64

H. S. W. MASSEY

(219) may be used to calculate the momentum loss cross section due to this effect. hIottg2has applied the Fermi-Thomas statistical method to determine U ( r ) for an alloy consisting of a metal such as copper, silver, or gold, with one valence electron per atom, containing in solid solution a small proportion of a metal with Z 1 valence electrons per atom. He obtains V ( r ) = (Ze2/r)e--r/a, (234) where ) (235) a2 = ( ? r / 3 ~ ,%2/4me2,

+

N Obeing the number of atoms per unit volume. If the perturbation method may be used and the electrons treated as completely free, the calculation of I ( @for this case is exactly similar to that for scattering of electrons by free atoms which has been discussed in Sec. 11.1. I ( @is given by (24) with a = h/2mva,

(236)

and Qm may be calculated as in (127) to give

Thus the increase in resistance due to 1 per cent of foreign metal in solid solution is, according to (237),

where y = h2/4m2v2a2,

(239) v being the velocity of the conduction electrons which is given from (229) by h v = - (3P2NS)5'd. m

This formula agrees with experimental results on the resistance of dilute solid solutions in copper, silver, '*and gold83 provided a is taken as 0.3 A, which is rather smaller than the value given by the statistical model. 3. The Resistance of Semi-Conductors

Since there are necessarily impurities present in a semi-conductor, both the sources of scattering discussed in Secs. VI.l and VI.2 must be present. In the course of a detailed study of the properties of silicon both as an excess semi-conductor (containing a small amount of phosphorus as

ELECTRON SCATTERING IN SOLIDS

65

impurity) and as a defect semi-conductor (containing a small amount of boron as impurity) Pearson and BardeenS4have determined the mobilities of the electrons responsible for the conduction, and we shall conclude with a brief discussion of their results. a. Non-degenerate Case. When the impurity concentration is not too high, the electrons or holes produced form an assembly of such low concentration that it may be treated by classical statistics. I n general the impurities will be only partially ionized so that scattering will arise not only from ionized but also neutral impurities. The contribution from the former collisions to the momentum loss cross section, and hence to the reciprocal of the mobility, has been calculated by Conwell and Weisskopf.S6 They simply consider the scattering of free electrons with a Maxwell distribution of energies corresponding t o a temperature T . Q,,, may be calculated for electrons of velocity v by taking I ( e ) for e > eo as given by the Rutherford scattering formula for a charge e / K , K being the dielectric constant. The limiting angle O0 is so small that the contribution from smaller angles can be neglected. Thus

as the upper limit may be taken as unity without serious error. To determine eo i t is supposed that the interaction of a particular ion and an electron is screened when they are at distances apart > d, 2d being the average distance between neighboring ions. For ordinary temperatures T , the velocity v of the electrons is so low that Born's approximation is no longer valid for the description of the collisions [see (37)]. On the other hand the classical theory gives satisfactory results. According to this theory the field a t a separation d determines the scattering at a n angle eo where eo = 2e2/mv2Kd. Hence Q~ N _ ( 2 r e 4 / ~ 2 m 2 v 4 ) log ( 2 2 / 4 ~ 4 . (242) To complete the calculation vQ, must be averaged over the Maxwell velocity distribution. Conwell and WeisskopfE6obtain finally

where

x = 6KduT/e2, N l being the number of ionized impurities per unit volume. The contribution from the scattering by the neutral centers is difficult to determine as it is likely to depend sensitively on the precise form of the scattering field, and we shall ignore it henceforward.

66

H. S. W. MASSEY

Whereas the resistance due to lattice vibration increases as T , (243) shows that the contribution from ionized impurity scattering varies as T-34 and should be mainly responsible for the resistance a t low temperatures. Pearson and Bardeens4 showed that in the samples they studied the mobility could be represented by an expression of the form l/p =

aT-35

+ bTM,

where a is of the order of magnitude to be expected from (243). b. Degenerate Case. If the electron or hole concentration due to the impurities is so dense that the assembly must be treated as a degenerate one, all the impurities can be assumed to be ionized and the scattering by neutral centers ignored. I n this case the effect of the ionized impurity scatterers may be calculated in the same way aa the increase of resistance in an alloy due to lattice distortion in the neighborhood of the foreign atom. The scattering potential (234) used in the latter case (Sec. VI.2) is replaced by U ( r ) = (E2/Kr)e-7/a,

(244)

where K is the dielectric constant and a is given by (235) with n the number of impurity centers per cubic centimeter. This gives as in Sec. VI 2, if Born’s approximation is applicable, l/p =

(2eam2/3~K2h3)f(y)

where

f(Y) and

=

log (1

+ Y> - Y/(l + Y)

y = (h2/4me2)(3n/7r)36.

(245) (246)

(247)

In this case the contribution to l/p is independent of temperature and (245) should represent the value of l/p at low temperatures where the effect of lattice scattering is negligible, Comparison with observation on five samples showed that (245) gives results of the correct order if f(y) N l.84 If the screening constant a is taken as given by Mott’s statistical treatments2 a smaller value of f(y) would be obtained, but it is hardly to be expected that the rather crude theory using Born’s approximation would give results of greater accuracy. REFERENCES 1. McKay, K. G. Secondary Rlectron Emission. Advances in Electronzcs, I, 66 (1948). 2. Thomson, G. P., and Cochrane, L. Theory and Practice of Electron Diffraction, Macmillan, New York, 1939. 3. Thomas, L. H. Proc. Cambrtdge Phzl. SOC.,23, 542 (1927). 4. Fermi, E. 2.Physik, 47, 73; 49, 550 (1928). 5. Bush, V . , and Caldwell, S. H. Phys. Rev., 38, 1898 (1931).

ELECTRON SCATTERING I N SOLIDS

67

6. Hartree, D. R. Rept. Prog. Phys. XI (1946-7). 7. hlott, N. F., and Massey, H. 8. W. The Theory of Atomic Collisions, Clarendon Press, Oxford, 2nd Edition, p. 114. 1949. 8. Bullard, E. C., and Massey, H. S. W. Proc. Cambridge Phil. Soc., 26,556 (1930). 9. Bethe, H. Ann. Physik, 6,325 (1930). 10. Debye, P. Ergeb. tech. Rontgenkunde, 3, 11 (1933). 11. Borries, B. von. Z. Naturjorsch., 4a, 51 (1949). 12. Mott, N. F., and hlassey, H. S. W. The Theory of Atomic Collisions, Clarendon Press, Oxford, 2nd Edition, p. 188. 1949. 13. Marton, L., and Schiff, L. I. J . Applied Phys., 12, 759 (1941). 14. Mott, N. F., and Massey, H. S. W. The Theory of Atomic Collisions, Clarendon Press, Oxford. 2nd Edition, p. 119. 1949. 15. Schiff, 1,. I. Quantum Mechanics, p. 169. 1949. 16. hIott, N. F., an'd hlassey, H. S. W. The Theory of Atomic Collisions, Clarendon Press, Oxford, 2nd Edition, Ch. IX. 1949. 17. Massey, H. S. W.,and Burhop, E. H. S. Electronic and Ionic Impact Phenomena, Clarcndon Press, Oxford, Ch. 111. 1952. 18. Buerhner, W. W.,van der Graaff, R. J . , and Feshbach, H. Phgs. Reu., 69, 452 (1946); Buechner, \T. W., van der Graaff, R. J., Sperduto, A., Burrill, 5;. A., and Feshbach, H., zbid., 72, 678 (1947). 19. hIott, N. F., Proc. Roc. SOC.(London),A124, 425 (1929); 136, 429 (193%. 20. Bartlett, J. H., and Welton, T. A. Phgs. Rev., 69, 281 (1941). 21. McKinley, W., and Feshbach, H. Phys. Rev., 74, 1759 (1948). 22. Massey, H. S. W., and Mohr, C. B. 0. Proc. Roy. SOC.(London), A177, 341 (1941). 23. Mohr, C. B. 0. Proc. Roy. SOC.(London),A182, 189 (1944). 24. Rose, M. E. Phys. Rev., 73, 279 (1948). 25. Elton, L. R. B. Proc. Phys. Soc. (London),A63, 1115 (1950). 26. Lyman, M., Hanson, A. O., and Scott, hi. B. B d l . Am. Phys. SOC.,26,3 (1950). 27. Parzen, G. Phys. Reti., 80, 355 (1950). 28. MacColl, L. A. Phys. Rev., 66, 699 (1939). 29. Gimpel, I., and Richardson, 0. Proc. Roy. Soc. (London), A182, 17 (1943). 30. Farnsworth, H. E. Phys. Rev., 20, 355 (1922); 26, 41 (1925). 31. Bruining, P. Physicu, 6,913 (1938). 32. Heisenberg, W. Physik Z., 32, 737 (1931). 33. Koppe, H. 2. Physik, 124, 658 (1948). 34. Mott, N. F., and hlassey, €1. S. W. The Theory of Atomic Collisions, Clarendon Press, Oxford, 2nd Edition, Ch. XI. 1949. 35. Burhop, E. H. S. Proc. Cambridge Phil. Soc., 36, 43 (1940). 3G. Clark, J. C. P h p . Reo. 48, 30 (1935), and Webster, D. L., Hansen, W. W., and Duveneck, F. B. tbzd.. 43, 851 (1933), for I< ionization of Ag; Smick, A. E., and Kirkpatrick, P., zbrd., 67, 153 (1945), and Pockman, L. T., Webster, D. L., Kirkpatrick, P., and Hanorth, K. ibid., 71,330 (1047) for K ionization of Ni; Webster, D. L., Pockman, L. T., and Kirkpatrick, P. ibzd., 44, 130 (1933) for L shells of Au. 37. Hayward, E. Phys. Rev., 72, 937 (1947). 38. Messel, H., and Ritson, D. hf. Phil. Mag., 41, 1129 (1950). 39. Rudberg, E. Phys. Reti., 60, 138 (1936). 40. Slater, J. C., and Rudberg, E. Phys. Rev. 60, 150 (1936). 41. Turnbull, J. C., and Farnsworth, H. E. Phys. Rev., 64, 509 (1938). 43. Reichertz, P. P., and Farnsworth, H. E. Phys. Rev.,76, 1903 (1949). 43. Ruthemann, G. Ann. Physik, 6, 113, 135 (1948).

68 44. 45. 46. 4i. 48. 40. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. i2. 73. 74. 75. 76. 77. i8. 79. 80. 81. 82. 83. 84. 85. 86. 87.

H. S. W. MASSEY

Bethe, H., Rose, M. E., and Smith, L. P. Proc. Am, Phil. SOC.,78, 573 (1938). Snyder, H. S., and Scott, W. T. Phys. Rev., 76, 220 (1949). Lewis, H. W. Phys. Rev., 78, 526 (1950). Butler, S. T. Proc. Phys. SOC.(London), A63, 599 (1950). Goutlsmit, S., and Saunderson, J. L. Phys. Rev., 67,24 (1940); 68, 36 (1940). \Yhittakcr, E. T., and Watson, G. N. Modern Analysis, Cambridge Univ. Press, Cambridge, 4th Edition, p. 373. 1927. Moli&re,G. 2. LVuturforsch., 3a, 78 (1948). Iculrhitsky, I,. A, and Latyschev, G. D. Phys. Rev., 61, 254 (1942). MoliBrc, G. 2. .?‘aiurforsch., 2a, 133 (1947). Goldschmidt-Clermont, G., King, D. T., Muirhead, H., and Ritson, R. M. Proc. Phys. SOC.(London), 61, 183 (1948). Corson, D. R. Phys. Rev., 80, 303 (1950). Rossi, B., and Griesen, K. Revs. Modern Phys., 13, 240 (1941). Scott, W.T. Phys. Rev., 76, 220 (1949). Fleischmann, R. 2. Physik 103, 113 (1936); Mitchell, A., and Langer, R. Phys. Rec., 62, 137 (1937). Bot.he, W. Ann Physik, 6, 44 (1949). Williams, E. J. Revs. Modern Phys., 17, 217 (1945). Bohr, -4. Kgl. Danske Vidensk. Sqlskab, 19, 1 (1948). Bethe, H., and Fermi, E. 2.Physik, 77, 296 (1932). Bloch, F. Z. Physik, 81, 363 (1933). Kramers, €1. A. Physicu, 13, 401 (1947). von Weiszacker, C. F. Ann. Physik, 17, 869 (1933). Swann, W.F. G. J. Franklin Inst., 226, 598 (1938). Fermi, E. Phys. Rev., 67, 485 (1940). Halpern, O., and Hall, H. Phys. Rev., 67,459 (1940); 73, 477 (1948). cercnkov, P. Compi. rend. acad. sci. U.R.S.S., 2, 451 (1934). Frank, I., and Tamm, Ig. Compt. rend. acud. sci. U.R.S.S., 14, 109 (1937). Crane, H. R., Olesen, N. L., and Chao, K. T. Phys. Rev., 67, 664 (1940). Hereford, F. 1,. Phys. Rev., 74, 574 (1948). Paul, W., and Reich, H. Z . Physik, 127, 429 (1950). Zajac, B., and Ross, M. Nature, 164, 311 (1949). Bleulrr, l?., and Ziinti, W. Helv. Phys. A d a , 19, 376 (1946). Glendennin, L. E. Nucleonics, 2, 12 (1948). Fowler, W.A,, Lauritsen, C. C., and Lauritsen, T. Revs. Modern Phys., 20, 236 (1948). Hereford, F. L., and Swann, C. P. Phys. Rev., 78, 726 (1950). Mott, S . F., and Jones, H. Properties of Metals and Alloys, Clarendon Press, Oxford, Ch. 11. 1936. Seitz, F. Modern Theory of Solids, Ch. IX. 1940. Mott, K. F., and Jones, H. Properties of Metals and Alloys, p. 252. 1936. Seitz, F. Modern Theory of Solids, Ch. XV. 1940. Mott, N . F. Proc. Cambridge Phil. SOC.,32, 281 (1936). hlott, N. F., and Jones, H. Properties of Metals and Alloys, Clarendon Press, Oxford, p. 289. 1936. Pearson, G. L., and Bardeen, J. Phys. Rev., 76, 865 (1949). Conwell, E., and Weisskopf, V. F. Phys. Rev., 69,258A (1946). Acheson, L. K., Phys. Rev., 82,488 (1951). Hanson, A . D., Land, L. H., Lyman, E. M., and Scott, M. B. Phys. Rev., 84, 634 (1951).

The Scintillation Counter G. A. MORTON Radio Corporation of America, RCA Laboratories Division, Princeton, New Jersey CONTENTS

Page I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 11. The Photomultiplier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Multiplier Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 1. Photoelectron Collection Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 2. Multiplication Statistics ....... .. .. .. . . 80 3. Gain . . . . . . . . . . . . . . . . . . ................................... 83 4. Spurious Pulse Output.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Resolving Times.. . . . . . . . . . . . . . . . . . . . . . IV. Phosphor Crystals.. . . . . . . . . . . . . . . . . . . . . . . V. Scintillation Counter Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Radiation Detection and Monitoring.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Scintillation Counter Spectrometry. . . . 3. Time Measurements.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

94 94 103 106

I . INTRODUCTION In the few years that the scintillation counter has been in general use it has been developed into one of the most valuable tools in the field of nuclear research for the detection of high-energy radiations. As such, it has been the subject of considerable analysis itself, in addition to having been the means of obtaining the solution of a number of interesting problems of nuclear physics. It is extremely difficult to trace out the history of the scintillation counter in any detail. The device is the logical evolution of one of the earliest forms of nuclear particle detectors, the Spinthariscope. The idea of electronically counting the flashes of light produced in the phosphor of a Spinthariscope by x-rays or nuclear radiation is not new but was not applied until quite recently. The first published account of a scintillation counter appears to be that by H. Kallman' in 1947 describing work that he had carried out in Berlin at that time. This was closely followed by articles by Coltman and Marshall2 and other workers in the field. The essential components of a scintillation counter are a phosphor crystal, a secondary emission multiplier, and some form of presentation 69

70

G . A . MORTON

device: for example, a pulse height selector and pulse counter, arranged as illustrated in Fig. 1. The nuclear radiation to be measured falls on the phosphor crystal. As each nuclear emission strikes the crystal, it gives up some or all of its energy and excites a fluorescent scintillation. The light from this flash causes the release of photoelectrons from the photocathode of the secondary emission multiplier. These initial electrons are multiplied by the cascaded dynodes of the tube and when collected result in a current pulse at the output. The electrical pulses thus formed are analyzed and counted by the circuit which follows the multiplier. The scintillation counter is superior in a number of very important respects to detectors which depend on the ionization of gas for their action. Phosphor crystals can be found which are quite efficient at PHOTOMULTIPLIER

FIG.1. Scintillation counter.

converting the energy of the incident particles into photons of radiation suitable to excite the multiplier. Therefore, nearly all the particles which are absorbed by the crystal produce a countable pulse. Furthermore, since the density of the crystal can be fairly high, a large fraction of the incident radiation, whether it be material particles, such as alpha or beta rays or photons as in the case of gamma rays, is absorbed by the phosphor. As a consequence, the efficiency of the device is quite high, for example, efficiencies of 50 per cent or more for gamma rays can readily be achieved with a scintillation counter. On the other hand, with the gas-ionization type detector, the interaction of the nuclear radiation is either with the walls of the counter or with the relatively low density of gas with which the counter is filled, so that it can only detect a relatively small fraction of the particles passing through it. Therefore, the efficiency of this class of detector is low, being for most types of Geiger counters, for example, only a fraction of a per cent. Also, since the number of light photons produced in a given scintillation is proportional to the energy absorbed by the crystal from the incident particle, the number of electrons released by the photocathode and consequently the size of the current pulse a t the output is a measure of the energy of the incident particle. This means that the scintillation detector may be employed as an energy analyzer or spectrometer without sacrifice of any of its other desirable qualities.

THE SCINTILLATION COUNTER

71

Finally, the scintillation counter has an extremely short resolving time. The multiplier being an electronic device operating at fairly high voltages is extremely fast in its action. Phosphor crystals have been found for which the duration of the flash representing a single scintillation is only a per cent or less of a microsecond. This means that the scintillation counter has a resolving time of only a few billionths of a second. On the other hand, an ionization type of detector, such as the Geiger counter, will not resolve events separated by less than a few microseconds. Therefore, the scintillation counter can be used to determine the chronological relationship between nuclear events where the time intervals are several orders of magnitude smaller than has heretofore been possible. This capability is of extreme importance in experimental nuclear research. Before considering in greater detail the performance of this device or describing some of the results which it has made possible, it would be well to consider the major components making up the scintillation counter in some detail. Two in particular are characteristic of this device, namely, the photomultiplier and the phosphor crystal. Each of these will be treated in some detail in succeeding sections. 11. THE PHOTOMULTIPLIER The photomultiplier3-6 is a device for obtaining a large electrical signal from a small amount of incident visible light radiation. It consists of a photocathode and a series of electrodes known as dynodes which have been so surfaced that electrons striking them produce secondary emission. The electrodes of a multiplier are so shaped that electrons from the photocathode are directed onto the first dynode. The secondary electrons produced at the first dynode are in turn made to focus on the second dynode. This cascading process is repeated for the subsequent dynodes and finally the secondary electrons from the last dynode are collected by an anode. It is evident that with this arrangement, if the secondary emission ratio of each dynode (that is, the number of secondary electrons which is on the average produced by each primary bombarding electron) is u, the initial photocurrent will be amplified by a factor uk where k is the number of dynodes. The factor uk is known as the gain G of the multiplier. Thus, a secondary emission photomultiplier is in fact a photocell and amplifier assembled in a single electron tube. At this point it might be asked why, since in nearly eyery case elaborate circuitry involving a number of vacuum tubes must follow the multiplier in a scintillation counter, an ordinary phototube and thermionic vacuum tube amplifier cannot be used instead of the photo-

72

G . A . MORTON

multiplier. The reason is that only a few photoelectrons are released from a photocathode by the light from a scintillation. This minute photocurrent must be amplified with an amplifier having an extremely short rise time (i.e., second), if it is to be useful as a scintillation counter. However, it is not possible to design an amplifier with the required extremely short rise time which a t the same time has the very high input impedance and high signal-to-noise ratio required to amplify the very small initial current. The photomultiplier, on the other hand, has, as will be discussed in greater detail later in this section, the required rapid rise time and at the same time functions as an almost completely noise-free amplifier. To date, the photomultiplier is the only photosensitive device known which meets the demands placed on this element in a scintillation counter. I

MAGNETIC

FIG.2.

2

3

MULTIPLIER

Magnetically focused multiplier.

A number of different classes of photomultipliers exist which are fundamentally suitable for scintillation counting. These differ primarily in the means for directing electrons from one dynode to the next. The most important classes are the magnetically focused multiplier, the electrostatically focused multiplier, and the unfocused multiplier. The magnetic multiplier depends upon crossed magnetic and electric fields which produce cycloidal-like electron trajectories, for directing the electrons from one stage to the next. Figure 2 illustrates schematically the electrode arrangement for this type of multiplier. The magnetic multiplier is not available commercially and has not been used for scintillation counting. One of the reasons for this is that it is rather critical in adjustment and requires a magnetic field which must be accurately controlled in intensity and orientation, if the multiplier is to operate satisfactorily. It does, however, possess certain advantages which will be discussed later on in this article. The electrostatically focused multiplier is the type most widely used in this country. I n this type of multiplier the dynodes are so shaped as to produce an electrostatic potential distribution between successive dynodes which satisfies two important conditions. The first of these is that electrons from the working surface of one dynode strike the working

THE SCINTILLATION COUNTER

73

area of the next. The second is that the electrostatic field at the surface of each dynode is in such a direction as to draw electrons away from it. Other conditions which must be satisfied by the electrode design of the tube are that sharp points and close spacings must be avoided to eliminate cold cathode discharge effects, free paths between widely separated dynodes must be eliminated in order to prevent ion feedback, and practical configurations permitting good tube design must be used. The structure of a typical unfocused multiplier is illustrated in Fig. 3. This is a venetian blind type of multiplier used fairly extensively abroad. The electrons strike the dynode from the left, producing secondary elec-

COLLECTOR

d

SCREEN

FIG.3.

“Venetian blind” multiplier.

trons which are drawn through the structure by the potential difference between the mesh screen and the venetian blind-like dynode. After passing through the screen these electrons strike the next dynode where they produce a second generation of secondary electrons. This process is cascaded for as many stages as is required to obtain the desired total gain. In this multiplier no attempt is made to cause the electrons to follow definite predetermined paths. A number of the multipliers which have been successfully used for scintillation counting and which are commercially available in this country and abroad are listed in Table I.6 The salient features of some of these multipliers warrant further discussion. All the multipliers listed in Table I have photocathodes based on an intermetallic compound Cs,Sb of cesium and antimony. The sensitive material is thought to be an internal photoemitter, that is, photons are absorbed in the bulk material in a depth of a few tens of angstrom units causing the excitation of photoelectrons which escape from the surface. This is in distinction to surface photoemitters, such as cesium-cesium oxide-silver, where the absorption of photons effective in releasing electrons occurs only at surface atoms. Two forms of cesium antimony photocathodes are employed, these

TABLEI. Tuhe Type Photocathode type area (cm2) spectral class peak response (angstroms) longwave cutoff (angstroms) sensitivity ( p a j l ) Gain number of stages volts per stage average gain Capacity coll. to last dynode (jtpf) coll. to total structure (ppf) Voltage overall (maximum) coll. to last dynode Current coll. (maximum, average) (ma) dark current (pa) Dimensions length (in.) diameter (in.) See footnote page 78.

Characteristics of commercial photomultipliers.

RCA 931A

RCA 1P21

RCA 1P22

RCA 1P28

RCA 5819

EM1 4588

EM1 5060

EM1 5311

Internal 1.9

Internal 1.9 s-4 4000 7000 40

Internal 1.9 5-8 4200 8000

Internal 1.9 s-5 3400 7000 15

Tube end 11 S-9 4800 7000 40

Internal 20 Like S-4

Tube end 0.7 Like S-9

Tube end 5 Like s-9

40

20

20

9 100 105

10 90 6 X lo5

9 150 106

11 160 107

11 160 107

s-4 4000 7000 10

3

9 100 108

9 100 2 x 108

9 100 2 - x 106

4 6.5

4 6.5

4 615

4 6.5

5 8

1250 250

1250 250

1250 250

1250 250

1250 150

1500 150

1 .o 0.25

0.1 0.1

1.o 0.25

2.5 -

0.75 0.05

0.03

3"16

3"16

3"16

1A

1A

56 2t

10 2

2

x

0

p g

o

2

0 2

8

1

180

180

1 0.01

1 0.1

S#

8%

2

2

75

THE SCINTILLATION COUNTER

being illustrated in Fig. 4, together with their respective spectral responses. For the first, the material is deposited on a solid metal back and electrons are emitted from the side on which the light is incident. The second form is a thin semi-transparent layer of the material on a transparent glass backing. Here the light is incident on the surface through the glass and electrons are emitted from the side opposite t h a t from which the light falls. It will be seen from Fig. 4 t h a t the spectral response has a maximum a t a slightly shorter wavelength for the first form of cesium antimony photocathode than for the second. Further. more, the quantum efficiency of the first form is slightly higher than t h a t

-GLASS

3000

4000 WAVE

SPECTRAL

5OOO LENGTH

6000

A

RESPONSE

FIG.4. Spectral response of CssSb photocathodes.

of the second. The quantum efficiency of the metal-backed materia a t its peak response is about 0.3 per cent per microamp per lumen response. Since sensitivities of 40 microamps per lumen or more can be easily achieved with this surface, quantum efficiencies above 10 per cent can be readily obtained. The semi-transparent cesium antimony photocathode has a somewhat lower quantum efficiency, it being 0.2 per cent per microamp per lumen. Thus, with the same sensitivity t o white light, that is 40 microamps per lumen, its quantum efficiency will be about 8 per cent. Obviously, if the wavelength of the incident light does not correspond t o that of the peak response, the quantum efficiency will be lower. The quantum efficiency for any wavelength can be readily determined with the aid of the spectral response curve given in Fig. 4,together with a n equation which takes account of the variation of energy per photon with wavelength. If yx, is the quantum efficiency a t Xo, the wavelength of the peak of the spectral response, the quantum efficiency ^/x a t wsvelength X will be:

where Rx is the response a t wavelength X as indicated by the response

76

G. A. MORTON

curve. A high quantum efficiency is of considerable importance in scintillation counting, as will become more apparent when the statistics of the situation are considered in a later section. The thermionic emission from the photocathode is a factor which cannot be ignored. If the thermionic emission a t room temperature causes a large number of electrons to enter the multiplier structure, these will contribute to spurious pulses in the output, which will form a background that may be objectionable or even intolerable. The thermionic emission from the cesium antimony type of photocathode at a given temperature varies'somewhat with the specific processing which has been

I

I

10

100

I

1000

1

l0,OOO

VOLTS

FIG.5. Secondary emission ratio of CstSb as a function of voltage.

given the material. Measurements on a number of these surfaces indicate that a fair value is 5000 electrons per square centimeter per second a t a temperature of 30°C. The thermionic emission increases rapidly as the temperature is raised, as would be expected from the Richardson equation. As has already been mentioned, the dynode surfaces are sensitized to have a high secondary emission ratio. The material used in this sensitization is essentially the same as that used on the photocathodes, namely, an intermetallic compound of cesium and antimony. The specific method of depositing and activating the material, however, may differ considerably from that employed for the photocathodes. The secondary emission ratio of the material is a function of the velocity of the impinging electrons. Figure 5 shows the variation of the secondary emission ratio of a typical cesium antimony surface as a function of the potential through which the bombarding primary electron falls.

THE SCINTILLATION COUNTER

77

This material is found t o be quite satisfactory as a secondary emitter. While the maximum secondary emission ratio is perhaps 25 per cent lower than the best practical secondary emitter known, namely, the cesium-sensitized cesium oxide-silver surface, i t is more stable and also more easily produced. Not only is the material found t o be fairly insensitive t o temperature changes, but also i t is quite stable under electron bombardment as long as current densities of 50 microamperes per square centimeter are not exceeded. At higher current densities there is a falling off of secondary emission ratio as the bombardment continues. Complete recovery from this fatigue effect can be expected if the secondary emissive surface is allowed t o remain a t room 6. diagram of type 931A multitemperature without bombardment for a pe- plier structure. riod of a few minutes t o several hours. Of the multipliers listed in Table I the RC'A 931A, 1P21, 1P22, and 1P28 are identical in their electrode design. The photocathodes in these tubes are metal electrodes followed by nine-stage multiplier units with the dynodes arranged in a circular pattern in order to obtain maximum space utilization. Figure 6 shows schematically the arrangement of this structure. The area of the photocathode in this tube is rather small, and the electrode is mounted well back inside the tube. This makes i t difficult t o obtain good optical coupling between the phosphor crystal and the photocathode. Other characteristics such as uniformity, stability, gain, and life are well suited for scintillation counting. The 931A has a metalbacked cesium-antimony photocathode of the Type S4. The RCA 1P21 is similar t o the 931A, but is processed t o have high gain and stability, low dark current and maximum uniformity. The same type of photocathode is used in the 1P28, but the tube is sealed in a Corning 9741 glass envelope which is transparent t o ultraviolet radiation out t o 2000 angstroms. The RCA 5819 eliminates the objection of the small, inaccessible photocathode mentioned in connection with the 931A. The photocathode is a l+-in. diameter disk forming the glass end of the tube, followed by a ten-stage multiplier structure. The arrangement of the photocathode and dynodes is illustrated in Fig. 7. The electrode structure is the same as that of the 931A, but the surface which in the former is a photocathode is in the 5819 so processed t h a t it can serve as the first dynode. The large end-on photocathode of this tube makes i t possible

@

78

G . A. MORTON

t o obtain good optical coupling with a phosphor crystal and, therefore, this tube has been found t o give excellent results for scintillation counting. The EM1 4588 and 5060 are both venetian blind type multipliers. The 4588 has a large area internal photocathode followed by a nine-stage structure. Because of its size, fairly efficient optical coupling can be obtained with this multiplier in spite of the fact that the photocathode is a n internal electrode. From the characteristics listed in Table I it will be seen that the gain for a given overall voltage is somewhat less than

J

PHOTOCATHODE

I 1 I

1

ACCELERATING

1 ELECTRODES$

'.

\

FIG 7. Schematic diagram of type 5819 multiplier structure. for a focused multiplier. Furthermore, the inefficiency characteristic of this t$ypeof unfocused multiplier makes the statistics slightly poorer. I n spite of the two unfavorable characteristics mentioned, the tube has given very good performance in scintillation counters. The EM1 5060 employs a n on-the-glass photocathode, but the area of this photocathode is only about one twenty-fifth t h a t of the 4588. The small area is t o minimize the thermionic current, and the on-the-glass cathode permits good optical coupling. This tube has also given excellent results. *

111. MULTIPLIER PERFORMANCE I n considering the performance characteristics of a multiplier which makes it suitable for scintillation counting, one must examine the factors which contribute t o obtaining a current pulse output which is most nearly proportional t o the number of photons striking the photocathode; those which permit the fastest rise time and those minimizing the spurious pulse output. The principal cause of the departure of proportionality between the current pulse from the multiplier and the number of photons striking the photocathode is the poor statistics involved. A scintillation causes the release of some small number 6 of electrons from the photocathode. Since the emission is a random process, there is a probable deviation in 6 proportional t o the square root of 6 itself. Therefore, the

* Added

in press.

Additional photomultipliers have been introduced by both

-

RCA and EMI. Some of these are: RCA 6199, like the 5819 but with 135-inch diameter; EM1 6262 approx. 3 in.2 photocathode area, 14 stage, gain lo8.

THE SCINTILLATION COUNTER

79

fractional root mean square deviation cannot be less than 1/43, where 6 is the number of electrons entering the multiplier. Furthermore, the whole multiplication process occurring in the multiplier is statistical in its nature which further increases the deviation. As will become increasingly apparent as the discussion proceeds, among the several ways of decreasing the deviation the most effective way of improving the statistics of the situation is by making 6 as large as possible. 1. Photoelectron Collection Eficiency

The two factors which determine the number of electrons entering the multiplier structure for a given number of incident photons on the photocathode are the quantum efficiency of the photocathode and the collection efficiency of the electron optical system which directs the electrons from the cathode on to the first dynode. The quantum efficiency of the photocathode has been discussed briefly in the preceding section. Its improvement rests on the discovery of new materials for sensitizing the photocathode or of new ways of activating known materials. The efficiency of photoelectron collection in a multiplier is primarily a matter of the electrode design. A multiplier which is faulty in this important aspect cannot be made t o perform well, no matter how it is used. . It is possible, however, b y incorrectly using a well-designed multiplier t o spoil the collection efficiency. The two most common causes of poor collection efficiency, where the inefficiency is due t o the manner of usage rather than of multiplier design, are the presence of a magnetic field in the neighborhood of the photocathode or incorrect voltages used on the multiplier. Occasionally a multiplier will incorporate magnetic materiais in its structure, which may become permanently magnetized causing poor collection efficiency even when a n external source of magnetic interference is absent. Such a multiplier can be readily demagnetized by passing it through a coil carrying alternating current (in doing this care should be taken not t o turn off the current through the coil until the multiplier has been moved some distance away from it). Where a multiplier is being used in an experiment demanding a high correlation between the intensity of light flashes and the current output pulses, as is the case for energy spectrometry, etc., it is well t o measure not only the gain and photosensitivity of the multiplier used, but also its collection efficiency. There are a number of procedures for doing this. One which uses essentially the same equipment required for spectrometric measurements is as follows. A small amount of light is allowed t o fall on the photocathode of a multiplier which has a pulse height discriminator and pulse counter as output circuit. An integrated pulse height curve is made of the pulse output by plotting the number of

80

G . A . MORTON

pulses per second n which exceed a given pulse height p as a function of p . Obviously, when this curve is extrapolated to zero pulse height, the pulse rate n,‘ must equal the number of electrons which enter the multiplier. A curve of this type is illustrated in Fig. 8. The number of electrons COUNTING

I

“P

RATE DO00

2

I

PULSE

HEIGHT

3

(ELECTRON

HEIGHTS)

FIQ.8. Photoelectron pulse height distribution.

per second n, which leave the photocathode can be calculated from the output current ioand the gain G of the multiplier by the relation:

The collection efficiency q p will therefore be:

If a given scintillation yields N photons at the photocathode of a multiplier, the number of electrons 6 which enter the multiplier and are useful in determining the size of the output current pulse will be 6

= YVPN

I t is evident that the quantum efficiency y of the photocathode and the collection efficiency q p are equally important in determining the effectiveness of the multiplier. 2. Multiplication Statistics

It was also mentioned that the process of multiplication contributes somewhat to increasing the mean square deviation of pulse height from their expected value. This is because the whole process of secondary emission is statistical in nature. In other words, if the average gain of the multiplier is given as G, this does not mean that every electron

THE SCINTILLATION COUNTER

81

passing through the multiplier leads t o exactly G electrons at the output. G is actually only the expected number of electrons and the probable deviation from this value must be calculated. The secondary emission ratio u of a dynode is in itself a statistical quantity and, as has been pointed out, the multiplier simply cascades the values of u. The exact distribution of secondary electrons from a dynode is not known. The distribution is, however, approximately that given by Poisson's law, namely, if u is the secondary emission ratio, the probability of exactly z electrons leaving the surface when it is bombarded by an electron is given by

Nevertheless, there is reason to believe that the actual distribution in the case of real secondary emitters and in particular of dynodes as used in a mulbiplier departs somewhat from this relationship. If a Poisson distribution is assumed, the root mean square deviation from the expected number of electrons z = u will be

49

= d u

I n striking the next dynode each of these electrons produces its secondary electrons in accordance with the same distribution. This type of cascading problem can be handled by means of a special generating function from the theory of probability. The form of this function F ( s ) is such that z = F'(1) AZ2 = F"(1) 4-F(1) - [F'(1)]'

For the multiplier problem the function takes the form for k stages: F(x)

. - fi-l(fi(fi+l

= fO(fl(f2(. m

*

-

. (f&>>>>)>>

2=0

and for the dynodes f l

- .

fk

j,(z>=

2

= e-cesz Z!

2=L)

Forming the generating function as indicated above leads to F ( % ) = e-6e6e-"eue . . . '

-

repeated k timea

82

G. A. MORTON

By differentiation and substituting x

=

z=

1

6Uk

as was t o be expected and

Since k is a relatively large number and moment reduces t o

-

AZ2 - 1

u

> 1 the

fractional second

a

6u-1

2 2

If photoelectrons are released one a t a time from the photocathode (note: this does not mean 6 = 1 but rather -fo = x) the fractional mean square AZ2 1 deviation of pulse heights will be 7= __. a-1 If, on the other hand, the distribution of secondary electrons for a dynode differs somewhat from a Poisson distribution so that for a secondary emission ratio of u the root mean square deviation is & the fractional mean square deviation for a k stage multiplier becomes

z

and for electrons emitted singly from the photocathode:

A22 2 2

-

E

a-1

The relation for 6 electrons from the photocathode is a n important one and will be used when the problem of employing a scintillation counter as an energy spectrometer is considered. A measurement of the distribution curve of the pulse heights obtained from a multiplier can be used t o evaluate e in the relation €/a - 1. Such a curve is made as described in connection with the determination of the photoelectron collection efficiency. For a typical RCA 5819 this type of measurement gives a value E = 1.54. The photoelectron distribution curve is very valuable in appraising the performance of a multiplier in a scintillation counter system. I n addition t o giving a means of evaluating E and q p it permits a rather direct determination of the pulse height produced on the average by an electron entering the multiplier.

THE SCINTILLATION COUNTER

83

3. Gain

The gain of a multiplier used for scintillation counting is not a t all critical as long as it remains constant throughout the measurement. The gain should be high enough so that the output pulse can be readily handled by ordinary vacuum tube circuits following the multiplier. This sets a gain of a few hundred thousand as the practical lower limit for a multiplier used for this purpose. If the gain is too high, that is 1 0 9 or more, the output current may become space-charged limited unless special precautions are taken. Multiplication factors lying anywhere between these two extremes are found to be perfectly satisfactory for scintillation counting. Since it is important to know the gain of the multiplier in order t o determine the. statistics of the situation, a word might be said about methods of making gain measurements. Since the ratio of output current to photoelectron current a t the photocathode is very large, it is usually impossible t o make a gain measurement simply by measuring these two currents. There are, however, several ways of getting around this difficulty. One is t o divide the multiplier into two or more sections. For example, a ten-stage multiplier with a gain of a million can be measured by first measuring the input and output current for the first five stages and then the input and the output current of the last five, the total gain being the product of the two values determined. An alternative method is t o first operate the multiplier a t a reduced voltage so that the overall gain is low. Under these conditions the gain of the multiplier can be measured simply by measuring input and output current. Keeping the multiplier voltage constant, the light level is then reduced until the output current is very small. The input current is then calculated. Next, keeping the incident light on the photocathode constant the voltage of the multiplier is raised to its normal value. The output current is then measured and the gain calculated from the ratio of the measured output current to the calculated input current. If the operating gain of a multiplier is extremely high, it may be necessary to carry out this procedure in three steps instead of two. Since the secondary emission ratio is a function of the potential difference through which the primary bombarding electron falls, the overall gain of a multiplier is extremely sensitive to the overall voltage. This can be readily seen from the following equations: a-kV G = uk ,- ( I G V ) ~ AG AV G,-k-v

84

G . A. MORTON

Referring to Fig. 5, it will be seen that the secondary emission ratio varies only a little less rapidly than linearly with bombarding voltages in the range normally used between dynodes of a multiplier. The gain is therefore almost proportional to the lcth power of the voltage where lc is the number of stages of the multiplier. Actual measurements of the variation of gain with voltage for a nine-stage 1P21 shows it to be proportional to the seventh power of the voltage. This means that where a scintillation counter is to be used under conditions where a quantitative measurement is made of the output current pulses, the overall voltage of the multiplier must be maintained at a very constant value.

4. Spurious Pulse Output When a secondary emission photomultiplier is measured in complete d a r k n e s ~ ,a~certain ?~ number of pulses per second will be observed in the output. Some few of these may be due t o cosmic rays reacting directly with the photocathode or other parts of the multiplier, but by far the largest number of the spurious pulses are internally generated. A number of causes may operate to produce the. dark current pulses. All but one of these causes are, however, nonfundamental in nature. Thermionic emission from the photocathode and to a lesser extent from the dynodes will contribute output pulses which are basic to the photomultiplier. For a given type of photocathode they cannot be eliminated except by lowering the temperature of the multiplier. Other nonfundamental causes of dark current pulses in the output are the ionization of any small amount of residual gas left in the tube and field emission from sharp points or edges of electrodes where high gradients may develop. Electrical leakage over insulating surfaces may contribute to a dark current a t the output, but usually does not produce spurious pulses. With a well-manufactured photomultiplier operated with normal voltages, the nonfundamental spurious pulse sources should be almost completely absent. The dark current pulse outputs of an RCA 931A and an RCA 5819 are shown in Fig. 9. The pulse height distribution curve for the 5819 is almost identical with the distribution curves obtained for photoelectrons from the photocathode. This is to be expected, since the large size of the photocathode makes it the major source of electrons producing the dark current pulses. With the 931A where the dynodes have nearly the same area as the photocathode, the form of the distribution curve is noticeably different. The curves shown are plotted in terms of electron heights entering the multiplier. In this form the distributions are essentially independent of voltage, until the voltage is raised to a point where other effects than thermionic emission appear.

85

THE SCIXTILLATION C O U N T E R

Since the primary cause of the dark pulses is thermionic emission, it is obviously strongly effected by the temperature a t which the tube is operated. By cooling the multiplier t o dry ice or liquid air temperature, the dark pulse rate can be reduced t o a very lorn value. I n the neighborhood of room temperature the number of dark pulses per second of any

0

2

4

PULSE

HEIGHT

6

8 (ELECTRCN

10

HEIGHTS]

FIG.9. Spurious pulse output from types 931A and 5819 photomultipliers.

given pulse height doubles with each ten-degree centigrade rise in temperature. 5 . Resolving Time

It has already been pointed out t h a t one of the important attributes of the scintillation counter is its very short resolving time. The limit to the resolving time is determined in part by multiplier performance and in part by the properties of the phosphor crystal employed. As will be shown somewhat later, i t is possible successfully t o use crystals whose flash durations are less than lop8second and where the rise time of the flash is even shorter. A cooled crystal of trans-stilbene is a n example of a phosphor showing this performance. Such time durations are very small indeed, in fact quite comparable

86

G . A. MORTON

with electron transit times. Therefore, i t is necessary t o examine the operation of the multiplier rather critically t o determine its limitations in this respect. When an electron starts from the photocathode of the multiplier and proceeds t o produce generations of secondary electrons which are eventually collected a s a current at the anode, a certain amount of time is required. This transit time itself does not, however, limit the resolving time of the multiplier. If all the electrons took exactly the same length of time in performing this operation, this time would simply constitute a delay which could be measured and allowed for in the experiment. The electrons in traversing the multiplier, however, do not necessarily take exactly the same length of time. The resultant transit time spread is the thing which ultimately limits the resolving time of a multiplier. A number of processes which occur as part of the operation of a secondary emission multiplier may contribute t o the transit time spread. Among the more important ones, which must be examined in detail, are: ( u ) emission time of secondary electrons, ( b ) initial velocity effects, (c) electron trajectory differences, and (d) space charge effects. Considering these in order: The exact emission time for secondary electrons has not yet been determined; however, some recent measurements seem t o indicate time constants as long as 3 X second. Other experiments have indicated t h a t a t least a certain fraction of the secondary electroiis are emitted in times less than second. Secondary electrons are emitted with a rather large range of initial velocities. A good secondary emitter will emit most of its electrons with initial velocities in the range of from 0 t o 3 v. It is quite obvious that an electron emitted with 3 v velocity in the direction of the next dynode mill reach i t before a n electron starting with zero initial velocity. It can be readily shown t h a t the fractional decrease in transit time of the higher velocity electrons over those emitted with zero initial velocity is approximately given by the relation

"=JZ t

Assuming now t h a t the multiplier is operated with 100 v per stage making V o = 100 v, a n electron leaving with a n initial velocity of 3 v directed toward the next dynode will require 17 per cent less time than one leaving with almost no velocity. Since for the type of structure under consideration, the transit time delay is the order of 3 X lop9 second, this decrease in transit time amounts t o about 5 X 10-lO second. Differences in trajectory lengths of electrons leaving various points on the dynode is perhaps the largest factor contributing t o the spread in

THE SCINTILLATION COUNTER

87

transit time. The effect of path length differences has been calculated for a typical linear electrostatic multiplier structure of the type illustrated in Fig. 10. Here the time required to traverse the shortest path is found to be 3 X second and the time difference between the longsecond. Including both the effect of est and shortest path 1.7 X initial velocity and the differences in path lengths, the maximum time spread in one stage is the order of 2 X second. The probable spread is then less than but close to half this value. Since the differences in transit times are more or less random in nature, the total spread for a

FIQ.10. Typical linear multiplier structure.

multiplier having k stages is not k times that for a single stage, but more nearly equal to the square root of k times this value. Thus, the transit time spread for a sixteen-stage multiplier of the type shown will be about 4 X 10-9 second. Experimentally with a sixteen-stage multiplier having a structure corresponding to that illustrated and operated under conditions such that the collector current is space charge limited to 35 milliamps, the maximum charge on a 150 micromicrofarad condenser developed by pulses corresponding to single electrons emitted from the photocathode is found to be about 1; v. This means that the time spread for the pulse from a single electron is approximately 5 x second, which is in good agreement with the value arrived a t above. It should be pointed out that for many experiments it is not necessary t o base the time accuracy upon the arrival of the entire charge which results from a single electron a t the photocathode. Frequently the circuitry following the multiplier can be triggered by as little as 10 per

88

G . A. MORTON

cent of the charge from a single electron. When this type of measurement is possible, it obviously leads to a considerable improvement in time resolution. Indeed, almost one order of magnitude in time resolution improvement can be obtained.

IV. PHOSPHOR CRYSTALS A wide variety of phosphorss-'7 are available for scintillation counters. The selection of the particular phosphor to be used depends upon the type and energy of the radiation investigated and upon the particular type of measurement that is being made with the scintillation counter. For alpha particle measurements,S~9the phosphor is generally in the form of a relatively thin screen of powdered fluorescent material mounted on a glass or plastic plate. This screen is mounted as close to the photocathode of the multiplier as possible in order to obtain good optical coupling. Screen thicknesses of only a few milligrams per square centimeter are optimum for this type of measurement, since the penetrating power of alpha particles is rather small. Silver-activated zinc sulfide has been found to be one of the most efficient materials to use for this type of screen. A well-prepared screen of this material will yield one photon per each one hundred electron volts or less energy of the incident particle. This type of phosphor, however, is rather slow, the duration of the scintillation being several tens of microseconds. For most alpha particle measurements this is not a serious objection. Where coincidences between alpha particles or an alpha particle and other types of radiation are being investigated, a zinc sulfide screen may not have adequate resolving time. Zinc oxide has only about 20 per cent the efficiency of zinc sulfide, but the duration of the scintillation is considerably shorter being about one microsecond. For still shorter resolving time the organic crystals may be used, but these are quite inefficient under alpha particle excitation. For gamma and beta rays the problem is somewhat different. Here the radiation is quite penetrating and it is necessary to use a phosphor crystal having a relatively large volume and high optical transparency, so that light generated inside the crystal can escape without too much attentuation. Materials which have been successfully used for scintillation counting of beta and gamma rays are of two classes, namely, inorganic phosphors and organic phosphors. The behavior of these two classes is quite different and probably the mechanisms of fluorescence are fundamentally unlike. All the organic phosphors which have been found satisfactory so far contain conjugated double bonded carbon atoms in benzene rings. The fluorescence is probably due to intramolecular energy transitions. The

THE SCINTILLATION COUNTER

89

fluorescent behavior of the organic phosphors is characterized by a very short duration of luminescence, which duration decreases as the temperature is decreased. The efficiency of the release of photons per unit energy of the incident particle is fairly good, but decreases a s the resolving time of the material decreases. One of the interesting properties exhibited by the organic phosphors is that they will form quite efficient mixed crystal phosphors. For example, naphthalene, which in itself is a rather inefficient phosphor, when mixed with 1 per cent or less of anthracene (a good phosphor) and crystallized forms a solid solution which is crystalline and nearly, if not wholly, as efficient as anthracene itself. So many examples are found of this property of forming a n efficient phosphor when a small amount of one material, usually a good phosphor, is dissolved in a large amount of material which in itself is inefficient, t h a t processes which are fundamental t o the basic mechanism of the production of fluorescence in organic materials must be involved. At present, the mechanism of the transfer of energy from the inert solvent t o the active centers of the solute is not understood. One possibility is t h a t ultraviolet radiation serves as the transfer link. Ultraviolet may be produced having a wavelength slightly longer than that of certain characteristic absorption edges of benzene rings of the solvent. The very electronic configuration that makes the solute a good phosphor may shift these characteristic absorption edges t o slightly longer wavelengths. Therefore, the solute strongly absorbs the ultraviolet produced in the solvent, transforming this energy into visible radiation by the fluorescent mechanism in the solute molecules. It is interesting t o note that this property holds for both liquid and solid solutions. I n the case of the inorganic materials the fluorescence is probably the result of transition involving the energy band structure of the crystal and energy levels associated with impurities or imperfection activator centers in the crystal rather than with transitions in individual molecules. This mechanism rules out the possibility of forming the type of mixed crystal phosphors mentioned in connection with the organic materials. The scintillation behavior of inorganic materials is characterized by a fluorescent flash of longer duration than that for organic materials, and the duration of the flash in general increases with decreasing temperature. The efficiency of some of the inorganic phosphors is considerably higher than that of most organic materials known. Furthermore, since some of the inorganic phosphors have a very high density, the net efficiency per volume for converting gamma rays t o visible light photons is great. Table I1 lists a number of phosphors which have been found useful

90

G. A. MORTON

for scintillation counting. These materials are grouped into inorganic phosphors, organic phosphors, mixed crystal phosphors, and liquid phosphors. The most important characteristics of the materials, namely, density, index of refraction, wavelength of radiation, duration of flash, and efficiency, are included in the table. I n giving the efficiencies no attempt is made to place the efficiency of the material on an absolute basis. Rather, the numbers from 1 to 5 are used to order the material in terms of their effectiveness; 1 being the most efficient and 5 the least. As a guide t o the significance of these numbers, materials designated as 1 produce more than 10,000 visible light photons per mev energy of the incident particle. Those numbered 2 produce approximately 10,000 photons per mev; 3 approximately 5000; 4, 2000; and 5, 1000 photons per mev. TABLE11. Crystal Phosphors. Name

ComSpectromposition Density Index eter

Inorganic 6.06 1.934 3.67 1.7745 7.90 2.2-2.3 4.06 1.955 3 . 1 8 1.434 Organic Anthracene 1 . 2 5 1.595 Trans-stilbene 1 . 1 6 1.622 1.23 Terphenyl Naphthalene 1 . 1 5 1.618 M i z e d Organic Naphthalene (anthracene) 1 . 1 5 1.618 Naphthalene (distyryl) 1 . 1 5 1.618 Diphenylene oxide (anthracene) Liquid Phosphors Terphenyl in xylene 0.8641 1.500 Terphenyl in benzene 0.879 1.501 Anthracene in phenyl ether 1.073 1.583

Calcium tungstate Sodium iodide Cadmium tungstate Lithium iodide Fluorite

Caw04 NaI(T1) CdWOh LiI(T1) CaFz

4300 A 4100 5200

Blue ~4000 4400 4100 -4000 -3500 4400 N4500 -4400

-4000 -4000 -4400

Time

>

3 x 10-7 > 10-6 10-6 10-7 3-4 2-1 -2 -5

x x

x x

10-8 10-8 10-8 10-8

4 x 10-8 1-3 X 10-8 -10-8

(fy;oapt)

Efficiency 1 1-2 1 2 3 2 3-4 2-3 5

3 2 3 >4 4

5

A number of the materials listed have such wide usage that they deserve separate mention. Sodium iodide activated with thalliumll is a very effective inorganic phosphor. Its efficiency as a phosphor is good, and the relatively high atomic number of the iodine makes it an excellent absorber of gamma rays. The flash duration of this material at room temperature is the order of 5 X 10-7 second. The material forms very nice transparent crystals; but the crystals are extremely sensitive to moisture. A rela-

THE SCINTILLATION COUNTER

91

tively short exposure t o the atmosphere may completely ruin one of these crystals. The instability of the material toward water vapor together with the rather long flash duration somewhat curtails its usefulness. The other alkali iodides activated with thallium are also useful as phosphor crystals. Cadmium tungstateI2 is an efficient phosphor and has a very high density. It can also be made into clear very stable crystals. Howei7er, the flash duration is quite long, being several microseconds so that it is not suited for work where speed is important. Calcium fluoride13 can be obtained in large clear crystals which are extremeIy stable. The flash duration for this material is the order of lo-' second, but the material is not a very efficient phosphor, which limits its usefulness. The organic crystal phosphor, anthracene,14 is probably the most widely used material in scintillation counters for the detection of beta and gamma rays. Although the efficiency of this material is not as good a s some of the inorganic phosphors, it is nevertheless good enough so that the deficiency in this property is not serious. The important feature of the crystal is that its flash duration is quite short, being 3 t o 4 X lo+ second a t room temperature and 1 t o 2 x 10-8 second when cooled t o liquid air temperature. Because of its great usefulness, i t is worth devoting a few paragraphs t o the description of its properties and method of preparation. Anthracene consists of three benzene rings linked together in a straight line. The rings are so joined as t o permit the formation of conjugated double-bonded carbon, which in turn allows the existence of T electrons, that, in accordance with present theories of organic fluorescence, are responsible for the emission of light. The material forms monoclinic crystals having a specific gravity of 1.25. The melting point of these crystals is about 215"C, a temperature which is high enough for most practical applications in scintillation counter work without being so high as t o make crystal synthesis difficult. The fluorescence is in the form of a relatively narrow band having a peak a t 4140 angstroms. The index of refraction of the crystal is about 1.5948. T o prepare a crystal of anthracene, first dissolve 20 g of the material in 100 cc of pure ethylene glycol. The ethylene glycol and anthracene are co-distilled and then precipitated, the anthracene being filtered from the solution. The ethylene glycol is recycled. After this process has been completed, the anthracene is washed in hot distilled water t o remove most of the ethylene glycol. The material is next dried in a vacuum desiccator. I n order t o remove the last traces of ethylene glycol the material should then be melted under vacuum. Next, the anthracene is

92

G . A . MORTON

distilled into the crucible in which the crystal is t o be grown. A crucible for this amount of material might consist of a pyrex tube with a conical tip ending in a small bulb a t the lower end and an entrance tube through which thc material is distilled into the vessel at the upper end. Eyelets or hooks as required t o support the crucible should be sealed near the top of the container. The furnace in which the anthracene is crystallized consists of a cylindrical pyrex or ceramic tube wound with heater wire in such a way t h a t the temperature in the upper half of the furnace is above the melting point of anthracene and there is a gradient of approximately 60°C per inch throughout the length of the furnace, the lower part being held only slightly above room temperature. The windings should be arranged in such a way that the isothermal lines are as flat and uniform as possible. .4n outsidc cylindrical baffle will increase the efficiency of the furnace and decrease its sensitivity t o external convection currents, etc. The crucible containing the anthracene is suspended in the furnace by a flexible wire which is wrapped around a drum that is turned by a slow speed motor mounted above the furnace. The speed of the motor is adjusted so as to lon-er the crucible a t a rate of about & in. per hour. The anthracene will be melted a s long as the crucible is in the upper part of the furnace, but as it is lowered through the 215°C isothermal surface, crystallization takes place starting a t the tip. A small single crystal (to act as a seed) should first form, and then as the crucible continues t o lower, the crystal should grow from the bottom up until the entire charge has crystallized. Occasionally more than one crystal will start a t the tip of the crucible. I t is then necessary t o raise the crystal back t o the upper high temperature part of the furnace and remelt the anthracene. Usually two or three tries are sufficient to obtain a good, single crystal. If the anthracene has been carefully prepared and purified, it should be possible t o obtain water-clear, single crystals of several cubic inches in volume by following this procedure. Trans-stilbene is another organic material which has been found to be very useful for certain types of investigations using scintillation counting. The efficiency of the material is lower than that of anthracene, but its flash duration is shorter, making i t useful where time relationships are t o be measured. The flash duration of the material a t room temperature is about 10-8 second. When the material is cooled t o liquid nitrogen second. temperature, the flash duration becomes less than 5 X Naphthalene itself is a poor phosphor, a t least in the visible region. However, the material may be useful a s the solvent for mixed crystals. With distyryl as a n activator the mixed crystal has an efficiency slightly

T H E SCINTILLATION COUKTER

93

higher than that of anthracene and there is some indication that a crystal grown of the solution may be somewhat more transparent to its own radiation than is a pure anthracene crystal. The flash duration of this mixed crystal lies between that of anthracene and that of trans-stilbene. Finally, i t is somewhat easier t o obtain large clear crystals of this material since the melting point of the solvent material is lower than the melting point of anthracene. As is evident from Table I1 the liquid phosphors are much less efficient than the crystalline material. However, the liquid material can be used in any size or shape desired which is a very great advantage for certain experiments. I n cosmic ray work, for example, where the energy of the incident particles is high so that the question of efficiency is not very important, this class of phosphor has found i m p x t a n t application. If liquid phosphors can be found having higher efficiencies than those known a t present, it may well be that they will replase entirely the crystal phosphors now in use for gamma-ray detection. Because of the necessity of a container, they are not as well suited for beta-particle detection except where the energies involved are extremely high. The detection and measurement of neutrons with scintillation counters is a much more specialized application. However, i t should be mentioned briefly. Where fast neutrons are involved, the organic materials and especially liquid phosphors are quite successful in converting the neutron energy into visible light scintillations. Here the low atomic number material of the phosphor serves to rapidly slow the neutron down absorbing its energy through collisions. These collisions in turn excite the fluorescent centers and give rise t o the emission of visible light photons. For thermal neutrons the situation is somewhat different in that the neutrons themselves do not have sufficient energy t o excite fluorescence. Therefore, the phosphor must incorporate nuclei which will capture neutrons and give up energy in doing so. Phosphors containing boron (10) and indium have both been successfully used for this purpose. Obviously i t would be possible t o incorporate fissionable material in the phosphor crystal and make use of the energy of fission t o excite the material. However, the latter method is a very extravagant way of accomplishing a rather simple end. A good deal remains t o be done in the field of phosphor materials for scintillation counting and active work in many research centers is in progress towards a better solution of this problem. As this work proceeds, marked improvements in available phosphors can confidently be expected.

94

G . A. MORTON

Ti. SCINTILLATIOX COUNTER APPLICATIONS 1 . Radiation Detection and Monitoring

The first application of the scintillation counter that might be considered is t h a t of using the device for detecting nuclear radiation. This may be for the purpose of making surveys for radioactive contamination, for observing tracer materials, the monitoring of nuclear reactors, or similar tasks. An example of this class of survey device which has shown considerable promise is the scintillation counter for alpha-particle detection. The rather low penetrating power of alpha particles makes them rather difficult t o detect with devices depending upon the ionization of a gas. It has been virtually impossible t o make a Geiger counter with thin enough malls t o be of much use for the detection of alpha particles. Proportional counters and ionization chambers can be equipped with windows covered by very thin organic films t o make them suitable for the detection of alpha particles. However, such devices are quite complicated in their electronics and difficult t o maintain in operation. On the other hand, the alpha-particle scintillation detector simply consists of a thin fluorescent screen close t o the photocathode of a multiplier. Where the device is to be used with ambient light, it is necessary t o coat the phosphor with a light-tight film. Such opaque films can be made thin enough so that the air-equivalent range loss of the alpha particles is only a few millimeters. Since in general alpha particles are quite energetic, the flashes produced a t the phosphor are large and consequently large output pulses are obtained. It is, therefore, not difficult t o arrange the circuits which follow the multiplier in such a way that only a few background counts are observed per hour in the absence of alpha-emitting material, and yet every alpha particle that strikes the screen will be counted. An alpha-particle sensitive scintillation counter which is t o be used as a survey instrument should h a r e as large a fluorescent screen as possible because of the very low tolerance level that has been established t o guard against the health hazard of alpha emitters. There is, however, a relationship between the size of the fluorescent screen that can be used and the size of the photocathode of the multiplier. It can be shown that if A , is the area of the fluorescent screen, and R its reflectivity t o its own radiation, and A , the area of the photocathode, the maximum fraction of the light produced by a scintillation that can be collected by the photocathode is given by the relation:

THE SCINTILLATION COUNTER

95

Inasmuch a s the value of R rarely exceeds 0.5 it is evident from this equation that, if a large fraction of the light from the scintillation is to be usefully collected, the fluorescent screen and photocathode should have approximately equaI areas. Consequently, a multiplier with a large photocathode is important for an alpha survey instrument. The scintillation counter is very sensitive a s a device for detecting gamma rays. The relatively high density of crystal phosphors makes them quite efficient at intercepting gamma rays and converting their energy t o visible scintillations. Furthermore, crystals can be made which are very transparent so that large volumes of the material may be used without too severe optical losses. Therefore, large crystals in combination with good multipliers can form gamma-ray detectors which have sensitivities th at are orders of magnitude greater than can be achieved with any device employing gas ionization. When such an arrangement is used as a survey instrument or radiation monitor, obviously the background due to cosmic rays and natural radioactivity will increase by the same factor as the radiation to be detected. However, because of the improved statistics thus achieved, a lower intensity of radiation being sought will give a meaningful signal. For example, a Geiger counter instrument with a n integration time of 1 second might have a natural background reading of ten counts per second. The root mean square deviation of this reading will be the square root of 10. Therefore, it would be difficult to detect a n increase of radiation of less than 30 per cent of background. On the other hand, a scintillation counter using a large crystaI might have a natural background count of 1000 counts per second. The statistical fluctuations a t such a counting rate would give a root mean square deviation of about 3 per cent, therefore a change of radiation intensity of a few per cent of background would give a recognizable signal. Thus, such a device would, for example, give warning of a source of radioactivity a t a considerably greater distance than would an instrument based upon a Geiger counter. Where the energy of the radiation to be detected is small and the ambient operating temperature high, it may be necessary t o use a pair of multipliers receiving light from the same crystal and connected in coincidence in such a way th at only when pulses occur a t the output of both multipliers simultaneously will the pulse be registered on the presentation instrument. The random pulses generated as a result of thermionic emission in the two multipliers will only rarely produce accidental coincidences which are counted, thus the multiplier background through such an arrangement is very greatly reduced. When the scintillation counter is used with a simple rate counting circuit, the meter reading is simply proportional to the number of

96

G.

A . MORTON

gamma-ray photons per second, quite independent of their energy SO that such a device does not read in Roentgen units and does not measure the radiation health hazard. More elaborate output circuits, however, can be used to cause the meter to read Roentgen units. Where the survey device is to be used a t fairly high radiation levels it is not necessary to employ a counting technique a t all. Instead, the photomultiplier simply integrates the light from the phosphor crystal and the multiplier output current is a measure of this light. * By properly selecting the crystal (e.g., a crystal composed of atoms having approximately the same atomic number as those of air) such an arrangement can also be made t o read in Roentgen units directly. The scintillation counter also has promise of being a very useful survey type beta-ray detector. It avoids the problem of a thin vacuum window which is a very serious problem with a Geiger counter. For beta-particle detection an organic crystal similar to that used for gammaray detection may be used, but its thickness can be considerably less because of the lower penetrating power of the beta particle. A l-mev beta particle will penetrate only about cm of anthracene. In order to give maximum discrimination against gamma rays the phosphor should be as thin as will give output pulse heights which can be adequately separated from background noise. Again the phosphor crystal must be covered with an opaque coating to exclude ambient light. This film may be much thicker, however, than for alpha particles. I n addition to their application for survey purposes, such devices may be used in connection with beta-particle detection for radioactive tracer work and for such devices as penetration type thickness gages for thin metals or plastics. It is relatively simple to make a scintillation counter which will detect either fast or slow neutrons. In almost all cases, neutrons are only found in the presence of fairly large amounts of gamma rays, and so far no satisfactory way has been devised for discriminating in favor of neutrons in a strong gamma-ray background. However, in certain special devices such as for neutron spectrometers, the scintillation counter has been used quite effectively as a neutron detector.

+

2. Scintillation Counter Spectrometry

It has already been pointed out that the number of photons from a phosphor crystal is proportional to the amount of energy absorbed from the incident nuclear particle. If these photons are directed onto the photocathode of a multiplier they will produce a number of photoelectrons proportional to their number. Consequently, the size of the output pulse from the multiplier will be related to the energy lost by the nuclear particle. Where the particle loses all its energy in the phosphor

THE SCINTILLATION COUNTER

97

or a known fraction thereof, obviously the device can be used as an energy spectrometer. However, since all of the processes are statistical, the system must be examined in some detail in order to determine the significance in terms of an energy spectrum of a given pulse height distribution obtained from the multiplier. In the discussion of the statistics of a multiplier, it was shown that if a series of pulses, each one due to the emission of 6 electrons from the photocathode, were examined a t the output of a multiplier, a distribution in pulse heights or amounts of charge per pulse would be found which had a standard deviation A, delta given by:

This means that if in a scintillation counter spectrometer, a sequence of monoenergetic nuclear particles which give up their entire energy to the phosphor crystal and thus each produced the same number of photons were detected, a distribution in pulse heights would be obtained rather than simply a single value of pulse height for the entire series. The position of the maximum of this distribution would correspond to the energy of the particle. Again, if the nuclear radiation whose spectrum is to be analyzed consists of two groups of monoenergetic particles with fairly widely separated energies, the pulse height spectrum obtained from the scintillation counter would be in the form of two separate approximately Gaussian distributions whose maxima would indicate the two energies of the particles being analyzed. When, however, the energies of the incident particles are so close together that the distributions corresponding to these energies overlap, the problem of analyzing the pulse height distribution obtained into the energy spectrum of the incident particles becomes more difficult. I n the most general case the incident particles will have a continuous energy distribution. To analyze this general case assume that the energy distribution curve of the incident particles is represented by G ( p ) in Fig. 11. Here the abscissa p is the number of photoelectrons released (average) at the multiplier by the particle of energy E , with E , = constant p . When such particles are measured with the scintillation counter they will giv? rise to a pulse height distribution curve given by F ( p ' ) shown in the same figure. A consideration of what is taking place in the system will show that the curve G ( p ) and F ( p ' ) are related by the following integral equation: F(P')

=

lo- G ( P ) f ( P , P

- P'WP

Where f(p, p - p') is the multiplier distribution curve for p electrons

98

G . A. MORTON

from the photocathode. Thus, each point on the pulse height distribution curve of the multiplier output is the result of scanning the curve G ( p ) by the distribution f(p, p - p ’ ) with p’ fixed.

PULSE.

HEIGHT

P

ENERGY

(PULSE

HEIGHT)

FIG.11. Representative energy and pulse height distributions.

The function f(p, p - p ’ ) can be fairly closely approximated by the Gaussian distribution: f(p, p - p’)

1 .\/ 2*kp

= ____

e-(p-p”~/2kp

The problem is now to reconstruct G ( p ) from the measured curve F(p’). It is not possible to obtain an exact solution of this integral equation, but by making the appropriate approximations it can be expanded and integrated giving the wanted distribution in terms of the measured pulse height distribution. The relations thus obtained are the following :

kP G(P) = F ( P ) - 4 F”(P) G’(P)

k

=

F’b) - ;iF”(P)

Higher order approximations can, of course, be derived if necessary. These formulas make it possible to compute the energy spectrum of the

THE SCINTILLATION COUNTER

99

radiation being observed from the pulse height distribution curve measured with the scintillation counter spectrometer. Beta-ray energy spectra are perhaps the most easily measured with a scintillation detector. Even here, however, it is necessary to take many precautions in order to avoid spurious effects. The sample should be mounted on a thin film of low-density material in order to avoid back scattering. This sample is placed close to the crystal in such a way as to minimize the fraction of beta particles striking the crystal but not giving up their entire energy to it. For example, the beta emitter is frequently

2000

loo0 PULSL

FIG.12. Pulse height distribution of

HEIGHT

Csl37

(redrawn from Nucleonics, ref. 19).

embedded entirely in the crystal, or it is placed between two crystals which avoid a good many of the problems associated with back scattering, reflection of beta particles from the crystal, etc. The beta particles which enter the crystal give up all their energy, to it producing scintillations whose integrated luminosities, i.e., total number of photons, are closely proportional to the energy of the particle. The light thus produced is received by the multiplier photocathode and gives rise to the pulse a t the output. These pulses are examined by means of pulse height discriminators, and a pulse height distribution is obtained. This distribution can be analyzed as outlined above to obtain the energy spectrum. This has been done for a number of beta emitters with very good results. Figures 12 and 13 indicate results

100

G . A. MORTON

obtained in this way by P. R. Bell for cesium (CsL3’),phosphorus and yttrium (ITg1). Figure 12 shows the beta-ray spectrumlg of Cs13’ together with the internal conversion electron a t 630-kev energy. Figure 13 shows a Kurie plot of phosphorus (F) compared with a similar plot’g for Ygl. It will be observed that the P32curve is a straight line on the Kurie plot (except at low energies where instrumental error introduces some curvature),

.5

I. 5

1.0

2.4

MEV

ENERGY

FIG.13. Kurie plots of

P3*

and

Y91

(redrawn from Nucleonics, ref. 19)

indicating that it is an allowed transition, whereas the Ygl plot cannot be represented by a straight line. Correcting for a degree of “forbidness,” the Ygl spectrum can be reduced to a straight line. A number of other substances have been examined, including such very weak beta-ray sources as Belo and K40. Gamma-ray energy spectrum measurements are less straightforward than those of beta rays becauce of the more complicated mechanism involved in the transfer of energy to the crystal phosphor by the incident radiation. At least three mechanisms of energy transfer may be involved in this process. The first is photoelectric conversion where the gamma ray interacts with one of the firmly bound electrons of an atom of the crystal and gives up essentially all its energy to this electron, thus causing it t o be ejected photoelectrically from the atom. With this type of

THE SCINTILLATION COUNTER

101

conversion the electron and, hence, the crystal receives essentially all the energy of the gamma particle. The second type of energy conversion is through so-called Compton collisions. Here the incoming gamma ray interacts with an essentially free electron in the crystal in a two-body collision. The gamma-ray energy will be only partially transferred to the electron with which it is interacting, and the fraction of this energy which the electron receives is a matter of probability. Consequentially, the scintillations will not have a luminosity corresponding t o the full energy of the gamma rays. The maximum energy which can be transferred to the crystal through a Compton collision is given by:

The energy transfer to the crystal forms a continuum from this maximum energy down to zero energy according to distribution laws governing the Compton process.

-PAIR

PROD.

ENERGY

FIG.14.

Cross section for absorption for iodine (redrawn from Nucleonics, ref. 20).

Finally, the gamma ray, if it is of sufficiently high energy may interact with the phosphor by producing an electron-positron pair. Here the amount of energy transferred to the crystal will be equal t o that of the gamma ray, minus the energy required for the pair-formation (approximately 1 mev). Figure 14 gives the theoretical cross-section curves for the three con-

102

G . A. MORTON

version processes in iodine of sodium iodide as computed by Hofstadter and McIntyre.20 Based on these curves, Figs. 15 and 16 show the theoretical pulse distribution expected for 0.51- and 2.04-mev particles

0.51 MEV

I

RAY

\

L.22 10

2

4

6

PULSE

8

HEIGHT

FIG. 15. Calculated pulse height distribution for a 0.51-mev gamma ray in NaI(T1) (redrawn from Nucleonics, ref. 20).

PULSE

HEIGHT

FIG. 16. Calculated pulse height distribution for a 2.04-mev gamma ray in NaI(T1) (redrawn from Nucleonics, ref. 20).

as computed by the above authors. Measurements made on the gamma rays from a number of materials, such as Au19*,Na24,and Ga66,confirmed these results. It will be evident from the above that the interpretation of pulse heights distributions obtained from a complicated gamma-ray spectrum

103

THE SCINTILLATION COUNTER

may be difficult indeed. It is fortunate, however, that gamma spectra are generally in the form of the discrete lines rather than a continuous distribution of energy as with beta rays. Therefore, unless the line structure of the spectrum being analyzed is extremely complicated, it is usually possible t o obtain an interpretation from the measured pulse heights distribution curves. An interesting procedure for using the Compton effect in measuring gamma-ray spectra was worked out by Hofstadter.21 It consists of arranging two scintillation counters, A and B, as shown in Fig. 17, in PHOTOMULTIPLIER

/

RECOIL ELECTRON

Fro. 17. Two-crystal gamma-ray spectrometer.

such a way t ha t their outputs are in coincidence, and only if a pulse occurs in counter B will the pulse be recorded from counter A . It can be shown from the Compton interaction equations th at if e is the angle formed at counter A between the incident gamma ray and the Compton scattered gamma ray 'which reached counter B, the following energy relations must be fulfilled:

E

=

' l1 4- [' 4- E,,,.

- E ,, 2

2mc2 hav

e

I")

If the angle 0 is kept constant, the energy given t o the Compton electron in crystal A will be proportional to the energy of the incident gamma ray. Therefore, a pulse height distribution from counter A for pulses which occur only when the scattered gamma ray reaches B will be a measure of the energy spectrum of the source. Figure 18 illustrates the spectrums obtained from ( 2 0 6 0 (1.17- and 1.33-mev gamma ray) as measured in this way. 3. Time Measurements I n addition to the example cited above, the coincidence method in general is a very important adjunct to the scintillation counter technique. It makes possible the reduction of spurious signals due t o multiplier

104

G . A. MORTON

dark current pulses. It provides means of distinguishing between different kinds of nuclear phenomena. It permits taking advantage of the extremely short resolving time capabilities of the device for the determination of chronological relationships between nuclear events, and can aid in many other ways. A large number of circuits have been developed for using scintillation counters in coincidence. Figure 19 illustrates a typical circuit using three

PULSE

HEIGHT

(VOLTS)

d B

FIG.18. Energy spectrum of C o ' O (redrawn from Phys. Rev.,:ef. a ' A

21).

CRYSTAL CHAVACTERISTICS

ZP' d

B

d'r2a

a

2a

+ DYNOOE

COLLECTOR COLLECTOR

DYNODE

FIG.19. Three-crystal diode coincidence circuit.

THE SCINTILLATION COUNTER

105

crystal diodes22in such a way that only when pulses appear from the two multipliers simultaneously does a pulse reach the presentation device. The coincidence method, employing a circuit with a delay line in one of its branches has been used in connection with the decay of short-lived isomers. The problem here is to determine the half-life of radioactive daughters of an initially radioactive atom. The arrangement of the apparatus, as used by DeBendetti, McGowan, and is illustrated CRYSTALS

I

AMPLIFIER

I COINCIDENCE

I REGISTER DELAY

FIG.20. Schematic diagram of delayed coincidence system

in Fig. 20. The material being investigated is placed between two scintillation counter chains. One includes a delay element and is arranged to respond to the nuclear particle released by the initial transition. The second chain responds to the radiation released by the daughter atom. When a source having only a single transition is placed in the apparatus, the delayed coincidence measurements give only a very small constant background due to accidental delayed coincidences. This is illustrated in the dotted curve of Fig. 20. On the other hand, when there is a double transition, the second having a half-life of the same order of magnitude as the transfer time of the delay element, the delayed coincidence gives a straight line on a semi-logarithm plot. The slope of the line is a measure of the half-life of the isomer. Some examples of the half-lives found for such isomers are given below: Ga72

8-

Ge72*

Y

___ -+

14 hr

2.9 x 10-7

P-

Y

sec Ge72

Yb177 --+ Lu177* A sec Lu177 1.8 hr 1.3 x 10-7 B- Au'97* Y ---f sec Aulg7 Hg197 2.3 hr 7 x 10-9 I

~

106

G . A . MORTON

I n order t o use the coincidence method to reduce the thermionic background of secondary emission multipliers two multipliers are arranged so they look a t a single phosphor crystal. The scintillation flash excites photoelectrons in both multipliers simultaneously and, consequently, gives a recordable pulse through the coincidence circuit. The thermionic emission, on the other hand, being a random process, produces only a relatively few number of accidental coincidences. By making the resolving time of the system short, that is comparable with the flash duration of the phosphor, the normal thermionic background of a multiplier can be reduced to a matter of a few counts per minute or even a few counts per hour. This is very useful when weak radioactive sources are being studied. I n the above article it has not been possible to cover completely either the operation of a scintillation counter or its many applications in full detail. However, the discussion may serve to indicate the general principles of the scintillation counter, its limitations, and its uses in nuclear physics. With the rapidly widening usage of the device and the continued study of its operation, it can be confidently expected that many improvements will be made in the performance, reliability, and applicability of the scintillation counter. However, even without these improvements the scintillation counter represents one of the most powerful detection means available to the nuclear physicists. REFERENCES 1. Kallmann, H. Natur u. Tech., July, 1947. 2. Coltman, J. W., and Marshall, F. H. Photomultiplier Radiation Detector. Phys. Rev., 72, No. 6, 528 (1947). 3. Zworykin, V. K., Morton, G. A., and Malter, L. The Secondary Emission Multiplier-A New Electronic Device. Proc. Inst. Radio Engrs., 24, No. 3, 351 (1936). 4. Rajchman, J. A., and Snyder, R. L. An Electrostatically Focused Multiplier Phototube. Electronics, 13, 20 (1940). 5. Engstrom, R. W. Multiplier Phototube Characteristics: Application to Low Light Levels. J. Optical SOC.Am., 37, 420 (1947). 6. Morton, G. A. Photomultipliers for Scintillation Counting. R C A Rev., 10, No. 4, 525 (1949). 7. Morton, G. A,, and Mitchell, J. A. Performance of 931-A Type Multiplier in a Scintillation Counter. R C A Rev., 9, No. 4, 632 (1948). 8. Sherr, R. Scintillation Counter for the Detection of Alpha Particles. Rev. Sei. Instruments, 18, 767 (1947). 9. Graves, J. D., and Dyson, J. P. Scintillation Counter for Laboratory Counting of Alpha Particles. Rev. Sn'. Instruments, 20, 560 (1949). 10. Properties of Scintillation Materials. Nucleonics, 6, No. 5, 70 (1950). 11. Hofstadter, R. The Detection of Gamma-Rays with Thallium Activated Sodium Iodide Crystals. Phys. Rev., 7 6 , 796 (1949). 12. Gillette, R. H. Calcium and Cadmium Tungstate as Scintillation Counter Crystals for Gamma-Ray Detection. Rev. Sci. Instruments, 21, 294 (1950).

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107

13. MacIntyre, W. J. Decay of Scintillations in Calcium Fluoride Crystals. Phys. Rev., 76, 1439 (1949). 14. Bell, P. R. The Use of Anthracene as a Scintillation Counter. Phys. Rev., 73, 1405 (1948). 15. Feazel, C. E., and Smith, C. D. Production of Large Crystals of Naphthalene and Anthracene. Rev. Sci. Instruments, 19, 817 (1948). 16. Gettings, H. T., et al. Relative Sensitivities of Some Organic Compounds for Scintillation Counting. Phys. Rev., 76, 205 (1949). 17. Hofstadter, R., Liebson, S. H., and Elliott, J. 0. Terphenyl and Dibenzyl Scintillation Counters. Phys. Rev., 78, 81 (1950). .18. Reynolds, G. T. Liquid Scintillation Counters. Nucleonics, 6 , NO.5 , 68 (1950). 19. Jordan, W. H., and Bell, P. R. Scintillation Counters. ATucleonics, 6 , NO.4, 30 (1949). 20. Hofstadter, R., and McIntyre, J. A. Gamma-Ray Spectroscopy with Crystals of NaI(T1). Nucleonics, 7 , No. 3, 32 (1950). 21. Hofstadter, R., and McIntyre, J. A. Measurement of Gamma-Ray Energies with Two Crystals in Coincidence. Phys. Rev., 78, 619 (1950). 22. Morton, 0.A., and Robinson, K. W. A Coincidence Scintillation Counter. Nucleonics, 4, No. 2, 25 (1949). 23. DeBenedetti, et al. Self-Delayed Coincidences with Scintillation Counters. Phys. Rev., 73, 140 (1948).

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Fluctuation Phenomena ALDERT VAN DER ZIEL Department of Electrical Engineering. Institute of Technology. University of Minnesota. Minnea.polis, Minnesota CONTENTS

Page 110 1 Correlation . . . . . . . . . . . . . ......................... 110 112 2 . Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I1. Fourier Analysis of Fluctuating Quantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 1. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 2 . Methods of Calculation of the Fourie; Spectrum. . . . . . . . . . . . . . . . . . . . . 114 a . From Statistical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 b . F r o m t h e Time Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 c . From the Fourier Analysis of a Single Elementary E v e n t . , . . . . . . . . . 115 d . From x ( t ) X ( t + w ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 I11. Application to Various Noise Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 117 1. Thermal Noise Generators . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 2 . Shot Noise in Diodes and Triodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 a . Noise in Diodes at Low Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b . Noise in Triodes at Low Frequencies. . . . . . . . . . . . . . . . . . . . . . . . . . 123 3 . Noise in Diodes and Triodes at High Frequenci . . . . . . . . . . . . . . . . . . . . 124 a . Noise in Saturated Diodes at High Frequencies . . . . . . . . . . . . . . . . . b . Exponential Part of the Characteristic . Total Emission Noise ... c . High-Frequency Noise in Space-Charge Limited Diodes . . . . . . . . . . . . 126 129 d Noise in Triodes a t High Frequencies., . . . . . . . . . . . . . . . . . . . . . . . . . . . e . Noise in Electron Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 f. Induced Grid Noise in Triodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g. Discussion of the Results of the Last Two Sections . . . . . . . . . . . . . . . . . 132 4 . Partition Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 133 a . Partition Noise in Pentodes and Hexodes., . . . . . . . . . . . . . . . . . . . . . 134 b . Induced Grid Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Secondary Emission Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6. Noise in Gas Discharge Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7 . Noise in Mixer Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a . Triode, Pentode, and Hexode Mixers . . . . . . . . . . . . . . . . . . b . Diode Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 c. Deflection Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 139 8 . Noise in Photocells and Photomultipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 9 Shot Noise in Semi-conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 10. Flicker Noise in Cathodes and Semi-Conductors . . . . . . . . . . . . . . . . . . . . . 11 Noise in Crystal Diodes and Transistors . . . . . . . . . . . . . . . 109

I . Introduction . . . . . . . . . . . . . .

.

.

. .

.........................

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ALDERT VAN DER ZIEL

Page IV. Noise in Receivers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 ..................................... 147 1. Noise Figure . . . . . . . . . . . 2. Noise Figures of Various rcuits.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 a. Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 b. Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 150 c. Noise in Triode and Pentode Circuits.. . . . . . . . . . . . . . . . . . . . . . . . . . . . d. Diode Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 References. .. ................................. . . . 153

I. INTRODUCTION The random motion of the free electrons in a conductor gives rise to a fluctuating voltage across its terminals; this effect is known as thermal noise. The random emission of electrons by the cathode of a vacuum tube gives rise to fluctuations in the tube current; this effect is known as shot noise. The name “spontaneous fluctuations of electricity ” would be the most appropriate one. However, in view of their acoustical effects, these fluctuations are now generally known under the name “noise.” Noise sets a very serious limit to the detection of all kinds of weak signals.1l In the discussion of some noise problems, an extensive mathematical analysis2~12-15-is cannot be avoided. In many cases, however, a simple Fourier analysis is sufficient. It is the aim of this paper to give a simple discussion of some important noise problems. In the measurement of noise, one takes the average value of the noise power over a sufficiently long time. In the calculations, however, we shall take average values over a large number of identical systems subjected to independent fluctuations (ensemble), in order to avoid confusion. Both methods give identical results. An average value will be denoted by . A quantity X ( t ) will be called a fluctuating quantity in this paper if X ( t ) = 0 but Xz(t) # 0. If X(t) # 0, one might better introduce [ X ( t )- X(l)] as the fluctuating quantity. It may in general be assumed that Xz(t> taken over an ensemble is independent of time. For if the elements of the ensemble all started at t = 0 with X ( t ) = XO,then x”(t)= Xo2 at t = to. Independent of the initial value Xo2, the expression Xz(t> will approach a stationary value X 2 for sufficiently large values of t ; X 2 is usually the only item of interest. 1. Correlation In our discussion of noise problems, we have to introduce the concept of correlation between fluctuating quantities.I7 Let x and y be two fluctuating quantities such that Z = Q = 0, then the correlation coefieient c is defined as:

FLUCTUATION PHENOMENA

111

= 3 . = 0 and c = 0; in that case If x and y are independent then the quantities are said to be uncorrelated. If # 0 the coefficient c is a good measure for the dependence of the one quantity upon the other one. If 0 < [cl < 1 then the quantities are said to be partially correlated; if Icl = 1, the quantities are said to be completely correlated. The most important case in noise problems is the case of linear correlation (at any rate as long as linear circuit theory can be applied) :

xy

y where a is a constant and

2

=

ax

+ z,

(1.2)

is uncorrelated with x. Then:

which shows that IcI 5 1. Correlation is very important if two fluctuating quantities x and y have to be added and the mean square value is taken:

c = 0 (no correlation) means that the quantities have to be added quadratically; - (1.4a) (29 y)Z = 2 2 y2,

+

+

]cI = 1 (complete correlation) means that the quantities have to be added linearly; = 2 5 2 dS*.y’i+ y2= (dz& dz)2. (I.4b) In many cases the correlation between the values of a certain fluctuating quantity X ( t ) a t different instants is also of interest.17 We shall often use correlation coefficients c(w) of the type:

+

c(w) = X ( t ) X ( t w)/X2(t); c ( - w ) = c(w), (1.5) c(w) is equal to unity a t w = 0 (normalization) and decreases more or less rapidly for w > 0. The decrease can usually be characterized by a single correlation time T O (for exceptions compare section 111.10) such that c(w) = 0 for w >> T O . In the case of fluctuating currents in tubes, T O is usually equal to the transit time of the electrons, for fluctuating signals across tuned circuits TOis equal to the time constant of the circuit. * * c ( - w ) = c(w) because X(u)X(u’) = X(u’)X(u). Putting u‘ = u + w, we have:

+

X ( u ) X ( u w ) = X(u’)X(u’ - w) = X(u)X(u- w), since an average value, taken over an ensemble, does not depend upon u.

112

ALDERT VAN DER ZIEL

2. Fourier Analysis

The most convenient way of calculating mean square values of fluctuating quantities is the method of Fourier analysis. I n order to show that it is permissible to use this method consider a fluctuating quantity Y ( t ) of a certain system (e.g., the noise output voltage of an amplifier) which is caused by a fluctuating quantity X ( t ) (e.g., the noise of the first input circuit or the noise of the first tube). X ( t ) is developed into a Fourier series for 0 < t < To,the sum X l ( t ) of this series is equal to X ( t ) for 0 < t < T o but differs from X ( t ) outside that interval. Though the values of X ( t ) for t < 0 may have some influence upon the values of Y ( t ) for t > 0, this influence will have died out after a certain time T I , depending upon the time constant of the system. Hence it is allowed t o use the Fourier representation X , ( t ) of X ( t ) for the interval - 00 < t < T o in order to calculate the values of Y ( t ) and of for 7'1 < t < T O . As is independent of time this will give the right value of For that reason i t i s allowed to apply a-c circuit analysis to noise problems in tubes and circuits and to apply the laws of vacuum tube electronics to noise problems in radio tubes.

m.

11. FOURIER ANALYSIS OF FLUCTUATING QUANTITIES

I. Theory16.16 Let X ( t ) be a fluctuating quantity which is continuous except in a To IX(u)Idu finite number of points of the interval 0 < t < T osuch that exists; then it is allowed to develop X ( t ) into a Fourier series for the time interval 0 < t < T o and the sum of this series is equal to X ( t ) for that time interval if X ( t ) is properly defined a t the discontinuities:*

/o

n=-

(D

f

To

(11.2)

The Fourier component x, for the frequency w,, is: Z, = a,eiw*t + a e - i w d

(11.3) * Sometimes discontinuous fluctuating quantities are introduced in the theoretical

discussion of a problem, b u t they are never measured as such; as every physical instrument has a finite rise time, these discontinuities will always be smoothed out. A perfect example is the convection current at a certain point in a radio tube; it is infinite if an electron passes that point and zero at all other instants. However, the fluctuating currents in the outer circuit are perfectly continuous.

113

FLUCTUATION PHENOMENA

and its mean square value taken over a n ensemble is:

=

/

4Af

X(u)X(u

0

=

+

W)

cos wnw dw

F(fniAf,

(11.4)

where Af = 1/To and (u'- u) = w.* Equation (11.4) shows that the Fourier spectrum F ( f n ) of X ( t ) is: F(fn>

= 4

lom

x(~>x(U

+ w ) cos wnw dw.

(11.5)

Having calculated the mean square values of the Fourier coefficients of X ( t ) , we can now draw the following conclusions: a. If 7 0 is the correlation time, then the Fourier spectrum F ( f n ) is independent of frequency if wnr0 << 1 :

F(fn)

=

Fo

=

4

I-

X(u)X(u

z,

=

n=-

00

2

(11.6)

can be calculated:

b. As soon as F ( f n ) is known,

Xz(t) =

+ w)dw.

2a,a_, =

2

F(fm)Af = l o W F ( f n ) d f n .(11.7)

n=O

n=O

+

c. If F ( f n ) is known, x ( u ) X ( u w ) can be calculated. For after a well-known theorem of Fourier analysis equation (11.5) can be reversed as : X ( u ) X ( u w) = F ( f n ) cos wnw df,. (11.8)

+

j-"

+

As X ( u ) X ( u w ) should be a bounded continuous function, the integral in (11.8) should converge for all values of w, including w = 0. In order t o ensure convergence F(fn) has t o satisfy the following conditions:68

* One can choose a small time 6 related to the correlation time 7 0 of X ( t ) such t h a t = 0 for I wI > 6. If To >> 6, it is allowed to replace the limits of integration --u and (To - u) by -6 and +6, as the area of integration is hardly changed by it. The limits of integration may then be extended again to - rn and + a as X ( u ) X ( u + w) = 0 for (wi> 8, so t h a t the second integral may be repIaced X ( u ) X ( u + w)

+

by the third one. Due t o the fact t h a t X ( u ) X ( u w) and cos w,w are symmetric in w , whereas sin w,w is antisymmetric, the third integral may be replaced by the fourth one.

114

ALDERT VAN DER ZIEL

a . F(fn)should vary slower than l/fnat very low frequencies. b. F ( f n ) should vary faster than l/fnat very high frequencies.* 2. Methods of Calculation of the Fourier Spectrum a. From Statistical Considerations. We shall derive Nyquist’s theorem for the thermal noise of a tuned circuit at a temperature T with the help of the equipartition 1aw.t The circuit, tuned at a frequency fo, is completely equivalent to a harmonic oscillator of frequency f o at the same temperature T . Let L be the self-induction, C the capacity, R the tuned circuit impedance, v the noise voltage across its terminals, and i the current through the coil, then:

+Liz+ +cvZ = kT(hfo/kT)[ehfo’kT - 11-’

=

kT p(f0);

+P= 4cVz

(11.9)

where h and k are Planck’s and Boltzmann’s constants, respectively. Describing the noise by a fluctuating emf E(1) in series with the tuned - circuit impedance R, we have for the Fourier components of E ( t ) : en2 = F(f,)Af and the mean square value of the voltage v across the tuned circuit is :

n=O

(11.10) as wo2LC = 1, (wnC - l / w , L ) = 2 ( w , - UO)CRand F(fn) = F ( f o ) over the bandwidth of the circuit in good approximation. Hence:

-

(11.11)

e2 = F ( j o ) A j = 4kTRp(fo)Af

* Violation of condition ( 6 ) may occur when X ( t ) is not bounded a t some points; in that case X ( t ) X ( t w ) will not be bounded at w = 0. This occurs only for the rather “artificial” quantities mentioned previously. It is a well-known fact that in the case of excess noise in semi-conductors, the spectrum varies as l/f in a rather wide frequency range.55 The above conditions show that deviations from the l/f law have to occur a t the very low and the very high-frequency end, though they do not tell us in what frequency range these deviations occur; that has to be decided by experiments. t According to the equipartition law, the average energy per degree of freedom is ) a harmonic oscillator) for any system satisfying the folequal to f k T (or f k T p ( J ~for lowing conditions: ( a ) the system is kept a t a uniform temperature T ;( b ) the energy which depends upon a certain number of independent variables can be written as a sum of quadratic terms in these variables; (c) each of the independent variables can -a. The number of degrees of freedom is equal to the number vary from - m to of independent variables (coordinates, velocities, etc.) which are used in the expression for the energy. The equipartition law holds for the tuned circuit because t h e above conditions are satisfied; the energy of the system is (tLi2 f C v z ) . The factor p c f o ) occurs because of quantum effects.

+

+

+

FLUCTUATION PHENOMENA

115

according to (11.9). This is known as Nyquist’s theorem.61 b. From the Time Average. X , = 1 / [~X ( u ) d u .

z2 = 1 / ~ ’JJ’ JOT X ( u ) X ( u ’ )du du’ = Fo/(2r)

(11.12)

if r >> rO.l7 We apply this to calculate shot effect in a saturated diode having a d-c current I,. Let - e be the electronic charge and N the number of electrons emitted during the time interval 7, then: I, = iVe/r. (11.13) The fluctuation ( N in the number of emitted electrons is equivalent to a time average current:*

m)

I,

=

e(N - R)/r; IT = e2iiT/r2= eI,/r.

(11.14)

According to (11.12):

i2 = FoAf

=

27T2Af= 2eIaAf

(11.15)

a result which was first derived by c. From the Fourier Analysis of a Single Elementary Event. If X ( t ) is the result of a large number of independent identical elementary processes occurring a t random’t then the Fourier spectrum can be calculated from a Fourier analysis of a single elementary process. If a, is the Fourier coefficient of X ( t ) and a,‘ the corresponding Fourier coefficient of the elementary event, then a, = Za,’ (sum taken over all events occurring in the interval To) and: - x2, = 2a,a-, = 2 N ~ n l a - d ~ (11.16)

m

where is the average number of events occurring during the time interval To. The contributions of the elementary events have to be added quadratically as they are independent. One can apply this method to the calculation of noise in radio tubes. It can be shown from energy considerations that the motion of an electron

* This is due t o the following theorem of probability theory. Let certain similar independent events occurring at random occur a t the average rate h. Then if n is the number of events occurring during a certain time interval T : 6 = AT;

(n -

ri)2

= A = AT.

t It is useful to clarify the meaning of the somewhat related expressions: “independent” and “random.” Events are said to be independent if any particular event does in no way influence the occurrence or nonoccurrence of subsequent events. Events are said to occur at random, e.g., a t random intervals or in a random form, size, or shape if any particular event does in no way affect any future event in its time of occurrence, form, size, or shape.

116

ALDERT VAN DER ZIEL

of charge -e between two electrodes of arbitrary shape gives rise to a current (von Engel and Steenbeck,’ p. 150) :

El4 I ( t ) = eu 7

(11.17)

in the circuit connecting the electrodes, u is the instantaneous velocity of the electron, E, the field strength at the position of the electron and V the potential difference between the electrodes. If T~ is the transit time of an electron, then an electron emitted at the instant t o gives rise to a current pulse (11.17) during the interval t o < t < t o T O . It should be emphasized that even though (11.17) is of general validity, its application to noise problems only holds for negligible space charge; this restriction which is due to (11.16) has not always been taken into acc0unt.3~~34 We apply this t o the calculation of the current in a lead connecting two adjacent grids at equal potential, if a saturated current loflows through the tube. The current pulse due to a single electron is e / r o for to < t < t o 7 0 and:

+

+

(11.18)

This is an illustration of the principle mentioned in Sec. 1.2: 2eIoAf represents the Fourier spectrum of the convection current entering the space between the grids, and the other term is the square of the modulus of the response of the outer circuit. d. From X ( t ) X ( t w). According to (1.5), this is equivalent to calculating and c(w). As an example, consider the problem of shot noise in semi-conductors. Let the drift velocity be such that it would take a conduction electron on the average a time T O to travel from one electrode to the other one if it lived long enough. Let the average life time of a conduction electron between its “creation” and its “captuse” be equal to T I and let 71 << 70. If I 0 is the average current and the average number of electrons moving between the electrodes, then :

m

+

m

I = iVe/To,

(11.19)

as each electron gives a pulse e/ro of duration 71. The fluctuation in number of moving electrons gives a current fluctuation : ~ ( t= )

(N - N)e/TO;

Pm = eIo/To.

(11.20)

In order to find c(w),we have to investigate what part of the electrons contributing t o I ( t ) at t = t o still contribute at t = ( t o w). As this

+

FLUCTUATION PHENOMENA

117

is a decay problem, we put: c(w)

=

(11.21)

e-w/rl.

Introducing this into (11.5) :

-

i2= F(fn)Af

=

+

2e10(2~1/70)[l (w,,~~)~]-lAf.

(II.22)

This result, which was derived by B e r n a m ~ n t ,Davydov ~~ and Gurev i ~ h and , ~ ~Gisolf,3* reduces to the full shot effect formula (II.18a) if 7 1

>> T o .

111. APPLICATION TO VARIOUSKOISEGENERATORS 1. Thermal Noise Generators In 1928 Nyquist61 published his classical paper on thermal noise and the only important additions to our knowledge of thermal noise have been the derivation of Nyquist’s theorem with the help of the electron theory and the discovery of the relation between thermal noise and black body radiation. Nyquist’s theorem (11.11) shows that the available noise power in the frequency interval Af is:

P, = $ 2 / R

=

kTAfp(f).

(111.1)

In order to show that this result is of universal validity, we follow Nyquist’s proof. Suppose two thermal noise generators kept at the temperature T existed which had different available noise powers in a certain frequency interval Af. Then these generators could be connected by means of a filter which either passed every frequency except those in the interval Af or which passed the frequencies of the interval A j only. In both cases the average noise power flowing from generator 1 to generator 2 would be different from the average noise power flowing from generator 2 to generator 1. But that is forbidden by the second law of thermodynamics. Hence the available noise powers of the generators are identical. As we proved (11.11) in one particular case, it now holds universally. p(f) = 1 a t low frequencies but starts to decrease if h f / k T 2 1 ; at room temperature this corresponds to a wavelength of 50 1.1. In practice it is therefore allowed to put p(f) = 1 at present. The occurrence of the factor p ( j ) in (111.1) is of great theoretical interest, and it would be worth while to test its presence a t low temperatures and cm waves. Equation (111.1) was verified experimentally in the r-f region first by Johnson,46later by many other^;^ the values of k which could be deduced from the measurements differed from the values obtained by other per cent. Recent accuracy is even better; methods by less than

+

118

ALDERT VAN DER ZIEL

thermal noise has been used for an accurate determination of temperature in the high temperature region’37 the results thus obtained differed by less than 0.1 per cent from the temperatures obtained by other methods. * As i t is allowed to apply normal circuit theory t o thermal noise problems, the noise of a resistance R may also be represented by a noise current generator dg of infinite internal resistance connected in parallel with R. i2 = 4kTgAf ( g = l/ R ). (I1I.2) Nyquist’s theorem not only holds for noise in resistors but it is also valid for any thermal noise generator. The theorem may therefore be stated as follows. A n y thermal noise generator generates as much noise as its equivalent circuit would do at the same temperature. We apply the above result to an antenna enclosed in a hollow sphere kept a t a temperature T . Its equivalent circuit is its radiation resistance R, and the available noise power is given by (111.1). I n this case as in so many other ones Nyquist’s theorem gives the noise output without any further calculation; whereas the exact calculation of the problem with the help of the radiation theory is rather lengthy, as can be judged from Burgess’ paper on this I n this problem the antenna noise is due to the interaction of the antenna and the black body radiation inside the hollow sphere. I n a conductor the cause is different-the noise is due to the interaction of the motion of the electrons with the vibrations of the crystal lattice. According t o the electron theory, the electrons in a conductor move more or less freely except for collisions with the lattice which cause the electrons t o be deflected (the free path length between two collisions is about cm). As the motion of electrons constitutes a current, the rapid change of direction of motion constitutes a rapidly fluctuating ~* and HellerIg showed that: current. B e r n a m ~ n t S, ~~~e n k e ,Bakker

Pa = kTAf

(111.3)

if it was assumed that after a collision the electrons were scattered isotropically in random directions. This result coincides with (111.1) except for the factor p(f). The reason for this discrepancy is that thr above assumption is not correct; in the collision process scattering over small angles is favored. Van der !Gelasshowed in a qualitative mannee that agreement with (111.1) would result if this scattering process was * I t has been objected5 that these noise measurements do not represent a genuine determination of k, as Nyquist’s theorem is “based” upon the assuinption that the equipartition law holds. This objection does not hold; the validity of the equipartition law in this case is not an assumption but ti direct consequenceof thermodynamics.

119

FLUCTUATION PHENOMENA

taken into account in the right manner; a quantitative calculation is rather difficult. As the thermal noise in a small part of a conductor is in thermal equilibrium with the lattice vibrations of that part, Nyquist's theorem can be extended to nonuniform circuits by assuming a noise emf of the type (11.11) in series with each resistance RlZ4where T is the temperature of R. This was verified experimentally by Williams,92who also showed that the noise in a tuned LCR circuit was completely determined by the temperature of R . It is useful to introduce two new concepts: the noise ratio n and the equivalent noise temperature T,. Let T be the normal room temperature, then the noise ratzo n of a n electric circuit i s deJined as the ratio of the available noise output power of the circuit to Ihe noise which would occui i f its equivalent circuit were kept at normal room temperature T. The equivalent noise temperature T , is defined as:

T , = nT.

(111.4)

The above definitions for n and T , are of general validity, they also hold for impedances which are obtained with the help of electronic circuits. As was shown by Percival,'j3 mil at^,^^ and Strutt and van der Ziel,*1 it is possible to obtain impedances with a low equivalent noise temperature in that way. The best result so far was obtained by Van Zolingengl who constructed an electronic damping for an evacuated electrometer which had an equivalent noise temperature of less than 1°K. 2. Shot Noise in Diodes and Triodes

The electrons emitted by a cathode have a certain velocity distribution; due to this velocity distribution the diode characteristic consists of three parts : the saturated region, the space-charge limited region, and the exponential region. If I is the saturation current, I, the anode current, V , the anode voltage, and T , the cathode temperature, then:

I, = I

(111.5)

for the saturated region ( V , so large that all electrons arrive at the anode) : I a -- I e c V d k T o (111.6) for the exponential region ( V , so much negative that only the electrons with an initial velocity > -V, volts arrive at the %node)and: '

Ia --

Ie-eVm/kTc

for the space-charge limited region in which

(111.7) z1

potential minimum of

ALDERT VAN DER ZIEL

120

depth -V,,, exists between potential minimum and anode (only the electrons with an initial velocity ? V , arrive a t the anode). a. Noise in Diodes at Low Frequencies. Except for Flicker effect (Sec. 111.10) it may be assumed that the emission of an electron is an independent event occurring a t random. For that reason Sch~ttky’s’~ theorem (11.15) should hold for the exponential as well as for the saturated region. This shows that the noise in those diodes can be represented by a noise current generator fiof infinite impedance connected in parallel with the diode. The measurements on noise in saturated diodes agree with (11.15); the values of the electronic charge e which were obtained that way6 differed from the values obtained by other methods by less than 6 per cent.* The validity of (11.15) for the exponential region was verified experimentally by Fiirth and M a c D ~ n a l d . ~ ~ I n the space-charge limited region the primary current fluctuations are considerably reduced by the space charge. For any increase in the emitted current will tend to increase the anode current; but it also gives rise to a deepening of the potential minimum, which in turn tends to decrease the anode current. The primary current d I , due t o the electrons which are emitted with an initial velocity between Vo and ( V , dV0) volts is:

+

dI,

=

Ie-vO/v+d(Vo/VT); V T = kT,/e.

(111.8)

Now let the current d I , show a fluctuation 61, then the corresponding fluctuation 61, in the anode current is:

61, = -y(V0S)Ip

(111.9)

The problem is now to calculate -y(Vo). If V o > V,, then the primary fluctuation 61, arrives at the anode, but it causes a deepening SV, of the potential minimum and this decreases the anode current by an amount ( I J V T ) SV, so that:

61, = T(VO)6IP= 61, - (I,/VT)6Vm.

(111.10)

If V o < V,, then the primary current does nol arrive a t the anode but it causes a deepening 6Vm of the potential minimum, and this decreases the anode current: (111.11) 61, = y(Vo)GI, = -(I,/V,)SV,.

6V,, and hence r(V0) can be calculated with the help of Langmuir’s diode theory. r(V0) = 0 for V O= 0 as those electrons do not deepen the 8

* It should be possible to obtain even more accurate agreement by comparing the noise of a saturated diode with the thermal noise of a resistor. The accuracy of the value for e l k which would be obtained that way might be better than 0.1 per cent.

FLUCTUATION PHENOMENA

121

potential minimum. r ( V o )= 1 for Vo = 00 as these electrons do not contribute t o the space charge either. y(V0) = - - C Q for V , = V , as those electrons come permanently t o rest in the potential minimum. A calculated curve ~ ( V O versus ) Vo is shown in Fig. 1. It shows that the

FIG.1. Shot effect reduction factor y as a function of the emission velocity V O (represented by the dimensiodess parameter X = ( V O V m ) / V ~ )$.1 = m means V J V T >> 1; r12 = ( V , V n ) / V ~where , V , is the anode voltage of the diode. Part X > 0 of curve represents the group of electrons which turn in front of the potential minimum. Part X < 0 represents those electrons which arrive at the anode.

-

+

electrons turning in front of the potential minimum (Vo < V,) give only a negligible contribution to a?. As the current d I , shows the full shot effect given by (11.15), we have for the Fourier components of the fluctuations in the anode current:

2

where I?,

=

lo“ 2 e d 1 4 f . /o

=

2e1~j

=

2eI,Af

O0

r2,

r ~ ( ~ 0 )

,2(Vo>e(v~-V~)/~~d(VO/VT)

(111.12)

the “noise suppression factor,” is given by the above integral.

122

ALDERT VAN DER ZIEL

I n the final result it is more convenient to express 7 in terms of the conductivity g of the diode: ia2 = 0 . 4kTcgAf. (111.13) This formula is true for the space-charge limited region and for the exponential region but does not hold for the saturated region of course. In the space-charge limited region e is always close to the limiting value:

e

=

3 ( i - T/4)

=

0.644,

(I11.14)

except near the end points of the region. I n the exponential region 0 = & as g = I a / V r in that region. But the formula: ia2 = 2eIar2Af (111.15)

is even more general. It holds in all three regions; r2 = 1in the exponential and saturated regions, whereas in the space-charge limited region :

(111.16) according to (111.12), (111.13) and the definition of V T . The above problem was treated more or less simultaneously by Schottky73and S ~ e n k e by , ~ ~Bakker (unpublished), by FbckG7and by N0rth.~8 We now consider a tube consisting of two equal cathodes opposite each other a t the same temperature T, for the case of zero total current. Nyquist's theorem should hold in this case and if g is the conductivity of the tube one would expect a noise current:

-

i2 = 4kT,gAf. (111.17) Diemer and Kno130 showed in a detailed discussion that (111.17) should be true and also proved experimentally that this was the case. The above result is also true if the cathodes are at the same temperature but have different work functions, contact potentials, and saturation currents such that the average current is again zero, for in this case Nyquist's theorem again holds except for fluctuations in work function. In the particular case in which there is no potential minimum between the cathodes this can also be shown as follows. One cathode is in the exponential and the other one in the saturated part of its characteristic. One gives an average current I, in one direction the other one the same average current in opposite direction. For both currents (11.15) holds and as the fluctuations of the two currents are independent they have to be added quadratically. Hence, as the conductivity is g = (eIa)/(kTc):

i2 = 2eIaAf -l- 2eI,Af

=

4kTcgAf.

(111.18)

FLUCTUATION PHENOMENA

123

The above result also holds if the two cathodes are a t different temperatures and if ‘they are biased in such a way that the average current is zero, provided that T , now denotes the temperature of th a t cathode which is in the exponential part of its characteristic. The reasonisthat, even though there is no thermal equilibrium (so that the laws of thermodynamics cannot be applied) the derivation which led t o (111.18) still holds. This means, for example, that in an electrometer triode with floating grid the noise of the input circuit is given by (111.18), if T , is the cathode temperature and g the input conductivity of the tube in this b. Noise in Triodes at Low Frequencies. After the discussion of noise in diodes the discussion for negative grid triodes can be short. Due t o the complicated grid structure the exact calculation of the problem is difficult, but fortunately a very good approximation exists. It is found that the triode characteristic is such as if the grid were replaced by a n equivalent anode a t a potential: v e =

.(V,

+ Va/P),

(111.19)

where V , is the grid voltage, V a the anode voltage, p the amplification factor and u a factor slightly less than unity. One would expect the noise of the triode and the noise of the equivalent diode to be the same. As, however, the Conductivity g of the equivalent diode and the transconductance gm of the triode are related as: gm =

(I I I .20)

Ug,

we have in this case according t o (111.16): -

i2 = 2eI,,PAf

= (O/u)

*

4kT,gmAf;

r2 - -2kTcg7ne eI,u

(111.21)

For more information about the factor CT compare North’s paper.58 experiment^^^ showed that formula (111.13) did not hold very well for diodes; the reason is th at low-velocity electrons have a rather large probability of being reflected a t the anode. It can be shown from simple considerations that this may increase the noise of the tube by a factor 2-4. At higher velocities the probability of reflection is very small, hence (111.21) should hold for triodes. This has been verified by experiment^.^^ It is useful t o introduce the concept of “equivalent noise resistance” a t this point. The equivalent noise resistance R, m a y be dejned such that i f a resistance R, were connected between grid and cathode and kept at normal room temperature it would give as much noise in the output as the lube itself. This means: i2 = 4kTR,,Aj * gm2, (111.22)

124

ALDERT VAN DER ZIEL

where T is normal room temperature. Hence, according to (111.21) : (I11.23) For nornial triodes with indirectly heated cathodes e = 2.5, but it may become as large as 4 for tubes with a large distance between the grid wires (u is smaller in th at case). The concept of equivalent noise resistance is a very useful one as it allows to compare the contributions of tbe input circuit and the first tube of an amplifier t o the total noise output of the amplifier. 3. Noise in Diodes and Triodes at High Frequencies

a. Noise in Saturated Diodes at High Frequencies. By applying the theory of Sec. 1 1 . 2 ~one obtains for the h-f noise in a plane saturated diode in which the field strength between cathode and anode is constant (negligible space charge) :

-

2

i 2 = Ze10Af l&d$?)]2;43(/3) = - (1 - e-@ - be-@), (111.24)

P2

a result first obtained by Ballantine.21 I n this equation I, is the diode current and P = j w . The function 1+3(/3)/2 is plotted against the transit = UT in Fig. 2. angle Duva1I3*shon-ed th at the expression for 7 will change somewhat if space charge is no longer negligible, but his result cannot be trusted as it is derived with the help of (11.16) which holds for negligible space charge only. The case of a saturated current flowing between two grids a t equipotential (as may, for example, be encountered in microwave disk-seal type noise diodes) was discussed in Sec. I1.2c, and the result is found in formula (11.18a). The theory for cylindrical diodes can be worked out along the same lines. We refer to the work b y Kompfner et aL50and by Johnson.41 The theory shows that in order t o keep the h-f calibration of a saturated diode noise generator valid even for high frequencies, one has to keep W T << 1. The condition that the transit time T of the electron is as short as possible calls for short electrode distances and large electron velocities (high anode voltages). Moreover, one has to keep the self-induction L of the electrode leads as small as possible, as it can give rise t o series resonance effects due to the diode capacity C. For that reason microwave diode noise generators use a coaxial diode matched to a cable.

FLUCTUATION PHENOMENA

125

At microwave frequencies it is no longer possible to keep W T << 1. I n that case one has to verify first that the structures satisfy the theoretical formulas; after that the formulas can be used in the noise calibration.50 Secondary electrons emitted by the anode do not give rise to any change in noise at low frequencies; at high frequencies they give rise to a new phenomenon which was investigated by D ~ v a l l . The ~ ~ secondary electrons cause a change in the shape of the current pulses due to the

emission of a single primary electron by the cathode; the current pulses get a “tail” of varying length and height, depending upon the energy with which the secondary electrons are emitted. J i d t = 0 for this tail, as the secondary electrons start from the anode and arrive back at the anode. A Fourier analysis of these pulses shows that a t high frequencies (WT >> 1) the noise may be several times the value given by Ballantine’s formula. b . Exponential Part of the Characteristic. Total Emisiion Noise.3 At high frequencies it is found that an important noise current flows to the anode of a diode, even if the anode voltage is so much negative that hardly any electrons can arrive at it. This effect is called total emission noise,s6 it is caused by the fact that the number of electrons emitted

126

ALDERT VAN DER ZIEL

within a (narrow) velocity range shows spontaneous fluctuations. I n the case of negligible space charge the electrons emitted by the cathode give current pulses of varying length and height (due t o the varying emission velocity) such t h a t Ji dt = 0. A Fourier analysis of these pulses shows that an important effect can be expected a t higher frequencies. If a n h-f voltage is applied t o the anode of a diode biased beyond cut-off, then it is found that on the average the electrons moving in the electric field gain energy. This is equivalent t o a h-f diode conductivity, the so-called total emission conductivity. 2 3 , 7 6 It is found experimentally and it can be proved theoretically from general consideratioils that both the total emission noise ? and the total emission conductivity y vary as w 2 in a wide frequency range. It is thus allowed t o describe both effects by saying that the equivalent noise temperature T , of the total emission conductivity is constant* in a wide frequency range. Experiments show that T , is about equal t o the cathode temperature T,. This is also \\-hat one would expect from a thermodynamical point of view. For as practically no direct current flows t o the anode it would not make any difference if the anode the negative anode voltage were replaced by a conductor a t cathode temperature T , and having a contact potential difference with respect t o the cathode equal t o the anode voltage. But this is a system kept a t a uniform temperature T,, and hence its noise temperature T , = T,. Only in case of an appreciable d-c anode current is there any reason t o expect that T , might be smaller than T,. The relation T , = T , was proved experimentally by van der Ziel and \'ersiiel.a6 It was also proved theoretically by direct computation for the case of negligible space charge.89 The casn, of strong space charge has been treated by Freeman his result cannot be trusted, however, as it depends upon (1I.lG). ? is proportional t o the saturation current T in the case of negligible space charge and should vary rather sloivly with I in the other case; this also follows from the above experiments. c. High-Frequemy Noise in Space-Charge Limited Diodes. Due t o the space charge the passage of an electron from cathode t o anode is not an independent event, so that the theory of Sec. 1 1 . 2 ~cannot be applied. As (111.13) and (111.15) hold only under the tacit assumption that 61, is the primary current fluctuation over a time interval long in comparison with the transit time of the electrons, the theory of Sec. III.2a cannot be adapted easily for the h-f region. Attempts3 in the direction of an exact theory of h-f noise have not yet been worked out; the main difficulty seems t o be t o give a proper h-f theory of the space between cathode and poten* Because 2 = m 2 A f = 4kl',gAf = 4kT,bw2Af, T , = a / ( 4 k b ) where a and b are

+

constants.

127

FLUCTUATION PHENOMENA

tial minimum. Fortunately an approximation method exists which makes use of the following simplifying assumptions: 1. The motion of electrons in the region between cathode and potential minimum can be neglected altogether. 2. The electrons pass through the potential minimum with a uniform velocity uo equal’to the average velocity (7rkT,/2m)-341when k is Boltzmann’s constant, m the electronic mass, and T , the cathode temperature. 3. The anode current has a value such that the field strength at the potential minimum is zero. A theory based upon these three assumptions gives about the right potential distribution between potential minimum and anode and the right (I,, V,) characteristic. Llewellynsl applied the above approximation in order to calculate the h-f diode conductivity, and Racks7 applied it to noise problems by investigating the influence of a small fluctuation in the initial velocity upon the anode current. Llewellyn investigated the following general problem. Consider an electron stream between two parallel planes 1 and 2. The total current I ( t ) = I, I l ( t ) which a t the instant t has the same value at any distance from the plane 1, consists of a d-c part 1 0 and a small current ripple I l ( t ) . Llewellyn was then able to express the a-c potential difference ( V , - V1) between the two planes in terms of 11, the initial velocity ripple and the initial acceleration ripple a t the plane 1. If E is the field strength, € 0 = 8.85 x farad per meter, I&$) a small ripple in the convection current at the instant t and at a distance x from plane 1 and A the electrode area, then:

+

I(t) = 1 0

+ I l ( t ) = + I c ( x , t ) + €OA aE ZJ

(111.25)

113

the latter term being the displacement current. As (aE/at) is related to the ripple in the acceleration, it is also possible to express ( V , - Vl), the convection current at the electrode 2 and the velocity ripple u2 at the electrode 2 in terms of I l ( t ) , the convection current Ic(O,t)at the electrode 1 and the velocity ripple u1 a t the electrode 1:

(V2 - V l ) = allIl(t) [Ic(z,t)lz =

u2

UZlIl(t)

= a3lIl(l)

+ alZIc(0,t)+ al3ul(t), + azzIc(0,t) + a23udt),

I

+ a3~Ic(o,t)+ a33ul(t)*

(111.26)

These equations are known as the Llewellyn-Peterson equations, the coefficients a11,a12 . . . etc. have been calculated by L l e ~ e l l y n . ~ ~ ~ 6 4 ~ 6 ~ I n our particular case plane 2 coincides with the anode and plane 1 with the potential minimum so that E = 0 and aE/dt = 0 a t plane 1. This means that the convection current Ic(O,t)at that plane:

IG(O,t) = I l ( t ) .

(III.25a)

128

ALDERT VAN DER ZIEL

Inserting this into (111.26) and neglecting a small term in the coefficient of I1 (cont,aining the average value U O of the initial velocity at the plane 1) we obtain:

where PI = j w r 1 and r1 the transit time from potential minimum to anode. First consider the case in which u1 = 0. Then (III.26a) gives for the complex impedance z1 of the diode (zl also takes into account the tube capacity) : 21 = 4&31>/gm. (III.26b) At low frequencies (pl = O ) , z1 = l/gm is equal to the internal resistance of the diode. Racka7observed that a fluctuation in the primary current will correspond to a fluctuation in the average velocity with which the electrons pass the potential minimum and this fluctuation in average velocity will give rise to a fluctuation Il in the anode current. I n order to calculate the h-f diode noise we put ( V 2 - Vl) = 0 in (III.26a), apply a Fourier analysis to the velocity fluctuation in order to calculate the velocity ripple u1, and identify the last term in (III.26a) as a noise emf. The mean square value of the current fluctuation is then found as:

i12

*

1211'

=

-

-

e 0 ~ 1 4 ~ ( P ~; ) 1eo2 ~ .=

(my

IOQ2

*G.

(111.27)

A detailed calculation shows that:

(

3

(111.28)

eo2 = 3 1 - - $kT,Af/g,,

-

which T, is the cathode temperature.

i12

-

= io2 =

-

At low frequencies (PI

( 1) - 4kTcgm.Aj,

eo2gm2= 3 1 - -

=

0): (I11.29)

which is identical with (111.13). Hence the method gives the correct expression for the h-f noise in diodes. Combining (111.29), (111.27), and (III.26b) we have at high frequencies: (111.30)

129

FLUCTUATION PHENOMENA

Figure 2 shows P/? as a function of lpll = w r 1 ; as may be seen from this figure, does not strongly depend upon frequency, though there is a dip around lpll = 27r. This result that the noise suppression factor r2 does not change very much with frequency is not inconsistent with measurements carried out by D u ~ a 1 1(large ~ ~ scale models) and by Kompfner et aL60 (coaxial diodes). d . Noise in Triodes at High Frequencies. Some measurements on total emission noise in triodes have been published. The noise temperature seems to be definitely smaller than the cathode temperature. It also seems that the total emission conductivity in triodes is smaller than for the corresponding diodes.3 Both effects might be due to the inhomogeneous potential distribution in the cathode-grid region if the tube current is nearly cut-off. The most important problem is the calculation of the noise in a space charge limited triode. Except for the fact that one has to add a factor u in the equation (111.29) for 2,it is allowed to use (111.30) as an expression for the noise current in the cathode lead of a triode. I n order to find the noise current in the anode lead of a triode, it is again useful to apply the Llewellyn-Peterson equations which give for the convection noise current at the grid plane:

where u is the average velocity a t the grid plane and (111.27):

il

follows from (111.32)

This convection current now enters the grid-anode space. If the influence of the space charge in the anode-grid region can be neglected, it gives rise to a current: (111.33) iz = ic43(P2) in the anode lead, 82 = jwn and 7 2 is the transit time from grid to anode.* Expressing the term loul/u in terms of io, (111.31) becomes: (111.34) Besides the numerical result it is interesting t o note that il, ic,and iz are all completely correlated with the initial velocity Jluctuation. The

* A more exact theory should also take into account that the electrons entering the grid-anode region have a small velocity ripple u2 which is completely correlated with i,. It gives rise to a small noise current in the anode lead which is completely correlated with i ) and which can usually be neglected.

130

ALDERT VAN DER ZIEL

validity of this fundamental relation will be tested in the next two sect ions. e. Noise in Electron Beams. Pierce' has applied the LlewellynPeterson relations to noise problems in traveling wave tubes. It is beyond the scope of this review t o discuss noise problems in these tubes except for a very interesting experiment by Cutler and Quate which has a direct bearing upon the above theory.2sa They investigated the magnitude of the noise current in an electron beam by moving a resonant cavity tuned a t 4200 megacycles along the beam and found maxima and minima in the noise which were explained theoretically. The theory makes use of equation (111.31). Let the transit time from cathode to anode in an electron gun be so large that &(PI) can be neglected in comparison to +P1e-@1 (this is the case if m1> 37r); (111.31) then gives for the convection noise current i, a t the anode of the gun : zc . = I0 - .jm1e-iO" . u1. (111.35) U

The Llewellyn-Peterson relations give that under those conditions the velocity fluctuation u2 a t the anode is: (111.36) i, and u2, which are completely correlated, are now used as the input boundary conditions to the drift tube. According t o Pierce? the beam in the drift region is capable of propagating two unattenuated space charge waves which can be expressed as functions of i, and u2. As these two waves propagate with different velocities there will be points along the beam where the two space charge waves are in phase (maximum noise) separated by points where the two waves have opposite phase (no noise). Figure 3 shows the observed noise plotted against distance along the beam (full-drawn curve) in comparison with the calculated noise (dotted curve). The calculated curve was derived with the help of equations (111.35) and (111.36). The rather good agreement between theory and experiment allows us to draw the following conclusions: (1) i, and u2 are completely correlated. Otherwise a practically complete compensation of the noise in the minima would not be possible.

* It has been suggested66that the same method might be used in order to get rid of a large amount of noise in pentodes at very high frequencies by designing a region in the tube such that it has full space charge. ( E = 0 at one of the electrodes.) Formula (111.34) will then be valid and hence (111.35) will result if the transit time T to the next electrode is chosen such that w > 3r. This means that the initial conY ection current fluctuations will then have disappeared.

131

FLUCTUATION PHENOMENA

The small residual amount of noise in the minima was found t o be due t o the interception of a small fraction of the electron beam by the cavity (partition noise). (2) T h e theory gives the right magnitude of the noise. The only discrepancy was that the theoretical curve had t o be shifted somewhat in order to obtain the best agreement with experiment. This small discrepancy is thought t o be due t o the use of (111.35) and (111.36), otherwise these equations seem t o be the right starting point. 10

I

I

I

I

11

w u)

9 12

5In

13

3 14

9

15

m

a

z 16 5 17 z

0

a in

; rJ

19

20 0

2 3 4 DISTANCE F R O M ANODE IN I N C H E S

5

6

FIG.3. Results of Cutler’s experiment on the noise power versus distance along a n electron beam. The distance is measured from the anode of the electron gun producing the beam. (Courtesy of Dr. Cutler.)

f. Induced Grid Noise in Triodes.20#60 Turning back t o triodes we observe that the noise current il in the cathode lead and the noise current iz in the anode lead are completely correlated. But as they have a phase difference, a current (il - i,) has t o flow t o the grid. Using (111.30) and (111.34) and employing a series expansion of the various functions we obtain for moderately high frequencies: (il

- iz) =

io(+jjw~1

+

g j j w ~ 2 ) ;(il

- i2)2

+

= Z2&o2(~1

2 ~ 2 ) ~ .(111.37)

The induced grid noise shouId therefore be proportional t o u 2 in a wide frequency range. This was verified experimentally by Bakker;,O i t cannot be considered as a verification of the above theory, however, as i t follows from very general considerations. Bellzza has expressed (il - iz)2 in terms of the increase AC in input capacity and van der Ziel

132

ALDERT VAN DER ZIEL

has given a n extension of his result with the help of the LlewellynPeterson equations.90a The induced grid noise should be completely correlated with tube noise. Strutt and van der %elsoshowed that under those conditions the induced grid noise might be used in order t o eliminate part, if not all, tube noise by properly detuning the input circuit. Kleen48proved that some noise reduction could be obtained in this way, whereas van der Ziel and Versnela6 showed t h a t a t least part of the induced grid noise was correlated with the tube noise and that a t 7-m wavelength this part had a phase difference of 90 degrees with respect t o the tube noise, as required by (111.37). Recent experiments carried out by the authorgob showed that for 654 and 6AC7 tubes (the latter used as a triode) a major part of the induced grid noise (about two-thirds of it) was not correlated t o tube noise. This is a serious difficulty of the above theory, but i t explains why the noise reducing schemes mentioned previously did not eliminate more tube noise. g. Discussion of the Results of the Last Two Sections. Due t o the occurrence of this uncorrelated part of the induced grid noise it does not seem t o be worth while t o investigate whether (111.37) agrees numerically with experiment as it was derived under the assumption of a complete correlation. The question is now where this uncorrelated part comes from. Most uncorrelated noise can be accounted for by the fact that the electrons can pass the grid wires at various distances.22 The shape of the current pulses flowing t o the grid will then vary a t random, which gjves rise t o an uncorrelated part of the induced grid noise. Part of the uncorrelated noise can be explained by tube inhomogeneit i e s g 7 If il = il’ illf and i2 = i,’ i2“ where i,’ and i,” and also iz‘ and i2” are uncorrelated, but il’and i2’ and also i,” and iz” are completely correlated, then il and iz are no longer completely correlated in general. It is also likely that part of the uncorrelated induced grid noise is caused by the fact that the three assumptions of Sec. 1 1 1 . 3 ~upon which the theory is based are rather crude, especially for tube structures in which the distance between cathode and potential minimum is a n appreciable fraction of the cathode-grid distance, as is true in many modern tubes. I n t h a t case it is understandable that at least part of the induced grid noise might not be correlated t o the tube noise, as one would not expect the theory t o hold well in that instance. On the other hand, this lack of correlation should not affect the beam experiment. For even if the convection noise current close t o the potential minimum were not correlated at all t o the velocity fluctuations, then

+

+

133

FLUCTUATION PHENOMENA

(111.35) and (111.36) would still be valid, provided that ur1 i&sufficiently large. For in that case the original convection current would become negligible at the anode. 4, Partition Noise

a. Partition Noise in Pentodes and Hexodes. I n studying the motion of electrons in multi-grid tubes one usually finds the following condition to prevail. Whether an electron arrives a t the anode or at the screen grids is compfetely random, mainly due to the random velocity component parallel to the cathode and the absence of space-charge effects outside the cathode-grid region. Due to the random distribution of the electrons over the various positive electrodes a new type of noise, partition noise, occurs. In the same notation as before we have for a pentode, if 2 is the noise in the cathode lead : ',I2

Af;

-

iC2= 2e(Ia

+ I2)rC2Af,

(111.38)

The interpretation of these equations is as follows. We split the instantaneous cathode current into a constant part and a fluctuating part i,. The part I z / ( I u I,) of the fluctuation will go to the screen grid, and the part Ia/(Ia 12)to the anode. This gives the first term in the equations. The constant current is divided a t random between screen grid and anode, it gives rise to a fluctuating current i, flowing from the screen grid to the anode (partition noise) ; this accounts for the second term in the equations.* The partition noise was treated simultaneously by Schottky74and Bakker18 and independently by North.Kg According to the above theory the noise currents in the screen grid lead and the anode lead are correlated. By feeding back the right part of the noise in the screen grid lead into the input circuit in the proper phase it is possible to get rid of the partition noise. This was first demonstrated by Strutt and van der !Gelsoand verified experimentally by

+ +

* The magnitude of 2 follows from the following theorem. Let certain similar independent events have the probability X to occur in the form A and the probability (1 - A) to occur in the form R, such that the form of an individual event is completely random. Counting n events, n1 are found to be of the form A and n2 of the form B, such that:

n1

= An;

122

=

(1 - X)n; (nl - ii,)'

=

(n, -

?&)2

= X(1

- X)n.

134

ALDERT VAN DER ZIEL

I n a hexode a similar theory can be applied.5g Noise is generated here a t the cathode, the first screen grid and the second screen grid. The ' partition noise generated at the second screen grid flows to the anode, the partition noise generated a t the first screen grid is properly distributed between the second screen grid and the anode and the shot noise generated a t the cathode is distributed between the various positive electrodes a t the proper rate. It is then found that the expression (111.39) for 2 also holds for a hexode, provided that I 2 represents the current flowing to the positive grids. The more positive electrodes are inrerted between cathode and anode, the more current will be intercepted and the larger the noise; for that reason the noise resistance of a hexode is usually much larger than for a pentode. Equation (111.39) can also be applied to those pentagrids in which the anode current is not influenced by the space charge in front of the second control grid. I n some cases, however, the space charge in front of the second control grid limits and controls the anode current; the current fluctuations will thus be partly suppressed by the space charge and 2 may be much smaller than would follow from (111.39). We obtain therefore for the noise resistance R, of a pentode (or hexode), if gm is the transconductance of the anode current and e afactor of 2.5-4 (Sec. 111.2a), according t o (111.39) and (111.13) : (111.40) This formula shows that partition noise is especially important for tubes with a large ratio 1 2 / g , . b. Induced Grid Noise. Due to the fact that a fluctuating current is flowing through the second control grid of a hexode or pentagrid, induced grid noise occurs. Some measurements have been carried out by Bakker,20from which it seems to follow that induced grid noise is much larger for these tubes than for a pentode. There are two reasons for it: (1) the transit times are usually much longer; (2) the tube current a t the second control grid is usually much noisier as it contains a large amount of partition noise. A good theoretical discussion of this kind of induced grid noise is still lacking for most hexode and pentagrid tubes; Bakker's theory is correct for the type of tube he measured. 5 . Secondary Emission N o i ~ e ' ~ . ~ ~

Consider a secondary emission cathode for which on the average each primary electron liberates 6 secondaries. If every primary liberated exactly 6 secondaries then no extra noise would result, but as the number

135

FLUCTUATION PHENOMENA

of secondaries per primary is fluctuating, a new type of noise, usually called secondary emission noise arises. Let Bn be the probability that a primary electron liberates n electrons. Then :

the latter equation defines a quantity K which will be used below. Suppose the primary beam is saturated and the primary current is I,. Then the part Ipn= /?,Ip of this primary current will liberate n electrons per primary. I,, shows fluctuations; if all the secondaries are collected a t the anode:

2

=

2

-

(2eIpnAf) n2 = 2eI,~6Af;

(111.42)

n=O

Zieglerg3measured K and 6 for various secondary emitters. K is usually 30 to 50 per cent larger than 6. If every primary had liberated 6 secondaries we would have had:

-

ia2= 2eIPa2Aj, so that the part:

-

',i

(III.42a)

= 2 e I , ( ~- S)SAj

(111.43)

is realIy the noise due to the fluctuations in secondary emission. If the primary current is not saturated we obtain:

-

-

+ 2 = 2e1,6(rP26 +

- 6)Af (111.44) is the primary current fluctuation and rP2 the noise suppression i,' = i p 2 6'-

K

where ?a factor of the primary current.

6. Noise in Gas Discharge Tubes

I n radio tubes containing small traces of gas the noise is found to be several times higher than would be expected according to the preceding theory. The reason for this large increase in noise is understood as follows. In an evacuated triode the noise is partially suppressed by space charge and? = 2eI,r24f where r2,the noise suppression factor, may have a value of 0.10 or less. If some gas is present, so that there is a small probability p that a primary electron will ionize a gas molecule, then this in itself would give a contribution 2eIapAf to 2. I n addition, however, the positive ions moving through the potential minimum with a very low speed (much smaller than of the average velocity of the electrons in the potential minimum) give rise to a large temporary increase in

136

ALDERT VAN DER ZIEL

anode current as they reduce the space charge in the potential minimum (Fig. 1). This increases the original current fluctuation SI due to the ionization by a large factor m, so that the actual contribution to ? becomes 2eI,pm2Af, this can be much larger than the shot noise current 2eI,I’*Af, even for small values of p . For a more exact theory compare Thompson and North’s paper.g2 Gas discharge tubes have been used recently as microwave noise standard^.^' The discharge tubes wbich are rather thin are usually inserted in a wave guide such that their axis makes an angle of about 10 degrees with the axis of the guide, this provides about a perfect match over a rather wide range of temperatures and frequencies. The “noise temperature ” of the gas discharge is approximately equal t o the “electron temperature” of the discharge. Noise ratios around 16 db are common; this property makes these discharge tubes valuable for measuring noise figures (Sec. IV) of 20 db or less. The fact that the noise temperature of the discharge is about equal to the electron temperature T,can be easily understood in the following way. The positive ions move so slowly that their influence can be neglected. The plasma electrons in the discharge can be considered as a free electron gas of temperature T. except for the convection current I flowing in the direction of the axis of the tube. The presence of the gas ions makes itself felt only in the fact that the free electrons suffer collisions. Let the average time between two collisions be r ; during two consecutive collisions the electrons move in a straight path and give rise to a current pulse in the outer circuit as discussed previously. If an electric field is applied to the gas, the electron gas is found to have a conddctivity G ( w ) . The random motion of the plasma electrons constitutes thermal noise for which Nyquist’s theorem holds (noise temperature T,). Superimposed upon this random motion is a forced motion of the electrons in the direction of the axis of the tube. The randomness in the free path length which is traveled between two collisions gives rise to a shot noise current i in the direction of the tube which has to be added quadratically t o the thermal noise. But as this shot noise current flows in a direction making an angle e with the direction of the E vector of the wave guide, the current in the direction of the E vector is i cos 0. The shot noise current can be calculated in a way as shown in Sec. 11.2d. We quote here the result obtained by Parzen and Goldstein‘j2for the available noise power P, of a gas discharge tube:

Pa = kT,Af

+3 cos2 0 (1 + N

2 +

w2T2)

Af

(111.45)

FLUCTUATION PHENOMENA

137

where N is the number of free electrons in the plasma and P o the d-c power dissipated in the tube. The second term in (111.45) is usually only a few per cent of the first one especially because in practical applications of gas discharge noise standards e is about 80 degrees.

7. Noise in Mixer Tubes a. Triode, Pentode, and Hexode mixer^.^^,^^*^^^ I n mixer tubes the anode current changes in the rhythm of the local oscillator voltage and may be zero during part of the cycle. I n order to find the i-f noise current in the output of the tube one has to take the average value of the noise over one complete cycle of the local oscillator voltage. Denoting this average by ( )*,, we have for a triode mixer in which local oscillator voltage and signal are both applied to the grid, if gmis the instantaneous transconductance of the tube :

-

(ia2)Av =

e

*

4ikT(gm)~vAf,

(111.46)

as gm is the only quantity which changes during a cycle. For a pentode and hexode mixer, things are a little more complicated. Let I,, Ia,and I2 denote the instantaneous cathode current, the instantaneous anode current, and the instantaneous screen grid current, respectively, and let gm denote the instantaneous transconductance of the cathode current; I , = (Ia I 2 ) of course. We then have for a pentode mixer in which the local oscillator voltage and the signal voltage are both applied to the grid, according to (111.39) and (111.13):

+

@)av

= e

*

4kT(gm)~,X2Af -k 2e(Ic)AvX(l- X)Af,

(111.47)

where = I a / I C . I n this case only I , and gmchange during the cycle but remains constant. In a hexode mixer, however, in which the local oscillator voltage is applied to the second control gird, I , and gm remain practically constant, but X changes in the rhythm of the local oscillator voltage. Hence:

-

(ia2)dV

=

€ ’

+

4kTgm(h2)rdf 2eIC(X(1- X)jAvA.f.

(111.48)

If g,, is the conversion transconductance, one can introduce the noise resistance of the tube according to the definition: (23.4,

= 4kTRnAf * gmc2.

(111.49)

For large oscillator voltages (gm)Av = g,, and gmcis about equal to one-fourth of the maximum transconductance so that the noise resistance of a triode mixer is about four times the noise resistance of a corresponding h-f triode under the most favorable circumstances. For hexodes values for R, of 100,000-200,000 ohms are common. Much larger values

138

ALDERT VAN DER ZIEL

occur for small local oscillator voltages because gmc becomes so small in that case. b. Diode Mixers.s An interesting noise compensation occurs in a diode mixer circuit.39 Let the input circuit have a conductivity Gi and let the output be short-circuited. Let w i be the input frequency, wm the intermediate frequency, and let v h cos be the local oscillator voltage. As the transconductance gm is a periodic function with period Wh, we develop it into a Fourier series: gm

=

90

+ 2gmc cos + uht

*

*

*

(111.50)

1

where g o = ( g m ) A v and gmcis the conversion transconductance. Let a small fluctuation peak in the diode current occur a t t = T . Developing this fluctuation peak into a Fourier series we obtain an h-f component a cos w i ( t - T ) and an i-f component u cos wm(t - T ) . If the input were also short-circuited, the latter would be the total i-f noise current. But if the input circuit has a conductivity Gi, an h-f voltage will be developed across the input and if wm = (oi - W h ) it will give rise to an i-f current: Fc

u cos [ ~ m ( t- T )

+

@h7];

Fc

=

gmc/(Gi

90).

(111.51)

Combining the two i-f currents, the square of the amplitude becomes: U2(1 - 2Fc COS WhT

+ Fez)

(111.52)

instead of a2. But according to (111.13) the instantaneous value of u2 a t a certain instant T is proportional to the instantaneous value of gma t that instant. Using (111.13) and substituting t = T into (111.50), the i-f noise is found by taking the average of (111.52) over a cycle:

whereas it would be equal to e .4kTg&f if the input were short-circuited, Therefore a compensation takes place, which is practically a complete one if gmc = go and Gi << go, so that F, = 1. The condition gmc = go means that the tube has to draw current during a small part of the cycle. For a fuller discussion we refer to papers on the subject.ag.** c. DeJlection Mixing ( H e r ~ Z d * ~ )In . a beam deflection mixer' tube a low average anode current (I,JAv is combined with a large conversion transconductance gmo in order to make a low noise tube, A sharply

FLUCTUATION PHENOMENA

139

focused beam passes along two input deflection plates and along two local oscillator deflection plates t o which a local oscillator voltage V = VI, cos Wht is applied. For v h = 0 the beam is intercepted by a wire; if v h > 0, the beam is deflected on and off the wire and the transconductance to the plate varies between a positive maximum and a negative minimum value. This gives an increase in gmcby a factor 2, as in normal mixing the transconductance changes from a maximum value to zero. Moreover, as the anode current is zero for v h = 0, the average anode current (Ia)A, will still be quite small even if v h is chosen such that gmc has an appreciable value. Due to the fact that a large part of the beam is permanently intercepted by the wire, it follows from (111.39) that the anode noise current 2 is such as if I,, were a saturated current. Applying (111.49), we find for the noise resistance: (111.54) For a tube designed for 1200 megacycles, R, was 30,000 ohms. As the input capacity of the tubes is small, high circuit impedances a t rather wide bandwidth have been obtained. Moreover, as the input circuit is balanced, there is little induced grid noise so that very good noise figures have been obtained even at 1200 rnegacycle~.~~ 8. Noise in Photocells and photomultiplier^^^

Noise in photocells follows Schottky's formula (111.15) i2 = 2eIAf, as the emission of a photoelectron is an independent random event. Very weak signals from a photocell have to be amplified; a very large anode resistance R in the photocell circuit is then needed. The limitation in sensitivity is the thermal noise of this resistor. An important improvement in sensitivity can be obtained by using secondary emission multiplication. If I , is the primary current and if there are n multiplier stages each having a secondary emission factor 6, then the output signal is 1,P. If there were no secondary emission noise the noise output would be : ia2= 2eI,62"Af. (111.55)

But the first multiplier stage gives a noise 7 = 2 e ( l , S ) ( ~ - S)Af which is multiplied in (n - 1) stages, the second stage gives a noise ? = 2 e ( I , P ) . (K - S)Af, which is multiplied in (n - 2 ) stages. Adding all contributions we obtain for n >> 1 and 6 > 1 : (III.55a)

140

ALDERT VAN DER ZIEL

The factor ( K - 1)/(6 - 1) which is usually between 1.2 and 1.5 indicates how little the noise-signal ratio is increased by the secondary emission. For very high amplifications one runs into trouble due to the “dark current ” (which is partly due to thermionic emission and partly to gas ionization), which gives rise to a noise background and limits the sensitivity. 9. Shot Noise in Semi-Conductors

A kind of noise closely related to shot noise in tubes might be expected to occur in semi-conductors. One can investigate this problem in various ways: ( a ) by assuming that the number of free electrons or holes fluctuates, thus causing a fluctuation in the r e s i ~ t a n c e ,(~b ~ ) by * ~assuming ~ that the creation or the “trapping” of a free electron or hole is an independent effect occurring a t random (Sec. II.2d) . 2 9 , 3 8 Both methods give identical results.g0 The effect should be negligible for metals but has importance for semi-conductors as shown by Herzog and van der Zie1.448 If T I is the average life of a free electron (or hole) and T O the average drift time of the elecfxon (or hole) from one electrode to the other one (TO is inversely proportional to the current I ) , then one can distinguish between two extreme cases: ( a ) I n bulk material T I < > T O so that practically all electrons enter the semi-conductor a t the negative electrode and leave it at the positive one. The noise should then be the full shot noise of a saturated diode as represented by (II.18a). This occurs in crystal diodes; Flicker effect over and above this shot effect is also p r e ~ e n t . ~ 10. Flicker Noise in Cathodes and Semi-Conductors

In saturated diodes a large amount of noise over and above shot noise occurs at low frequencies (Flicker e f f e ~ t ) .If~ current ~ ~ ~ ~ flows through a semi-conductor, then a large amount of noise over and above thermal noise and shot noise is generated.28*53.55 Both effects can be described by a constant current generator 4 2 of infinite impedance in parallel with the device under consideration. It is found that in both cases the noise can be described by a formula of the type:

FLUCTUATION PHENOMENA

i2

=

KIaf-“j

141 (111.56)

in a wide range of currents I and frequencies f down to frequencies below 1 cycle per second. A similar formula also holds for excess noise in carbon microphones, granular resistance elements, photoconductors, crystal diodes, and transistors. Due to the similarity of the law (111.56), one might better label all these excess noises by the name Flicker effect. Usually a is close to 2, b is often close to 1. These noises often consist of two types, one is a rushing sound somewhat similar qualitatively to thermal noise and shot noise, the other is a frying or rough sound which occurs in erratic bursts. These noise “bursts” require a large time constant of the indicating instrument in noise measuring equipment in order to prevent the deflection of the instrument from fluctuating erratically. If diodes are compared having the same current but different cathode areas A , we find that P should be inversely proportional to A (because if n identical saturated diodes are connected in parallel both 3; and I are multiplied by a factor n). Hence, other things being equal, tubes with a larger cathode area should have a lower Flicker effect. In semi-conductors ? should be inversely proportional to the length L and the cross-sectional area A of the conductor, that is 2 should be inversely proportional to the volume V (for if n identical conductors are connected in series or in parallel, 7 is divided by a factor N in both cases). This makes it understandable why Flicker noise is so important in crystal diodes as it is mainly generated in the thin barrier layer surrounding the contact. Both phenomena seem to be governed by a diffusion phenomenon.s2*68 I n the case of tubes the emission of an electron is not an independent event occurring at random, but (‘active specks” on the cathode emit a number of electrons in an irregular sequence during their lifetime. According to Schottkyl7l the effect is caused by foreign atoms on the surface of the emitter; they decrease the work function 4, their migration over the surface causes 4 to fluctuate and this in turn gives rise to current fluctuations. In the case of semi-conductors the creation or trapping of electrons (or holes) is no longer an independent event occurring a t random, but the probability may depend upon the presence of foreign atoms or lattice distortions. A migration of these atoms through the conductor may thus “modulate” the current passing through it, thus causing excess noise which can be described by a resistance fluctuation.66 The occurrence of the factor I 2 in (111.56) is easy to understand. In electron tubes the fluctuations &$ in work function give rise to a fluctuation 61 in current; it follows from Richardson’s equation for the satura-

142

ALDERT VAN DER ZIEL

tion current I that 61 is proportional to I . In semi-conductors a fluctuation 6R in resistance gives rise to a voltage fluctuation I6R across its terminals. Carrying out a Fourier analysis it is found that i'i is proportional to I 2 in both cases. The frequency dependence is more difficult to explain. One might perhaps think that such a diffusion process would give rise to an exponential correlation function of the type ecW/*. In that case one would expect?' (compare Sec. II.2d) :

2 = const. T ( 1 + W V ) - ' A ~ ,

(111.57)

which is constant at very low frequencies and varies as the square of the frequency at higher frequencies in disagreement with (111.56). Cathodes with N O"emission centers'' a t the surface of average life time T and emitting on the average N electrons during their life would give Schottky's formula: i2 = %NeIAj(l w ~ T ~ )=- 2~ ( 1 2 / N o ) A f ~ ( l u ~ T ~ ) - ~(III.57a) .

+

+

Agreement with experiment can be obtained by introducing a wide distribution of correlation times T : ~ O

dP

= g(r)dT;

We then obtain:

-

i2

=

const.

[ h" ~

h"

g(T)dT = 1.

(111.58)

( f1

O ~ T ~ ) - ' ~ ( T ) ~Af. T]

(I11.59)

The difficulty is thus removed one step back, as one only has t o account for the distribution function g(r).* Richardson68has shown that the diffusion processes mentioned above might be interpreted as leading to a wide distribution of correlation times. As diffusion may be a more or less slow phenomenon, it can account for relaxation times up to many seconds or minutes. A detailed investigation of several models by Richardson gave the following results: (1) I n a system comprising a high-resistance layer modulated by the three-dimensional diffusion of particles (or heat) 2would be proportional t o f-54. (2) In a system composed of a localized contact disturbed by a diffusing surface layer 2 would be constant a t low frequencies and would vary as fF2 a t high frequencies.

* In particular the distribution function < < much slower than 1 / ~for 7 <

in which g(7) varies as a / . in a region and much faster than 1,'. for r > 7 2 gives a noise spectrum which varies as f-1 for 1/72 < w < l/n, varies slower than l/f at very low frequencies and faster than l/f a t very high frequencies (usually This agrees with the experimental data. goes aa l/fz).

T~

7

72;

T~

FLUCTUATION PHENOMENA

143

(3) In a system involving the contact between relatively large areas of rough surfaces covered with diffusing surface layers 3 would be proportional to f-’ in a wide frequency range as required by experiments. Miller*5“ studied diffusion processes of particles, such as impurity atoms, which are able to “modulate” currents and found that 3 varied as f-N at low frequencies, as f-94 in a wide frequency range and as f+ at high frequencies. Macfarlane also studied several diffusionmechanisms. s2s All these examples show that the most likely explanation of the frequency dependence is a sort of diffusion mechanism. But any mechanism which gives a wide distribution of correlation times of the right shape will of course do the same. Macfarlanes2proposed a theory of Flicker effect based upon Sproull’s theoryI9 of cathode emission. The theory is nonlinear, for the time constant of the decay of an ‘(active speck” of the cathode depends upon its size; the larger the speck the more violently it decays. By introducing a wide gaussian distribution in the size of the specks (equivalent to a wide distribution in correlation times) Macfarlane obtained a formula of the type (111.56). Unfortunately, the theory seems to require that 3 becomes independent of frequency below a few hundred cycles, whereas Bogle’s workz5seems to indicate that (111.56) is valid down to 1 cycle (actually correlation times up to a few hundred seconds were observed). There does not seem to be any indication either that big specks decay much more violently than the small specks. In oxide-coated cathodes Flicker effect is not necessarily a surface phenomenon. The oxide layer is a semi-conductor, which will show fluctuations in conductivity. As the emission current of an oxide-coated cathode seems to be proportional to the conductivity of the coating, the fluctuations in conductivity might contribute to the Flicker effect as we11.90 I n space-charge-limited diodes the Flicker effect is less than in corresponding saturated diodes.72 Let I , be the anode current, g m the transconductance and V T = kT,/e, 61 and 61, the fluctuation in emission current and anode current, respectively, then: 61, = (aIa/aI)61 = (gmVr/I)6 1

according to Langmuir’s theory of the diode characteristic. Denoting the corresponding Fourier coefficients by i and i,, respectively, one finds:

2 where

2

=

-

-

7 ( g m V , / I ) 2= Ggm2; ~~2 = izVT2/12

represents the equivalent noise emf at the input.

* Miller’s process seems to be identical with Richardson’s first model.

(I11.SO) The only

144

ALDERT VAN DER ZIEL

exceptions are diodes with W-cathodes, where the noise is increased considerably by space charge; this effect is due to the emission of positive ions which wander around in the potential minimum and cause current pulses of 10-2 - 10-6 seconds duration (anomalous Flicker effect).8.~25*60a Van Wij ngaardengo0carried out careful Flicker noise measurements and obtained the following results. For W-filaments he found only noise of the type (III.57a); above 10 cycles Flicker noise was small in comparison t o shot noise. For Th-W-diodes the Flicker noise was of the type (111.56) with a = 2 and b = 1. For oxide-coated cathodes the noise could often be described by a formula:

i2

= A/f

+ B7/(1 + w%.")

(III.6Oa)

in which A and B both varied as 12. Calculating N Ofrom the second term he found values of the order of 2 X 1Olo for his cathodes. This

number coincides with his estimated number of free Ba-atoms a t the surface and thus identifies Schottky's emission centers here as individual Ba-atoms. In other cases he found:

-

ve2 = (Ao/f)ebra

(III.60b)

in which both A Oand b depended strongly upon the cathode temperature; he attributed this noise to a fluctuation in the conductivity of the coating. In measuring noise in apparently homogeneous semi-conductors one must be very careful that the end contacts carrying the d-c currents do not act as crystal rectifiers; otherwise most of the resistance may be localized in the contacts and the main part of the excess noise may be generated there. For that reason one should provide extra contacts somewhere along the conductor and measure the noise emf between those contacts only. The most reliable results will be obtained with single crystals. Interesting measurements on germanium single crystals were carried out by Montgomery and Sh0ckley.6~ They used a single crystal that had three extra contacts A , B, and C close together such that noise could be measured between each of them. If the electrons or holes which contributed to the noise between the points A and B also contributed to the noise between the points B and C one would expect a correlation between the noise emf's vAB and vBC. As v A C = vAB vBC, one would have:

+

+ G2+ 2c - -

(111.61) d V A B 2 ' vBC2 where c is the correlation coefficient between vAB and v A C . Hence by it is possible to calculate c. c changed measuring vAc2, v n B 2 and >v appreciably with surface treatment (sand blasting, presumably due to the changes in surface recombination) or by changing the bias voltage. V>

=

V Z i

FLUCTUATION PHENOMENA

145

The single crystals used by Montgomery and Shockley were electron conductors, but some holes with short life time ( = 10W sec) were present which generated the excess noise. The observations fitted best with the idea of lumped sources of holes. * These measurements were carried out a t audio frequencies. Herzog and van der Ziel measured the noise ratio n of such single crystals over a wider range of frequencies and varying currents and found that the experiments could be described by a formula :44a

n

=

1

+ A/f + B/(1 + w 2 ~ 1 2 )+ C/(l + w27z2)

(111.62)

with T~ = 10-6 sec and 7 2 much smaller; A , B, and C were proportional to 12. The first term is due t o thermal noise, the second to the excess noise mentioned above, the third term is ascribed t o the shot effect of the holes causing the excess noise (because the value of T~ corresponds with the life time of the holes) and the fourth term is ascribed to the shot effect of the electrons. 1 1 . Noise i n Crystal Diodes and Transistors

A marked difference exists between the noise in the backward and in the forward direction of a crystal diode. I n the forward direction there is some Flicker effect a t lower frequencies, but a t higher frequencies the noise often remains more or less constant; this constant part might be interpreted as shot noise. In the backward direction the noise decreases with increasing frequency even above 30 megacycles; it might be identified largely as Flicker effect, though some shot noise will be present. A good summary of earlier work is found in Torrey and Whitmer, Crystal rectifier^.^ As a typical example of recent measurements we give some data obtained by Kno1.t Knol measured the ratio I d / I in 1N34 crystals and the ratio T , / T between 1 and 15 megacycles with I as a parameter; T is room temperature, T , the equivalent noise temperature of the differential resistance R = d V / d I , and I d is the equivalent saturated diode current of a crystal carrying a d-c current I ; T , / T = 20RId of course. I n the forward direction Id/I waa practically constant between 1 and 15 megacycles. Values for Ia/I which were much smaller than unity were observed, especially for currents between 1 and 5 ma. I n an ordinary diode one would call this “space charge suppression of shot noise,” *T.R.E. Conference on electron tubes and solid state devices. Ann Arbor, Michigan, June, 1950. t Unpublished. I am indebted to Dr. Knol, N. V. Philips’ Gloeilampen-fabricken, Eindhoven, HoIland, for allowing me to publish these data.

146

ALDERT VAN DER ZIEL

but in this case at least part (if not all) of it is due to a feedback effect caused by the bulk resistance of the germanium.9 I n the backward direction the noise was strongly frequency dependent, and Id/I was always much larger than unity; Id/I varied somewhat slower than f-' at room temperature and somewhat faster than f-' at -70°C. In the forward direction Ia/I decreased with decreasing temperature; in the backward direction Id/I increased with decreasing temperature, especially a t the longer wavelengths. T,/T was found t o be rather high in the backward direction; quite apart from the Flicker effect this would be expected even for pure shot effect, because the differential resistance R is so large in that case. T,/T = 1 for zero current of course; with increasing current, T,/T goes

F

FIG.4. Equivalent network for the noise of a transitor; Z,, Zb, Zc, and Z, are the characteristic impedances of the transitor; V , represents the emitter noise emf, V , the collector noise emf, i, is the emitter noise current.

through a minimum which may be as low as 0.50 and then increases again. A value T,/T = 4 is not surprising in the absence of Flicker effect, for the characteristic in the forward direction is exponential for low voltages and in a diode with an exponential characteristic T J T , was also found to be (Section III.2a). We mentioned Knolls results about the frequency dependence of the Flicker noise. Other measurements seem to indicate a f-' frequency d e ~ e n d e n c ewhereas ,~~ Mooer~ found ~ ~ ~several cases in which the Flicker noise in crystal diodes varied as f-36 at low frequencies and as f-34 a t higher frequencies. This shows that different crystal diodes have widely different noise properties. Noise in transistor^^^ is closely related to noise in crystal diodes, because a transistor can be considered as a crystal diode with two point contacts instead of one. In an N type transistor, the input contact, which is called the emitter ( e ) , is positive with respect to the base ( b ) ; the output contact, which is called the collector ( c ) , is negative with respect to the base. An equivalent circuit of a transistor is represented in

FLUCTUATION PHENOMENA

147

Fig. 4. The noise has to be represented by an input noise emf v6 and an output noise emf v c ; both are partly correlated. This correlation is due to the conduction mechanism in a transistor, the current from the emitter largely consists of holes; a large part of this hole current flows to the collector and modulates the current voltage characteristic of the collector. Both C and 2 vary about inversely proportional to the frequency, and 2 is usually much smaller than 2.. It is common to characterize the noisiness of a transistor by mentioning its noise figure a t 1000 cycles. A noise figure of 50 db a t 1000 cycles is not uncommon. This huge amount of noise is mainly due to 2, it increases if the collector voltage is made more negative and it also depends slightly upon the emitter current I,. The fact that 2 is so large is in agreement with the fact that a crystal diode operated in the back direction a t rather large currents (0.5-1 ma) gives rise to a huge amount of Flicker noise a t 1000 cycles. N-P-N junction transistors have a much lower noise figure.

IV. NOISE IN RECEIVERS

I. Noise Figure6,sVLo Just as the noise ratio n characterizes the noisiness of a noise generator, so the noise figure F of a receiver characterizes the noisiness of a ‘ receiver.33,35s4**s0It is defined as follows. Let the actual antenna of the receiver be replaced by a dummy antenna (noise ratio of 1) kept a t room temperature. The noise output power of the receiver is such as if the receiver itself were noiseless and the dummy antenna had a noise ratio F.* If the actual antenna has a noise ratio n,, then the eflective noise figure Feffof the receiver13 is defined in analogy with the noise figure F ; the only difference is that the words “dummy antenna” have to be replaced by “actual antenna.”t Obviously : (IV.1) F.fr = n, (F - 1).

+

Noise figures are often expressed in db. ; the reason is that in comparing two receivers, the ratio of their noise figures is the determining factor. If several amplifier stages are connected in cascade, having noise figures F1, F z , Fa, etc., respectively, then the noise figure F of the whole amplifier can be determined by a method first given by F r i i ~ . ~ ~

* Another definition is: F is the ratio of the available noise output power of the receiver to t h a t part which is due to the thermal noise of the dummy antenna. t An ideal receiver is one for which F = 1. Usually, one tends to design a receiver such that F is a minimum. If n, > ( F - l ) , then F,rf = n,; in that case, very little can be gained by decreasing F . This is the case for good receivers in the 5- to 30megacycle region, as n, is very large in that region.13

148

ALDERT VAN DER ZIEL

I n order to discuss this method, the circuit elements belonging to the antenna, to the first stage, to the second stage, etc., must first be defined properly. The dummy antenna is considered all by itself. The coupling elements which couple the dummy antenna to the first stage are considered to belong to the first stage; the coupling elements which couple the output electrode of the first stage to the input of the second stage are considered to belong t o the second stage, etc. We can now define the noise figure F of the first stage for that particular coupling between antenna and input, which is actually used. One can also define the available power gain 91, for that particular coupling as: 91

=

Available signal power a t output electrode Available signal power at the antenna

The first stage as seen from its output electrode has an internal resistance

R 1and is coupled t o the input of the second stage. The noise figure F z of the second stage is defined for that particular coupling. The definition of gz for that particular coupling is similar to the definition of gl, as is the output resistance Rz of the second stage. We are now able to calculate the noise figure F of a number of stages. Looking a t the output of the first stage, the noise ratio of that output is: n1 = F l g l .

(IV.2)

This means that in analogy to (IV.l), the noise of the first two stages combined is such as if the output of the first stage had a noise ratio n =

n1

+ ( F z - 1) = F l g l + (Fz- 1).

(IV.3)

In analogy to (IV.2), we have for the noise figure of the two combined stages : F = n/gi = Fi (Fz - l)/gi. (IV.4)

+

In an analogous way, we have for more stages in cascade Friis' formula:

This formula holds as long as the available gain can be defined for each of the stages, that is as long as R1, R2,etc., are positive.* We see that F = F1if g1 is sufficiently large. In other cases, the noise of the second stage is also important.

* Formula (IV.4) shows t h a t it is sense t o use an h-f stage of noise factor F 1 in front of a receiver of noise figure F t if F < F f . Obviously this means F1 < Fz;but there is also a condition for the available gain g1 of the stage as F < Fs means: F1

+ ( F z - l)/gl

< F z or g1 > (Fz - 1 ) / ( F 2 - PI).

If g1 < 1 the stage cannot serve any useful purpose.

FLUCTUATION PHENOMENA

149

This is especially the case with radar receivers having a crystal mixer as their first stage. The “gain” of the mixer stage is actually a power loss ( g l < l), the noise figure of the receiver is determined by the output noise ratio n of the crystal mixer, the power gain g 1 of the mixer stage and the noise figure Fz of the first i-f stage. Combining (IV.4) and (IV.3), we have therefore for the noise figure F of the radar receiver9 (IV.5) 2. Noise Figures of Various Circuits

a. Measurement. The noise ratio n of a noise source can be measured by comparing its noise output to the output from a known noise source.8s As the noise figure F of a receiver is in fact a noise ratio, F can be measured in a similar way. Saturated diodes are often used as a standard noise may be used as well. ~ o u r c ebut , ~ hot ~ ~ ~ ~ ~or gas discharge One way is t o compare the noise output power of a receiver a dummy antenna of noise ratio 1 to the noise output powtx of receiver dummy antenna of known noise ratio nu (e.g., gas discharge tube). If the measured noise powers are Po and PI, respectively, then according to (IV.1):

+

+

+ F - 1)/F

(nu

=

P l / P o or F

=

(nu - l ) P 1 / ( P 1- PO). (IV.6)

For the best accuracy, nu and F should have the same order of magnitude. If a noise diode is used in parallel with the dummy resistance R , the saturated diode current is changed from zero t o such a value Id that the output noise power of the receiver is doubled. Then:*

F

=

(e/2kT)IdR = 2QIdR.

(IV.7)

I n a wide-band receiver, one has t o distinguish between the “overall” noise figure F’,8 which is the value measured in the above way and the noise figure F for a small region of the amplified frequency band. If one wants t o measure F , one has t o use the wide-band amplifier as a preamplifier for a narrow-band receiver; tuning the latter t o the various frequencies gives F as a function of frequency. The available gain g also depends upon frequency; the relation between F’ and F ( f ) is:

F’

k- g ( f M h=F ( f ) g ( f ) d f . =

(IV.8)

If g ( f ) is constant inside a band of width B and zero outside t h a t band, then F’ corresponds to the average value of F ( f ) taken over the band.

* According

to the definition of F :

2eZ&fR2 = F . 4 k T R A f ; F

=

(e/2kT)ZdR.

150

ALDERT VAN DER ZIEL

F‘ generally depends upon bandwidth whereas F does not. Strictly speaking, the discussion of Sec. IV.l holds for F and not for F‘. If the bandwidth of the input circuit of the first amplifier stage is equal t o or larger than the overall bandwidth of the amplifier, F’ and F will differ very little. I t is often useful t o measure F as a function of the transformed anteima resistance R, in order t o find the most suitable In t h a t case, one may connect the dummy transformed antenna resistance R, and the noise diode right across the input circuit of the amplifier. One usually finds, experimentally :

F

=

A

+ B / R , + CR,,

(IV.9)

which has a minimum value:

+- 1/m

F,,, = A 2 for R, = 2/B/C. (IV.10) If a wide band is required, it is often better to choose a value of R, which is a few times smaller than d / B / C ; as the minimum in (IV.9) is rather flat, this does not increase F very much, and i t results in a flatter frequency response. Another way to niden the bandwidth of the input circuit is to use an input band-pass filter; it does not improve the noise figure, hoivever. 5iib I n all measurements, it is advisable to check the linearity of the amplifier with a noise diode and to make sure that the detecting instrument really measures power. -1crystal diode acts as a quadratic detector as long as the detected current does not escrecl a few microamperes. 0. C a l ~ z i l a f i o n . ~I n~ order to calculate the noise figure of an amplifier stage. one considers the output of the stage to be short-circuited* and determines the contributions of antenna noise, tuned circuit noise, induced grid noise, and tube noise to the mean square value ? of the noise current in the short-circuited output lead. Let those contributions be a?,b2, c 2 , and d2, then according to the definition of F : t F

= (a2

+ b2 + c2 + d’)/a2.

(IV.11)

One usually finds a theoretical formula of the type (IV.9). c. Noise in Triode and Peirtode Circuits. 3 . 6 , 1 0 I n low-noise amplifiers, one often uses a neut,ralized triode or a grounded grid circuit as a first stage. A favored combination is a neutralized triode followed by a * T h i s does not alter the signal-to-noise ratio of the stage, as the signal-noise uol/aye ratio at the o\itput terminals is equal to the signal-noise current ratio in the lead short-circuiting the terminals. This short circuit eliminatcs the feedback and thus simplifies the calciilations. iBecause of the correlated part of induced grid noise, it is riot always allowed to add c arid d quadratically (compare Sec. III.3f).

151

FLUCTUATION PHENOMENA

grounded grid.g1a I n the first circuit, the anode impedance is kept lo^ and the anode grid capacity is tuned, both in order to reduce feedback. I n the grounded grid circuit, the cathode is used as the input electrode; i t has a low input impedance ( l / g m ) and a low anode-cathode capacity (especially if some screening is applied) so that i t is perfectly stable too. It is best suited for u-h-f disk-seal triodes. Though the grounded grid triode has a lorn input impedance, both circuits have identical noise figures under identical conditions. *9 This is due t o a feedback effect;s7 the tube noise flows through the input circuit as well as through the output circuit.* If the constants A , B, and C of (IV.9) are calculated for a grounded grid circuit, one finds :

A

=

1

4-2Rn/R1; B

as usually (R,/R1)2

=

(e/ZkT)Id 4-Rn/RI2

=

<< 201dR,&,we may write:

201d

+ Rn/RI2; C

=

R,;

(IV.12)

I n these equations, Rn is the noise resistance of the tube; the input circuit noise and the uncorrelated component of induced grid noise are represented by the “equivalent saturated diode current” I d , ? and R1 represents the input impedance of the tube tuned circuit.$ If I d is mainly determined by induced grid noise (and not by circuit noise) it should vary as w 2 in a wide frequency range and (F,,, - 1) should be roughly proportional t o w . The above theory holds for the neutralized triode too, except for the effect of the uncorrelated part of induced grid noise (see footnote). It also holds for a pentode except for some feedback effects;87F is somewhat larger here as R, is larger than for a triode. Diemer and Kno131 measured a noise figure of 7 db a t 10 cm for an especially prepared disk-seal triode in which they tried t o keep the transit time of the electrons small (small cathode-grid distance) and as * If both circuits have identical transformed antenna resistances and identical

+

tuned input circuit impedances and if both input circuits are tuned to minimum noise figure, the two will give identical noise figures. The neutralized triode is usually tuned to a maximum input signal, and therefore its noise figure is slightly larger than for the grounded grid circuit. The difference is not very important in many cases; it would be zero if the induced grid noise had no correlated component. t The indured grid noise and the circuit noise can be represented by a noise current of infinite impedance connected across the input. We now define I d by generator <2 the relation: ? = 2eIdA.f. $ As the noise figure is not affected by feedback,80,81one should take for R , that value which would exist if there were no feedback effects through the interelectrode capacities.

152

ALDERT VAN DER ZIEL

uniform as possible (smaller uncorrelated part of induced grid noise) and in which the oxide emission layer was largely eliminated (this layer gives a n important contribution t o R1 and I d a t microwave frequencies). This is better than normal crystal diode mixerss ( F = 12-15 db) or traveling wave tubes7 ( F = 10-15 db). d. Diode mixer^.^^^ Though thermionic diode mixers are sometimes used in the region below 600 megacycles, microwave mixer stages generally make use of crystal diode mixers, as the latter give a better noise figure a t microwave frequencies. According t o (IV.5) the determining factors for the noise figure of a receiver starting with a diode mixer in the first stage, are N1, Fz, and g l . For thermionic diode mixers, g1 seems t o decrease rather rapidly with increasing frequency, due t o total emission conductivity and transit time effects, whereas n1 increases because the noise compensation of Sec. III.7b becomes less effective. Crystal diodes do not show these effects. Representative figures for crystal diodes a t 30-megacycle intermediate frequency are: nl = 2; F z = 1.5; g = Q; F = 15 ( = 12 db). F as a function of the local oscillator (1-0) voltage shows a minimum at a certain voltage, because g 1 and nl both increase with voltage, but at a different rate. F as a function of the intermediate frequency f o shows a rather flat minimum, usually between 20 and 100 megacycles, because n1 decreases with f o and ( F , - 1) is roughly proportional t o j o , whereas g 1 is independent of fo. As the microwave circuits often show a considerable image frequency response which in turn influences the gain g 1 and the noise figure F , i t is advisable t o choose the image frequency response such t h a t g 1 is a maxim~m.8*4~ As a n oscillator circuit shows response t o signals of a frequency f slightly different from the oscillator frequency font, a n oscillator will generate noise sidebands.3*8 The oscillator noise power decreases with increasing If - .l;of I n the mixing process, the local oscillator signal will beat with the local oscillator noise, thus resulting in a considerable i-f noise output and a n important increase in F . Besides using a high intermediate frequency and a low-noise oscillator, this effect may also be decreased considerably by using balanced mixers. If either h-f is pushpull, 1-0 single, and i-f push-pull or if h-f is single, 1-0 push-pull, and i-f push-pull, then the local oscillator noise will not give a response in the i-f circuit if the mixer stage is perfectly balanced. ACKNOWLEDGEMENT The writer is indebted to Dr. C. C. Cutler, Dr. K. S. Knol, Dr. D. 0. North, and Dr. R. M. Ryder for permitting use of figures or unpublished material in this review

FLUCTUATION P H E N O M E N A

153

and to the Engineering Experiment Station of the University of Minnesota for preparation of some of the drawings. REFERENCES BOOKS 1. von Engel, A., and Steenbeck, M. Elektrische Gasentladungen, Vol. I. Springer, Berlin, 1932. 2. Goldman, S. Frequency Analysis, Modulation and Noise. McGraw-Hill, New York, 1948. 3. Hamilton, D. R., Knipp, J. K., and Kuper, J. B. H. Klystrons and Microwave Triodes. McGraw-Hill, New York, 1948. 4. Lawson, J. L., and Uhlenbeck, G. E. Threshold Signals. McGraw-Hill, New York, 1950. 5. Moullin, E. B. Spontaneous Fluctuations of Voltage. Clarendon Press, Oxford, 1938. 6. Moxon, L. A. Recent Advances in Radio Receivers. University Press, Cambridge, 1949. 7. Pierce, J. R. Travelling Wave Amplifiers. Van Nostrand, New York, 1950. 8. Pound, R. V. Microwave Mixers. McGraw-Hill, New York, 1948. 8a. Rothe, H., and Kleen, W. Elektronen-rohren als Anfangstufenverstarker. Becker and Erler, Leipzig, 1944. 9. Torrey, H. C., and Whitmer, C. H. Crystal Rectifiers. McGraw-Hill, New York, 1948. 10. Valley, G. E., and Wallman, H. Vacuum Tube Amplifiers. McGraw-Hill, New York, 1948. REVIEWPAPERS 11. 12. 13. 14. 15. 16. 17.

Barnes, R. B., and Silverman, S. Rev. Modern Phys., 6, 162 (1934). Chandrasekhar, S. Rev. Modern Phys., 16, 1 (1943). Herbstreit, J. W. Advances i n Electronics, I, 347 (1948). MaeDonald, D. K. C. Repts. Progress Phys., 12, 56 (1949). Rice, S. 0. Bell System Tech. J., 23, 282 (1944); 24, 46 (1945). Wang, M. C., and Uhlenbeck, G. E. Rev. Modern Phys., 17, 323 (1945). Zernike, F. Handbuch der Physik, Vol. 111. 4 1 9 4 9 2 , Springer, Berlin, 1928.

PAPERS 18. Bakker, C. J. Physicu, 6, 581 (1938). 19. Bakker, C. J., and Heller, G. Physicu, 6, 262 (1939). 20. Bakker, C. J. Physicu, 8, 23 (1941). 21. Ballantine, S. ,I. Franklin Inst., 206, 159 (1928). 22. Bell, R. L. Wireless Engr., 26, 294 (1948). 22a. Bell, R. L. Wireless Engr., 27, 86 (1950). 23. Begovich, N. A. J . Applied Phys., 20, 457 (1949). 24. Bernamont, J. Ann. phys., 7, 71 (1937). 25. Bogle, H. Technical Monograph, No 137, Appl. Phys. Lab., John Hopkins Univ., 1948. 26. Brillouin, I,. Helv. Phys. Acla, 7, 47, Supplement 1934. 27. Burgess, R. Proc. Phys. SOC.(London),63, 293 (1941). 28. Christensen, C. J., and Pearson, G. L. Bell System Tech. J . , 15, 197 (1936). 28a. Cutler, C. C., and Quate, C. F. Phys. Rev., 80, 875 (1950).

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ALDERT VAN DER ZIEL

Davydov, B., and Gurevich, B. J . Phys. U.S.S.R., 7, 138 (1943). Diemer, G., and Knol, K. S. Phzlzps Research Rept., 6, 131 (1950). Diemer, G., and Knol, K. S. Philips Research Rept., 6, 153 (1950). Duvall, G., E. Tech. Rept. No. 82, Research Lab. of Electronics, M.I.T., 1948. Frans, K. Elek. Nachr. Tech., 16, 92 (1939); Z. Hochfr. Elektroak., 69, 105 (1942). 34. Freeman, J. J. J . Research Natl. Bur. Standards, 42, 757 (1949). 35. Friis, H. T. Proc. Znst. Radio Engrs., 32, 419 (1944). 36. Fiirth, R., and hfacDonald, D. K. C. Nature, 167, 841 (1946). 37. Garrison, J. B., and Lawson, A. W. Rev. Sci. Instruments, 20, 785 (1949). 38. Gisolf, J. H. Physica, 16, 825 (1949). 39. Haantjes, J., and Tellegen, B. D. H. Phalzps Research Rept., 2, 401 (1947). 40. Hayner, L. J., and Kurrelmeyer, B. Phys. Rev., 62, 952 (1937). 41. Herold, E. W. RCA Rev., 4, 324 (1940). 42. Herold, E. W., and Malter, L. Proc. Znst. Radio Engrs., 31, 423-438; 491-510; 567-582 (1943). 42a. Herold, E. W. Proc. Znst. Radio Engrs., 30,84 (1942). 43. Herold, E. W. Proc. Znst. Radio Engrs., 34, 184 (1946); Electronics, 22,76 (May 1949). 44. Herold, E. W., Bush, R. R., and Ferris, W. R. Proc. Znst. Radio Engrs., 33, 603 (1945). 44a. Hersog, G. B., and van der Ziel, A. Phys. Rev., 84, 1249 (1951). 45. Johnson, J. B. Phys. Rev., 26, 71 (1925). 46. Johnson, J. B. Phys. Rev., 32, 97 (1928). 47. Johnson, H. RCA Rev., 8, 169 (1947). 48. Kleen, W. Telejunkenrohre, 23, 274 (1941). 49. Kleen, W. Frequenz, 3, 209 (1949). 50. Kompfner, R., Hatton, J., Schneider, E. E., and Dresel, L. A. C. J . Znst. Elec. Engrs. (London), 93, Pt. IIIA, 1436 (1946). 50a. Kronenberger, K. 2. angew. Phys., 3, 1 (1951). 50b. Lebenbaum, M. L. Proc. Inst. Radio Engrs., 38, 75 (1950). 51. Llewellyn, F. B. Bell System Tech. J . , 14, 632 (1935). 52. Macfarlane, G. G. Proc. Phys. SOC.(London), 69, 366 (1947). 52a. Macfarlane, G. G. Proc. Phys. SOC.(London), 63, 807 (1950). 53. Meyer, E., and Thiede, H. Elek. Nachr. Tech., 12, 237 (1935). 54. Milatz, J. M. W. Nederland. Tzjdschr. Nutzu.uk., 8, 19 (1941). 54a. Melman, I. J. Tele-Tech., 9,36 (July 1950). 55. Miller, P. H., Jr. Proc. Znst. Radio Engrs., 36, 252 (1947). 55a. Miller, W. Tech. Rept. No. 11, U. of Pennsylvania, Bu Ships Contract Nobs 34144, 1948. 56. Montgomery, H. C., and Shockley, W. Phys. Rev., 78, 646 (1950). 56a. Mooers, H. T. NEC Proc., Vol. 5, 1949. 57. Mumford, W. W. Bell System Tech, J., 28, 608 (1949). 58. North, D. 0. RCA Rev., 4, 441 (1940); 6, 106 (1941). 59. North, D. 0. RCA Rev., 6,244 (1940). 60. North, D. O., and Ferris, W. R. Proc. Inst. Radio Engrs., 29, 49 (1941). 61. Nyquist, H. Phys. Rev., 32, 110 (1928). 62. Parsen, P., and Goldstein, L. Phys. Rev., 79, 190 (1950). 63. Percival, W. S. Wireless Engr., 16, 237 (1939). 64. Peterson, L. S., and Llewellyn, F. B. Proc. Znst. Radio Engrs., 32,144 (1944); 33, 458 (1945).

29. 30. 31. 32. 33.

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155

Peterson, L. S. Proc. Inst. Radio Engrs., 36, 1264 (1947). Peterson, L. S. Bell System Tech. J . , 27, 593 (1948). Rack, A. J. Bell System Tech. J., 17, 502 (1938). Richardson, R. J. Bell System Tech. J., 29, 119 (1950). Ryder, R. M., and Kircher, R. J. Bell System Tech. J . , 28, 367 (1049). Schottky, W. Ann. Physik, 67, 541 (1918). Schottky, W. Phys. Rev., 28, 74 (1926). Schottky, W. Physica, 4, 175 (1037). Schottky, W. Wiss. Verogent. Siemens-Werken, 16, 1 (1937). Schottky, W. Ann. Physik, 32, 195 (1038). Shockley, W.and Pierce, J. R. Proc. Znst. Radio Engrs., 26, 321 (1938). Smyth, C. N. Nature, 167, 841 (1’346). Spenke, E. Wiss. Veroflent Siemens-Werken, 16, 19 (1937). Spenke, E. Wiss.Verogent Siemens-Werken, 18, 55 (1939). Sproull, R. L. Phys. Reu., 67, 166 (1945). Strutt, b l . J. O., and van der Ziel, A. Physica, 8, 1 (1941); 9, 1003 (1942); 10, 823 (1943). 81. Strutt, M. J. O., and van der Ziel, A. Physica, 9, 513 (1942). 82. Thompson, B. J., and North, D. 0. RCA Rev., 6, 371 (1941). 83. Ullrich, E. H., and Rogers, D. C. J . Inst. Elect. Engrs., 93,Pt. IIIA, 1347 (1946). 84. van der Ziel, A. Physica, 9, 177 (1942). 85. van der Ziel, A. Philips Research Rept., 2, 321 (1947). 86. van der Ziel, A., and Versnel, A. Nature, 169, 640 (1947); Philips Research Rept., 3, 13 (1948). 87. van der Ziel, A., and Versnel, A. Philips Research Rept. 3, 121; 255 (1948). 88. van der Ziel, A. J . Applied Phys., 21, 300 (1050). 89. van der Ziel, A. Proc. Znst. Radio Engrs., 38, 562 (1950). 90. van der Ziel, A. Physica, 16, 359 (1050). 90a. van der Ziel, A. WireZcss Engr., 28, 226 (1051). 90b. van der Ziel, A. Canad. J. Techn., 29, 540 (1051). 9Oc. van Wijngaarden, J. G. Ph. D. Thesis, Amsterdam, 1051. 91. van Zolingen, J. J. Ph. D. Thesis, Vtrecht, 1048. 91a. Wallman, H., MacNee, A. B., and Gadsden, C. P. Pror. Znst. Radio Engrs., 36, 700 (1948). 92. Williams, F. C. J . Znst. Elec. Engrs., 83, TG (1938). 93. Ziegler, M. Physica, 3, 1; 307 (1936). 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

N o t e added in proof:

Measurements on BTL 1553 (WE 41612) grounded grid triodes a t 4000 megacycles indicate a very low input resistance (10 ohms) and a rather high noise figure (15 db).* Both effects are probably due to total emission damping.

* Bowen,

A. E. and hlumford, W. W. Bell System Tech. J., 29, 531 (1950). Rohertson, S. D. Bell System Tech. J., 28, 619 (1949).

This Page Intentionally Left Blank

Electronic Digital Computers CHARLES Ti.

L. SMITH

Ofice of Naval Research, Washington, D.C. CONTENTS

I. Introduction. . . . . . . . . . . . . . . . . ... ........................ 11. Input-Output. . . . . . . . . . . . . . . . ................................ 111. Internal Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Arithmetic and Control Organs ................................

Page 157 160 161 171

V. Whirlwind.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. SEAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .....................................................

174 180 185

I.

INTRODUCTION

The development of high-speed automatically sequenced electronic digital computers has been one of the more spectacular achievements of recent years. Unfortunately, promise has frequently far outstripped performance, and actual progress has a t times seemed heart-breakingly slow. However, during 1950, several machines of rather advanced design were completed, tested t o the point where satisfactory operation appeared assured, and put into operation. It is therefore appropriate that this volume should contain some account of the present state of the art. It is obviously inappropriate t o trace the history of digital computer development in a n article devoted t o electronic machines, as several of the earlier successful machines, such as the Bell Telephone Laboratories relay calculators and the Mark I and Mark I1 developed by Professor &ken of the Harvard Computation Laboratory, used electromechanical elements throughout. Furthermore, it is not considered profitable here t o give equal consideration t o all the existing machines, either built or in construction.* It is felt t h a t a more useful treatment will consist of a general discussion of syst.ems, in which we consider briefly what functions must be performed, followed by consideration of the electronic devices and the circuitry used for the performance of these functions. This will be followed by a rather more detailed treatment of two computers,

* See Chapter 10 of High Speed Computing Devices, by the Staff of the Engineering Research Associates, Inc., McGraw-Hill, 1950, for a review of machines and projects in this country. Very complete bibliographies are given a t the ends of the chapters. For this reason, we have not deemed it necessary to include bibliographical information here. 157

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CHARLES V. L. SMITH

Whirlwind and SEAC, which were put in operation during 1950. Thus we shall generally restrict ourselves t o the current state of the art as exemplified in these two systems whose operability can be regarded as established. However, we shall feel free t o depart a t times from this principle: thus a n account of the Selectron storage tube, and of the use of the conventional cathode ray tube used as a storage device are included, though neither had been, a t the time of writing, incorporated in this country in a fully operable computer. We shall first consider the functions which an automatic digital computer must perform. Consider the analogy of a human operator provided with an ordinary desk type calculator, which can perform the operations of arithmetic. He is furnished with a sheet of instructions showing him what operations t o perform in what sequence, and he is given the numerical data of the problem. He himself reads and interprets instructions, inserts the data into the calculator, and causes i t t o perform the appropriate operation. The result of this operation must then be set aside or stored either for future use in the computation, or as part of the desired answer t o the problem. The latter numbers are finally written down and turned over t o the person who initiated the problem as the answer. Thus the following functions are distinguishable: (1) “input” t o the system, ( 2 ) a n “arithmetic organ,” (3) a “control organ,” (4) a “storage organ” (or “memory”), (5) a n “output” from the system. Another point that should be noted is that the input t o the system contains two kinds of information: (I) instructions, or orders, (2) numerical data t o be processed. I n the current technical jargon, any group of symbols introduced into the system is called a “word,” whether i t is a n “order” or a “number.” A system performing the five functions which were distinguished above can be realized physically in a great number of ways. Thus the earlier machines possessed only limited storage capacity, and each instruction was read into the machine from the input just before it was t o be executed. I n later designs the orders and the numerical data are both read into the storage, as far as its capacity permits, before operation is to begin, and the order words are delivered from this memory t o the control in sequence. We may also point out t h a t the storage may be multifold in character; that is, i t may employ several methods of storing information, one of low capacity but from which information may be extracted very rapidly, a second of greater capacity and lower speed, and so on. We may a t this point draw a very general block diagram (Fig. 1) of a n automatic digital computer. It should be pointed out t h a t the input and

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output functions may both be performed by the same device, which may also be designed to act as an auxiliary means of storage. Before passing to a review of the devices used to perform the functions enumerated above, it is best to make several rather miscellaneous remarks. First, as devices which possess but two stable states are particularly simple, as for example, the familiar Eccles-Jordan trigger circuit, it is very natural and convenient to use the binary number system in a computer, at least internally, with provision made for converting the notation used in the input into binary form within the machine. It is of course also possible to use other schemes of notation suitably encoded.

FIG.1. Block diagram of computer functions.

Thus in the binary-coded decimal system, each decimal digit is converted into its binary form and so is represented by four binary digits or “bits,” to use Shannon’s terminology. We favor the use of the binary system, as it seems to lead to the most natural physical realization, but hesitate to dogmatize, as other methods of encoding the information have their champions. Secondly, data transmission may be either serial or parallel, that is, pulses representing the bits of a word may all be transmitted sequentially over a single wire, or a separate wire may be assigned to each bit, all bits being then transmitted simultaneously. Of course, combinations of these two schemes can be used; for example, if we use a binary coded decimal representation, we may assign four wires to the four bits used to encode each decimal digit, so that those representing each decimal digit are transmitted in parallel, while the decimal digits are transmitted serially. Similarly the arithmetic unit may be either serial or parallel-we will have more to say about this later. Hence we can designate a machine as serial-serial, serial-parallel, parallel-serial, or parallel-parallel-all four types are possible, though which type the designer chooses will depend upon various considerations, such as type of storage to be used and desired speed of computation.

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Thirdly, considerable divergence in the mode of representing numbers is possible. Thus we may agree that in every case the decimal point lies in some fixed position, as for example, directly in ftont of the first digit, so that all numbers are treated as proper fractions: this is attractive because it makes the engineering design simpler, but throws upon the user of the machine the task of keeping track of the scale factors or shifts that must be introduced in order to prevent the numbers from growing beyond the word length available. Or we may permit the decimal point to shift about in a natural way during the computation; for example, each number may be represented as a proper fraction in binary positional notation times a power of two. These two schemes result in “fixed decimal point ” and “floating decimal point” machines respectively. We shall now turn t o consideration of the way in which the required machine functions can be physically realized.

11. INPUT-OUTPUT Although much experimental work has been done on the use of magnetizable wire and tape as a means of input, output, and auxiliary storage, at the time of writing it must be admitted that no device of this kind has yet been incorporated in a machine of proved operability. The probability is high, however, that if this were being written a year hence, quite a different situation would be revealed. At the moment, input and output by means of Teletype tape is popular, and this is entirely reasonable as it was mostly a question of adapting existing equipment rather than of undertaking extensive development. In considering the advantages and disadvantages of various input and output media, it is necessary to keep in mind the use to which the computer is to be put. The emphasis so far has been on machines for performing scientific computations. I n this case the high-speed input and output are desirable but not indispensable, though magnetizable media clearly would be useful because of their adaptability as auxiliary storage devices. This is because the amount of numerical data of the problem may be quite limited, while the quantity of intermediate results, which must be temporarily held in the memory as the computation progresses, but which are of no interest in the final result, may be quite large. High-speed input and output media become of great importance, however, in the case of a machine designed to process very large quantities of data, the actual processing in each case being rather simple; an illustration would be a machine whose purpose was to mechanize a filing system in a large commercial establishment. As such machines are certainly feasible provided input-output-storage media of satisfactory speed and

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capacity are available, and as the potential market is enormous, we may confidently expect that really satisfactory devices of this kind will not be long in development. As we have said, much work has already been done on input and output by means of “magnetic” (that is, magnetizable) media of various forms: wire, metallic tape, or paper tape coated with a thin layer of a suitable substance, such as magnetite. A suitable recording “head” consists of an iron ring shaped core having a small gap in its circumference and carrying a winding. The head is so mounted that the medium is either in contact with the core a t the gap or very nearly so, the direction of motion of the medium being in the plane of the core. If information is t o be recorded, the medium is set in motion and the winding of the head is energized in a suitable way. For example, if the information t o be recorded consists of numbers expressed in binary notation, we may apply a pulse of current in one direction for each one, and a pulse in the opposite direction for each zero, the medium being originally in a demagnetized state. At each pulse, a considerable portion of the flux does not cross the high-reluctance gap in the core of the head, but rather takes the low-reluctance path through the magnetizable medium, leaving a permanently magnetized spot, of one polarity for a one, but of the opposite for a zero. To read this information, the medium is similarly caused t o move past the gap of a head; as each spot passes the gap, the flux in the core of the head varies, causing a n induced emf in the winding of the head-this emf is of course of one form for a one, but of another for a zero, and so the recorded information may be recovered. Needless t o say, a variety of methods of recording are possible, of which one has been mentioned; another simple possibility is t o store ones as magnetized, but zeros as unmagnetized spots.

111. INTERNAL STORAGE Storage devices may be classified in a variety of ways. Without entering into a n overly elaborate discussion, we can consider some basic distinctions. First, the storage can be permanent, as in the case of magnetized spots on a magnetizable medium, or it can be of such a character t h a t it must be continuously regenerated, in which case the term “volatile” has been suggested. Secondly, a definite item of stored information may be available only periodically, or i t may be availableat all times: the terms “cyclic” and “noncyclic” have been suggested for these two cases. Thirdly, the storage may be of such a nature that each item is freely alterable, or i t may not: we can use the terms “erasable” and “nonerasable” t o cover this distinction.* Fourth, the stored items * ERA, pp. 304-305 for a rather full discussion of these classifications.

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may remain fixed with respect to the storage device, or they may constantly be in motion relative to it. We describe these conditions as “static ” and ‘(dynamic.”” In the history of the development of automatic digital computers, a great variety of internal storage devices have been used. The earlier machines used mechanical or electromechanical devices, for example, loops of punched paper tape or banks of relays. These devices will not concern us further. Two parameters often considered in assessing the merit of a storage system are the “capacity,” which can be specified as the number of bits stored or, if one prefers, by the number of words of specified length, and the “access time,” which is the time needed to withdraw a desired word from storage. Storage devices of fairly large capacity will be considered below; however, it is not inappropriate here to call attention to the use of the flip-flop register for storing a single number with very small access time. This is naturally a costly device, but one that is practically unavoidable in certain parts of a computer, for example, in a parallel arithmetic unit. We will have more to say about this later on. The types of storage that will be discussed are as follows: (a)magnetic drum, (6) acoustic delay line, and ( c ) electrostatic storage tube, arranged in the order of decreasing access time. The first of these is a completely satisfactory device if one is content with an access time of several milliseconds and desires very large capacity. However, access time can be materially reduced by skilful coding. The second has been discussed at great length in recent years, but only within the past year (1950) was a machine using it placed in productive operation in this country. A similar remark applies to the third. The magnetic drum does not differ in principle from magnetic tape; in fact, it is quite possible merely to wrap a tape about a drum, though it is naturally more satisfactory to apply a magnetizable coating directly to the metal surface. Ring type tape heads may be used for recording and reading the data, which is naturally disposed in a number of parallel circumferential tracks, which may be placed fairly close together-about ten t o the inch is conservative. Clearly, to obtain a small access time, it is necessary to rotate the drum at high speed, which implies that the heads must not be in contact with the surface; a spacing of about two-thousandths of an inch is not too hard to obtain and is not too great to give reasonable strength of magnetization and output signals. Access time can be reduced by various expedients. Thus the drum may be caused to rotate at higher speed, the information may be recorded

* ERA, pp. 304-305 for a rather full discussion of these classifications.

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more than once (which of course decreases the capacity), or several reading heads may be assigned to each circumferential track. Capacity is a function of the packing density, or number of magnetized spots per inch, the number of parallel tracks per inch length of drum, and the physical dimensions. It has been said that ten tracks per inch of drum length is easily obt,ained, while one hundred bits per inch of circumference is fairly conservative. Thus a drum 20 in. long and 25 in. in circumference can easily store a half million bits. Many successful magnetic drum storage systems have been built, for example, by Professor Aiken of Harvard and by Professor P. L. Morton of the University of California. They are commercially available from the Engineering Research Associates. The acoustic or sonic delay line has been much studied and has been chosen as the storage device for several computers: the EDVAC, UNIVAC, EDSAC (in England), SEAC, and the machine being built by the Raytheon Manufacturing Company. Of these, EDSAC was put in operation in 1949 and SEAC in 1950, so me can consider this type of storage as of proved worth. In principle, acoustic delay line storage is quite simple. A tube of liquid or a rod of solid material is provided a t both ends with transducers effecting the conversion of electrical energy t o acoustic energy and the reverse. Quartz crystals are commonly used t o perform this function. If now the transducer a t one end is excited by a voltage pulse, it is set into mechanical vibration, and this vibration is transmitted by the solid or liquid material; arriving a t the far end, the vibration mechanically excites the transducer, causing a pulse of radio-frequency voltage to appear across its terminals. The input pulse may be one polarity, or it may be a pulse of radio frequency voltage of frequency near that of the crystal a t resonance; the output is necessarily a pulse of r-f voltage, whose shape naturally shows considerable deterioration from that of the input. The output must now be amplified, reshaped, and reapplied to the input. One method is t o pass it through a detector t o recover the distorted pulse envelope and t o use this voltage t o gate a standard pulse into the input. Thus a train of pulses may be caused t o circulate continually through the loop consisting of the delay line and the external circuitry. Each pulse is available periodically a t some definite point in the loop-just how often of course depends upon the length of the line and the velocity of propagation of acoustic energy in the medium. Thus trains of pulses may be kept in circulation as long as desired: when it is desired t o recover one, it is clearly necessary t o wait on the average a time equal t o one-half the transmission time of the line. It has been stated that either solids or liquids may be used as the

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acoustic transmission medium. Fused quartz and magnesium alloys have been Ihr subject of experiment, but mercury is the most popular material. The mismatch in acoustic impedance between it and quartz is not as bad as in the case of most other liquids. The geiicral form of a mercury delay line has been described. We now must consider the factors that determine how much information can be stored. The velocity of an acoustic wave in mercury a t 17°C is 1.46 meters pcr millisecond. This is subject t o a variation of one part in three thousand per degree centigrade. It has been found possible to space pulses as densely as four per microsecond; this density however requires very close control on the temperature or the line. Information can also be stored in the form of electrostatic charge. A number of mcthods have been advocated, some tested and a few found worthy of development. We will concern ourselves here only with electrostatic storage tubes for computer applications. As it is convenient to represent all information within a computer in binary coded form, the storage device needs t o possess just tn-o stable storage states. It must be possible readily t o insert information in and extract it from the device, and t o hold it there indefinitely without deterioration. Of course large capacity is also desired. The devices t o be considered below are the following: the Whirlwind storage tube, the Selectron, and the ordinary cathode ray tube used as a storage device. We shall discuss them in t h a t order. All depend upon the fact that it is possible t o obtain secondary electron emission ratios greater than unity.* Figure 2 illustrates the essential features of the Whirlwind tube. At one end appear two electron guns: the read-write gun provides a sharply focused beam of high-velocity electrons, which may be deflected by the usual methods; the holding gun provides a diffuse beam of lorn-velocity electrons. Lit the other end of the tube appears the metal signal plate, the front of this is covcrcd with a sheet of mica 0.005 in. thick, upon the surface of which is a mosaic of small beryllium squares. A grounded collector screen (100 meshes per inch) is mounted 0.015 in. in front of the storage surface T o write on the storage surface, it is first necessary t o apply deflection voltages t o direct the beam t o the desired location, after which a positive or a negative spot can he written. The process of writing positive is merely t o turn on the nrite-read beam. If the spot bombarded by the electron beam is below collector potential, the emitted electrons, 11hich * We treat the I f hirlwind tuhe here rather than under the Whirlwind computer for unity in presentation.

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are more numerous than the bombarding ones, move t o the collector, and the potential of the bombarded spot increases until the potential difference between it and the collector is zero. This is a point of equilibrium, for no secondaries are attracted t o the collector. If the area has previously been a t collector potential, no change takes place. To write negative, we observe that if the spot t o be bombarded has been above collector potential before the beam is turned on, all the secondaries return t o the storage surface which becomes more negative until the spot reaches collector potential. Thus the bombarded spot always reaches collector potential. This provides the clue t o the process 0-3553s

r-$68

PULSE GRID TO WRITE OR READ

b r W R I T I N G - READING BEAM DEFLECTED TO SELECTED SPOT

/

SIGNAL PLATE MOSAIC

WRll

COLLECTOR DIELECTRIC -100 VOLTS

SIGNAL OUT

+ I J--$

FIG.2.

SIGNAL PLATE GATE DURING WRITE MINUS

Simplified diagram of Whirlwind storage tube.

of writing negative. Just before beam turn on, the signal plate potential is raised t o +lo0 v ; when bombardment ceases, the potential of the bombarded spot has fallen t o that of the collector, or zero volts. Immediately thereafter the signal plate potential is dropped t o zero volts, which brings the potential of the bombarded spot t o -100 v, while the potentials of all other spots return t o their values previous t o the raising of the signal plate potential. Note t h a t the value of 100 v is not arbitrary: it is determined by the holding gun potential, as we shall immediately see. Information once written on the storage surface is not permanent. Deterioration will take place due t o leakage, t o the effects of reading, and t o secondary electrons resulting from bombardment of other spots, so t h a t it is necessary t o provide a means of continuous regeneration, which will be referred t o as “holding.” As remarked before, this is the function of the electron gun which provides a diffuse spray of low-velocity electrons, uniformly spread over the storage plate.

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I n the case of a negatively charged spot, we consider two situations as possible: (I) the spot potential is slightly above the holding gun potential (-100 v), (2) i t is slightly below t h a t value. I n the first case, the electrons from the holding gun strike the spot with such low velocity that a secondary emission ratio of less than unity results, so t h a t the spot accumulates negative charge, and its potential approaches t h a t of the holding gun. I n the second, the electrons from the holding gun never reach the spot, and the effect of leakage is t o raise the spot potential toward t h a t of the holding gun, a level which has therefore been shown t o be stable. Now consider a positively charged spot in the two cases: (1) potential above zero volts (the collector potential), ( 2 ) below zero volts. I n both cases the electrons of the holding beam arrive with sufficient velocity t o give a secondary emission ratio of about two t o one. I n the first case, the secondaries are attracted back t o the storage surface and so negative charge accumulates which brings the spot potential back down toward that of the collector. I n the second case, secondaries are attracted t o the collector, and the spot charge becomes more positive, raising this spot potential toward t h a t of the collector. Thus collector potential is also a stable spot potential. Now consider the reading process. This can be done by discharging the spot by means of the high-velocity (read-write) electron beam. The change in charge is of course capacitatively coupled t o the signal plate, so t h a t a n output signal is available. If just before the reading beam is turned on, the signal plate potential is dropped t o a point between zero and - 100 v, the reading process consists of charging or discharging the spot t o this level, and zeros and ones thus give output signals of opposite polarities. I n the Whirlwind installation, the electron beam is intensity modulated a t 10 megacycles per second during the reading process, as the radio-frequency output signal can be easily separated from the large pulse voltage used t o drop the signal plate potential during the reading process. The first bank of sixteen tubes installed in the Whirlwind computer are a t present being operated conservatively t o store 256 bits per tube, though greater density probably can be achieved with the existing tubes. Development is going ahead both on changes in tube and in its mode of operation, and it is expected t h a t considerably greater capacity will be realized. The present access time is about 20 microseconds, though it appears reasonable t o believe t h a t this will be eventually substantially reduced. A means of electrostatic storage using conventional cathode ray tubes, first proposed by F. C. Williams in England, has aroused such

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interest in this country, and similar methods are being employed in a number of computer projects here, the pioneer work in applying Williams’ ideas having been done by J. H. Bigelow a t the Institute for Advanced Study. Although in no case (at the time of writing) has a computer incorporating this type of storage been put into productive operation, it is considered advisable to give some account of the principles here. It is reasonable to believe that perhaps several computers utilizing various forms of the “Williams storage’’ will be completed within the next year. This scheme also depends on secondary emission properties, in this case of the phosphor. An additional electrode is placed just outside the face of the tube. Clearly if the deflection voltages appropriate to a definite location on the screen of the tube are applied, and the beam is then turned on, the spot at which it strikes the screen will charge positively t o an equilibrium value due t o secondary emission. A different charge distribution can be obtained in a number of ways, a simple one being first t o turn the beam on, then off, then t o displace it very slightly and finally t o turn it on again. We may refer to these adjacent spots as the “ A ” and “ B ” locations. Thus two distinct charge distributions can be created, one of which can be used to represent a binary zero, the other a binary one. T o read, we need only direct the beam t o the A location and then turn it on, for it can be shown that the wave forms of the displacement current t o the external signal plate, and hence voltages developed in a resistor connected from plate t o ground are different, the initial swings being in different directions in the two cases. The stored information deteriorates fairly rapidly on account of surface leakage, so that it is necessary t o provide a means of restoring it periodically. This should be done every tenth of a second or less. As only one electron beam is available, it must be used for reading, writing, and restoring; the usual scheme is t o rewrite each bit when it is read, and t o interpose “regeneration” and “action” (read or write) cycles in an orderly fashion, being sure that the information in every storage location in the tube is regenerated in some sufficiently small interval of time. The Williams, type of storage has the great advantage of requiring no tube development (at least initially). It is necessary t o exercise care in selecting satisfactory tubes, as dead spots,” where no storage is possible, must be avoided, and techniques for doing this have been developed. It seems likely that some modifications would make cathode ray tubes more suitable for this use; for example, better gun design would permit greater storage density, while greater care in the application of the phosphorescent coating would no doubt improve performance and result in fewer tubes found t o be unsatisfactory. Storage density of 1024 bits per tube seems reasonable, and has been

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obtained at the Institute for Advanced Study, though it is necessary to emphasize that this has not yet been achieved in a computer that has been placed in productive operation in this country. Dr. Williams

FIG.3. The Selectron

achieved this density in England, but he was using only a few tubes in an experimental computer. Moreover, he was operating his tubes in a serial mode, while only by using parallel storage can really low access time be obtained. Adaptations of the Williams storage in this country are universally of parallel character. The serial mode sets less exacting requirements for the circuitry, as only one set of deflection potentials

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must be established with precision, while in the parallel mode, this must be true of both sets. In operation in the parallel mode, an access time of 10 microseconds is feasible. The Selectron, developed by Dr. J. Rajchman of the RCA Laboratories, depends also upon secondary emission, but uses an ingenious method of directing the electron current t o the desired locations which avoids the necessity of reproducing deflection voltages accurately. T Y P I C A L ELECTRON PATHS FOR: STORING E L E M E N T AT1 OWLTS I 7 l V . 17bV. ~ R E A D I N Q READING

PLATE

PLATE

-

CATHODES 0 VOLTS VERTICAL SELECTlhG E A R S OWLTS OR -ZOOVOLTS -HORIZONTAL SELECTING BARS 0 VOLTS OR -i!OOVOLlS COLLECTOR P L A T E ti75 VOLTS STORING E Y E L E T S 0 O R ~ ~ T S W L T S WRITING PLATE 3 8 O v o ~ T sPOSITIVE PULSE READING PLATE -125 VOLTS D.C. looVOLTS POSITIVE PULSE FARADAY CAGE 4 4 0 0 VOLTS READING O U T P U T WIRES ~ S I O V O L T S FLUORESCENT

MONITORING LIGHT SIGNAL

SCREEN

SECONDARY E L E C T R O N S PRODUCING ELECTRONIC OUTPUT SIGNAL

SELECTRON STRUCTURE FIG.4. Structure of the Selectron.

The present tube (SB256) is 3 in. in diameter by 8 in. long. Figure 3 gives the appearance of the tube, and Fig. 4 illustrates the internal structure. It contains eight elongated cathodes separating a set of nine vertical selection bars. On either side of the plane of the cathodes there is, in a plane parallel t o that of the cathodes, a set of eighteen selecting bars a t right angles t o the vertical set; these are called the horizontal selecting bars. The horizontal and vertical selecting bars form a set of 256 windows. On either side of the horizontal selecting bars and parallel to their plane is a metal plate (the “collector”) having a round hole for each “window.” Beyond these are sheets of mica carrying a hollow metal eyelet for each hole in the collector. Next come two parallel metal plates, each having a hole for each window: these are the “writing”

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and “reading” plates. Then finally there is a Faraday cage formed by two parallel perforated plates, the remaining walls being solid. The outer perforated plate is placed against a glass plate coated with a fluorescent material. In the central plane of the cage is a set of nine wires spaced to be between the holes in the perforated plates and connected by a common lead t o the stem. These are called the ‘(reading wires.” The cathode is held at ground potential, the collector at +175 v, and the cage a t +400 v ; the reading and writing plate potentials are varied t o perform the operations, as we shall see. If the four selecting bars defining a given window are all a t cathode potential, electrons from the cathode are focused into eyelets. These are electrically floating. They will adjust their potentials so that the net electron current t o them is zero. Two stable values of eyelet potential exist: cathode potential and collector potential. Thus we have again a means of storing binary coded information. To write, a particular location is selected by assuring that the four bars defining it are all a t ground potential, while all others are made sufficiently negative. Electron current t o a window is interrupted if a t least one of the bars defining the window is made sufficiently negative. A positive pulse having a sharply rising leading edge, a flat top, and a gradually falling trailing edge, is applied to the writing plate which was quiescently a t cathode potential. Capacitative coupling raises the potential of the selected eyelet to the vicinity of collector potential or above, thus assuring that the electron current to the eyelet will bring it to collector potential. The flat top of the writing pulse lasts long enough for this t o take place. To write “positive,” the current t o the eyelet is permitted t o continue to flow during the decay of the writing pulse. This permits the eyelet to remain a t collector potential despite the tendency of the falling collector potential to drag it down. To write 1I negative,” the eyelet current is interrupted during the decay of the writing pulse, so that the eyelet potential is dragged down to cathode potential. Thus a selected eyelet can be forced to assume either of the two possible stable potentials. The reading plate is held negative (- 125 v) except when the reading operation is t o be performed, when it is raised to a relatively positive value (-25 v). The reading process consists of selecting the eyelet to be read and pulsing the reading plate positive. Then if the eyelet is a t cathode potential, no current passes through the eyelet and therefore none through the hole in the reading plate; if the eyelet is a t collector potential, electron current flows through t o the Faraday cage, where, upon striking the fluorescent screen, it releases secondary electrons which,

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being collected by the reading wires, are available t o produce an output signal. The selectron system is illustrated in Fig. 4. Only eighteen leads are required to perform selections on the 256 storage elements.

IV. ARITHMETICAND CONTROL ORGANS* The arithmetical and control organs can assume many forms, so that it is not practicable t o discuss all that have been proposed. Naturally one must, for example, expect the logical organization and the circuitry to differ in the case of serial and parallel arithmetic organs. I n this section we shall content ourselves with a rather general discussion. Specific examples will be given in the treatment of the Whirlwind and SEAC computers. In general, the basic circuits employed are not particularly complicated and are rather few in number. We have t o deal with large aggregates of fairly simple building blocks. The basic problem is reliability. Rather wide margins must be allowed for in design in order t o avoid as far as possible the effects of variation of the circuit parameters from their nominal values and the effects of aging. We shall first consider the arithmetic organ. It clearly must in any case contain both elements for the temporary storage of the numbers upon which a given operation is t o be performed, elements for the adding and subtracting of numbers (multiplication and division are built up out of successive additions and subtractions) , and elements which cause the desired operation to be carried out upon the receipt of instructions from the central control. A device which can hold a number is generally referred to as a “register.” In an arithmetic organ it is necessary t o hold briefly the numbers upon which operations are t o be performed. The registers that are used for this must be of such a character that information can speedily be inserted in them or ext.racted from them. Thus a register consisting of a set of flip-flops, one for each bit t o be held, with the necessary gating circuits for read-in and read-out is very common. It is furthermore necessary for certain purposes t o provide means of shifting the information held in a register t o the right or t o the left. One application of this is in the conversion from parallel t o serial transmission; if the bits are transmitted to the flip-flops of the register, an output provided, say, from the left end, and the contents then shifted left a number of times equal to the number of bits held by the register, clearly the information held

* See Chapters 4 and 13 of “High Speed Computing Devices” by the Staff of Engineering Research Associates, McGraw-Hill, 1950, for a large variety of switching and gating circuits and adders.

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will emerge as a time sequence of pulses. The reverse transformation is also possible. This type of conversion is used, for example, in communicating between the serial input t o SEAC and the parallel Williams storage organ which is now in the process of construction. Another use of a shifting register is in performing the multiplication process. This will be discussed later. Registers, both shifting and nonshifting, for parallel arithmetic organs are readily built u p of flip-flops, one for each bit of the word, expressed in binary notation, and gates for effecting read-in, read-out, and shifting operations, while for serial arithmetic organs they assume the character of delay lines one work in length. Examples will be given when we discuss Whirlwind and SEAC. However, i t is useful here t o call attention t o the shifting registers of the Institute for Advanced Study computer, which is, a t the time of writing, nearing completion. These consist of two ranks of flip-flops, which can readily be cleared t o hold all zeros or all ones. Circuits are provided for shifting the contents of each flip-flop of the lower rank t o the one standing directly above it, and for shifting the contents of each flip-flop of the upper rank down t o the one of the lower rank in the preceding or following column. The shift-right process, for example, consists in first clearing the flip-flops of the upper rank, then, by opening the vertical gates, placing in them the contents of those of the lower rank. The latter are then cleared, and the shift-right-down gates are opened t o force each flip-flop of the lower rank t o agree in its contents with the one in the preceding column of the upper rank. I n this shifting process information is never (‘in transit”: furthermore no flip-flop is ever commanded t o change its state, but is definitely set into the state which it is t o assume. Addition in a parallel arithmetic organ is effected by adding simultaneously all pairs of digits of equal positional order in the two numbers t o be added: then of course provision must be made t o add in the carries. I n a serial adder, the two digits of lowest positional order are added first, the carry is delayed one pulse time and added in with the sum of the two digits of next higher order, and so on. Examples of both will appear under our discussion of Whirlwind and SEAC. The Institute for Advanced Study computer incorporates a n adder of quite different character-binary digits of a given column are added in the form of adding currents in a resistor t o give a sum voltage, and t o this is added a voltage representing the carry from the column of next lower order. Additional equipment, called the “digit resolver,” is needed t o interpret the voltages thus produced as binary ones and zeros. Multiplication is generally built up of successive additions and shifts. Certain features of the binary number system make division rather

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simpler than in other systems. It is built u p of a succession of additions, subtractions, and shifts. The control organ generally performs three functions: successive orders must be procured from the storage and interpreted or decoded, t o find what operation is next t o be performed, and in what location (or locations) in the storage the needed number (or numbers) are located. Thus we can, if we wish, distinguish main control, arithmetic control, and storage control as functions, though this need not be reflected in the physical organization of the equipment. Great variety exists in the means of effecting these functions. We would expect in any case t o find th a t a good deal of the task of the control is t o make selections and perform switching operations. The well-known diode matrix is frequently used for this purpose. We shall find examples in both Whirlwind and SEAC. We may also expect t o find counters for keeping track of the successive instructions and a register into which each order is placed as it is extracted from the storage. It is well t o emphasize the fact th at current and past designs of circuits for both the arithmetic and the control organs utilize conventional vacuum tubes originally developed for communication equipment. I n both these organs, the tubes are generally operated in a n off-on mode (there is an exception in the case of SEAC), for which they presumably were not designed. It is evident that long tube life is needed in a system incorporating several thousand tubes if an intolerable failure rate is t o be avoided. This is both a tube and a circuit problem. Certainly circuit design for wide operating margins and the avoidance of operating conditions known to be detrimental to tube life are incumbent upon the designer in order t o get the best results with existing tube types, while selection of tubes before installation is also helpful. The effect of off-on operation has been shown t o lead, in the case of tubes whose cathodes are made of “active” nickel t o the formation of a n interface between the nickel sleeve and the oxide coating, which effectively introduces an impedance in the cathode lead consisting of a resistance and a capacitance in parallel. This causes degeneration, as shown in reduced plate current. The remedy is t o use tubes whose cathode sleeves are made of passive nickel, which contains less than 0.01 per cent of silicon. Considerably improved tubes are definitely needed for computer applications. A beginning a t least has been made in this direction. The Radio Corporation of America manufactures three tube types designed for computer work. Features of the design include: good initial electrical characteristics, which remain stable for long periods, good

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structure for freedom from intermittent interelement short circuits, freedom from grid emission, long heater life, and the lowest possible heater power consumption. Sylvania also designed for the Whirlwind project a pentode (7AK7) with characteristics especially suited for operation in a gate circuit. If electronic computers develop in importance in our economy, we will surely see more developments of this sort.

V. WHIRLWIND The Whirlwind computer was developed by the Servomechanisms Laboratory of the Massachusetts Institute of Technology under a contract with the Office of Naval Research. The program has emphasized both reliability and high operating speed and has included research leading to the development of the special storage tube that has already been described. As high operating speed was desired, parallel data transmission and a parallel arithmetic organ were fundamental features of the design. The basic block diagram of Fig. 1 is of course still valid. For Whirlwind this may be slightly modified by showing all the blocks communicating with a digit transfer bus, which is physically composed of sixteen coaxial cables, one for each bit of the sixteen bit words, while separate interconnections exist between the control and each of the other blocks. The binary system is used t,hroughout. At present, information may be inserted in other notations and a special subprogram inserted in the storage which causes the arithmetic organ to convert each incoming word into binary notation before it is placed in the storage. The word length within the machine is sixteen bits. Words signifying numbers consist of a sign and fifteen binary digits, the binary point being interpreted t o come between the sign and the first bit, so that all numbers are treated as proper fractions. A plus sign is signified by zero, minus by one. Negative numbers are represented by the minus sign and the “ones complement” of the absolute value, which is found by subtracting it fromO.llll . . . 1, and thus has zeros or ones when the absolute value has ones or zeros respectively. Instruction words contain a specification of the next operation to be performed (first five bits) and the storage location of the operand (last eleven bits). Thus a “single address” code is used. An account of the instructions used will be given after the discussion of the control and arithmetic organs. For initial operation of Whirlwind a punched paper tape system was devised, which need not detain us. A photographic film reader-recorder developed by Eastman Kodak is also available. This unit stores each binary word in two lines. On the first line each position holding a one

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is represented by a n exposed spot, while on the second, exposed spots represent zeros, so t h a t we may regard the first line as holding the number, the second, its complement, since the absence of a n exposed spot in any position obviously can be interpreted as representing a zero. There are one hundred lines per inch of film; it can be moved as fast as 20 in. per second or i t can be moved line by line. The unit can be used as either a reader or a recorder, though changing its function from one t o the other must be done manually. Reading and recording are both performed by light obtained from the moving spot on the face of a cathode ray tube. At the sweep speed used (one sweep every 50 microseconds) each recorded row is very nearly perpendicular t o the length of the film. The film must be of course developed continuously and rapidly right after the recording process, if intermediate results are t o be held on it and made available for further use in the computer. I n this way the combination of a reader and a recorder can be made t o function as an auxiliary storage device, though the need for developing the film after recording and the fact t h a t the information cannot be erased or altered would presumably make this function more readily handled by means of a magnetic tape device. To permit communication between the Kodak reader-recorders and the internal storage, a n input-output element is included. This contains an in-out register for temporarily holding a word t o be recorded or a word read; i t serves as a parallel-serial conversion device, since the bits of each word are read off the film serially and must be transmitted within the computer in parallel. This function of a shifting register has already been mentioned. A comparison register is provided for checking purposes and a n in-out control, which coordinates the operations of the computer and the reader-recorder. As the input-output and storage organs of Whirlwind have now been treated, we shall proceed t o consider the arithmetic and control organs. Before going on t o the structure, both logical and electrical, of these, it must be noted that all timing of computer operations originates in the control, a part of which is called the master clock. This contains a number of circuits for the distribution of timing pulses; the heart of i t is the pulse generator, which is merely a n oscillator whose frequency is 2 megacycles per second, shaping circuits t o provide a 2-megacycle train of pulses, and a scale-of-two counter t o provide a 1-megacycle train of pulses. The 2-megacycle pulses are used only in the arithmetic organ, while the 1-megacycle pulses are used as the fundamental timing pulses of the central control, in the storage control, and t o control the in-out element. The clock also contains a scale of sixteen counter which receives the 1-megacycle pulses and provides pulses a t a repetition rate

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of 62.5 k.c.p.s. t o time the “restoration” operation, of which we shall have something t o say when we discuss the gate tube. It also contains a clock pulse control, which essentially is a pulse distributor. The most generally used individual circuits in Whirlwind are: the flip-flop, the gate tube, the delay element, and the (‘mixer.” These are the basic building blocks, though other circuits occur for amplification, impedance matching, pulse inversion, etc. The Whirlwind flip-flop is basically the familiar Eccles-Jordan circuit. Features are that the cathodes of both tubes are connected and returned to ground by means of a resistor, which permits triggering by a positive pulse in the cathode circuit, and the the cross-over resistors have condensers connected in parallel with them t o improve switching speed. Negative grid inputs also provide triggering action. Cathode triggering is used in the “restoration” process, which will be discussed in the second paragraph below. Grid triggering is used for two purposes: (1) to clear the flip-flop t o a specified state, (2) to transmit information to it. The gate tube is a pentode with two inputs: a positive pulse to the control grid and an “enabling” or “disabling” voltage to the suppressor. If the suppressor voltage is made sufficiently low, the plate current is cut off, and a positive pulse applied t o the control grid has no effect on the plate voltage. I n this case the gate is said t o be ‘(disabled.” Thus plate current, and therefore plate voltage, is affected only if a positive pulse is applied t o the control grid while the suppressor voltage is sufficiently high, or, as we may say, while the gate is enabled. The gate thus functions as a logical (‘and” circuit, a pulse output signifying the simultaneous presence of a pulse input and that of an enabling signal. When a positive pulse output is desired, or a remote load is to be driven, a pulse transformer is used in the pentode plate circuit. The gate tube suppressor is in many cases driven by a flip-flop plate voltage. This would cause no trouble if direct coupling were used. However, it is desired t o avoid this, as it leads t o the necessity of operating different circuits a t different d-c voltage levels. However, if a-c coupling is used, the difficulty arises that the state of the flip-flop may not change for a period of time which is long in comparison with the time constant of the suppressor circuit of the gate tube. To avoid the consequences of this situation, the charge on the coupling capacitor is periodically restored. The coupling from flip-flop plate t o suppressor is by means of a capacitor. The anode of a crystal diode is connected to the suppressor of the gate, while the cathode is connected t o a negative d-c voltage which provides a bias, the gate cathode being grounded. Every 16 microseconds a pair of positive pulses 1 microsecond apart is applied to

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the flip-flop cathode. The net effect is of course t o leave the flip-flop in the condition in which it was before the pair of “restorer” pulses arrived, but t o restore the charge on the coupling capacitor. Delays are introduced where needed by two methods: a n electrical delay line or a one-shot multivibrator. The so-called mixer is a logical “ o r ” circuit. The simplest form consists of two diodes with anodes connected; the common anode lead, from which the output is taken, is connected t o a positive voltage supply through a resistor, and the inputs are negative pulses applied t o the cathodes. Supposing for simplicity t h a t these start from ground and fall t o - E volts, i t is clear t h a t the output voltage will be slightly above ground when no pulse is applied t o either input, but will fall t o slightly above - E volts if a pulse is applied t o either input. Other forms are of course possible. The logical structure of the computer depends upon the building blocks just discussed. Important ensembles of these simple circuits are the registers, counters, and switches of which the arithmetic and the control organs are chiefly built up. The switches are diode matrices driven by flip-flops. A very simple form is shown on p. 42 of the ERA volume on computers t o which reference has already been made. If there are n flip-flops, there are 2” output leads, corresponding t o the 2” possible conditions of the flip-flops, and for each of these conditions one of the output leads is “selected” in the sense that its voltage is equal t o E b b , while the other voltages are lower. If the output leads drive the suppressors of gate tubes, the circuit can obviously be so arranged t h a t the selected lead enables its gate, while the others disable theirs. Note t h a t the switch can be thought of as a decoder, as it gives a n interpretation (by means of the selection of outputs) of each binary word inserted in the flip-flops. Switches of this type are used in the control t o supply pulses t o the requisite points in the proper time sequence, for example, by controlling gates as noted above. The counters are simple binary counters, which need not be discussed. The registers are simply sets of flip-flops, one for each bit of the basic sixteen bit word, with means of clearing them and of inserting information in and extracting it from them. The control contains, in addition t o the clock, which provides the timed trains of pulses needed throughout the computer, a program counter which contains the location in the storage of the instruction t o be executed, a program register, into which the instruction is read from the storage, and matrix switches which interpret respectively the first five and the last eleven bits of the instruction. The first of these selects one of thirty-two possible operations (all of these are not used), while the

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second selects one of 2048 possible locations in the storage, from which the number t o be operated upon is t o be extracted. As we noted before, instruction words are stored in consecutively numbered storage locations; hence upon the completion of an order the program counter is stepped once, so t h a t i t will then hold the storage location of the next instruction t o be executed. An exception occurs in the case of the subprogram order, when the address of the first order of the subprogram t o be executed is inserted in the program counter. The arithmetic organ contains basically: (1) three registers, the A and B registers and the accumulator; (2) certain subsidiary binary storage elements, such as the sign control flip-flop which remembers the correct sign of the result of the multiplication or division being performed; (3) the arithmetic control flip-flops, which control the supply of operating pulses. Into the A register is introduced each number brought from the storage into the arithmetic organ. It holds the addend, subtrahend multiplicand, and divisor, respectively in the four arithmetical operations. Gates are provided by which the contents of the A register may be read into the accumulator, which must be done in the adding process (for subtracting, the complement is read in). The accumulator is a shifting register provided with special equipment t o enable it t o form the sum of the number resident in it and that read in from the A register. An incoming pulse from a flip-flop of the A register flips the corresponding stage of the accumulator t o ((one” if it held a “zero,” and t o “zero” if it held a “one.” I n the latter case a carry pulse is produced which sets t o ((one” a carry flip-flop. An ingenious high-speed carry circuit then adds in the carries. The B register is a n auxiliary device; for example, into i t are sent digits which are shifted out of one end of the accumulator during a shifting process, as occurs in multiplication. I n this process, the multiplier is first inserted in the B register: then the least significant bit is inspected; if it is a ((one,”the contents of the A register are added into the accumulator; if it is a ((zero,” nothing happens. The contents of the B register are then shifted one column t o the right, the last bit being lost, while the contents of the accumulator are similarly shifted, the least significant bit being however inserted in the column left vacant in the B register. This process continues sixteen times, a counter being obviously required t o call a halt after sixteen steps. All the multiplier disappears, but in the end the accumulator holds the sixteen most significant bits of the product, while the B register holds the least significant sixteen bits. During division the quotient is built up in the B register. We will not take the space to describe the process here.

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It should be added that means are provided for giving a n alarm whenever a sum is equal t o or greater than unity. Total addition time of 72 psec., and total multiplication time of 87 mec. are goals, depending upon reducing access ‘time t o 6 psec. from the present value of 25 psec. Present values are higher as conservatism in the early stages of operation of the storage dictates the use of a longer access time t o assure reliability in operation of the storage tubes. The Whirlwind order code contains instructions of five types: (1) tape orders, which control the communication between the computer and the input and output; ( 2 ) transfer orders, which control the transmission of information from the arithmetic organ t o the storage; (3) subprogram orders, which cause the control t a take its next instruction from an arbitrary storage location instead of the next location; (4) add orders; (5) multiply orders (in this last group we include division and shifting left or right). These will not be described in detail. As a n example, the order designated as (‘ca x” causes the accumulator and B register t o be cleared t o zero, and then the word is held in storage location “ x ” t o be transferred t o the accumulator. Thus t o add two numbers requires two orders, while t o transfer their sum from the accumulator back t o storage requires a transfer order. This is the general arithmetical procedure: first one operand is read froD the storage into the accumulator; the next order specifies the other operand and the operation: the result may be left in the accumulator for further processing or transferred back t o the storage. I t is not feasible t o go further into detail concerning the Whirlwind computer. However, two additional features may well be mentioned. First, in the course of the development program certain standard test units were built. A variable frequency clock pulse generator, a pulse mixer, a register panel (consisting of one flip-flop and a gate circuit), and a gate and delay unit. By means of these, i t was possible t o build elaborate test setups and even t o simulate the operation of parts of the computer not yet installed. It is clear from our discussion t h a t a computer could be built u p of these elements. Second, Whirlwind has built into it a rationalized preventive maintenance scheme, called “marginal checking.” This depends upon the fact that component failure is ordinarily the result of a progressive deterioration. If the circuit containing the component is caused t o operate in a n abnormal way, the component may be caused t o fail. The marginal checking process is an orderly way of temporarily causing such abnormal operation for the purpose of causing t o fail those components which are on the verge of failure under normal conditions. Consider the marginal checking of a flip-flop. I n this circuit each

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tube, when conducting, must be able t o hold the other in a non-conducting state. As a tube deteriorates, its plate current falls off, and this reduces the bias applied t o the grid of the other tube. If one tube deteriorates faster than the other, the balance in the circuit is destroyed, and this may reach the point where switching can no longer take place. Marginal checking here is accomplished by inserting variable voltages in the screen leads of the two tubes, and selectively varying the screen voltages. Raising one tube’s screen voltage raises also its control grid cut-off voltage. Thus if the “off” tube’s screen voltage is raised the extent t o which it must be raised before the “ o n ” tube can no longer hold it in a cut-off condition, is a measure of the plate current margin of the “ o n ” tube. The spurious switching of the flip-flop can be automatically detected by applying sensing pulses t o the gate tube connected t o the plate of either tube of t8heflip-flop. I n Whirlwind the marginal checking routine has been largely automatized, t o the extent that the whole system can be checked in 15 minutes. Marginal checking was first tried with a n experimental five-bit multiplier containing 400 vacuum tubes. I n one period of 45 days marginal checking applied just before each day’s operations discovered 16 tubes, 7 crystals, and 4 resistors whose margins were too low. These were replaced as discovered, with the result t h a t trouble-free operation was obtained throughout the period. VI. SEAC The “ S E A C ” was developed a t the National Bureau of Standards under sponsorship of the Department of the Air Force. It is a binary machine. Transfer is serial, as is tfheArithmetic organ, a natural choice since mercury line storage is used. The design was so conceived as t o result as soon as possible in a workable computer, which dictated the decision t o use mercury storage; however, provision was made t o permit the incorporation of a Williams type storage also when its feasibility should be demonstrated: it appears likely t h a t this will be done in the near future. The basic word length is forty-five bits. A number word consists of forty-four numerical bits and a sign. Two types of instruction words are available. A four-address instruction contains, in addition t o a specification of the operation t o be performed, the addresses in the storage (1) from which the operands are t o be extracted, ( 2 ) t o which the result is t o be returned, and (3) a t which the next instruction is to be found. A three-address instruction contains the specification of the operation, addresses of the operands, and that t o which the result is t o

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be delivered; in this case, instructions are arranged in consecutively numbered addresses in the storage, which are consulted sequentially, unless some branching operation intervenes, when the natural sequence is interrupted. Words are represented as trains of half-microsecond pulses, a pulse for a “one,” no pulse for “zero,” these pulses being supplied by a “clock” at a prf of 1 mcps. Input and output at present can be accomplished by two methods: (1) both by perforated paper tapes, (2) input by a manually operated keyboard, output by a teletype printer. These are expected to be replaced by magnetic tape devices in the near future and so need not concern us further.

FIG.5. A single SEAC mercury line and associated equipment.

The internal storage is of the mercury line type, five hundred and twelve words being held in sixty-four mercury lines. The total delay per line is 384 microseconds, allowing for eight words each followed by a space of 3 microseconds. Average access time is therefore 192 microseconds. The pulses representing binary ones modulate an 8-mcps carrier, and in this form are applied to the line input. ‘They are somewhat “smeared” in transmission, emerging however as pulses of the carrier signal not over 1 microsecond in length, the attenuation being 60 db. The recirculation system of each line consists of an amplifier, a detector t o recover the pulse envelope, a pulse reshaper, read-in and read-out gates, and a modulator; an 8-mcps oscillator supplies the carrier frequency. A photograph of a mercury line and its recirculation system is shown in Fig. 5 . The mercury storage was built for NBS by the Technitrol Corporation of Philadelphia. The circuitry of SEAC is sufficiently unusual to merit rather more

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detailed discussion than the limitations of space will permit us t o devote t o it, but it ib hoped that the main features will be made clear. The feature tliat first strikes one upon examining the SEAC circuits is the way in Xvhich the vacuum tubes are employed. Logical operations are performed by crystal diodes in various combinations, while beampower tubes with pulse transformers in the output circuit are essentially used only t o supply power. The use of pulse transformers is very convenient in several respect s : (1) inversion of pulse polarity gives a positive output for n poiitive input, v-hile if more than one secondary is used, a single tube can be used t o supply both positive and negative-going pulses for a positive input ; ( 2 ) d-c isolation is automatically achieved, so t h a t all tubes can be operated a t the same d-c level; (3) as the tube delivers maximum pon-tr at voltage gain greater than unity, while a comparatively small voltagc swing is needed a t the output, the pulse transformers are used t o step down the plate voltage, which means t h a t rather high current can be delivered a t low impedance, and that therefore it is not necessary t o be unduly concerned with the capacity that is t o be driven; unshielded signal leads can therefore be employed. The usual output signal amplitude is 18 v, and u p t o 120 ma can be delivered safely t o the load, 5 : 1 and 7 :1 step-down ratios being used in the pulse transformers. Of course the use of pulse transformers has its disadvantages too: (1) more delay per stage is introduced than with the more conventional video circuitry, and (2) the d-c component of the signal is lost; the base line of the output from the transformer secondary can shift with varying density of the pulse traiii. Ho\vever, these are far from fatal. The second is the more serioub, but it was found that this effect could be miiiimized hy so opcruting the tubes that the design load line intersects the zero bias plate characteristic well below its “knee.” I t has been said that logical operations are performed by corn binations of crystd diodes. Positive-going pulscs are used t o transmit information in SEAC, which dictates the structure of the logical “ a n d ” and “ o r ” circuits used. The schematic in Fig. G shows many features that are fouiitl throughoiit the SEAC. Thus a t point C we have several diode cathodes with a common cathode connection which is returned t o a -65 v d-c line by way of a resistor. Inputs are positive information pulses applied to the plates. If any one of the plates is driven positive, all the cathodes rise with it in voltage. Hence this circuit is a physical realization of the logical sum* of the inputs. A t point A are shown two * The logical sum of t n o or more sets of elements consists of those elements which belong to a t least one of the sets. Thus it is equivalent to the word “or.” The logical product of t n o or more sets of elements consists of the elements common to all the sets and is thus equivalent to the word “and.” T h e usual symbols for sum and product are used.

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diodes, their plates connected to this point, while inputs may be applied to their cathodes. As long as a t least one cathode is held at a level below 3.62 v, clearly the voltage at point A will be only slightly higher than that of the lower cathode. For the voltage at A to rise, it is necessary for both inputs to rise simultaneously. This circuit therefore gives us the physical realization of the logical product of the inputs. We also call attention to the beam-power tube and pulse transformer combination which is used throughout the SEAC circuitary. Complicated logical functions can be built up by properly cascading the logical elementary circuits; of course the resistor values must be properly adjusted, and care must be taken that sufficient current is available to drive the distributed capacities.

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FIG.6. Typical SEAC circuitry.

A simple combination of the basic tetrode circuit with an “and” gate results in the “regenerative reclocking ” scheme used throughout the computer. An input pulse and a clock pulse are both applied to the inputs of an ((and” circuit whose output is connected to one input of an L‘orllcircuit. The terminal of the secondary of the transformer which will swing positive when a positive pulse is applied to the grid of the tetrode is connected to one input of an (‘and” circuit and a clock pulse to the other, the output of the crand” circuit being connected to the other input of the “or” circuit. Finally the “or” circuit output is connected to the tetrode’s control grid. Thus, upon a positive input pulse being received, the tetrode’s grid will not go positive until the rise of the clock pulse. The output of the transformer secondary and the clock pulse together will then hold the grid voltage up until the fall of the clock pulse. Thus in each vacuum tube stage the information pulses are reshaped and retimed against a standard reference. A slight extension of the above scheme, utilizing a second feedback path from the transformer secondary to the grid circuit via a delay line and an “and” circuit the other input to which is a clock pulse, and whose output is fed to the “or” circuit previously mentioned, results in a circuit

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which is such that, if a pulse is once fed to it, it will keep the pulse circulating through the delay line indefinitely. Of course it is necessary so to adjust the line’s delay that the total transmission time around the loop is 1 microsecond (or a multiple thereof). Thus the circuit has at its output an information pulse (or the lack of one) every microsecond if one is inserted and can be described as a “dynamic flip-flop.” An inhibiting circuit must of course be incorporated so that the flip-flop can be cleared when desired. Dynamic registers and shifting registers can of course be built up of dynamic flip-flops. Actually if the total delay around the loop is made 5 microseconds instead of 1 microsecond, each circuit can hold five bits of information, and thus a register more than ample to hold a forty-five bit word can be constructed using only nine vacuum tubes. The performance of addition in the binary system using a serial adder is particularly simple. This depends on the fact that the sum of two bits is “zero” if both are “ones” or “zeros” (in the former case of course a carry must be generated), while it is one ” if the first is (‘zero ” and the second “one,” or if the first is (‘one” and the second “zero.” Thus if the bits being added are A and B, and we use A (not A ) to be “zero’’ if A is one and vice versa, the expression A . B A . B certainly gives the sum, while A B gives the carry,* and it is obvious that this can readily be instrumented by means of the simple “and” and “or ” circuits already described. This combination gives a so-called half-adder, for we have made no provision for adding in the carry to the sum of the next pair of bits to arrive. A cascade of two half-adders, with a delay line to retard the addition of the carry, forms a serial adder. A serial adder whose output is passed through a delay line one word in length and is then used as one adder input functions as an accumulator. For suppose one number inserted. This is in effect added to “zero” and sent through the delay line, arriving again at one adder input in synchronism with the second number. The adder forms the sum of these and keeps it circulating through the delay line feedback loop until either another addend is inserted, or the contents of the accumulator are read out, and the feedback path is inhibited to clear the accumulator. For subtraction, it is necessary to incorporate also ( I complementors,” which merely replace the “zeros” and “ones” of the number to be subtracted by “ones” and (‘zeros” respectively. The arithmetic organ of SEAC consists essentially of t,he adder loop (accumulator) , (multip1)icand loop, and (mu1tip)lier loop, plus of course the necessary complementers, and a counter to keep track of the steps * Here addition and multiplication and course used in the “logical” sense.

-

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in the multiplication process. Multiplication is built up by means of successive additions and shifts. The control organ contains a n instruction register, which receives from the storage the instruction t o be executed, an instruction operation decoder which is a dynamically operated crystal diode matrix, and circuitry t o decode the address information, select the mercury lines in which the operands are stored, and the correct position of the operands within their lines, and to provide the necessary timing so that the desired operands will be correctly extracted from the storage. The SEAC instruction code is simple. There are seven basic orders: addition, subtraction, multiplication, division, comparison, logical transfer, and input-output control. Operation times, including access time to the storage, are (average values): addition and subtraction 0.9 millisecond, multiplication and division 3.0 milliseconds.

VII. CONCLUSION The Whirlwind and SEAC machines have been described because they represent the developments that came to fruition during 1950, and hence, at the time of writing, represent the state of the art. This, however, is a very fluid entity. A considerable number of development programs seem about to reach successful conclusions, but, since they had not done so by the end of 1950, they were not given consideration in the present discussion.

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Modulation of Continuous-Wave Magnetrons* J. S. DONAL, JR. Radio Corporation of America, R C A Laboratories Division, Princeton, New Jersey CONTENTS

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.

111.

IV.

V.

VI.

VII.

Page 188

1 . Modulation Characteristics Desired. . . . . . . . . . . 2. Amplitude Modulation. . . . . . . . . . . . . . . . . . . . . . 3. Frequency Xlodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 4. Mixed hlodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Frequency Modulation or Control by Spiral Electron Beams. . . . . . . . . . . . 194 1. Effect of Longitudinal Magnetic Field., . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 196 2. Determination of Electronic Admittance. . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Determination of the Frequency Change Due to the Guns . . . . . . . . . .L. 197 4. Variation of AW with Changes in Parameters.. . . . . . . . . . . . . . . . . . . . . . . 199 5. Use of Spiral Beams 6. Evaluation . . . . . . . . . . . ..................................... 201 Frequency Modulation . . . . . . . . . . . 201 1. Hot-Resonance Studies of Magnetrons . . . . . . . . . . . . . . . . . . . 202 2. Bulk Effects of Spac 205 3. Experimental Applications, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Evaluation.. . . . . . . . . . . . . . . . . . . . . ...................... 206 Voltage Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 1. Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................. 209 2. Discussion of Voltage Tuning . . . . . . . . . . . . . . . . . . . 210 3. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amplitude Modulation Using Absorption by a Spiral Electron Beam 1 . Attainable Electronic Conductance and Power Absorption. . . . . . . . 2. Example of an R F Circuit for hlagnetron Modulation.. . . . . . . . . . . . . . 214 215 3. Predicted Modulation Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. A Developmental Absorption Modulation System. . . . . . . . . . . 5. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amplitude Modulation by Means of the Electron Coupler. . . . . . . . . 1. Behavior of the Beam in the Output Cavity of the Coupler. . 2. Modulation of the Power in the Load.. . . . . . . . . . . . . . . . . . . . . 3. Construction and Performance of a Typical Coupler.. . . . . . . . . . . . . . . . 223 4. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Control or Modulation by Injection Phase Locking.. . . . . . . . . . . . . . . . . . . 225 1. Phase Locking under Static Conditions .................... 226 a. Graphical Treatment. . . . . . . . . ............ . . . . . . . . 227 b. Analytical Expression for the 1, . . . . . . . . 228

* Condensed from a monograph of the same title based upon lectures delivered at the Summer Electronics Symposium, University of Michigan, 1950. 187

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J . S . DOXAL. JR .

Page 230 2 . Frequency Control of Modulated Oscillators. . . . . . . . . . . . . . . . . . . . . . . a. Variation of Phase Modulation with Static Phase Difference . . . . . . . 231 b . Injection Lockirlg for Automatic Frequency Control . . . . . . . . . . . . . . 231 232 3 . Out-Phase lfodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . 1~:raluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 \-I11. .4rnplitude llotlulation by Plate Modulation of a Magnetron with Simul234 tancous Frequency Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Performance of a Plate-Modulated Magnetron . . . . . . . . . . . . . . . . . . . . . 235 a. Modulation Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 b . LIodulation Linearity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 c . A4mplitudcModulation Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 d . Characteristics of the Frequency-Control Beams . . . . . . . . . . . . . . . . . . 237 e . Pushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 2 . Phase-Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 a. Perforinance of Loop with Circuit Components of Infinite Bandwidth 241 h . Perforniance of a Practical Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 c . TSxperiniental R.esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 3 . Frequency Control Used in Addition to Phase Control . . . . . . . . . . . . . . 245 4 . Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 I S . The Tnjcrtion Xlagnetron as the Possihle Means of Producing Amplitude o r E’reqiieney JIodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 I . T h e Principles of the Injection Magnetron . . . . . . . . . . . . . . . . . . . . . 247 2 . Characteristics with the Control-Anode Voltage Constant . . . . . . . . . . . 249 3 . Performance as a Function of Control-Anode Voltage . . . . . . . . . . . . . 250 4 . Variation of Rod Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 5 . Lorn-Current Behavior of the Injection Magnetron . . . . . . . . . . . . . . . . . . 251 6. Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 S . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 I~eferences ........................................................ 254

I . INTRODUCTION I t is rather obvious that the increasiiig use of radio for broadcasting and communication purposes will require the use of higher frequencies and. for some services. inconveniently large continuous powers . The output power of conventional triodes or tetrodes is limited t o a few kilowatts a t a thousand megacycles. while a t higher frequencies their output is decreased still farther . The cw magnetron has a n efficiency of 50 to 70 per cent a t microwave frequencies . Not only is this efficiency the highest afforded by microwave tubes. but powers of tens of kilowatts a t 1000 megacycles. decreasing t o perhaps a few kilowatts a t 10.000 megacycles. can be developed with comparative ease . The magnetron is basically a self-excited oscillator. however. with the result that it is difficult t o employ the tube for conventional amplitude or frequency modulation within the exacting specifications of commercial and military systems. Nevertheless. many methods are now available. or in the

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course of development, for magnetron modulation. These procedures meet the requirements of many practical systems. Pulse modulation is not included in this discussion, since this type of modulation is well known and imposes much less severe requirements on the tube than does conventional amplitude modulation. However, the methods of frequency control t o be described are applicable to pulsed tubes. There are only a limited number of fundamentally different ways to modulate a magnetron. For example, amplitude modulation is produced by variation of the power input, of the power derived from the electron stream, or of the power permitted to reach the load. Frequency modulation may be produced either by altering the frequency a t which a

++

FIG.1. Simplified equivalent circuit of the magnetron.

fixed resonant circuit is driven by the electron stream, or by changing the naiural resonant frequency of this circuit. There are many variations of these procedures, but an understanding of the behavior of the magnetron when the fundamental methods are used is necessary if the -# variations are t o be properly evaluated. Figure 1 shows a simplified equivalent circuit for the magnetron. Y eis the electronic admittance, the subscript T refers to the tank circuit, and Y L ’ is the load admittance after transformation by the coupling mechanism. GT represents a conductance accounting for the losses in the tank circuit. Since the condition for oscillation requires that the sum of the admittances a t any plane in the circuit shall be zero it can be shown‘ that, after separation of the real and imaginary portion of this relation:

--Be

=

2Y,,

(T) 0

Wo

+

I3L’

where Qo, Qext, and Q Lare the unloaded, external, and loaded Q’s, respectively, of the system, w 0 is the resonant angular frequency of the tank circuit, w is the angular frequency of operation, and Yo,,the characteristic admittance of the tank circuit, is given by: 1 Yo, = d c / L = w o e = (3) WOL

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J . S. DONAL, JR.

SlaterPhas espressed the conductance and susceptance relations in a somelchat different, and often more convenient, form:

where (Qext)o is the value of external Q Jvith a matched load and GL and BL are the normalized values of conductance and susceptance of the load. Since the power derived from the electron stream is

I "Ti

FIG.2. Variation of electronic conductance and susceptance with R F voltage.

either (1) or (4) n ill give information on the variations of the power in the load if we have a knowledge of the behavior of Vrf as a function of G,. Either (2) or ( 5 ) may be solved for w to determine the operating frequency as a function of the electronic susceptance, of the loading, or of the value of s o . I t must not be assumed that all the characteristics of the magnetron can be calculated, although much of the behavior can be predicted qualitatively. As an example, the forms of the variations of G, and Be with Ti,f are show1 in Fig. 2.2 As will be shown below, these curves make equations (1) to ( 5 ) more useful than mould otherwise be the case. I n addition to relations such as those of Fig. 2 , a few general rules can be ~ t a t e d . ~ , .First, " . ~ Be does not vary when BL is altered, so that w is a linear fuiiction of RL from (5). Secondly, Be is a function of G, from Fig. 2. As a result, when G L alone is varied, altering G,, the frequency of operation is changed. On the other hand, a variation of B L alone does not result in a change of power output, since Be is independent of BL. Thirdly, B , is a function of anode voltage, so that the operating frequency is a function of anode voltage, from (2). This is the phenomenon of

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191

frequency pushing which is of considerable importance in the following sections. Fourthly, G, is not a function of anode voltage in a n equilibrium state. This is obvious from (1) since GT and GL’ are not affected by voltage. While Be is a function of anode voltage and G, would be expected to vary when Be changes, from Fig. 2, there is actually a different G, curve for each anode voltage. The value of G, is the same on the new curve even though Vrris i n c r e a ~ e d . ~ I n the light of the above equations and rules, more specific consideration may be given t o methods for magnetron modulation. 1. Modulation Characteristics Desired

The modulating power, and particularly the modulating voltage, should be as small as possible. For either amplitude or frequency modulation the system efficiency should be high, particularly if high rf powers are t o be produced. Several of the methods for amplitude modulation t o be described are inherently absorption methods in t h a t the power input remains constant while the load power is altered. Such procedures have low efficiency averaged over the modulation cycle. Very little amplitude modulation should be mixed with frequency modulation, for although this can often be removed by limiting, the process is wasteful of energy. Frequency or phase modulation mixed with desired amplitude modulation is even more serious, for i t results in interference and distortion which cannot be tolerated, except t o a small degree, in most systems. The absence of mixed modulation is the most difficult criterion t o meet in modulating a magnetron. For frequency modulation, the available frequency deviation should be as large as possible. It should preferably be linear with the modulating voltage. For amplitude modulation, the available modulation factor should be large t o avoid waste of carrier power. This factor is required by regulation t o be a t least 0.74 for television, as an example. During amplitude modulation, the rf voltage across the load should be linear with the modulation voltage a t the magnetron or a t some point well along in the modulator stages. For constant modulating voltage, either the frequency deviation or the modulation factor should be reasonably independent of modulation rate, i.e., the system should have a bandwidth sufficient for the type of service contemplated. 2. Amplitude Modulation

The first basic method for the production of amplitude modulation is variation of the power input. When the anode voltage of a magnetron is altered, both the power output and the frequency change. The latter effect is considered in paragraphs 2 and 3, below. The power output is

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J. S. DONAL, JR.

not proportional t o the input, for the electronic efficiency is a function of anode voltage. The efficiency would be expected2 to decrease steadily as the voltage is raised above that for which oscillation begins. As the rf voltage increases, the electrons tend t o be drawn directly to the anode, the interaction conditions become less favorable, and the rf currents may actually decrease. As the cut-off voltage is approached, the electronic efficiency decreases to zer0.~9~The simple theory does not hold a t very low currents, for the electronic efficiency decreases again as the current is reduced. This is attributed partly t o leakage currents and partly to poor phase focusing at very low rf fields.' At a fixed loading and magnetic field, therefore, both the electronic efficiency and the total efficiency pass through a maximum as the anode voltage is increased. The dc current is proportional t o the dc voltage over most of the operating range, but the variation in efficiency must be considered in predicting the shape of the modulation characteristic. A t a fixed loading and anode current, the electronic efficiency increases rapidly with magnetic field. Thus, frequency modulation devices, within the magnetron, may limit the efficiency if the frequency modulation requires a low magnetic field. The second and third basic methods for obtaining amplitude modulation are variation of the power derived from the electron stream and variation of the power permitted t o reach the load. An example of a combination of those methods is the use of electronic absorption means within the magnetron. This alters G,, from (1). Decreasing G T and G , (from some mean value of loading) raises V,, from Fig. 2, but it is not obvious what happens t o the power, G,Vd2,delivered by the electrons. As in the case of high anode voltages, however, an increase of rf voltage ultimately decreases the electronic efficiency. The increase in Qo would result in an increase in circuit efficiency

but the decrease in electronic efficiency overcomes this effect. Since the magnetron should be designed for an optimum combination of electronic and circuit efficiencies with no extra internal loading, the above case is somewhat academic. An increase in GT, however, is easy t o achieve electronically. This reduces the rf voltage, from Fig. 2, and the electronic efficiency falls on account of poor phase focusing. The circuit efficiency also falls from (7), and the power output is decreased. As Slater has noted2 the product -GeVrr2 starts from zero a t zero rf voltage (Fig. 2), passes through a maximum and falls rapidly as G , decreases.

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

193

As another combination of the same two basic modulation methods, variation of load conductance, GL, may be used t o amplitude modulate a magnetron. As with a variation of GT, Ge is altered and, again, the resulting rf voltage must be considered, as well as the circuit efficiency. A reduced load conductance raises Q L and reduces qc from (7). The rf voltage becomes too high (Fig. 2) for proper phasing of the electrons with the rf field and the electronic efficiency falls. Both effects reduce the power to the load. When the value of GL is increased, qc increases, with the result that the power in the load is raised until the reduced rf voltage makes the phasing inadequate. The reduced electronic efficiency then becomes the controlling factor. I n addition, for the average magnetron, the power in the load decreases, for too high a GL, because of losses in the output ~ o u p l i n g . ~ The use alone of the third fundamental method of amplitude modulation, that is, variation of the power reaching the load without altering the input or the power generated, remains to be considered. This can be done only by diverting power from the load without changing the loading on the magnetron. Section VI describes the electron coupler, a device for this purpose. 3. Frequency Modulation

The general procedure for frequency modulation can be seen by inspection of (2) or (5). The operating frequency, w , can be changed if the anode voltage is varied to alter Be. This utilizes the frequency pushing for frequency modulation. Again, if B, is changed (Be is not affected), the frequency changes. An external reactance tube in parallel with the load may be considered t o vary BL, or power injected from a second oscillator (Sec. VII) may be used to vary the susceptance of a fictitious load. Finally, a reactance change produced within the cavities of the magnetron (Sec. 11) alters w o and w , for constant Be and BL.

4 . Mixed Modulation Mixed modulation is so undesirable, and so difficult to avoid, that it merits special consideration. The most efficient method for amplitude modulation, variation of anode voltage, was suggested in the preceding paragraph as a means of frequency modulation. For proper amplitude modulation, the frequency changes must be minimized, a procedure discussed at length in Secs. VII and VIII. Altering GT or GL,t o vary G, and yield amplitude modulation, varies the frequency, since Be is a function of G,. The effect is rather small and can largely be removed (Sec. V) or controlled. The electron coupler (Sec. VI) and out-phase modulation (Sec. VII)

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J. S. DONAL, JR.

do not vary either the plate voltage or the Q's of the magnetron. These methods are, therefore, reasonably free of incidental frequency modulation. The injection magnetron (Sec. IX) is a special tube in which the anode current, rather than the anode voltage, is altered. Be and the frequency are varied to a smaller degree than is the case for plate modulation. Frequency modulation by variation of w 0 (Sec. 11) gives, theoretically, no change in amplitude. I n practice, a few per cent of amplitude modulation is found. Reactance section modulation (Sec. 111) may be considered to vary BL or to vary wo. In its present state of development, the associated amplitude modulation is often severe. Voltage tuning (Sec. IV) uses enhanced pushing to accomplish frequency modulation, but the large changes in amplitude that would normally be caused by the variation in plate voltage are much reduced by the abnormal operating conditions imposed on the magnetron. Frequency modulation by injection of power from a second source can give very small associated amplitude modulation. None of the modulation procedures described below is perfect, although they meet perhaps all but one of the desired performance characteristics. Four of the eight methods discussed have not been described in the literature at the time this is written, although in several cases papers are nearing publication. At least six of the procedures are still under development, in several instances by their originators. The methods, whether complete or not, are of such interest that they warrant a comparative review a t this time. 11. FREQUENCY MODULATION OR

CONTROL BY SPIRAL ELECTRON BEAMS This procedure5v6is analogous to mechanical tuning carried out either by changing the resonant frequency of the magnetron tank circuit or by changing the resonant frequency of a cavity tightly coupled t o the magnetron to alter the frequency of oscillation. The tuning is performed by electron beams positioned either in the resonant cavities of the magnetron or in an external cavity. The two major differences from mechanical tuning are ( a ) the frequency may be altered by only about 1 per cent and ( b ) the frequency may be varied at high rates by grid control of the current in the auxiliary beam or beams. There is virtually no loading introduced by the beams and, since the frequency change is small, there is no change in the electronic efficiency. The power output of the magnetron is thus unchanged. Free electrons, in an oscillating electromagnetic field, are caused to' oscihte and thus induce image currents on the surfaces of the field boundaries. Since these currents are proportional to the field amplitude,

M O D UL AT ION O F CONTINUOUS-WAVE MAGPU'ETRONS

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a linear admittance function can be set up and treated as a conventional circuit element in the proper equivalent circuit. The induced currents are not, in general, in phase with the field. The real p a r t of the electronic admittance represents a n energy transfer between the electrons and the field, and the imaginary part represents a change in the resonant frequency of the system. 1, Effect of Longitudinal Magnetic Field

The electrons are projected into the resonant structure in a direction perpendicular t o the oscillating rf field and parallel t o a constant magnetic

1

FIG.3. Electron position, induced current and phase of current.

field. The dc energy in the beam is dissipated a t a collector plate. The rf field causes a rotation of the electrons a t cyclotron frequency, so t h a t the induced currents due t o this rotation are in phase with the field only if the angular frequency of the field is equal t o Belm. The physical situation is illustrated in Fig. 3. The electrons are projected between the plates in the direction a-b. Suppose that w , the frequency of the field, E , is greater than w,, the cyclotron frequency. As the field builds up during the first half cycle, the electrons are accelerated toward one plate and begin t o describe a circle with angular frequency wC. The electron lags behind the field, however, and when the electron has reached position 2 and has attained a radius of r p the induced current, it, lags behind the field by the angle 6. A t the end of each succeeding

196

J . S. DONAL, JR.

revolution the electron has gained more energy and has increased its radius of rotation, with a consequent increase in the induced current, but the induced current lags the field by the additional angle, 4, per cycle. When the phase lag exceeds the 90 degrees of position 5 , the electron is retarded during each cycle, so that the radius and current decrease, but the phase lag continues to increase. Suppose all electrons are removed a t position 6. I n a continuous beam there are electrons a t all positions so that the total effectivecurrent is the vector sum I’ with a resistive and reactive component. This situation would yield both a frequency change and a loading. However, if the transit time is adjusted so that the electrons leave at position 8, there is no resistive component. The current lags the voltage by 90 degrees just as the current through an inductance lags the potential difference across it. If the plates of Fig. 3 formed a resonant circuit with an inductance, the additional parallel electronic inductive reactance would increase the resonant frequency. If w had been made less than wc, the effective current would have been found t o lead the field, E , and the frequency of a resonant circuit would be decreased. 2. Determination of Electronic Admitta.nce

Only a summary of the procedure of Smith and Shulmans can be given here. They solved the equations of motion, for the electfrons in the crossed fields, for the instantaneous velocity in the direction perpendicular t o the boundary planes. This permitted the evaluation of the current induced by a n oscillating element, of known axial velocity, of a beam of total current I,. Integration yielded the total induced current in terms of the rf field amplitude, Eo,the transit time, T, and the plateseparation, d, or e - sin e IeI lo (1 -e;os e I = E,--? m 2d + j 02 where

e

=

(w,-

W)T.

Since the electronic admittance is given by

the expression of r in terms of the length L of the plates and the beam voltage, Vo, gives

)

=

G,

+ jB,.

(10)

A plot Y eversus 8 is given in Fig. 4. For e = 0, corresponding to w e = w, there is no phase shift between the induced currents and the field, and a

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

197

pure conductance and loading is presented to. the circuit. For 0 = k2?r, corresponding to the removal of electrons a t position 8 of Fig. 3, Ye is purely reactive. This is the pure frequency modulation case, attained by proper adjustment of B , for a fixed w or transit time. For 0 = A n , the frequency change is a maximum but the loading (or amplitude modulation) may be too severe for some applications. I .C

.4

..

.:

c FIG.4. Electronic conductance and susceptance as a function of 0 .

3. Determination of the Frequency Change Due to the Guns

The resonant cavity and the beam passing through it may be assumed to have the equivalent circuit of Fig. 5, where the product of Co and the square of the rf voltage at the parallel plates containing the beam is the total stored energy in the circuit. The circuit susceptance is given by the usual approximation 2CaAw, where Aw is the change in the resonant angular frequency, wg, caused by the beam. Since this must be the

198

J. S. DONAL, JR.

negative of the imaginary portion of

(lo), A w is found to be

A @ = - L2 - - lo 1 sin 8 - 0

wvoco

AU is zero at e = 0 (Fig. 4). A t modulation is zero,

e

Aw(27r) =

e2

= + 2 ~ for ,

(11)

which value the amplitude

L2 I 0 1 8d2 Vo 2 ~ C o

--.

Equation (11) does not contain the rf field and, furthermore, it would appear that Aw can be increased without limit by decreasing d or by increasing the transit time, 7, a t constant 8 since r 2 is proportional to BEAM /

FIG.5. Equivalent circuit of resonant cavity and beam.

L * / V O . This is by no means the case, for if the spiral diameter exceeds d / 2 , electrons will be removed from the beam, causing a reduction in frequency change and the occurrence of loading. The maximum spiral radius is given by lrlmax =

e r

Eom w,8

(w #

4.

(13)

In addition to grazing, space charge must be considered, for IO in (11) is related to V o . Smith and Shulman have obtained a more general expression for the maximum fractional AU which is obtainable under

space-charge-limited conditions and without removal of electrons by the walls in the region of maximum spiral diameter:

Here, F is a factor introduced by Haeff (see Sec. V) and is roughly unity for most practical cases. C: is, in general, the interplate capacitance in the region subtended by the beam, and Co is the total effective system capacitance defined earlier. The value of rm.,=of (13) must be equal to 2d, and the emission from the cathode must be space-charge limited.

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

199

This expression is for a single beam. The total Aw/wo is proportional to the number of beams used. The reader is referred to the literature’ for an illuminating example of the practical use of equations (12) and (14).

4. Variations of

Aw with Changes in Parameters

From ( l l ) , if 0 is maintained constant by adjusting H , A w varies as V$*’”/V or as V s as long as the current is space-charge limited. From (13), there will be decreasing tendency for electrons t o graze the walls. If V o remains constant and I0 is varied by adjusting the grid bias, the frequency change zs linear with the beam current.

MAGNETRON VANES BEAM

FIG.6. Section of magnetron showing position of beams.

From (12) or (14) the Aw is limited by the obtainable cathode current density. A change in the type of cathode to remove this limitation would permit an increase in Vo, and (at constant 0) Aw would increase as I P . From (14), Aw is proportional to wo so that with a properly designed structure fewer guns need be placed in the tube as the carrier frequency is raised and space becomes limited. From (11) there is no variation with Eo, and hence with the power output of the magnetron as long as grazing does not occur. However, when a tube is scaled t o a higher power, the maximum obtainable Au varies as 1/V.. from (14) or as l/d&.This usually means that Aw varies inversely as the anode voltage when voltage scaling is employed. 6. Use of Spiral Beams in Practical Magnetrons The beams can, of course, be placed in external cavities coupled to the magnetron and this has been accomplished successfully in spite of the

200

J. S. DONAL, JR.

FIG.7 . Variation of frequency change with beam current.

FIG.8. Experimental variation of loading and A f with U ~ / W O .

MODULATION OF CONTINUOUS-WAVE MAGNETRONS

201

coupling problems arising from efforts to minimize the effects of the increased stored energy in the system. The presence of the desired rf and fixed magnetic fields makes it rather more natural to pass the beams through the cavities in a direction perpendicular to the plane of Fig. 6. A t least two such tubes have been developed and described in the literature. A 25-watt cw magnetron a t 4000 megacycles' yielded a frequency deviation of about 2.5 megacycles. Figure 7 shows the degree to which the Aw was linear with beam current while Fig. 8 shows the variation of loading and Aw with wc/wo where 0 G (wc - COO).. It is worth noting that Aw was not quite zero at 0 = 0, nor was the loading quite a maximum at 0 = 0. This tube employed two grid-controlled beams at 40 v and 10 ma per beam. A l-kw cw tube a t 900 megacycless gave a frequency deviation, a t the value of e for minimum loading, of about + 4 megacycles. At the low carrier frequency, nine guns were required, using 300 to 500 v at a current per gun of 100 ma. 6. Evaluation

+

One of the principal advantages of this method is its simplicity and reliability. Over a period of five years very few tube failures have been encountered. This was to be expected, for the electron guns can be elementary triode or tetrode structures using receiving-tube parts. The compensating disadvantage is the fact that the tubes seldom have had a frequency deviation greater than +0.5 per cent of the carrier frequency, although theoretically this could be increased substantially. The necessary modulating power is extremely low, since the grids of the guns are normally always negative and the capacitance to the other electrodes is low. Theoretically, the frequency deviation is independent of modulation rate up to tens of megacycles6since the beams are changing the resonant frequency of the cavity system. The loading is seldom zero at the t9 = 27 point, as predicted by theory. It is not severe, however. A decrease in power of perhaps 5 per cent may be expected in practice when the beams are biased on. The utility of spiral beams for frequency control of the magnetron should be emphasized. They offer an almost ideal means for controlling the frequency at any desired rate, using a signal derived by comparison of the magnetron frequency with a standard such as a resonant cavity or a crystal controlled oscillator. 111. FREQUENCY MODULATION BY ELECTRON CLOUDS

Split-anode magnetrons and similar structures have been frequency modulated by associated nonoscillating anode structures enclosed in the

202

3. 6. DONAL, JR.

same envelope. In this as yet unpublished work, carried on several years ago by the General Electric Company, an increase in anode voltage of the nonoscillating reactance section caused a space-charge cloud t o expand and present an increased capacitance. Since the reactance section was closely coupled t o the magnetron proper, the system frequency was decreased, in some cases by as much as 5 t o 8 per cent. The carrier frequencies used ranged from 400 to about 800 megacycles. A comprehensive study of frequency modulation by electron clouds has been carried on in the Electrical Engineering Department of the University of M i ~ h i g a n .The ~ ~ objectives ~ ~ ~ ~ ~of this work were the study of the properties of space-charge clouds and the use of the clouds to frequency modulate interdigital and multicavity magnetrons operating a t several thousand megacycles. 1. Hot-Resonance Studies of Magnetrons

In applying this ingenious technique, first suggested by W. G. Dow, the experimental procedure was much the same as that employed in conventional cold-resonance work, with the exceptions that the magnetron cathode was heated and plate voltages below that necessary for oscillation were applied. Measured values of unloaded Q, input conductance a t resonance, and resonant wavelength thus reflected the effects of the space charge upon the cold-resonance values. To choose a single example from the large body of data presented in the Michigan reports, Fig. 9 shows, for a driven magnetron, the variation of the resonant wavelength, XO, and anode current, with anode voltage. Three domains of anode voltage are of interest.12 The first of these extends from zero voltage to about 450 volts. I n this region the space-charge cloud is expanding without the formation of well-defined spokes of space charge. The angular velocity of the outer edge of the space-charge cloud is below that of the traveling electromagnetic wave on the anode. The space charge exhibits the bulk properties which will be shown t o be useful for frequency modulation. The second range of anode voltage extends from about 450 to 750 v. At about 450 v the boundary angular velocity of the space-charge cloud reaches synchronism with the traveling electromagnetic wave. Above this voltage the electrons, which normally move with an angular velocity above that for synchronism, are slowed and phased t o form spokes. The spokes of charge induce currents in the anode which are so phased with respect t o the potentials on the anode that the capacitance of the system and the resonant wavelength are increased. While the relative phase of the induced currents and the anode potential remains constant, the

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

203

spokes expand rapidly with anode voltage and the slope of the curve of Xo is increased, sometimes quite sharply. The third region of anode potential is above about 750 v. At this value the spokes reach the anode and there is a net delivery of power t o t,he rf field. The spoke starts t o advance in phase with respect t o the rf field and there is a n increasing component of induced current in phase

FIG.9.

Magnetron wavelength and current as a function of anode voltage.

with the field corresponding t o the increase in power delivered. The capacitive effect of the spokes decreases and the resonant wavelength decreases. This effect is the ordinary pushing of the magnetron, or change in operating frequency with current. 2. Bulk Efects of Space Charge

When a magnetron is t o be frequency modulated it is largely the bulk effects of the space charge in the nonoscillating reactance section which are of interest. These can alter the frequency in either direction, as will be shown below. If Xo is t o be decreased, the synchronous region of rapidly increasing XO must be avoided. If XO is to be increased the synchronous region of anode potential may be included in some cases, but anode current may be drawn by the reactance section and there may be severe loading.

204

J. S . DONAL, JR.

The propagation of waves in the magnetron space charge was considered for a number of different conditions of interest in this project. The problem was simplified by neglecting both the damping term and the effect of space variations in the steady state velocity and charge density distributions in the magnetron space-charge swarm. The effect of the steady magnetic field on the rf electron velocities, which was neglected in the analysis by Blewett and Ramo13 was taken into account. Propagation transverse and parallel t o the direction of the steady magnetic field was considered. Probably the most interesting conclusion is that in each case the propagation constant is double valued. For the case of propagation transverse t o the magnetic field, this corresponds t o polarization of the E vector either parallel or perpendicular t o the magnetic field. For the case of propagation parallel t o the field, the two values correspond t o right- and left-hand circular polarization. It is possible that the results of Welch are not valid a t frequencies near the cyclotron resonance, since damping cannot be neglected in this region. Lamb and Phillips1* have treated this case rigorously. Their result is in agreement with t h a t of Welch a t frequencies somewhat removed from the cyclotron resonance. The cyclotron resonance was not of major interest in this frequency modulation project. The results of the analysis for propagation in a direction transverse t o the direction of the static magnetic field are shown in Fig. 10 in the form of effective dielectric constant of the space-charge medium. The ratio of the radius of the cathode t o the radius of the space-charge cloud was assumed for simplicity t o be very much less than unity. The values of dielectric constant are plotted as a function of w,/wC, the ratio of the operating angular frequency t o the cyclotron angular frequency. The dotted curve is for a wave polarized parallel t o the static magnetic field, while the solid curves are obtained when the wave is polarized perpendicular t o the static magnetic field. The solid curves of Fig. 10 will be discussed, since the situation in the conventional magnetron interaction space geometry is best approximated by this case. When the dielectric constant, E , , is negative, the phase velocity is imaginary and a wave will not propagate within the space charge. When er is greater than unity, the phase velocity is less than the velocity of light, and capacitance between cathode and anode is increased by the space charge. When eV lies between zero and one, the phase velocity exceeds the velocity of light and the space charge d'ecreases the anode-cathode capacitance. The effect with cr negat>iveis usually the greatest, for the space-charge cloud acts like a n expanding metallic conductor as the anode voltage is increased. This produces a large increase in the resonant wavelength of the reactance section. From

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

205

Fig. 10, er is negative, and operation is carried out far from the perturbations found near the cyclotron frequency) when the ratio of the operating angular frequency t o the cyclotron angular frequency ( w f / w c ) is less than 0.36. This corresponds to a high magnetic field, well above that which could make the operating frequency equal t o the cyclotron frequency. The increase in Xo shown below 450 v in Fig. 9 is due t o a negative value of er. Welch and Brewer16have confirmed the predictions based upon Fig. 10 by hot-resonance measurements on a magnetron. The radius of the

FIG.10. Dielectric constant of magnetron space charge as a function of w ~ / w c .

space-charge cloud is constant for a constant ratio of anode voltage t o the square of the magnetic field. For a small value of E,/B2, B can be made quite high before oscillation starts, so that w f / w C can be made less than 0.36. As B is reduced, with E,/B2 maintained constant, E, is increasingly far from the values necessary for oscillation, SO that high values of w f / w e can be investigated. The experimental values of Xo varied with B in a manner to be expected from Fig. 10. 3. Experimental Applications

In general, two separate anode structures, within the same envelope and electrically connected) have been used for frequency modulation. One of the most successful forms of the tube, designed for a power output of about 500 watts at a wavelength of 13 cm, is shown in Fig. 11.16 The coaxial cavity was one-half wavelength long and loaded a t its two highvoltage points by vanes protruding from the outer conductor through slots in the center conductor. The cathodes of the two interdigital structures were held a t different dc potentials so that the potential of the modulator

206

J. S. DONAL, JR.

cathode could be varied. This resulted in a variation in the diameter of the space-charge cloud in the modulator section and, therefore, in the capacitance presented by this cloud. Low values of w , / w ~ were used so that the expanding cloud increased the resonant wavelength of the system. In order to obtain a useful change in capacitance it was necessary t o provide for a large increase in cloud diameter before the anode voltage attained a value resulting in oscillation of the modulator section. Welchg

FIG.11. Oscillating and modulating structures enclosed in a single envelope.

has shown that this end can be accomplished by using fewer anode segments in the modulator section without using impractically low ratios of anode to cathode radii. For a tube of the type shown in Fig. 11, the expected changes in the diameter of the modulator space-charge sheath were duplicated by metal cylinders inserted in a model of the tube. The results predicted a change in the operating frequency of about 2.5 per cent. In a tube oscillating a t 13 cm a change in anode voltage of the modulator section from zero to about 500 Y resulted in a frequency change of about 1 per cent.

4. Evaluation This work is still in progress and has not yet reached the point at which experimental measurements of frequency modulation have been

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

207

obtained in quantity. Several other tube structures are under investigation. The theoretical treatments in the reports already issued have in themselves been a contribution to the art. The method is potentially capable of producing very large frequency changes but, as the workers a t the University of Michigan have pointed out, there may be serious losses in the space charge which could result in associated amplitude modulation. In the experimental results so far obtained, some current has been drawn t o the modulator anodes. It will be necessary to obtain frequency modulation without drawing excessive anode current in order t o limit the required modulating power. IV. VOLTAGE TUNING

It will be remembered from the Introduction that the frequency of oscillation of a normal magnetron is determined by the susceptances of the electron stream, of t%e tank circuit, and of the effective load. The resonant frequency of the tank circuit is usually the determining factor as regards the frequency of operation, so that the latter varies a few per cent a t most from the cold-resonant frequency. Figure 9 illustrated this fact for a representative tube. After oscillation begins, the power output of a conventional tube increases very rapidly, while the frequency increases perhaps 1 per cent of the carrier frequency. It is well known that the pushing, or change of frequency with voltage or current, can be increased markedly by increasing the loading on the magnetron, but even under this condition the total increase in frequency, from the start of oscillation to maximum safe power output, is seldom more than a few per cent. Wilbur and Peters’? have found, however, that under certain special conditions the change in frequency with anode voltage may be as much as a factor of 4 t o 1. The effect was observed in split anode magnetrons and tubes of similar structure. The necessary conditions for “voltage tuning,” as the above effect has been called, are ( a ) extremely heavy loading of the magnetron and ( b ) cathode emission partially or completely temperature limited. With these limitations it would appear that the conditions in the electron stream, rather than resonance in the tank circuit, are the factors determining the frequency of operation. The pushing, in megacycles per volt, is several times that of conventional tubes. More important, however, is the fact that while a relatively small increase in voltage will draw a current resulting in the destruction of a conventional tube, under the conditions of voltage tuning the anode voltage may be increased several fold before dissipation limits are exceeded. The power output and efficiency are comparatively low, compared t o that expected for a magnetron of similar structure operated under normal conditions, particularly

208

J. S. DONAL, JR.

if it is desired t h a t the power output remain relatively constant in order t o avoid amplitude variations when the frequency is varied. 1. Experimental Results

All the results reported by Wilbur and Peters were obtained with magnetrons generally similar t o split anode or interdigital tubes, in which leads extending through the envelope wall permitted very heavy loading. The operating frequencies were in the range below 1000 megacycles. One group of tubes investigated had output powers from 10 to 200 watts. v)

5 V 2 0

W

I

750-

{ 160

650 700

I

$

600-

Z

3

0

1400

O 1600

1

' " 2000 2200 ANODE VOLTAGE

I800

'

~ 2400

~ 2600

0 ~

FIG.12. Voltage tuning of a 4-vane tropotron.

A s an example, the results obtained with a four-vane "tropotron" are shown in Fig. 12. Two different values of external loading are indicated by the subscripts L I and Lz. For the first loading (LI),in particular, the frequency was nearly doubled. The power output was a more sensitive function of loading than was the frequency variation. The power output was rather low in the range in which i t was reasonably independent of voltage. A large number of miniature magnetrons were tested by Wilbur and Peters. These split anode and interdigital tubes were capable of producing up t o 1 or 2 watts of output power when operated a t normal loading and with space-charge ,limited emission. With the heavy loading and temperature-limited emission required for voltage tuning, the power output was only a few milliwatts, but the frequency could be varied by

~

~

MODULATION OF CONTINUOUS-WAVE MAGNETRONS

factors of a t least four t o one. had a low noise factor.

209

The tubes were stable in operation and

2. Discussion of Voltage Tuning

I n spite of the reduced efficiency and power output of the tubes, voltage tuning may come t o be of very considerable importance as a means of obtaining frequency modulation. Certainly little is known a t this time of the mechanism behind the effect,and much further investigation will be required t o see if useful radiated power is obtainable under the required loading conditions. With the support of the Signal Corps, a comprehensive study of voltage tuning has been started at the University of Michigan. ‘ The object of the program is the development of useful voltage-tuned tubes at frequencies of several thousand megacycles. H. W. Welch, Jr., and his co-workers have pointed out12 several unusual properties of voltage tuning in addition to the heavy loading, low efficiency, and temperaturelimited emission noted above. For example, a t the very low Q used it is possible that Q’s of the same order in the transmission line t o the load will result in difficulties due to long line effect. Since the low Q must increase the circuit efficiency, the observed decrease in overall efficiency must be due to a marked decrease in electronic efficiency. The decrease in maximum-current boundary, usually associated with 1ow-Q operation, is not found under the conditions used for voltage tuning. Finally, voltage tuning is essentially the usual pushing enhanced by the heavy loading. The Michigan work has been initiated only recently and has SO far been devoted to a general study of pushing, current boundaries, 1ow-Q operation and space-charge theory of the magnetron. By assuming that the space-charge swarm is a modified constantcurrent generator and by considering the variation of the total conductance and susceptance of the tank circuit and load as a function of the change of frequency with plate voltage, it has already been possible to calculate a pushing characteristic in reasonable agreement with experimental results. The qualitative description of pushing is perhaps of more interest here. Between the voltage a t which the electron angular velocity becomes synchronous with the rotating electromagnetic wave and the voltage producing oscillation, the space-charge spokes expand in constant phase with respect to the wave on the anode. A spoke passes under an anode segment when the voltage on this segment is a maximum, but the current induced in the anode has already passed through a maximum and is zero a t this instant. The spoke thus contributes a loading current and increases the effective system capacitance,

210

J. S. DONAL, JR.

with a reduction in resonant frequency. As oscillation builds up, power must be contributed b y the electron stream. There must be a component of current in phase with the rf field. To accomplish this end, the spacecharge spokes advance in phase, and the induced current advances in phase with respect t o the rf field. This reduces the capacitative effect of the spokes and the resonant wavelength of the system decreases (Fig. 9) t o yield the usual pushing phenomenon. By application, t o the assumed space-charge distribution, of methods for calculating induced currents, i t is expected that this qualitative picture can be placed on a quantitative footing so that pushing under conditions of very heavy loading can be better understood. At the upper current boundary a magnetron either stops oscillating or shifts modes. It is rather strange that the effect does not appear to be unduly serious under the conditions of voltage tuning, although heavy loading reduces the boundary current in a tube operated under normal conditions. Welch has pointed out that the current boundary is affected by both cathode and space-charge limitations, by a space-charge density insufficient t o induce adequate current in the anode structure, b y transittime limitation of current through the spokes, and by inadequate phase focusing a t very high currents. Under normal operating conditions the maximum current is usually, but not always, increased by a n increase in cathode temperature. An explanation must be found for the elevated current boundary observed by the General Electric workers when the Q is low and the emission is limited. A tube has been constructed12 in which the resonant cavity is outside of a glass envelope containing a n interdigital anode structure. This will permit gross changes in the cavity and loading for a study of 1ow-Q operation. Fundamental studies of magnetron space charge, as a n aid t o a n understanding of voltage tuning, are being carried on with a diode magnetron, termed a “trajectron.” With this tube the electron trajectories in the space charge will be studied in a manner similar to that employed by Reverdin and Marton.lgab A beam of electrons will be passed through the diode in a n axial direction. Except for the axial velocity, the electrons in the beam may be expected t o have the same motion as electrons emitted from the cathode. Thus the beam displacement, observed on a fluorescent screen, should duplicate the radial motion of emitted electrons during the time of transit of the beam through the interaction space. S. Evaluation To date, voltage tuning has been restricted t o special types of tubes and t o low frequencies. It has not been demonstrated that power can

MODULATION OF CONTINUOUS-WAVE MAGNETRONS

211

be delivered t o a useful load without practical difficulties arising from long-line effects. The method is of such potential value, however, that i t merits the above description of the initial phase of the Michigan work on the subject. The problems that must be solved are interesting because they require a study of precisely those magnetron characteristics which are the most complex and, heretofore, the most neglected.

V. AMPLITUDEMODULATION USINGABSORPTION BY A SPIRAL ELECTRON BEAM The method for frequency modulation described in See. I1 used a beam of electrons projected through a resonant cavity which might be a cavity of the magnetron, for example. Equation (10) gave both components of the resulting electronic admittance in terms of e = ( B e / m - W ) T , and Fig. 4 showed that the conductance term, that producing a change in the Q of the resonant circuit, is a maximum a t e = 0 while the reactive effects vanish. A method of amplitude modulation by absorption has been developed which makes use of these properties of the spiral beam.20 Beams placed within a magnetron for purposes of frequency modulation could be used t o produce pure amplitude modulation. This is inadvisable for two reasons, however. First, the adjustment of 0 t o zero means that w = w,, or that the magnetic field applied t o the beams is that for which the carrier frequency is cyclotron frequency. Without a special structure, this same magnetic field is applied t o the magnetron, and it is too low for good efficiency in the case of most tubes. Secondly, absorption of power by the beams results in a higher value of GT in ( l ) , in a higher G,, and, usually, in a higher electronic efficiency. Thus, the power developed in the tube is increased, which tends t o cancel the power reduction in the load and t o reduce the range of amplitude modulation for a given change in beam current. For these reasons the absorption beam is placed in a n external cavity coupled t o the magnetron by means of a circuit described below. i. Attainable Electronic Conductance and Power Absorption Using (10) and Fig. 4 the electronic conductance presented by the beam a t 0 = 0 is L2 I0 G,(O) = - - * 8d2 Vo Since r

=

L/(2e/mVo)s6,the conductance may be written

G,(O)

=

e I. r2 - - . -. md2 4

212

J. S. DONAL, JR.

The form of the envelope of the beam for 0 = 0 is shown in Fig. 13. An instantaneous view would show the electrons lined up along the directrix of a cone or, in the practical case, forming a pencil beam the size of the cathode. Equations (15) and (16) are independent of the rf voltage between the plates, but if this is so high t h a t electrons strike the pole faces, r and G,(O) become functions of Vfi. The power absorbed is a function of Vrt under normal nongrazing conditions, for

P

1 v2 Vd2Ge = - . - . -L2 I 0 watts. 2 16 d2 Vo

=-

If Vrt and V o are both several hundred volts and L/d is about 5, values within the usual ranges employed, a n ampere of beam current will

BEAM AT ANY INSTANT

FIG.13. Envelope of a n absorption beam.

absorb several hundred watts. From (15), which is in practical units, an ampere of beam current a t a beam potential, Vo, of 1000 and L / d = 5 indicates a conductance of 0.003 mho. This is transformed by the loop coupling the external absorption tube t o the transmission line t o a much higher conductance presented t o the line. With the usual coupling loop the corresponding resistance presented t o the line would be a few ohms, so that the modulation possibilities are extremely good. The efficiency of absorption by electrons in a spiral beam can be considerably greater than is the case for a triode, for example. If each

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

2 13

of the N electrons per second in a beam absorbs a n energy of $mu2where v is the velocity of collection, i t can be shown that the energy absorbed by each electron is P I N and, using (17),

The energy absorbed by each electron in a triode is simply (V,,)e, but the term in brackets in (18) can be made substantially larger than unity. The absorption efficiency of the spiral beam is the higher of the two by this factor.

CATHODE

-T UT

POLE FACES OF L E N G T H " ~ ' FIG. 14. Placement of absorption-beam cathode.

Just as was the case for the frequency change in (11) and (12) of See. 11, L / d or T cannot be decreased indefinitely in (15) or (16), for collection of electrons will occur and G will not be a linear function of 10. I n the rf circuit t o be described, a t least, the fact that r becomes a variable after collection occurs results in a very poor modulation characteristic. The rotational energy absorbed by each electron, proportional t o wc2r2 may be used t o express the total power absorbed, and using (17) the maximum radius attained by the electrons, which determines the power absorbed, is

If the poles are spaced apart by d and the cathode is a strip of width t, rmaris limited t o $(d - t ) . (See Fig. 14.) The optimum design of the absorption tube is obtained by a series of simple approximations. One starts with a n rf voltage determined from circuit considerations, a maximum allowable cathode current density

214

J. S. DONAL, JR.

with an assumed pole spacing, pole length, and cathode size, and with the maximum allowable cathode current. The beam voltage is then calculated from relations such as those of Haeff.21 This gives the conductance or power absorbed, from (15) or (17), but the r,,, of (19) must be less than +(d - t ) . If r,,, can be increased, the length (and transit time) can be increased t o increase G, but if r,,, is too large, the length and the resulting G must be decreased. If the value of G calculated is unsatisfactory, the dimension of the cathode (if it is a strip) parallel t o the faces of the poles may be increased, the type of cathode may be changed or structures may be used in parallel.

FIG.1.5. RF circuit used for absorption modulation.

2. Example of a n RF Circuit for Magnetron Modulation Figure 15 shows a circuit which has been used for absorption modulation of a magnetron. It is basically the circuit used earlier by Parkerzz for absorption modulation with triodes. The power output of the magnetrons used n as found t o be closely proportional t o the conductance ( G L L ) , presented t o the tube, to a power u = 0.33. A 400-ohm shunt load prevented complete unloading of the magnetron and possible poor spectrum. The conductance, G,, presented by the absorption tube is the electronic conductance after transformation by the coupling loop. Keglecting losses and the shunt load, i t is obvious that with the absorption beam off the main transmission line is short circuited, which reduces the power in the load t o zero. The magnetron efficiency is reduced by reducing its loading. Conversely, a very high beam conductance would make GJIrvery lo\\ and would present oiily GL t o the magnetron. This would make the poner in the load a maximum. A straightforward circuit analysis yields the powers of Fig. 16, plotted in terms of their ratios t o the matched-load poncr output of the magnetron. From a krtou-ledge of the transformed beam conductance, as a function of beam current or control-grid voltage, the system performance can be determined.

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

215

3. Predicted Modulation Characteristics

Assuming a 400-ohm shunt load and a 50-ohm useful load it can be shown from a n analysis of the circuit of Fig. 15 th a t the rf voltage across the line outside the absorption tube would be (200P,,)55 where Po, is the matched load output of the magnetron, if a = 0, i.e., if there were no losses in the absorption tube with the beam cut off.' For a 1-kw magnetron, for example, such voltages would be expected to result in electron

a=& = ABSORPTION GL

TU B E CONDUCTANCE CONDUCTANCE OF U S E F U L L O A D

FIG.16. Variation of RF powers in absorption system.

collection since within the tube they are increased by the coupling coefficient. Theoretical modulation characteristics have been determined20 and are shown in Fig. 17. At low values of coupling coefficient and high values of Po, the undesirable dotted curves would be followed at low beam currents. Fortunately, the small losses in the absorption tube, corresponding t o a value of a (Fig. 16) of about 0.04, reduce the rf voltage and prevent electron collection a t the poles, although such losses reduce the maximum modulation factor to about 0.75.

4. A Developmental Absorption Modulation System I n a laboratory modulation system an 850-Mc 1-kw cw magnetron was amplitude modulated b y the tube and cavity shown in Fig. 18. T o provide easy replacement and experimental control of the cavity resonant frequency and the coupling t o the circuit of Fig. 15, the beam was enclosed in a glass capsule with wall coatings to provide pole faces. The necessary axial magnetic field was provided by a solenoidal magnet,

J. S. DONAL, JR.

216

FIG.17. Theoretical modulation characteristics. ABSORPTION T U B E

COLLECTOR W A L L COATING

A N T CAVITY

L I N E TO MAGNETRON AND A N T E N N A

FIG.18. View of absorption tube in its resonant cavity.

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

FIG.19. Photograph of developmental absorption modulation system.

217

2 18

J. S. DONAL, JR.

shown encased, in the photograph of the equipment of Fig. 19. The grid-controlled electron beam in the absorption tube was operated a t 600 v and about 150 ma. The maximum value of conductance developed by the beam was about 0.04 mho, corresponding to a value of a. of two in Fig. 16, so th a t the maximum power in the load was approximately 60 per cent of the matched-load power output of the magnetron. Actually, the power in the load was limited t o about 500 watts by failure of the glass walls of the absorption tube under the high rf voltages in the tube a t low beam currents, but this cause of failure could have been eliminated by building the tubes of a material having lower loss, such as a ceramic. With the magnetron used, the system efficiency was somewhat less than 40 per cent a t the peaks of the modulation cycle. The average efficiency during the modulation cycle was thus quite low, a n unfortunate property of all absorption modulation systems, although this low efficiency was partially compensated by the absence of the usual driver stages of a conventional system. The grid was a t all times negative, the grid swing was only about 15 v, and the grid capacitance was only a few micromicrofarads. The power delivered by the modulator t o its plate load was therefore less than 1 watt. The modulation bandwidth of the system was in excess of 10 megacycles. The depth of modulation attainable corresponded t o a modulation factor of 0.75 and there was excellent linearity of the rf voltage across the load as a function of grid voltage. The frequency stability of the system during modulation is of fundamental interest in a comparative study of methods of modulation. From the nature of the rf circuit of Fig. 15 the loading of the magnetron was changed during the modulation cycle, although this change was one of conductance only. As discussed in the Introduction, a change i n G, resulting from such a change in GL" causes a variation of Be and of the frequency. I n the absorption system, however, it was possible to introduce a very slight amount of reactance, by adjustment of the line lengths and magnetic field, so that the point of operation on the Rieke diagram followed a contour of constant frequency very closely. As a result the frequency varied less than +15 kc in 825 megacycles. This change could have been reduced further, and the average frequency could have been controlled, by a feedback ldop such as that described in Sec. VIII. 5. Evaluation The method meets all of the desired performance criteria for a n amplitude modulation system except that of high average efficiency

MODULATIOK O F CONTINUOUS-WAVE MAGSETRONS

219

during the modulation cycle. I n common with all absorption systems, this arrangement has poor efficiency. The small frequency change during the modulation cycle could be corrected by a feedback loop. The linearity, depth of modulation, and bandwidth are satisfactory. The output power required from the modulator is very low.

TI. AMPLITUDE AIODULATION BY J I E A N S COCPLER

O F THE

ELECTRON

The spiral-beam absorption tube of Sec. V varied the load on the oscillator slightly and, as a result, caused a small amount of frequency modulation during the modulation cycle. While the frequency change U H F POWER SOURCE

ELECTRON COUPLER

FIG.20. Basic schematic diagram for use of coupler.

was only 15 kc, this variation would produce a large phase modulation a t low frequencies and would require a further control mechanism, such as a feedback loop, for some applications. The electron ~ o u p l e r , on ~~~*~ the other hand, is a device which provides variation of the power in the useful load with no change in the load presented to the oscillator and, hence, no change in frequency. I n principle, the electron coupler absorbs a constant amount of energy from the oscillator and transfers this energy t o a second circuit in which the energy can be dissipated or sent t o the load without any reaction on the primary circuit. The basic block diagram is shown in Fig. 20. I n practice, a resonant cavity forms the only load on a magnetron, and a constunt-current spiral beam traverses this cavity t o absorb a constant amount of power. A longitudinal magnetic field makes the cyclotron frequency of rotation of electrons in the beam equal t o the resonant frequency of the resonant cavity (and equal t o the oscillator frequency) precisely as in the case of the absorption tube of Sec. V. Instead of dissipating the energy a t a collector plate, however, the beam passes through a n aperture into a second resonant cavity shown in

220

J . S. DONAL, JR.

Fig. 21, tuned to the frequency of the oscillator. The beam excites this second cavity and gives up all or a controllable portion of its energy. The energy given up is transferred t o the load; the energy retained by the beam is dissipated a t a collector plate beyond the output cavity. The modulation is thus by absorption and results in a low average efficiency during the modulation cycle as was the case for the system of Sec. IT. Equations (1.5) and (16) for the determination of the electronic conductance of the absorption beam are applicable t o the coupler. This conductance is transformed by the loop coupling the input cavity of the electron coupler t o the transmission line and, if the line is matched, forms OUTPUT RESONANT CAVITY I N P U T RESONANT CAVITY

COLLECTOR

ELECTRON GUN

FIG.21. Internal structure of electron coupler.

the load presented to the output of the magnetron. Since the input cavity of the coupler is heavily loaded by the electron beam, it is necessary only that the load presented to the magnetron be constant. I t is usually most convenient t o match the coupler t o the line, however, for othernise the magnetron load would be a function of the transmission line length. The design criteria for the beam and input cavity of the electron coupler are the same as those of Sec. II-. I t is particularly important that electrons are not collected a t the pole faces, since such collection reduces the power remaining in the beam and the power available in the output cavity. 1. Behavior of the Beam in the Output Cavity of the Coupler The resonant cavitics used in the coupler were cylindrical, with the pole faces mounted on extensions from the walls as shown in Fig. 21. I n practice the second cavity was rotated 90 degrees with respect t o the

MODULATION O F COSTINUOUS-TVAVE MAGSETRONS

22 1

input cavity t o minimize coupling between the cavities. X s a result, there was no detectable power in the output cavity when the beam 11-as turned off and no evidence that conditions in the output cavity affected the input cavity. The cone-directrix beam in the first cavity becomes the element of a cylinder in the field-free space between the cavities and ~ r o u l dcontinue as an element of a cylinder through the second cavity if there were no rf fields there. If the output cavity were driven 180 degrees out of phase (neglecting the 90-degree physical rotation of the structure) with the rf voltages in the input cavity, the beam would be collapsed. Actually, the rotating electrons of the beam induce currents in the output cavity which, in turn, produce rf voltages which are 180 degrees out of phase with those in the input cavity (again neglecting the 90-degree physical rotation) and the spiral beam collapses and gives up its energy t o the cavity. I n the special case of identical geometries, beam voltages and rf fields in the two cavities, the envelopes of the spiral beams would be identical except for inversion of the second cone. All the energy absorbed in the first cavity would be transferred t o the second. Only the dc energy of the beam, attained before it enters the first cavity, would be dissipated a t the collector. If the transit time in the second cavity were decreased, by increasing the beam voltage, the beam would fail t o collapse and energy would be left t o be dissipated a t the collector. An increase in transit time would cause the beam t o collapse, giving up its energy, but i t would then reabsorb energy again from the fields in the cavity and dissipate this portion a t the collector. It can be shown that a n increase in the loading of the output cavity by the useful load produces the same effect upon the beam as does a decrease in transit time, and vice versa. C u c ~ i a has * ~ solved the equations of motion for the electrons in the second cavity (Region 111 of Fig. 22) for the components of velocity and displacement in the plane perpendicular t o the pole faces. These are as follows: 1 -lel [(E1rl- E 3 ~ 3 ) ] /?&I = W,TO - -2 le' E3r3 = m 2m

where w,ro is the angular velocity a t the entrance to the second cavity, wC is the cyclotron angular frequency and the symbols E and r indicate the rf fields and the transit times in the respective regions. Both velocity and displacement are zero when

222

J. S. DONAL, JR.

If lr is the length of the poles in the input cavity, the distance into the

w

a

El

z 0 W

W

a d

FIG.22.

Envelopes of Electron Trajectories.

pole-face region of the output cavity at which convergence occurs is given by

where the values of V are the beam voltages in the respective cavities. 6. Modulation of the Power in the Load

Several points of beam convergence in the output cavity are shown in Fig. 22. Suppose that the lengths of the poles and the beam voltages

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

223

are equal in the two cavities It can be shown that the rf fields will be equal, and convergence will take place at the exit of the pole faces in the secondary cavity if the load resistance, transformed into the tube and presented to the beam, is given by

Variation of the beam voltage in the second cavity only, to alter the transit time there, will shift the convergence point as predicted by (22). If the beam voltage is reduced to give-convergence at I , (Fig. 22),.the power given up will be reabsorbed and dissipated at the collector, for the power content of the beam is proportional to the square of its radius of rotation and the exit and entrance radii are equal. Modulation by increase of transit time encounters space-charge limitations and instabilities, however, and an increase of beam voltage is preferable. If the convergence is moved to l d , for example, or to a point twice the poleface length from the entrance, one-quarter of the power originally in the beam remains to be dissipated while three-fourths of the original power has been extracted and transferred to the useful load. Modulation by decrease in transit time is, of course, preferable to modulation of the current by varying the potential of the control grid of the gun, for such modulation would result in a large change in the loading on the oscillator and in a very large change in the system frequency. 3. Construction a.nd Performance of a Typical Coupler A photograph of a typical coupler for use a t 825 megacycles is shown in Fig. 23. The diameter of the structure is about 4 in. Tuning of each cavity is accomplished by varying, through bellows, capacities in shunt with the poles. The tuners and the seals closing off the coaxial lines are in planes 90 degrees apart because of the rotation of the poles mentioned earlier. The grid-controlled electron gun provides about 100 ma of beam current at about 500 v. The collector plate forming the top of the envelope is water cooled to dissipate the dc power of the beam plus rf power not transferred to the load. The rf power output of the experimental tubes was from 50 to 70 per cent of the rf input. The principal cause of the loss was probably dispersion of the beam and loss of outer electrons a t the pole faces of the input cavity. In the 800-900 megacycle range, the peak power in the load was about one-half kilowatt, limited by the oscillator used and the transfer efficiency of the coupler rather than by the power handling capability of the beam. A modulation characteristic is shown in Fig. 24. The available

I

0

~

"

N 0

"

b

"

"

0 m

'

0

m

PERCENT OF MAXIMUM VOLTAGE APPEARING ACROSS OUTPUT LOAD 0

-

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

225

modulation factor approaches 100 per cent in voltage. The linearity is not particularly good and the modulation voltage is high, although no current need be handled by the modulator, for the electrons are collected at an electrode, held at a constant potential, beyond the cavity. Those determinations of bandwidth made so far indicate merely t h a t i t is in excess of 5 megacycles. There was no measurable change in the system frequency during the modulation cycle. 4. Evaluation The most important advantage of the electron coupler is the elimination of changes of loading on the oscillator, with consequent changes in system frequency, as the power in the load is altered. Methods of modulation which require less modulating voltage and provide better linearity are under investigation. The most obvious disadvantage of the method lies in the fact t h a t it is an absorption system with the characteristic low average efficiency over the modulation cycle. The efficiency is further reduced by the transfer efficiency of the coupler. Since the frequency of the magnetron can be stabilized, against variations caused by changes in temperature or voltage, by the inclusion of frequency control guns and very simple circuits, the electron coupler should be useful in systems in which frequency stability is more important than efficiency. Of course the oscillator t o be modulated need not be a magnetron. I n considering spiral beams for handling power at higher frequencies, it should be remembered that for the same spiral radius the power absorbed by the beam varies as the square of the frequency. VII. CONTROL OR MODULATION BY INJECTION PHASE LOCKING Locking or synchronization of conventional oscillators has been studied by a number of workers. The term locking implies that not only are the frequencies of the locking and controlled oscillators the same but there is also a definite phase relationship between the rf voltages. From what has been said concerning the low inherent stability of self-excited oscillators, the locking of such oscillators t o a stable control oscillator js of obvious importance in the microwave field. E. E. Davidz5rz6J78-b has described a method for the phase control of microwave tubes which utilizes the injection of power via the output circuit of the oscillator t o be controlled. I n addition t o frequency stabilization, this procedure permits phase or frequency modulation or, using two oscillators, amplitude modulation by variation of their relative phases. The general phase-control characteristics of the system are as follows.

226

J.

S.

DONAL, JR.

If the frequency of an uncontrolled oscillator is modulated by an amount independent of modulation frequency, the rf phase modulation is inversely proportional to the modulation frequency. In the case of the phaselocked oscillator, however, the phase modulation is independent of modulation frequency up to perhaps 10 kc. Therefore, the frequency deviation of the locked oscillator is proportional to modulation frequency up to perhaps 10 kc. At modulation rates much above the audio range, the locked phase modulation decreases, as will be seen in greater detail below. For a constant-phase deviation, it is obvious that a t modulation frequencies approaching zero, the locked frequency deviation approaches zero. 1. Phase Locking under Static Conditions David has described the operation of the injection-locking system by reference to the chart giving the frequency and power output of the magnetron or klystron t o be controlled as a function of the magnitude

FIQ.25. Schematic Diagram of Injection Locking System.

and phase of the reflection coefficient. Suppose the oscillator delivers power to a matched load, i.e., the reflection coefficient, p, is zero. If the oscillator frequency, w’, is altered by a change in its dc conditions, it is obvious that a change in loading could correct the frequency change. The injected locking power performs this function automatically. Thus it is found that a strong injected signal of frequency w 1 causes the oscillator to assume the frequency w1 and t o ‘(track” until w 1 - LO’ becomes too great, at which point the lock is broken. The point of operation of the oscillator shifts, in general, to a new power output and to a point on the frequency contour wl. The locking power appears as if reflected from a load and the magnitude and phase of the resulting reflection coefficient uniquely specify the new power and the new frequency, WI. The simplified locking circuit is shown in Fig. 25. It is assumed that the locking power, P,, propagates only toward the controlled oscillator 0, that none of the output of 0 reaches the locking oscillator, OL,and that the frequency, phase and amplitude of the voltage of O L are independent variables. If PI is the total power going to the right in the line from the locked oscillator and lpl is the magnitude of the reflection coeEcieni,

MODULATION O F CONTINUOCS-WAVE MAGNETRONS

PL

227 (24)

= lPl2PI.

From (24) and the fact t h a t Po, the power output of the oscillator as specified on the reflection coefficient chart, must be zero when lpl = 1, we have Po = PI - P,. (25)

a. Graphical Treatment. If the locking power is held constant, as is usually the case, the oscillator must see a fictitious load which changes

-3162 FREQUENCY (MC)

FIG.26. Rieke diagram of velocity modulation tube.

with frequency in such a manner that the reflected power is constant. The contours of constant locking power, or loci of points of operation of the oscillator with the locking power constant, may be calculated from (24) and (25). Figure 26 is the chart of a klystron in the reflection coefficient plane. If a point such as -4 is chosen, a t a Po of 14 mw and with a IpI of 0.6, (24) and ( 2 5 ) yield a value of PL of 7.8 mw. A number of such calculations permit the contours of constant locking power of Fig. 27 t o be constructed. The value of PL calculated as a n example is shown a t point B. It is interesting that point A' of Fig. 26, on the 10-mw contour gives a value of PL of 12.7 mw, or a value of P L larger than Po.

228

J. S. DONAL, JR.

The oscillator must operate a t a point on the contour of known PI,, specifically a t the intersection of this contour with the frequency contour corresponding t o the locking frequency. If there is no such intersection the osciiiator will not be locked a t this frequency. Figure 28 shows the locking contours superimposed on the frequency contours of Fig. 26. The dots a t the points of targency are the breakout points. It is to be noted particularly that less locking power is required for control of the oscillator over a smaller range. David’s experimental contours were in 180.

FIG.2’7. Contours of constant locking power.

escellent agreenient with the theoretical contours, as mere the experimentally determined frequeiicies a t which the lock was broken. Since the locking contours intersect each frequency contour twice there 11-ould appear t o be two possible values of power output for each frequency but it has been shown t h a t the stable points are those only on the portions of the contours which are concave upward in the figures. Since the contours of constant PL can be closely approximated by circles for small P L , a rapid means for computing the synchronized behavior of an oscillator is available. b. A n a l y t i c a l E x p r e s s i o n for the Locking R a n y c . Only the case of operation into a matched load, before the application of the locking

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

229

signal, is considered here and in ( a ) , above. Pitts and Wickszs have analyzed the mismatched load case. SlaterZ9has shown that for GL = I and B L = 0 (normalized valu&) the complete normalized load admittance is given by y L = 1 - ~[,,[~~[(wI-o)c+BI = 1 - 2[,,[@" (26) The second form holds for the locked condition in which w1 = W , where w is the instantaneous frequency of the oscillator. I n ( 2 6 ) , Ipl is the reflec-

- - - - REFLECTED

OR LOCKING F R E Q U E N C Y (MC)

POWER(MW)

FIG.28. Locking contours superimposed on frequency contours.

tion coefficient of the apparent load and 6 is both the phase of the reflection coefficient and the phase difference between the locked and locking oscillators. If this value of Y Lis substituted in the ordinary expression for the condition for oscillation [see (4)and ( 5 ) of the Introduction] with GL = 1 and BL = 0,

230

J. S. DONAL, JR.

A comparison with the corresponding expressions for a n ordinary matched load shows t h a t the locking signal adds the last term in each expression. These are the load conductance and susceptance introduced by the locking signal. If 1pI is set equal t o zero in (as), t o give the matched load condition, u1 becomes u’, the matched-load angular frequency, or (29) Combining this with (28),

If lpI is assumed t o be constant ( P Lsmall), w 1 - w’ is a maximum when sin 0 = k 1, giving the basic expression relating the static locking range and the system parameters

This locking range is consistent with the tangency condition on the locking range of Fig. 28 for the assumed small values of IpI. The equality of the phase of the reflection coefficient with the phase difference between the two oscillators is now obvious, as well. I n addition, (31) permits (with 24) the calculation of the required locking power for a desired locking range. 2. Frequency Control of Modulated Oscillators The static case, treated above, is of interest for the adjustment of the oscillator frequency or for stabilization of this frequency against, very slow changes such as those caused by variations in temperature of the oscillator. Often, however, it is desired t o stabilize the frequency against power pack hum or, a most important case, against changes in frequency resulting from deliberate voltage changes incident t o plate modulation. An entirely different situation would arise if the oscillator were t o be frequency stabilized against slow frequency changes but phase or frequency modulated in addition. All these cases require a knowledge of the phase deviations of the locked oscillator. From these the frequency deviations can be determined, for +_Af

=

fm(+AO),

(32)

where Af and A0 are the amplitudes of the frequency and phase deviations, respectively. From (30), the phase angle, 0, between the two oscillators is given by

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

23 1

It is assumed that, as a contour of constant locking power is traversed, PO is constant, a reasonable assumption as may be seen from Fig. 28. IpI is then constant. The phase angle between the oscillators, or the phase angle of the locked oscillator if the phase of the locking oscillator is held constant, is a function only of the free-running frequency, w'. Since it will simplify the discussion if e is varied symmetrically about its zero value, changes in 0 will be assumed to be small so that sin 0 can be replaced by 0. An equal purpose would be served by assuming that W' varies in such a manner as t o produce a linear variation in 8. I n either STABILIZED KLYSTRON

-

PHASE SENSITIVE .DETECTOR OSCILLOSCOPE

MAGNETRON

FIG.29. Practical injection-locking circuit.

case e is sinusoidally modulated by sine-wave modulation of w' with a deviation A d . As long as the amplitude of the phase deviation A0 is constant, Af is proportional t o the modulation rate from (32). a,. Variation of Phase Modulation with Static Phase Diference. The phase modulation for a given Aw' is not constant over the static locking range. David shows that if the phase deviation, AO, is small, a deviation, Aw', of the free running frequency results in a phase deviation

Thus, A 0 is a function of 0 and rises from a minimum at w1 = w', or e = 0, to a very high value near the breakout point, e = -190'. This is of importance when the oscillator is to be stabilized to give a minimum phase or frequency deviation. b. In,jection Locking for Automatic Frequency Control. A practical injection circuit is shown in Fig. 29. A directional coupler with an attenuation of about 10 db was used to direct the major portion of the magnetron power to the useful load. This means, however, that 90 per cent of the locking power was dissipated and only 10 per cent was

232

J. S. DONAL, JR.

directed toward the magnetron, although this is not necessarily a permanent limitation of the system. The stabilization fa.ctor, H , of the control system is defined as the ratio of the unlocked frequency deviation t o the locked frequency deviation. This can be shown t o be

The stabilization factor increases as the square root of the locking power and varies inversely as urn,which follows, of course, from (32) if A0 is independent of urn. For slow changes such as temperature variations the locked frequency deviations are limited only by the stability of the control oscillator, since am.in t h a t case would be very small.

FIG.30. Vector diagrams of out-phase amplitude modulation

As a n example, for a 300-Mc tube with a n external Q of 3000 and with a IpI of 0.1, H would be 8 X lo3 at a 120-cycle hum frequency. H would decrease t o 8, however, a t frn = 120 kc. Equation (35) holds only for H much greater than unity, or, for the example chosen, for fm < < lo6. A t higher frequencies the phase is unable t o change sufficiently rapidly and i t would appear that an increase in H is t o be expected. Since the phase cannot keep up with the variation in w', neither (33) nor (34) hold a t high modulation rates. 3. Out-Phase Modulation

Out-phase modulation is a procedure for obtaining amplitude modulation, familiar in the literature of conventional tubes. The relative rf phase of two oscillators is varied in such a manner that when the voltages from the two oscillators are in phase a t the reference plane, the total power goes t o the useful load, but when the rf voltages are 180 degrees out of phase, all the power is dissipated and the power in the load is zero. Use of injection locking t o accomplish this end was suggested by E. E. David and tested experimentally by W. P. S ~ h n e i d e r . ~ The ~ system vectorial relationships are shown in Fig. 30. The two portions of the figure represent the two halves of the modulation cycle. The vectors

MODULATION OF CONTINUOUS-WAVE MAGNETRONS

233

W , represent the carrier voltage of the control oscillator, the two portions of the vector indicating that this voltage is inverted in phase as presented t o one of the two controlled klystrons. Elf, and Erf,are the vectors representing the carrier voltages of the controlled klystrons, while el and 0 2 are the rf phase differences between the locking oscillator and the controlled oscillators. I n the unmodulated condition both klystron oscillators are in phase with the locking source. The repeller voltages were then modulated in push-pull t o advance the phase of one oscillator and retard that of the other. Here the inverse sinusoidal variation of e given in (33) is most useful, because the total rf voltage is proportional t o sin 8 and, hence, linear with variations in the free-running frequency w'. It is necessary t o choose two oscillators of equal output and equal linear variations of free-running frequency with repeller voltage. Furthermore, this frequency must not vary with temperature, or the unmodulated phase relationships will be disturbed. With the modulation shown in Fig. 30 only the amplitude modulation sidebands are supplied. If the unmodulated phase difference between the two oscillators were made 90 degrees and each oscillator were modulated +45 degrees, the carrier would be supplied. The modulation characteristic would no longer be inherently linear, however. Schneider's experimental results were excellent, although the particular circuit used required a total locking power greater than the output power of the oscillators. The minimum power in the load was 30 d b below the maximum power and the linearity in the audio frequency range was almost perfect. The carrier frequency was 9200 megacycles. Both David and Schneider considered the bandwith a t some length. Present theory is adequate only for low modulation factors, where sin 0 may be replaced by 8, with the limit on Aw' placed by Schneider a t 0.7 [Iplwo/(QeXt)o]. Under these conditions the rf amplitude is down 3 db a t

Thus for a 3000-Mc tube with = 300 and IpI = 0.1, the response would be down 3 db at f m = 1 megacycle. Under the condition of higher carrier frequency and greater IpI used in Schneider's experimental work the conventional bandwidth was both calculated and measured t o be about 3 megacycles. It is interesting that the expected value of fm for a decrease in response by 3 d b is IpI times the total rf bandwidth expected from the ratio w/&. While the bandwidth has been determined for only small modulation factors, it may well be roughly the same for deeper modulation. Preemphasis should be quite practical for the improvement of bandwidth.

234

J. S. DONAL, J R .

4. Evaluation As a method of frequency control of magnetrons, injection locking offers the advantage t h a t no frequency-control guns are required. However, the locking power may be rather large if a wide locking range or a high stabilization factor is desired. The stabilization factor, H , has not been measured at high modulation r a t p and, simultaneously, high modulation depths, nor can i t be calculated from existing theory. This theory, applicable t o either the frequency control or t o out-phase modulation, predicts a n increase in H at high rates provided the modulation factor is kept low. If phase control by injection is used t o produce out-phase amplitude modulation, the overall efficiency is low; the arrangement is effectively a n absorption system since the input t o the oscillators is constant. This may not be a serious disadvantage for low-power systems. The available modulation factor is extremely high, approaching unity, and the linearity is intrinsically good. Any spurious frequency modulation is probably associated with second-order nonlinearities arising from assymmetries. The bandwidth is as yet little understood when the modulation factor is high, but i t appears t o be limited a t low modulation factors t o a value considerably less than that determined by the loaded Q of the oscillator. Pre-emphasis should be effective for improving the response. This method is in a n early stage of development, and it is highly probable t h a t some of its limitations will be removed. I n particular, i t should be possible t o reduce or t o eliminate the loss of locking power resulting from the use of the directional coupler of Fig. 29. VIII. AMPLITUDE MODULATION BY PLATEMODULATION OF

MAGNETRON WITH

A

SIMULTANEOUS FREQUENCY c O N T R O L 3 1 * 3 2

Amplitude modulation by the spiral-beam absorption tube (Sec. V), by the coupler (Sec. VI), and by out-phase modulation (Sec. VII) are all absorption methods, in that the input remains constant while the power output is varied. The average efficiency during the modulation cycle is low for all these procedures, a consideration which is particularly import a n t in high-power systems. Plate modulation of a magnetron, on the other hand, would yield much higher efficiency, but it has been believed that the characteristics of such a system would be poor with regard t o linearity, bandwidth, attainable depth of modulation and, in particular, frequency stability. I n the last case, the pushing during the modulation cycle would be expected t o give an intolerable amount of mixed frequency modulation. However, the simplicity and high efficiency of a platemodulation system warranted serious consideration of the method,

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

235

particularly since frequency control by spiral beams (Sec. 11) offered a means for the automatic stabilization of the frequency. In considering the stabilization of a magnetron it is not always obvious whether one should use a phase-control or a frequency-control system. The first yields, ideally, a controlled phase deviation which is independent of modulation rate, while in the second case the frequency deviation should be independent of rate. Since A0 = Af/fm, the phase control system gives a vanishingly small frequency deviation as the modulation rate is reduced to zero and, since the carrier frequency of any system must be extremely stable, the phase control system might be preferred. While there is evidence that frequency modulation can under certain circumstances cause severe mhltipath effects, such frequency modulation is usually of the constant deviation type with very large phase modulation a t low frequencies, again pointing to phase control as the better choice for use with amplitude modulation for television applications. Both phase and frequency control will be considered here, with greater emphasis on the first because of the high carrier stability it affords. While the frequency control may be of interest independently, it will be treated largely as a means of improving the phase control. The modulation characteristics to be expected from plate modulation will be considered first, followed by a description of the methods of stabilization. 1. Performance of a Plate-Modulated Magnetron The tube employed was the developmental 1 kw cw tube described in Sec. 11. The carrier frequency in this work was 825 megacycles. The magnetron was equipped with either nine or eleven internal frequencycontrol beams with a total beam current of about 1 amp at 500 v. The total range of frequency control available with this tube was 6 or 7 megacycles. A schematic diagram of the modulation system is shown in Fig. 31. The magnetron anode is grounded so that the rf lines may be a t ground potential. The modulator output stage is in series with the “plate” supply and serves as a variable impedance for control of the potential on the magnetron cathode. Thus when the drop across the modulator is increased from 200 to 400 v, the magnetron cathode-anode potential difference is decreased by 200 v. The phase-control signal, described below, is applied to the grids of the control guns in parallel with a frequency-compensation signal derived directly from the modulator chain. a. Modulation Factor. The modulation factor is defined as the difference between the minimum and maximum amplitudes of the modulation envelope divided by twice the carrier amplitude. It is

236

J. S. DONAL, JR.

important t h a t this factor be high if intelligence is t o be transmitted without waste of carrier power and production of interference. For example, in television practice the modulation factor is approximately 0.75, corresponding t o a minimum power of about 2 per cent of the peak power. Magnetron mode shifts a t high currents limit the peak power and, with this upper limit fixed, low-current discontinuities in power or frequency determine the available modulation factor. With the cw tubes used, the upper mode shift never occurred below 2.5 kw. The lowMAGNETRON

TO

T O PHASE-CONTROL

MAGNETRON HEATER AND

FIG.31.

Block diagram of magrletron plate modulation.

current discontinuities often occurred a t 60 t o 100 watts output statically but dynamically the power could be reduced smoothly t o 30 t o 40 watts. The available modulation factor was thus 0.75 or more. b. Modulation Linearity. Since the dynamic impedance of a magnetron is low the power output is a linear function of the current t o a first approximation. Because of a n efficiency rising with current and the slight increase in voltage, the rf power output varied, with these tubes, approximately a ,t':i or the rf voltage across the load varied as ia35. Since the current in magnetrons is roughly linear with change in voltage, this is by no means the desired characteristic of rf voltage linear with applied voltage. However, the current in the magnetron, which is the load for the tetrode modulator output stage, varied as the three-halves power of the modulator input, so that the rf voltage was linear with the grid voltage of the modulator. A typical linearity characteristic is shown in Fig. 32. The rf voltage across the load is plotted vertically,

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

237

and the grid drive is plotted horizontally. The required peak to peak modulating voltage at the magnetron cathode is 200 to 250 v. RF voltage versus anode voltage characteristics of magnetrons usually show deviations from smooth curves due to slight changes in the magnetron impedance. It is most important from a practical standpoint that the modulator used by insensitive to these impedance changes so that deviations from linearity will not occur in the overall characteristic. c. Amplitude Modulation Bmdwidlh. As might be expected, the frequency response of the amplitude modulation is roughly that to be expected from the loaded Q of the tube. The loaded Q of these tubes

FIG.32.

Oscilloscope presentation of modulation characteristic.

was slightly in excess of 100, and at 825 megacycles the response was down the conventional 3 db at a modulation rate somewhat less than 4 megacycles. The response curve deviates somewhat from that of a single RC circuit. d. Cho.racteristics of the Frequency-Control Beams. These characteristics have an important bearing on the operation of the phase of frequency-control systems. It is obvious, for example, that the total frequency-control range of the beams must exceed the pushing during the modulation cycle. The frequency change must be independent of modulation rate over a wide range of rates. Theoretically, the bandwidth should be in excess of 100 megacycles under the conditions employed (Sec. 11). The small amount of loading actually mixed with the frequency modulation, even at the magnetic field for which such loading should disappear, makes experimental determinations of bandwidth difficult and inaccurate, due to the unknown phase relationships between the frequency and amplitude modulations. It may be said that the bandwidth of the beams is certainly in excess of 5 megacycles and may approach the theoretical value.

238

J. S. DONAL, JR.

The frequency change due t o the beams is roughly proportional t o beam current and, therefore, t o the three-halves power of the controlgrid voltage. The megacycles per volt yielded by the beams is therefore a function of the average bias and of the amplitude of the correcting signal a t the grid. e. Pushing. The frequency change during the modulation cycle, to be corrected by the control systems, was about 6 megacycles for a modulation factor of 0.75 and a peak power of 2.5 kw. The frequency change per unit change in current was much less above the mid-current range than below this range. Figure 33 shows a curve of frequency

u $

3

0

U

z

-I

W

3

0 W

a -2

Lr

z

0

= -3 W

z

20 -4 w

>

c d

i

mJ

a

-5

0

2

6

8

P R O P O R T I O N A T E R - F VOLTAGE

FIG.33.

10 ACROSS

12

14

THE LOAD

Magnetron frequency versus RF output.

versus rf voltage across the load. It is obvious that if the pushing is t o be minimized while maintaining the modulation factor constant the tube should be operated at the highest practical peak power. Pushing decreases rapidly as the load is mismatched t o the line in such a direction as t o decrease the magnetron loading. This is t o be expected from the increased stability a t the higher loaded Q. The decrease in pushing in the high-current range is relatively greater than for the low-current range. An interesting observation is t h a t any residual loading by the control beams reduces the Q and increases the pushing. When the correcting signal on the guns is varied as the tube is modulated, the Q and pushing vary slightly during the modulation cycle, an effect which should be taken into account in designing the frequency control system.

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

239

6. Phase-Control System

The method of phase control was largely the development of D. S. Bond and D. G. Moore.32 A schematic diagram of the circuit is shown in Fig. 34. About 0.1 watt a t 825 megacycles, derived from a crystal controlled oscillator, and about 1 watt from the magnetron are supplied to the input terminals of a phase-comparison system which is a balanced modulator consisting of a diplexer, 3 3 filters, matching sections, and diode rectifiers. A wide-band combination of a dc amplifier and a cathode follower couples from the diodes to the grids of the frequency-control 825 MC

AMPLIFIER

AMPLIFIER (FIG. 31)

FIG.34. Block diagram of phase-control system.

guns. When the magnetron and locking-oscillator frequencies are not synchronous, but the beat note is within the pass band of the system, the beat signal brings the two oscillators into synchronism. After this occurs, there is not only zero difference in frequency between the oscillators but there is also a definite rf phase relationship maintained, for the output of the rectifiers and the signal a t the grids of the control beams is of a polarity and amplitude proportional t o the phase departure from quadrature. I n the static case, for example, when the free-running frequency of the magnetron is equal t o that of the control oscillator, there is no dc signal, other than bias, supplied t o the guns. When the freerunning frequency of the magnetron is altered, the locked magnetron frequency is unaltered but a new equilibrium is set up in which the relative rf phase at the diplexer differs from 90 degrees. The static locking range is exceeded, and breakout occurs, when the rf phase differ-

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ence is more than 590" from the quadrature condition. The range of phase locking is thus identical with that, of the injection locking of Sec. VII. The phase-control system is a form of feedback loop. As in feedback loops in general, spontaneous oscillation will occur a t the frequency for which the total phase shift around the circuit is 180 degrees unless the Nyquist criterion3* for stability is met, i.e., unless the loop gain is less than unity at this frequency. Fortunately, a correction network can be used t o so shape the gain and phase that the gain is high a t low modulation frequencies, yet the stability requirement is satisfied. CIRCUIT OF FIG. 3 4 F R O M D I P L E X E R TO FREQUENCY C O N T R O L GUNS I N C L U S I V E

\

FIG.35. Schematic representation of feed-back loop.

We are interested chiefly in the stabilization factor or compression ratio, H , which is the high ratio of the unlocked frequency deviation, due t o the pushing of the magnetron, t o the locked frequency deviation. This must be distinguished from pb, the gain of the feedback loop. Figure 35 shows the loop schematically. E,, is analogous t o AfuL, the unlocked frequency deviation, and Eoutis analogous t o AfL, the locked frequency deviation. From the figure, the output is passed through the loop with a gain of p@, so that

The quantities in (37) and (38) are vectors. The phase-control loop has two very important properties. First, the signal a t the gun grids produces a frequency change, but the signal from the diodes is proportional to a phase change. T h i s integration process results in there being a 90-degree phase shzft in the loop at all modulation rates, in addition to the usu0.1 phase shifts in the circuit components.

24 1

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

Secondly, it can be shown that, associated with the 90-degree phase shift, the loop g k , NO, is proportional to l/f,,,,aside from the gazn characteristics of the circuit components. a. Performance of Loop with Circuit Components of Infinite Bandwidth. This is an illuminating if somewhat academic case. An assumed gain characteristic is shown in Fig. 36. The total phase shift around the loop is 90 degrees and independent of frequency. In the Nyquist diagram of Fig. 37, each successive pp vector is plotted, as usual, a t an angle, a, from the negative end of the line O A , equal to the total phase shift in the loop. In the present case this phase shift is always 90 degrees.

0

0.2 0.4 0.6 0.6 1.0 1.2 1.4 MODULATION RATE f m ( M E G A C Y C L E S )

1.6

FIG.36. Gain versus modulation frequency for circuit of infinite bandwidth.

The unit vector is OA and the values of H = 1 - pp have been drawn in the figure. The values of compression ratio, H,are plotted as a function of rate, fm, in Fig. 38. The values of rf phase deviation, AO, are of particular interest. The magnetron pushing was assumed to be f l megacycle a t a rate of 1 megacycle and the unlocked phase deviations Since the compreswere calculated from the relation * A 8 = *Af/fm. sion ratio applies to the phase as well as to the frequency, the locked phase deviations were obtained from the relation AOL = AOUL/H. From Fig. 38, H never becomes less than unity in the infinite bandwidth case, so there can never be amplification of the phase or frequency deviations. The locked phase deviation, whether the components hove Jinite or infinite bandwidth, is independent of rate at loco frequencies, since unity is negligible compared to pB and H , itself, is proportional to l/fm as is A&,. From Fig. 37, when ,u/3 = 1, H = 4 2 and AOL is 0.707 of AOuL. AOL is also 0.707 of its value a t very low frequencies, or the locked phase deviation has fallen 3 db.

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J. S. DONAL, JR.

FIG.37. Nyquist diagram for circuit of infinite bandwidth.

FIG.38. Performance of feed-back loop with circuit of infinite bandwidth.

From See. VII it will be remembered that expression for the compression ratio, H , of (35) holds only when H is large, while the bandwidth of the phase control, (36), holds only for low depths of modulation. With these limitations the analogy t o the present infinite bandwidth case is very interesting. If David’s H is assumed t o be actually p/3 (the

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

243

H of this section approached p/3 a t low frequencies), one would expect from the preceding paragraph t h a t the phase deviation should be down 3 d b when H = 1. This is the case, for placing H = 1 in (35) gives precisely the condition of (36). b. Performance of a Pmctical Loop. I n a practical loop the circuit components add enough phase shift t o make the total phase shift 180 degrees a t a frequency of a few megacycles. I n Fig. 39 the circuitcomponent phase shift is assumed t o be linear with fm, the case often found in practice. For simplicity, p/3 is again assumed t o be proportional to l/fmsince the individual circuit components are usually quite flat t o a high frequency. The Nyquist diagram is shown in Fig. 40.

FIG.39. Gain and phase curves for circuit of finite bandwidth.

Each value of p/3 is plotted a t its corresponding phase angle, or 90 degrees plus the phase shifts of Fig. 37. The loop cannot oscillate, for po is less than unity when the total phase shift is 180" degrees, but when H = 1 - p/3 becomes less than unity (the tip of the p/3 vector within the unit circle) the phase and frequency deviations are amplified rather than compressed. I n Fig. 41, 1/H becomes much greater than one and this amplification extends over a rather wide range of frequencies about the frequency a t which the phase shift is 180 degrees. The degree of amplification shown is not particularly significant since it is a function merely of the amount by which pP differs from unity a t the singing frequency. It is quite obvious, however, that the bandwidths of the components of the loop should be made as wide as possible. c. Experimental Results. At this writing, the quantitative results have been obtained largely a t modulation rates below 20 kc. The

J. S. DONAL, JR.

244

C I R C U I T COMPONENT P H A S E A N G L E FOR

#,g FOR

fm=(fm)i

fm=(fm)c

H=I

-fib

FOR

(frn)i,~T~. PHASE SHIFT A R O U N D LOOP \

\

I

P\l/ \

A

I

I

FIG.40. Nyquist diagram for circuit of finite bandwidth.

FIG.41. Performance of feed-back loop with circuit of finite bandwidth.

magnetron was modulated with a modulation factor of about 0.75, for which the uncontrolled pushing mas k 2 megacycles. The correction network was used to eliminate singing yet increase the loop gain a t low frequencies. At a modulation rate of 5 kc, H was 1300 or the locked frequency deviation was about 1.5 kc. H was inversely proportional to

MODULATION O F CONTINUOUS-WAVE MAGNETROSS

245

the frequency as expected, so that i t rose t o 6500 a t 1 kc and about 50,000 a t the hum frequency of 120 cps. Since H varied as l/fm,the phase modulation was approximately constant throughout the audio range. From the value of H given above, the phase modulation was only k 18 degrees a t 5 kc, for example. This compares favorably with existing conventional transmitters. The megacycles per volt of the control beams is a factor in the loop gain. For low modulation factors, such as those t o be expected from hum modulation, the guns could be biased t o the steepest portion of their characteristics t o increase the loop gain about a factor of two and raise the compression of hum modulation t o a factor of 100,000. The loop gain a t lorn frequencies could be increased still further by the correction network. I n this method the low-frequency compression ratio is not limited by the locking power as was the case for injection locking (equation 35). 3, Frequency Control Used in Addition to Phase Control

While few experimental results have been obtained a t modulation rates in the megacycle region, amplification as predicted in paragraph 3(b) above has been encountered. I n addition t o broad banding of the loop, two other methods of control, used in parallel with the phasecontrol system, have been investigated. The first of these is direct compensation, whereby a signal derived from the modulator chain (see Fig. 31) is adjusted in phase, shape, and amplitude and applied t o the grids of the guns. This type of correction differs in two respects from the phase control. It yields a , m u c h lower compression ratio at low modulation rates but, contrary t o the results with the phase control system, the frequency correction can be constant with modulation rate and, furthermore, no amplification need be encountered. The improved control a t high frequencies is largely due t o the fact that the correcting signal can occur a t the same time as the signal t o be corrected, i.e., there need be no phase delay as in the phase-control loop. As much as 15 t o 20 d b of compression ratio has been obtained over a frequency range of one octave in the megacycle range of modulation rates, with 10 db over a range of frequency of 20 octaves. If the highgain region corresponded t o the amplification region of the phase-control loop, the amplification could be corrected t o compression. Thus, when the direct compensation and its phase-control loop are used together they act independently, and the total compression ratio is the product of the individual ratios of the two systems. The phase-control system acts as usual, but upon a magnetron with a pushing reduced by the compensation. Although the compression ratios quoted in the last paragraph may be

246

J. S. DONAL, JR.

obtained without difficulty b y use of the direct compensation, the longtime stability might be improved if a frequency discriminator were used in a second feedback loop. This is in a n early developmental state. As with compensation, H may be constant over a wide frequency range, rather than proportional t o l/fm. To correct any amplification produc2d by the phase-control loop, the singing frequency of the frequency-control loop must be very much the higher of the two. There must be a frequency margin wide enough t o permit the loop gain t o be adjusted from less than unity at the singing frequency t o a high value a t the singing frequency of the phase-control loop. This broad banding is made easier, however, by the fact that there is no initial 90-degree phase shift in the frequency-control loop.

4. Evaluation This work is still in progress a t this writing (November, 1950). It offers a very good chance of making magnetrons useful devices for conventional amplitude modulation, as is also the case for the injectionlocking system of Sec. VII. If the spurious frequency modulation can be controlled adequately, advantage can be taken not only of the intrinsically high efficiency of the magnetron but in particular of the fact that plate modulation maintains this high efficiency whereas absoqtion modulation seriously reduces i t during the modulation cycle. The bandwidth and modulation characteristics of the magnetron appear t o be satisfactory for most purposes. At low modulation rates the compression ratio of the phase control loop can be made very high. The values attained can probably be approached by injection locking, a t least by t h a t of the form described in See. VII, only for values of p close t o unity, or values of locking power nearly equal t o the power delivered t o the load, yet the power required from the control oscillator is only 0.1 watt for a 1-kw magnetron. If the unmodulated carrier of an uncontrolled magnetron is heterodyned into the audio range, low frequency f m noise and hum modulation result in a n extremely rough note. The locked magnetron, on the other hand, sounds like a crystal-controlled oscillator. Since H approaches infinity a t zero modulation rate, the carrier frequency stability is equal t o that of the crystal-controlled oscillator. At very high modulation rates, theory predicts amplification by the phase-control loop, and this is confirmed experimentally, although direct compensation or a frequency-control loop could help t o correct the situation. A fundamental improvement would result from an increase in the loop singing frequency. I n the case of injection phase control, on the other hand, the theory predicts a decrease in phase modulation and,

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247

hence, on increase in compression ratio a t high modulation rates. At present, however, the injection theory is valid only for low modulation factors and little is known of the behavior of the compression ratio wit,h frequency under other conditions. IX. THEINJECTION MAGNETRON AS THE POSSIBLE: MEANSOF PRODUCING AMPLITUDE OR FREQUENCY h$ODULATION Some of the disadvantages of the magnetron, when plate modulated for the production of amplitude modulation, were mentioned in Sec. VIII. Thus, with some tubes it is difficult to obtain deep modulation and the inherent nonlinearity of the modulation must be corrected. Compared with grid modulation, both the current and the voltage to be furnished by the modulator are high. Perhaps most important, the frequency change during the modulation cycle must be reduced by a large factor if the system is to be acceptable for the transmission of information. The injection magnetron proposed by A. M. Clogston* yields a good spectrum a t much lower relative powers than is the case for a conventional tube. Although there appears t o be no significant, improvement in the inherent linearity and the modulation voltage is somewhat higher th a n in conventional plate modulation, the current t o be supplied by the modulator is greatly reduced. From preliminary results, the frequency change during the modulation cycle is reduced by a factor of a t least ten compared with the pushing of conventional tubes at the same frequency. Finally, a linear frequency modulation can be produced if desired. 1. The Principles of the Injection Magnetron

I n the conventional tube a sheath of space charge surrounds the cathode and expands in diameter as the anode voltage is increased. The angular velocity of the electrons in the sheath increases as a function of the sheath diameter until, without rf fields, the outer edge of the sheath reaches the anode. Before this happens, currents induced in the anode structure cause a traveling wave t o appear on the anode if the applied magnetic field is in the correct range. These rf fields cause a grouping of the outer electrons of the sheath into spokes due to a phasing process. During this phasing process the power output of the tube jumps rather suddenly from zero to a finite value and thereafter increases rapidly as

* A. M. Clogston, United States patent 2,530,948, November 21, 1950, and The Injection Magnetron, unpublished report of the Bell Telephone Laboratories, October 30, 1947. Preliminary work was begun at the M.I.T. Radiation Laboratory during 1946. Some of this material was presented at thc 1948 I.R.E. Conference on Electron Devices. Permission to discuss this material has been granted by the author.

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J. S. DONAL, JR.

the anode voltage is raised, as the phase difference between the induced currents and the rf voltage decreases. The latter change results in a rather large change in the frequency of oscillation. The chain of events in the injection magnetron is quite different because the anode voltage is held constant while the anode current is controlled by a separate means. A simplified sectional drawing of the tube is shown in Fig. 42." As used b y Clogston the anode was a conventional sixteen-vane structure for 4000 megacycles, but the usual cathode was replaced by a molybdenum rod. The emitting cathode was coaxial with this rod but separated from it. Surrounding the emitting cathode was a control cylinder with a n internal diameter equal t o t h a t of the anode.

MAGNETRON

FIG.

42. Simplified sectional view of injection magnetron.

The current t o the resonant-anode structure was controlled by the control-anode voltage. The mechanism of control may be explained as follows. In a conventional magnetron, omission of cathode-end shields causes large currents t o flow out the ends of the anode structure t o the lids of the tube a t anode potential. I n the injection magnetron the hat between the structures is omitted and the axial flow of electrons supplies a sheath of electrons around the molybdenum rod. This sheath is expanded by the anode voltage, which is higher than that on the control anode, and electron resonance and oscillation occur. As pointed out by Clogston, this process of axial repulsion by the space charge is t o be expected, for the space-charge density in the sheath surrounding the hot cathode is very large, possibly fifty times t h a t in a cylindrical diode without magnetic field. The calculated voltages corresponding t o the longitudinal motion have been found t o be a substantial fraction of the

* Figures 42 to 45 are adapted from figures in the report of A. M. Clogston, loc. c i t .

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

249

voltages corresponding t o the rotational motion of the electrons in the space charge.

2. Characteristics with Control-Anode Voltage Constant The mode of operation of the injection tube is best seen from the performance when the oscillating-anode voltage, V A ,is varied as would be done in a conventional tube. With constant magnetic field, and the rod and cathode voltages both zero, the control-anode voltage, Vc, was held a t 500 v. Typical results are shown in Fig. 43. The most notice-

200

600

1000

1400

I800

A N O D E VOLTAGE (VA)

FIG.43. Performance when the anode voltage of a n injection magnetron is varied.

able features are the current and power peaks over a range of V Aof about 200 v. At low V1 most of the electrons contribute t o the control-anode current, I,. I A then increases much as it does in a conventional tube before oscillation starts although in the case of the latter tube, in particular, such currents are not explained by theory. At the outset of oscillation there is (Fig. 43) the rapid increase in current and power t o be expected, followed by a decrease in both. The decrease in power, due the electronic angular velocity becoming too high, is only rarely seen in conventional tubes, but a decrease in efficiency is always seen, due either to this effect or t o the very high rf fields collecting electrons, as the cut-off voltage is approached, before proper interaction occurs. The current never decreases in a conventional tube although its rate of increase may decrease if the cathode does not fail first. The action of the injection system might be considered as analogous t o an emission limitation. The power peak in Fig. 43 occurs between the Hartree voltage ( V H )

250

J . S. DOWAL, JR.

and the cut-off voltage (V,) where it is usually assumed to appear in conventional tubes, although in the latter case oscillation often occurs, as pointed out by Clogston, below the Hartree voltage. 3. Performance as a Function of Control-Anode Voltage

From the viewpoint of amplitude modulation, the most significant results were obtained when the anode voltage was held a t a value near that giving the peaks in Fig. 43 and the control-anode voltage was varied. The result is shown in Fig. 44. As in Fig. 43 changes in the values of the nominally constant voltages change the details but not the general character of the curves. In Fig. 44, the power output rises smoothly

CONTROL ANODE VOLTS (Vc)

FIG 44. Performance of an injection magnetron as a function of control-anode voltage.

from a very low value, as the efficiency increases, and is nearly linear with V,. Above a low power the power output is very roughly proportional t o the current, as in conventional tubes. The saturation of the power curve sets in as the control-anode current increases, evidence that when the sheath diameter in the control system becomes rather large some electrons enter the main anode a t too great a radius for either efficient spoke formation or for return t o the cathode of electrons in such a phase as t o absorb energy from the rf field. It is to be noted particularly that the oscillator frequency is double valued and that its change is very small. This result is a plausible effect of the rod potential remaining constant. Over the same range of power the frequency change in a conventional tube might be expected t o be ten or twenty times as great.

MODULATION O F CONTINUOUS-WAVE MAGNETRONS

25 1

4. Variation of Rod Potential Although the results so far obtained are very preliminary in nature, it is this form of operation which provides a linear frequency change. With V Aa t 1250 v and V , a t 500 v as in Figs. 44 and 43, respectively, the altering of V Rgave the variations of Fig. 45. The decrease of Po t o zero at negative and high positive values of VR would be expected from the behavior of the rod current, In. When IR is reduced t o below zero no electrons are returned t o the magnetron cathode and rejection of

ROD VOLTAGE (VR)

FIG.45.

Performance of a n injection magnetron as a function of rod potential.

unwanted power-absorbing electrons is faulty. When V Ris SO high that most of the injected electrons are collected directly, the number available for interaction is reduced. The frequency variation, while small compared t o the carrier frequency, is quite linear with V E ,and for some purposes the associated amplitude modulation would not be harmful. The range of frequency variation is probably susceptible of great improvement. 5. Low-Current Behavior of the Injection Magnetron

For most conventional tubes the leakage current t o the anode is 5 t o 10 per cent of the normal operating current a t the point of onset of the oscillation. Oscillation starts discontinuously a t a few per cent of the rated power output (see Sec. VIII), and the spectrum is likely t o be poor a t the very low powers. By contrast, the three or four samples of the injection magnetron tested by Clogston oscillated smoothly, when the control-anode voltage was reduced, down to 2 ma compared with the normal operating current of about 50 ma. The power decreased smoothly

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J. S. DONAL, JR.

t o perhaps 100 mw out of the normal rating of 25 watts. Most important of all, the spectrum was not impaired at the low powers; on the cont rnry measurements showed that the spectrum improved a t low p o ~ ~ e r sBelow . a few hundred milliwatts the noise figure was comparable t o that of a lclystron. 6 . Evaluation

It should be realized that a t the time this is written the development work on the injection magnetron is incomplete. It is obvious that other types of injection mechanism could be employed. Only a few tubes have been tested and all these were of a similar structure. Adaptation t o other frequencies and powers will doubtless be made, with much more complete and improved results. The low noise levels found when operation is carried out a t very low currents offer several possibilities. The available depth of amplitude modulation is increased. The tube might be useful as a local oscillator. Finally, good low-current operation means t h a t such a tube for operation a t wavelengths of 1 ern or less could have a size large enough for convenient construction yet operate a t cathode current densities available from eyisting cathodes. Although the available frequency modulation may be considered small by some standards and the band of frequency deviation that is free from appreciable amplitude modulation may be considered narrow, both these aspects may well be improved by further development. During amplitude modulation the power output is proportional t o the control voltage, as in most conventional magnetrons. It would, of course, be more desirable t o have the square root of the power output proportional t o the control voltage. The required modulation voltage is higher than for plate modulation with ordinary tubes, but the anode current need not be carried by the modulator. The disadvantages cited in the preceding paragraph could in some cases be minor, however, compared with the advantage of the small frequency changr observed during the modulation cycle. This would simplify the problem of frequency control by control guns (Scc. VII) or injection locking (Sec. VIII). There are as yet no available data on control bandwidth characteristics peculiar t o the injection magnetron or, for that matter, on the bandwidth of the amplitude modulation. However, no inhcrrnt limitations are t o be expected. Pulsed injection magnetrons w o d d require less pulse power. In addition, the starting of oscillation a t lower levels might make locking of the pulsed tube, by injection from a controlled source, a less difficult procedure.

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253

X. CONCLUSIONS Each of the methods described above has been evaluated to some degree a t the ends of the respective sections. Space will not be taken here t o summarize the performance characteristics of the modulation systems. The above evaluations would perhaps bear rereading in the light of the performance criteria stated in the Introduction. It should be re-emphasized that much of this work is not only unpublished but is still under development. Present inadequacies of performance will doubtless be removed by further investigation. Work carried on outside of the United States has not been included in this discussion for the reasonthat the writer could not conveniently, as in the case of other methods, add t o the interpretation of the literature by personal contact with the originators of the work. Specific attention should be directed, however, t o the papers of Gutton and O r t ~ s i . ~ ~ , ~ ~ Spiral electron beams should perhaps be considered the standard method for frequency modulation, for the performance of the beams is nearly ideal except for limited deviation. Reactance-section tuning and voltage tuning are not yet fully developed, but they promise great improvement in the attainable deviation. Of the methods for amplitude modulation, the procedures employing spiral-beam absorption, the electron coupler and out-phase modulation are those most free from mixed frequency modulation. These are all absorption methods, however, with low efficiency averaged over the modulation cycle. Plate modulation has the desired high efficiency and feedback loop or injection locking should effectively eliminate the associated frequency pushing. The injection magnetron, also, would be expected to have high efficiency. The somewhat lower pushing of this tube should yield t o control by the methods suggested for use with plate modulation. Frequency-control procedures, making use of a feedback loop or injection locking, are important in themselves, since many other systems, including those based upon pulse modulation, could be improved by application of these control methods. The large amount of effort being devoted t o the modulation and control of magnetrons is evidence of the possibilities these tubes are considered to have for uses in which high powers and high frequencies are required. ACKNOWLEDGMENTS The following journals have kindly granted permission for the use of the figures listed: Reviews of Modern Physics, Fig. 2 ; Proceedings of the Institute of Radio Engi-

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J, S . DONAL, JR.

neers, Figs. 3 to 10, inclusive, and 15 to 19, inclusive; RCA Review, Figs. 20, 21, and 22; l
REFERENCES 1. Fisk, J. B., Hagstrum, H. D., and Hartman, D. L. The Magnetron as a Generator of Centimeter Waves. Bell System Tech. J . , 26, 167 (1946). 2. Slater, J. C. llicrowave Electronics. I). Van Sostrand, New York, 1950. Ch. 9 and 13. 3. Collins, G. B., editor. Microwave Magnetrons. McGraw-Hill, New York, 1948. 4. Reich. H. J., editor. Very High Frequency Techniques. McGraiv-Hill, New Yorli, 194T. (Vol. 1, Ch. 21, G. Hok.) 5. Smith, Lloyd P., and Shulman, Carl. Frequency Modulation and Control by Electron Beams. Unpublished RCA Laboratories Report (Feb. 14, 1945). 6. Smith, Lloyd P., and Shulmen, Carl. Frequency Modulation and Control by I3ectron Beams. Proc. Inst. Radio Engrs., 36, 644 (1947). 7. Kilgore, G. R., Shulman, Carl I., and Kurshan, J. A Frequency-Modulated Magnetron for Super-High Frequencies. Proc. Inst. Radio Engrs., 36, 657 (1947). 8. nonal, J. S., Jr., Bush, R. R., Cnccia, C. L., and Hegbar, H. R. A 1-Kilowatt Frequency Modulated Magnetron for 900 Megacycles. Proc. Znst. Radio Engrs., 36, 664 (1947). 9. Welch, H. W.,J r . Space-Charge Effects and Frequency Characteristics of C-W 3Iagnetrons Relative t o the Problem of Frequency Modulation. Tech. Rept. S o . 1, Contract S o . W-36-039-sc-32245, Dept. of Elec. Eng., Univ. of Michigan (Sox.. 15, 1948). 10. Kelch, H. \I7.,Jr., Black, J. R., Brewer, G. R., and Hok, G. Theoretical Study, Design and Construction of C-\V Magnetrons for Frequency Modulation. Tech. Itept. No. 3, Contract No. 1\'-36-039-sc-32245, Dept. of Elec. Eng., Univ. of Xlichigan (May 27, 1949). 11. i\-elch, H. LV., Jr. Effects of Space Charge on Frequency Characteristics of Magnetrons. Proc. Znst. Radio Engrs., 38, 1434 (1950). 12. Welch, H. K., Jr., Black, J. R., Brewer, G. R., Xeedle, J. S., and Peterson, W. Theoretiral Study, Design and Construction of C-W Magnetrons for Frequency IIodulation. Qiiart. Rept. S o . 2., Contract W-36-039-sc-35561, Dept. of Elec. Eng., Univ. of Michigan (July, 1950). 13. Blelvctt, J. P., and Itamo, S. High-Frequency Behavior of a Space Charge Rotating in a Magnetic Field. Phys. Rev., 67, 635 (1940).

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14. Lamb, W. E., Jr., and Phillips, M. Space-Charge Frequency Dependence of a Magnetron Cavity. J . Applied Phys., 18, 230 (1947). 15. Welch, H W., Jr., Black, J. R., Brewer, G. R., and Hok, G. Theoretical Study, Design and Construction of C-W Magnetrons for Frequency Modulation. Quart. Rept. No. 1, Contract No. W-36-039-sc-35561, Dept. of Elec. Eng., Univ. of Michigan (April, 1950). 16. Welch, H. W., Jr., Black, J. R., and Brewer, G. R. Theoretical Study, Design and Construction of C-W Magnetrons for Frequency Modulation. Interim Rept. Contract No. R-36-039-sc-35561, Dept. of Elec. Eng., Univ. of Michigan (Dec. 15, 1949). 17. Wilbur, D. A., and Peters, P. H., Jr. Wide-Band Voltage Tuning of Magnetrons. Paper delivered before the Natl. Acad. of Sci., Schenectady, New York (Oct. 10, 1950). 18. Welch, H. W., Jr., Ruthberg, S., Peterson, W., and Batten, H. W. Tech. Rept. KO. 4, Contract No. W-36-039-sc-35561, Dept. of Elec. Eng., Univ. of Michigan (Dec., 1950). 19a. Reverdin, D., and Marton, L. Space-Charge Distribution in a D C Cut-off Magnetron. Paper delivered before Mexico meeting of Am. Phys. SOC.,Mexico City, June 22, 1950. 19b. Reverdin, D. L. Electron Optical Fploration of Space Charge in a Cut-Off Magnetron. J . Applied Phys., 22, 257 (1951). 20. Donal, J. S., Jr., and Bush, R. R. A Spiral Beam Method for the Amplitude Modulation of Magnetrons. Proc. Inst. Radio Engrs, 37, 375 (1949). 21. Haeff, A. V. Space-Charge Effects in Electron Beams. Proc. Znst. Radao Engrs., 21, 586 (1939). 22. Parker, W. N. A Unique Method of Modulation for High-Fidelity Television Transmitters. Proc. Znst. Radio Engrs., 26, 946 (1938). 23. Cuccia, C. L. The Electron Coupler-A Developmental Tube for Amplitude Modulation and Power Control a t Ultra-High Frequencies. R C A Rev., 10, 270 (1949). 24. Cuccia, C. L., and Donal, J. S., Jr. The Electron Coupler-A Spiral-Beam U H F Modulator. Electronics, 23, 80 (1950). 25. David, E . E., Jr. Locking Phenomena in hlicrowave Oscillators. Tech. Rept. No. 63, Res. Lab. of Electronics, Mass. Inst. of Tech. (April 8, 1948). 26. David, E. E., Jr. Some Aspects of R-F Phase Control in Microwave Oscillators. Tech. Rept. No. 100, Res. Lab. of Electronics, Mass. Inst. of Tech. (June 11, 1949). 27a. David, E. E., Jr. Some Aspects of R-F Phase Control in Microwave Oscillators. Thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Res. Lab. of Electronics, Mass. Inst. of Tech. (May, 1950). 27b. David, E. E., Jr. Transient Starting of a Magnetron as Described by the Inhomogeneous Van der Pol Equation. Tech. Rept. No. 168, Res. Lab. of Electronics, Mass. Inst. of Tech. (August 16, 1950). 28. Pitts, J. C., and Wicks, W. F. Locking Phenomena in Microwave Oscillators with Mismatched Loads. Thesis submitted in partial fulfillment of the requirement for the degree of Bachelor of Science, Res. Lab. of Electronics, Mass. Inst. of Tech. (1949). 29. Slater, J. C. The Phasing of Magnetrons. Tech. Rept .No. 35, Res. Lab. of Electronics, Mass. Inst. of Tech. (April 3, 1947).

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30. Schneider, 11’. P. Amplitude Modulation of Microwave Oscillators. Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, Res. Lab. of Electronics, Mass. Inst. of Tech. (May, 1950). 31. Donal, J. S., Jr. A Preliminary Report on an Amplitude-Modulated Transmitter Employing A Crystal Controlled Magnetron. Unpublished RCA Laboratories Report (March 15, 1950). 32. Bond, D. S., and Moore, D. G. (Pt. 1 ) ; Donal, J. S., Jr. (Pt. 2). An Experimental Amplitude Modulated Transmitter Employing a Crystal-Controlled Magnetron ; I. The Frequency Control System; 11. Frequency-Controlled Plate Modulation of the Magnetron. Paper delivered a t S e w England Radio Eng. Meeting; (.lpril 15, 1950). 33. Brown, G. W., Morrison, W. C., Behrend, W. L., and Reddeck, J. G. Method of Multiple Operation of Transmitter Tubes Particularly Adapted for Television Transmission in the U.H.F. Band. RCA Rev., 10, 161 (1949). 34. Nyquist, H. Regeneration Theory. Bell System Tech. .I 11, . 126 , (1932) vol. 11, pp. 126-147; (January, 1932). 35. Gutton, H., and Ortusi, J. A. Ultra-High-Frequency Modulation on Wave Guides. J . Brit. Znst. Radio Engrs., 7, 205 (1947). 36. Gutton, H., and Ortusi, J. A. Modulation sur Guides des Ondes Centimetriques. L’Onde Elect., 27, 307 (1947).

The Magnetic Airborne Detector WINFIELD E . FROMM Airborne Instruments Laboratory. Inc., Mineola. New York CONTENTS Page ...... . . . . . 258 ..................................... 258 2 . The Detection Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 3. The Magnetic Field of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 4 . The Magnetic Field of the Submarine., . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 5. Problems Peculiar to Detection from Aircraft . . . . . . . . . . . . . . . . . . . . . . . 262 I1. Types of Magnetic Anomaly Detectors ........................... 263 1. Magnetometers . . . . . . . . . . . . . . . . . . . ........................... 263 a . The Schmidt Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 b . The Coil Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 264 c . The Earth Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . d . The Saturable-Core Magnetometer. . . . . . . . . . . . . . . . . . . . . . . . . 264 e. The Variable-Resistance Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . 266 f. The Electron-Beam Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 2. Gradiometers . . . . . .......................... 266 Airborne Detector . . . . . . . . . . . . . 267 I11. Historical Developme 268 IV . The Saturable-Core Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 2. Single-Coil Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 3. Magnetometer Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 272 a . Even Harmonic Magnetometer Bridge., . . . . . . . . . . . . . . . . . . . . . . . . b. Peak Type Magnetometer Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 4 . Quantitative Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 V. Magnetic Stabilization and Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 1 Stabilization and Orientation in the Earth's Magnetic Field . . . . . . . . 280 2 . Methods of Magnet 'lization and Orientation. . . . . . . . . . . . . . . . 283 3. Special Methods ... ..................................... 290 a . Three-Component Unstabilized Total Eield hlagnetomcter . . . . . . . . 290 b . Three-Component Stabilized Total Field Magnetometer . . . . . . . . . . 291 292 VI . Magnetic Airborne Detector System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Universal Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 2 . Drive Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 3. Servo Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 4. Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 V I I . The Noise Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 1. Instrumental Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 a . Electrical Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 b. Magnetic Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 c . Stabilization Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 d . Magnetometer Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 257

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2. Aircraft Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Noise from Sources External to the -4ircraft.. . . . . . . . . . . . . . . . . . . . . . . a. Time Variations in the Earth’s Field.. . . . . . . . . . . . . . . . . . . . . . . . . . . b. Space Variations in the Earth’s Field.. . . . . . . . . . . . . . . . . . . . . . . . . . VIII. Conclusion. .. ....................... Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page 296 297 297 297 298 298

I. INTRODUCTION i. Scope of the Present Article The detection from aircraft of disturbances or anomalies in the earth’s magnetic field is a relatively recent development; virtually all the work has been done since 1940. The need of the Allies in 1941 and the next several years for means of detecting submerged submarines from the air led t o intensive research, development, engineering, and production of magnetic airborne detectors (MAD). These were in use on military patrol aircraft as early as 1942 and were used with varying degrees of success during the remainder of World War 11. Since 1945 various forms of the wartime MAD have been used by government and commercial groups in geophysical surveying throughout the world. Although numerous methods are known by which a n object, such as a submarine t h a t causes disturbances in the earth’s magnetic or gravitational fields, may be detected, the present article is restricted, except for historical background, t o a consideration of the only method used widely in aircraft during World War 11. This method employs the saturablecore magnetometer as the basic detection element. The remainder of the introduction will consider the problem of detecting submarines, the magnetic fields involved, and problems peculiar t o detection from aircraft. Some of the methods of magnetic airborne detection t h a t could be and have been used will then be reviewed, with a n appraisal of their merits. A brief historical review of magnetic airborne detection will be followed by fairly extensive descriptions of the saturable-core magnetometer and its theory, stabilization requirements of MAD, and practical magnetic stabilization methods. A MAD system typical of those used in World War I1 will then be described, and finally, consideration will be given t o noise sources and their significance in MAD systems. 2. The Detection Problem The detection of a submerged submarine by magnetic means requires the measurement of a small anomaly in the earth’s magnetic field caused by the presence of a ferromagnetic submarine. A t distances greater than

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50 or 100 f t from the submarine, the magnetic field of the submarine is much smaller than the earth’s field, and, as the distance is increased still farther, the submarine’s field decreases as the inverse cube of the distance. The field eventually becomes lost in the various electrical and magnetic noises that determine the minimum signal that the l I A \ Dcan detect. The detection problem is then one of detecting a weak local field in the presence of a strong and relatively uniform ambient field. The added requirement of doing this from a n unstable base such as an airplane complicates the problem. The many phases of the problem will be considered in the following pages. 3. The Magnetic Field of the Earth The characteristics of the earth’s magnetic field have been known for many years.’ Magnetically, the earth acts as a huge magnetic dipole nearly aligned on the north-south axis of the globe. The north magnetic pole is located below the southern polar region and the south magnetic pole below the northern polar region. Thus in the northern hemisphere the magnetic lines of force are inclined downward, while the converse is true in the southern hemisphere. At the magnetic equator (near the geographic equator) the lines of force are horizontal. The surface intensity of the field varies from 25,000 gammas (1 gamma = lop5 oersted) a t the magnetic equator t o about 70,000 gammas a t the magnetic poles. For most purposes the earth’s field is regarded as being uniformly distributed, but in sensitive measurements of magnetic anomalies such a generalization is inadequate and the various gradients in the Farth’s field must be considered. The vertical gradient of the total intensity lies between 0.005 gamma per foot and 0.01 gamma per foot. The northsouth horizontal gradient is about 0.0015 gamma per foot. Another characteristic of the earth’s field that must be considered in sensitive measurements is the time variation of the total field intensity. The magnitude of this variation can be great (an estreme example is a magnetic storm), but on the average the low-frequency variation is about 0.03 gamma in amplitude. The significance of the field gradients and time variations will be examined in more detail in the section on noise. At most, these characteristics of the field are of secondary importance. The primary importance of the earth’s magnetic field as far as the MAD is concerned lies in the following three factors: a. Because of the magnitude of the earth’s field, the actual detection problem becomes one of distinguishing a local small anomaly from a large total field. This anomaly is seldom greater than 1 part in 10,000 in the

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case of submarines. Anomalies due t o geological sources may be much larger. h. Because of the relative uniformity of the direction of the earth’s field, that field can be used as a magnetic reference vector for use in stabilizing the magnetic detection elements. c. The intensity of the earth’s field is high enough so that i t can easily induce significant magnetic moments in ferromagnetic bodies. Thus, even though a submarine may have no permanent moment, the induced moment due to the earth’s field may be large enough t o produce a detectable field several hundred feet away.

4. The Magnetic Field

of the Submarine

Considered in detail, the magnetization of a submarine is complicated. The modern sea-going submarine is large enough so that its various sections may have individual magnetic characteristics. However, a t distances greater than approximately the length of the submarine, the effect of each individual magnetized portion is small relative t o that of the overall magnetic moment so that for all normal considerations of its magnetic field the submarine may be considered as a single magnetic dipole. The axis of this dipole may or may not be aligned with the axis of the submarine; in general, the two axes are not aligned. Furthermore, the relative alignment is not fixed, changing with heading, position, and time. When viewed as a simple dipole, the equivalent magnetic moment of the submarine can be regarded as a magnetic vector with six components. The six components consist of permanent and induced longitudinal, transverse, and vertical moments. The resultant of these six vectors is the equivalent total magnetic moment, whose magnitude and direction are both variable. The permanent momeiits of the submarine depend upon its size and history. These moments, especially the longitudinal, may be large (10’ cgs units for a small submarine, 107 cgs units for a large one), unless the submarine has been degaussed recently. Degaussing reduces the moments by a considerable factor. Modern practice is to degauss submarines periodically t o minimize permanent moments. The induced moments depcnd upon the size of the submarine, its magnetic latitude, and its magnetic heading. These moments are of the same order of magnitude as the permanent moments. However, the induced moments are not as easily reduced; continuous degaussing carefully synchronized with heading and position is required. Such degaussing can be achieved but, because of practical difficulties, it was not used during World War 11.

26 1

MAGNETIC AIRBORNE DETECTOR

This brief introduction t o permanent and induced moments shows t h a t the resultant total moment may vary radically with even a simple change in heading of the submarine. For instance, a submarine heading north in northern latitudes with a permanent longitudinal moment of lo8 cgs units adding t o a longitudinal induced moment of the same magnitude will have a total longitudinal moment of 2 X lo8 cgs units. This is a large moment. If the submarine now reverses its heading, the permanent

PRRllNG

FIG.1. How the magnetic anomaly produced by a submarine is detected by a magnetometer.

and induced moments will exactly cancel, and the resultant moment is zero. A submarine operating a t high latitudes generally has a strong and constant vertical permanent component, unless i t has been reduced by degaussing. There is usually a fairly strong longitudinal magnetization which is normally stronger on north-south than on east-west headings. I n equatorial waters the vertical component tends t o become quite small, and the longitudinal component will be weak on east-west headings if the submarine has been degaussed recently. Under these circumstances only the weak athwartship moment may be available for detection. The manner in which the magnetic anomaly produced by a submarine is-detected is shown in Fig. 1. Figure 1A shows the equivalent magnetic dipole of the submarine and the resultant magnetic field. Figure 1B

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illustrates a detection element with its axis stabilized along the earth’s magnetic field vector. The detection element is sensitive only t o changes in magnetic field along its axis as it is carried by a n aircraft through the magnetic anomaly of the submarine. Figure 1C is a plot of the magnitude of this anomaly and represents the change in the magnitude of the earth’s field vector along the horizontal path of the aircraft at a given altitude. Quantitatively, the strength of the magnetic dipole field is given by

where F

=

M r

=

dipole field strength in gammas dipole moment in cgs units = distance from the dipole in centimeters a = angle between dipole axis and radius vector t o the point a t which the field is measured. It is particularly important t o note in (1) that the field strength is inversely proportional t o the cube of the distance. It is this fact t h a t determines the ultimate distance from the submarine a t which i t can be detected. For instance, with a typical submarine having a moment of loy cgs units the magnitude of a magnetic anomaly a t a distance of 400 ft would be about 10 gammas. At 800 ft the anomaly would be about 1.25 gammas, etc. Figure 2 shows a static contour map of the magnitude of the magnetic field of a typical submarine (los cgs moment). The map is for the component of magnetic field parallel t o the earth’s field on a horizontal plane 200 ft above the submarine. 5. Problems Peculiar to Detection f r o m Aircraft

Because the magnetic fields of submarines are so weak, the MAD must be extremely sensitive and must have a low inherent noise level. Furthermore, as will be seen in Sec. V, the normal stability requirements on the orientation of the detection element are such that a maximum error of only 5 or 6 minutes of arc can be tolerated for even the most violent velocities and accelerations encountered during flight. Lastly, the operational noise level is dependent upon many factors not ordinarily encountered in the use of electronic equipment. Magnetic signals (noise) arise from electrical disturbances in the aircraft, relative movement of magnetic bodies within the aircraft with respect t o the detection element, time variations in the earth’s magnetic field due t o magnetic storms, space variations in the earth’s magnetic field due t o geological

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disturbances in the earth’s surface, and vertical and horizontal gradients in the normal earth’s field. (See Sec. VII.) These noise sources affect the MAD similarly in geophysical prospecting, although not to the same extent as in submarine detection.

f

/

I / I I

I \

01

\ \

1“SAMHA)

FIG.2. Static contour map showing magnitude of component parallel to earth’s field at 200-ft level of the magnetic anomaly due to a submarine.

11. TYPESOF MAGNETIC ANOMALYDETECTORS

Though the magnetic airborne detector was developed recently, methods and instruments for detecting magnetic anomalies have been known for years, especially in connection with geophysical exploration and studies of the earth’s magnetic field. The instruments may be classed in two groups: (1) magnetometers, which are strictly defined as instruments whose outputs are proportional t o the magnitude of the total field or some component thereof, and (2) gradiometers, which are instruments whose outputs are proportional to the space rate of change of the total intensity or some component of it, or to a higher order space derivative. I n general, a gradiometer consists of a pair of magnetometers separated by a distance such th at the magnetic field between the two locations varies approximately linearly with distance. 1 . Magnetometers a. The Schmidt Magnetometer. Before the introduction of the magnetic airborne detector, the Schmidt magnetometer2was the most widely

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used instrument in magnetic prospecting, especially in connection with oil exploration. It consists of a carefully suspended magnetic system, a telescope, and a scale arranged for measuring deflections caused by changes in the field being measured. Though considered highly sensitive for oil exploration, i t is relatively insensitive for submarine detection; i t is not suitable for use in aircraft. b. T h e Coil Inductor. A simple coil of many turns that is translated through a nonuniform field will produce a n output voltage proportional t o the time rate of change of flux linking it, and hence proportional t o both the speed of translation and the field gradient. It is not a true magnetometer but is listed here as a special case because it has been used in practical systems. The translation of the coil must be stabilized because any rotation (except that about the coil’s own axis) will produce variations in the output, even in a uniform field. The coil inductor is characterized by low sensitivity. A coil 50 cm square with 100,000 turns has a sensitivity of only one-third t o one-half that of a saturable-core magnetometer (see below) for ordinary submarine signals. This fact and the need for the same accuracy of stabilization as for the saturable-core magnetometer have often discouraged the use of the coil inductor. However, it was used in a n early British gradiometer system, and it was also used (with a n iron core) in the Japanese MAD of World War 11. c. T h e Earth Inductor. This magnetometer consists of a coil spinning about a n axis lying in the plane of the coil and passing through its center. The axis is maintained perpendicular t o the ambient (earth’s magnetic) field. The voltage induced in the coil is proportional to the rate of spin and t o the magnitude of the total ambient field, in addition to the usual factors of area and number of turns. The submarine produces a signal that appears as amplitude modulation of the relatively high-frequency induced voltage. T o be more sensitive than the coil inductor, the coil of the earth inductor must have approximately the same area and number of turns as the inductor coil and must spin faster than about one revolution per second. Sensitivity increases directly as the rate of spin. The required stabilization accuracy is identical t o t h a t required for the simple coil inductor and for the saturable-core magnetometer. The mechanical difficulties of driving and stabilizing the earth inductor are not negligible. Furthermore, there is a disadvantage electrically in that slip rings are required as contacts. d . T h e Saturable-Core Magnetometer. The magnetically sensitive element of the saturable-core magnet0meter3,~consists of a coil on a ferromagnetic core as shown in Fig. 3A. I n practice the coil is aligned

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and maintained parallel t o the earth’s magnetic field. The coil surrounding the core is excited with a n alternating current. The magnetic saturation of the core introduces harmonics of the excitation frequency into the terminal voltage of the coil. Polarization of the core material by the ambient field alters the distribution of energy among these harmonics, in general introducing or increasing even-order harmonics. Any even-order harmonic-or a combination of even-order harmonicsmay be selected by bridges or filters, amplified, and rectified t o yield a n output that is a measure of the ambient field. AMBIENT FIELD

’ -

I

I (8)

I 1 FILTER

iz

b 1

OUTPUT

2f

FIG.3. A. Single-coil magnetometer with second harmonic output. tometer bridge with second harmonic output.

B. Magne-

The saturable-core magnetometer in various forms was used in virtually all magnetic airborne detectors developed in the United States during World War 11, and it is still in commercial use in detectors being flown in geophysical surveys. The saturable-core magnetometers are most efficiently used in pairs, as shown in Fig. 3B. The magnetometers are connected so t h a t the ambient field aids the driving flux in one and opposes the driving flux in the other. The even harmonic output of a four-element bridge consisting of the pair of magnetometers and two identical resistive or reactive driving elements is then proportional t o the ambient field. When used in this manner the saturable-core magnetometer bridge becomes an extremely sensitive indicator of changes in the field.

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This magnetometer requires the same accurate alignment and stabilization in the ambient field as the coil and earth inductors. e. The Variable-Resistance Magnetometer. When the temperature of certain materials is in the vicinity of the superconducting range, their electrical resistance is very sensitive t o the strength of a surrounding magnetic field. This principle did not see practical application during the last war. f. The Electron-Beam Magnetometer. It is possible t o use the deflection of a low-velocity electron beam as a measure of ambient field strength. This deflection may be detected by means of specially constructed tubes with suitable anode arrays5 or linear resistance elements. A magnetometer of this type has been proposed many times as a compass. All but the first of these magnetometers are possible types for magnetic airborne detection. I n all, the output is proportional t o the component of the field t h a t is parallel or perpendicular t o some specific axis of the sensitive element itself. I n the coil inductor it is the component perpendicular t o the plane of the coil. I n the earth inductor i t is the component perpendicular t o the spin axis of the coil. I n the saturablecore magnetometer i t is the component parallel t o the effective magnetic axis of the coil. I n the variable resistance magnetometer i t is the component related t o some axis of symmetry of the sensitive element, and in the electron-beam magnetometer it is the component of field perpendicular t o the electron velocity. Hence, in employing a magnetometer it is necessary t o eliminate or a t least minimize rotation of the sensitive element with respect t o the field in a t least one degree of freedom, and in some cases, two degrees of freedom. Otherwise, components will appear in the output that will correspond t o movement of the element in the field rather than t o actual variations of the field strength. For single-element magnetometers, therefore, some form of stabilized platform is required. This requirement may be relaxed or eliminated, however, by utilizing a n array of sensitive elements whose total output is invariant under any rotation. I n this arrangement the requirements for stabilization are replaced by requirements for a n accurate alignment of the various elements and for a precise combination of their separate outputs. Methods for doing this are described more fully in Sec. V. 2. Gradiometers

An airborne gradiometer can be constructed with a pair of magnetometers of any of the five types considered suitable for airborne detection. The gradiometer may be constructed either by stabilizing each of two magnetometers independently so that their axes remain parallel or by aligning their axes parallel and connecting them by a rigid framework. The distance between the two magnetometers should be such t h a t the

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magnetic field between the two locations varies approximately linearly with distance. The ultimate limits of gradiometers make them inferior in performance to the earth inductor and saturable-core magnetometers. Because the saturable-core magnetometer was used almost exclusively during World War 11, the remainder of the present article will be devoted to systems employing it as the magnetic detection element. 111. HISTORICAL DEVELOPMENT OF THE MAGNETIC AIRBORNE DETECTOR The concept of using the magnetic anomaly created by the ferromagnetic hull of a submarine t o detect its presence is old. During World War I large loops were used to detect the magnetic field of a submarine, and this method of detection has been used since that time for harbor protection. However, in the twenty years following World War I little, if any, effort was made to develop a reliable instrument for installation in what was then becoming a most important military carrier-the airplane. Thus, in 1939 when World War I1 began, only optical methods existed for detecting surfaced submarines, and no means existed for detecting submerged submarines from aircraft. It was not until 1940 that intensive development on magnetic airborne detectors began, first in Great Britain and later the same year in the United States. However, not until the spring of 1942 were the first satisfactory MAD sets (these employed the saturable-core magnetometer) being installed on U.S. Navy blimps and U.S. Army Air Force search airplanes. (Surprisingly enough, the first microwave radars for surface search were being installed a t the same time.) British MAD developments were such that by early 1941 a two-coil gradiometer was being tested operationally. This gradiometer consisted of coils about 1 ft in diameter, mounted coaxially in a supporting framework and separated by about 8 f t . Because this gradiometer system measured the space rate of change of the magnetic gradient, which varies inversely as the fifth power of the distance from the submarine, its performance was poor and its possibilities very limited. However, its development was continued in the United States until late in 1941, at which time it became apparent that the saturable-core magnetometer was more promising. Development of other magnetometers, including the gradiometer, was therefore terminated. Japanese development of MAD was not begun until the middle of 1942. In early 1943 the first model of an equipment employing a gyroscope-stabilized, iron-core coil inductor was tested, and although the detection range was low, the need for such a device was regarded as

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urgent enough t o justify its production. Numerous equipments were produced, and although a later system employing a coil with permalloy core in a n oscillator circuit was developed, its detection range was only slightly greater, and the coil inductor system was used throughout the war. It is interesting t o note that the Japanese stabilized the axis of the coil inductor in a vertical position rather than parallel t o the earth’s field. Stabilization noise in the Japanese system was therefore somewhat high and partially accounted for the low range that was obtained. The saturable-core magnetometer was first considered for use in sensitive magnetic devices by Victor V. Vacquier4 of the Gulf Research and Development Company. Its development was begun by Gulf late in 1940 for geophysical prospecting. However, the possibility of using the saturable-core magnetometer on aircraft for submarine detection was soon recognized. Early in 1941 the National Defense Research Committee assumed sponsorship of MAD development and by late 1941 the first MAD with a saturable-core magnetometer had been flown successfully, signals being obtained 400 f t from test submarines. This first instrument employed gyroscopic stabilization. h few improved models of this early equipment were produced and installed. However, the practical difficulties involved in gyroscopic stabilization led t o the development of methods for using the earth’s magnetic field to control the stabilization of the magnetometer. Equipment employing this principle was developed by the Western Electric Company (with the Naval Ordnance Laboratory) and by Airborne Instruments Laboratory. The latter group, operating as a part of the Division of War Research of Columbia University (under contract to the Office of Scientific Research and Development), soon was asked t o assume the major responsibility for MAD development and continued intensive effort until late in 1944. Similar work took place in Germany but t o the author’s knowledge no equipment reached the stage of operational use. Information on some of the German work and a theory of the device similar in some respects t o that presented here have been published only recently. Since 1945, magnetically stabilized saturable-core magnetometers have been used in geophysical prospecting718all over the world with considerable success. IV. THE SATURABLE-CORE ~TAGNETOMETER* The basic principles of the saturable-core magnetometer and the magnetic amplifier are the same. The magnetic amplifier has received wide treatment in the literature, but the saturable-core magnetometer * The author is indebted to Dr. E. G. Fubini of Airborne Instruments Laboratory Inc., for the material in this section.

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has received relatively little attention. Because of this and because there are significant differences in the two types of magnetic devices, a summary of the theory of the magnetometer is given in this section. 1. Introduction

A saturable-core magnetometer consists usually of a strip or cylinder of saturable magnetic material surrounded b y a coil, across which a n alternating driving voltage is impressed. The size of the strip or cylinder is relatively small; lengths employed are in the order of inches and the ratios of length t o width or diameter may be from 5 t o 100. The magnetic core may be closed, as in a toroid, or may be open, as in a strip. The open strip or cylindrical form of core is employed t o measure very small external magnetic fields. I n doing this, the nonlinear characteristics of the saturable material are employed. The basic reason why such nonlinearity can be employed is easily understood if one realizes t h a t there is a radical change in the electrical constants of the coil circuit when the core of a magnetometer goes into saturation. Since the time at which switching occurs between the unsaturated and saturated conditions is a function of the total magnetic field applied t o the core, it is possible t o measure variations in this field by comparing the different effects produced as the magnetometer goes into positive saturation (external field aiding driving field) and negative saturation (external field opposing driving field). Many methods can be employed in applying the saturable-core principle t o the measurement of a magnetic field, but in this section only a few t h a t have been widely used will be described. Sinusoidal driving voltages will be assumed, but i t should be understood t h a t nonsinusoidal drives may be found advantageous in some cases. I n this section we shall consider qualitatively the single-coil magnetometer and show that its output contains even harmonics of the driving voltage that are sensitive t o a n external magnetic field. We shall then describe magnetometer bridges with two magnetometers in opposition. These bridges possess certain advantages over the single magnetometer. Lastly, we shall examine quantitatively the operation of magnetometers both singly and in bridges. A graphical rather than analytical analysis will be used in this quantitative examination. 9. Single-Coil Magnetometer

Let a single-coil magnetometer with a strip or cylindrical core of saturable magnetic material be driven in and out of saturation by means of a sinusoidal voltage generator, as shown in Fig. 4A. Let us assume that no external magnetic field exists. Because the driving voltage is sinusoidal and contains no even harmonics, and since the magnetization

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curve for the core material is identical for both positive and negative fields, phenomena occurring a t saturation in the first half cycle are repeated exactly, except for sign, in the next half cycle. Symmetry is thus preserved, and neither the current flowing in the magnetometer nor TER

-/ I

I

I

SATURATION

I

DRIVE CURRENT WITH NO

I I

I

-4

I I I I

(B)

FIG.4. A. Schematic diagram of single-coil magnetometer. effect of magnetic bias on current drive of magnetometer.

B. Graph showing

the voltage appearing across it 11ill contain even harmonics. However, except for the extreme cases of zero or infinite generator impedances, both the current and the voltage will contain odd harmonics. Consider now the case where a n esternal magnetic field H is present, as shown by the dotted arrow in Fig. 4A. This corresponds (as shown in Fig. 4B) essentially to biasing the driving current relative t o the magnetization curve of the material. Now the saturation phenomena in the

27 1

MAGNETIC A I R B O R N E D E T E C T O R

first half cycle are not repeated exactly in the second half cycle. The reason is that saturation occurs earlier in the first half cycle (if the external field is aiding the driving field), and later in the second half cycle, so that the time between positive and negative saturation is no longer equal to exactly half the period of the driving voltage. It is quite obvious, a t least qualitatively, that under this condition even harmonics will be present in the complex magnetometer current and voltage and that the amplitude of these harmonics will be dependent on the magnitude of the external field. Here is, therefore, a method of detecting the presence of an external field. For instance, with a sinusMAGNETOMETER NO. I

1

AMBIENT FIELD H

MAGNETOMETER NO. 2

FIQ. 5. Schematic diagram of magnetometer bridge. shown dashed.

Unbalance resistor Ra

oidal current drive, one could measure the second, fourth, sixth, etc., harmonic of the fundamental frequency in the complex waveform of the voltage appearing across the magnetometer coil. It should also be noted a t this time that the phase of the even harmonics reverses as the external field passes through zero. Thus the amplitude and polarity of an external field may be measured by means of a phase-sensitive detector. 3. Magnetometer Bridges

The method of measurement of the magnetic field described in the previous paragraph has been used in some of the magnetometers that have seen very satisfactory practical use. The system can, however, be modified by using two magnetometers in opposition rather than a single magnetometer; by this is meant a combination of magnetometers as shown in Fig. 5 where the windings L1 and L z are wound in opposite directions on a single core or a pair of cores. For the reasons explained in the previous paragraph, if no magnetic field is present and if the circuit is electrically balanced, no output will appear a t the terminals of the

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W I N F I E L D E. FROMM

detector because of the symmetry characteristics mentioned above. However, the presence of an external field has a different effect on coil L1 as compared t o coil Lz. In effect, since the two windings are wound in opposite directions, the external field tends to make L1 saturate earlier than L2 during half of the cycle and later than Lz during the other half. I n this condition symmetry no longer exists and a voltage of some complex form will be present a t the detector output. It should be clear that this voltage will contain only even harmonics because all odd harmonics are cancelled by the symmetry of the circuit. The voltage a t the detector output will obviously acquire a maximum amplitude during the short time interval when one winding is saturated while the other is not. It is possible therefore to design a device that will measure the external magnetic field by measuring the second or some other even harmonic at the detector output and to take advantage of the circuit symmetry t o decrease the odd harmonics. Unavoidable unbalances in the bridge will prevent the complete cancellation of the fundamental and odd harmonics. It must be emphasized, however, that no unbalance except one due t o an outside magnetic field or equivalent will introduce even harmonics. The reason why a bridge unbalance does not create even harmonics, while the presence of a magnetic field does, is of interest. The difference is due t o the different nature of an electrical unbalance in the bridge and a magnetic unbalance due to an outside field. Consider for instance the case in which resistance R , is connected across L1while no resistance is connected across L2 (Fig. 5 ) . The magnitude of the current in saturation will always be greater in L z than in L1and for this reason Ll will go out of saturation earlier than L2 for both positive and negative cycles of the drive. The presence of an outside field, on the contrary, has, as stated before, a very different effect. During half of the cycle L1 will go out of saturation earlier than L 2 ;during the other half of the cycle L1 will go out of saturation later than L2. a. Even Harmonic Magnetometer Bridge. A magnetometer bridge connected as the one of Fig. 5 without the unbalance resistor R , lends itself to measurements of magnetic field through the determination of the even harmonic content in a fashion quite similar to that described in paragraph 2 . The advantage of employing the balanced circuit as compared to the employment of the single-ended magnetometer is a reduction in the amount of fundamental and odd harmonics that need to be filtered out of the detector output. It may be interesting to note a t this point that in the theoretical case of a bridge with a perfect electric balance, the output of the detector would consist of pulses as shown in Fig. 6, all of the same polarity, whose width is approximately proportional to the external field and whose amplitude changes as a function

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273

of the magnetic field present. A more detailed explanation of the process by which these pulses take place will be given in paragraph 4. b. Peak T y p e Magnetometer Bridge. It has been explained that a resistance placed across one of the magnetometer coils tends to produce a t the detector output a voltage of a peculiar shape containing (in the absence of outside fields) only odd harmonics. It will be explained in paragraph 4 that this voltage consists actually of puIses of opposite polarity whose width is a function of the amount of the resistance unbalance and whose amplitude also changes with the amount of unbalance. Pulses from a bridge of this type are shown in Fig. 7. If under these conditions of bridge unbalance a magnetic field is applied, we can I--

-

I I

m

t

I

I

I

DEGREES

FIG. 6. Typical output of balanced magnetometer bridge with large external magnetic field.

consider from a qualitative point of view that the .bridge is closer to balance during half of the cycle and farther from balance during the other half. The width of the positive pulse will therefore be different from that of the negative pulse, and th6 presence of an outside field can therefore be detected by measuring this difference.

4. Quantitative Considerations An explanation of the form of voltages and currents flowing in the magnetometer circuit cannot take into account all the details of the problem without introducing unsurmountable analytical difficulties. The best procedure for a quantitative study is to consider the effect of a saturable core as equivalent to switching the circuit from one consisting of a pure resistance (case of saturated core) to one consisting of resistance and reactance (when t>hecore is nonsaturated). On this basis a computation can be made with straightforward and elementary procedures. It must be remembered however that this assumption neglects hysteresis

274

WINFIELD E. FItOMM

losses, curvature of the corners of the magnetization curve, and the small but important finite inductance of the magnetometer in saturation. Experience shows t h a t these approximations, with the exception of the latter, can be made with the materials that are usually employed in the 70 r

-20 -30

-

UNBALANCE RESISTOR=480 OHMS

-40 -

-50 -60

-

-70

FIG. 7. Pulse output of unbalanced magnetometer bridge with zero external magnetic field.

magnetometer. The finite inductance present during saturation prevents the very steep discontinuities in current shown, for instance, in Fig. 8. With reference t o Fig. 8 the current is computed in the coil of a magnetometer whose characteristics are as follows: impedance in saturation, 120 j 0 ohms; impedance out of saturation a t 400 cycles, 240 j550 ohms; saturation level, 15 ma; internal impedance of generator, 120 j 0 ohms; maximum emf of the generator, 19.7 v (sinusoidal).

+

+

+

MAGNETIC A I R B O R N E D E T E C T O R

275

L

-90

FIG.8. Current waveforms in single-coil magnetometer with zero external magnetic field.

The curves drawn in Fig. 8 are as follows. Curve A is the current t h a t would flow in the magnetometer coil if it were always in saturation. We call this current the saturation current. Curve B is the current t h a t would flow in the magnetometer coil if its impedance were always that of the unsaturated case. We call this the below-saturation current.

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WINFIELD E. FROMM

The solid line (curve C) is the net current that mill actually flow under the conditions listed above. Beginning from point P I the current is above saturation and therefore the current of the magnetometer is controlled by curve A down t o an angle of about 170” at which the magnetometer goes out of saturation. The current a t this point Pz cannot change suddenly because of the presence of the inductance and therefore a transient takes place along curve P2-P,. This transient is computed with reference t o curve B because the current tends to approach exponentially the “permanent” current curve represented by it. A t point P a the current has gone through zero and increased negatively to the negative saturation value a t point P,. The current then rises in a steep discontinuity to point Pq corresponding again to curve A, the saturation current. (Were the finite inductance actually present during saturation taken into account, the rise from P 3 to Pq would be exponential.) Curve A is followed until the magnetometer goes out of saturation at point Pg and a transient takes place from point P s t o point P s identical to that described for the transient from P z t o Pa. The previous procedure leads to the determination of the net current (curve C, solid line, Fig. 8) flowing in the coil of the magnetometer. Once this current is determined all problems regarding the application of a magnetometer can be solved. For instance, if one desires to determine the shape of the voltage across the magnetometer coil, one must subtract the voltage drop across the internal impedance of the generator from its generated emf. When this is done a voltage of the type shown in Fig. 9 will be obtained. In order to determine the behavior of a magnetometer in the presence of an external field, one must visualize the difference introduced in the curves of Fig. 8 by a change in the value of the current a t which saturation occurs. For instance, for the magnetometer of the characteristics described above, a negative field (i.e., one aiding a negative current) of 10 gammas requires an increase in the positive saturation level from 15 to about 15.0004 ma and a decrease of the negative saturation level from 15 to 14.9996 ma. An accurate graphical analysis for this case cannot be carried out of course without a large increase in the scale of the diagram, but an understanding-of the nature of the phenomenon can be obtained by direct observation of the current shape of Fig. 8. Assuming such a field is present, the current required for saturation will be increased a t points Pz and Pe and will be decreased a t points P , and Pa. For this reason the sharp increase in current from point Psto point P I will occur slightly later than the time shown in the diagram. The rise in current from point P3 to point P , will occur slightly earlier. For this reason the current shape is no longer 180” antisymmetrical; this means

MAGNETIC AIRBORNE DETECTOR

277

that what occurs around 76" in the positive cycle differs from what occurs 180' later a t 256" in the negative cycle. The tlitfcrence in timing of each rise is very small. For instance, a n exact aiialysis of the case shown in Fig. 8 would show that a field of 10 gammas in this magnetometer would cause a time difference of the order of 3 millimicroscconds. The effect of inductance during saturation can be computed t o a first approximation by assuming that these pulses are applied t o a circuit containing resistance R and inductance L in series. The result is that

r

L Voltage waveform across single-coil inagnctometer with zero extcriid

FIG. 9. magnetic field.

the width of the pulses is controlled by the time constant R / L of the circuit, while their amplitude is a function of the product of the width times the amplitude of the narrow pulses predicted by the simplified theory outlined above. If the balanced circuit of Fig. 5 is employed, the current present a t the detector output will consist of the difference between two curves each sirnilair t o curve C of Fig. 8 but with modified saturation levels because of the presence of an external field. The saturation levels of the two magnetometers are always shifted in opposite directions (one increased, one decreased) since the coils are wound in opposite directions. It is quite evident that a small shift in the value of the saturation current

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WINFIELD E. FROMM

levels will leave the regions of the curve between PI and P Zand between

P , and P 6 unchanged so that during the time corresponding t o the intervals between about 76" and 170" and between 256' and 350" the output a t the detector terminals is zero. At 76" and a t 256" there will be a pulse of about 65-ma amplitude, which according t o this simplified theory would be a few millimicroseconds wide. During the time interval corresponding t o the transients between P z and P B ,and P5 and P,, there will be a current yave shape corresponding to the difference between the transients, and opposite in polarity from the pulse immediately following it. \;Ii hile it is impossible to draw current shapes corresponding to the output of a balanced bridge for fields as low as 10 gammas, the shape of the current can be visualized if one refers t o that computed for much larger outside fields. For instance, for a n outside field of the order of 250,000 gammas the theoretical shape of the current a t the detector output has a form shown in Fig. 6 . Of course the width of the pulses is much larger, and in this case is equal t o 250 microseconds. It is obvious from a n observation of Fig. 6 that only even harmonics are present a t the detector output as was explained in a qualitative fashion earlier. The effect of an unbalance resistor RB across one of the windings of the balanced magnetometer bridge of Fig. 5 is much more difficult t o visualize because a resistance in parallel with one winding has the effect of changing several of the important parameters. I n this case winding L1 behaves as if it were supplied by a generator at a lower emf and lower internal resistance. It is possible by a n analytical approach to determine the actual shape of the current output in the case of small unbalances as those employed in practice; however, the complication of the mathematics is such as t o make it much more desirable t o resort again to a graphical illustration. For instance, in Fig. 7 is given the shape of the current a t the detector output for the case of the magnetometer bridge of Fig. 5 with unbalance resistor R3. The value of the unbalancing resistor is here assumed t o be 480 ohms. This is between 50 and 150 times lower than the values employed in practice. For this reason, while the shape of the current is representative of the effect of unbalancing resistors, the width of the corresponding pulse has been greatly increased. In the case of Fig. 7 it is apparent that since the computation was made assuming that no external field was present, the current wave contains only odd harmonics. The width of the pulse is about 125 microseconds. The effect of a n external field is t o increase the width of the pulses in proportion with the magnitude of the field in the same manner as described for the balanced bridge. The amplitude of the pulses in the case where the saturation impedance is purely resistive changes only slightly with an external field present. I n practical cases, however, the

.

MAGNETIC AIRBORNE DETECTOR

279

amplitude becomes nearly proportional to the field because of the reasons given above. We must remember that in our analysis we have neglected the curvat)ure of the magnetization curve. This as well as the finite inductance of the magnetometer in saturation prevents steps of current as sharp as those shown in Fig. 8. I n practice, where these characteristics may not be neglected, the amplitude as well as the width of the pulses changes both for the balanced (even harmonic) and unbalanced (peak type) magnetometers. The finite inductance of the magnetometer in saturation is probably more important in determining the rise time of the steps than the curvature of the magnetization curve. The balanced output pulses of the unbalanced bridge definitely change therefore in amplitude as the external field changes. The change is in one direction, t h a t is, positive pulses increase and negative pulses decrease, or vice versa, as we would expect with the presence of even harmonics. The unbalanced bridge has an advantage over the balanced in that the signal pulses are above the “noise” level, even with zero external field. Consequently, it is often used as the magnetometer bridge in both detector and servo applications. I n this section we have indicated how the saturable-core elements may be used as magnetometers, either singly or in bridges. Two types of bridges have been described, the balanced and the unbalanced. The unbalanced is characterized by a n electric unbalance purposely inserted by means of a resistive (or sometimes reactive) element, and the output of which consists of pulses symmetrical about the base line in the absence of a n external field. The balanced bridge is characterized by even harmonic output only in the presence of an external magnetic field. The methods by which both of these bridges, particularly the unbalanced one, can be used in magnetic stabilization are described in the next section. V. MAGNETIC STABILIZATION A N D ORIENTATION Each of the five types of magnetometers suitable for airborne use produce outputs that are proportional t o that component of field parallel or perpendicular t o some specific axis of the magnetometer, except for the coil inductor whose output, as we have seen, is proportional t o the change in a component of the field. Because of this and the fact that the earth’s magnetic field is always present as a strong ambient field, a magnetometer must be stabilized accurately if the detector noise level is t o ’ b e kept low enough so that very small signals can be identified. This section will consider some of the aspects of magnetic stabilization, the importance of proper orientation of the magnetometer, methods of

280

W I N F I E L D E. FROMM

magnetic stabilization and orientation, and special methods by which the stabilization requirements may be relaxed. 1. Stabilization and Orientation in the Ea,rth’s Magnetic Field Figure 10 shows a simplified diagram of a saturable-core magnetometer stabilized with respect t o the earth’s field. Usually i t is desired t o stabilize the magnetometer parallel t o the earth’s field, and that is the intention in Fig. 10. However, a n initial misalignment angle 4 and a dynamic stabilization error angle 6 can both affect the orientation angle of the magnetometer. These angles are indicated in the figure.

/”

EARTH’S MAGNETIC FIELD

MAGNETOMETER

0=

INITIAL MISALIGNMENT ANGLE OF MAGNETOMETER WITH EARTH FIELD VECTOR

8 = DYNAMIC STABILIZATION ERROR ANGLE

FIG. 10. Diagram showing initial misalignment and dynamic stabilization error angles of a detector magnetometer.

In some geophysical applications it is necessary t o measure continuously the magnitude of the earth’s field. I n such cases the initial misalignment angle 4 causes a direct, static error equal t o H(1 - cos 4). If a stabilization error angle 6 exists, the dynamic error then becomes H[1 - cos (4 6)]. This may be greater or less than the static error but, t o a first approximation, its average value will equal the static error. If we are interested in measuring only the changes in the earth’s field (or, more strictly, the external field H ) , as is the case in submarine detection from aircraft and in some geophysical applications, the dynamic error is the only one of significance. It is, however, a function of both angles 4 and 6. I n this case the noise signal caused by imperfect stabilization of the magnetometer is

+

MAGNETIC A I R B O R N E D E T E C T O R Xn =

H[COS 4 - cos (4

= H[cos 4 (1

where

+ e)] + sin 4 sin el

- cos 0 )

28 1 (2) (31

X, = noise signal H 4

magnitude of earth's magnetic field initial misalignment angle of magnetometer with the earth field vector 0 = dynamic stabilization error angle. From (2) we note first that if e = 0, the noise signal is zero, no matter what the misalignment. Secondly, if 0 is small (as i t is in practice) S,, as given by (3), is a minimum when 4 = 0" and a maximum when 4 = 90". Thus, if 4 = O", S,, = H(1 - cos e), and, if 0 is small, X,, = H ( l - 1 P / 2 ) = H 0 2 / 2 H , where e is in radians. If 4 = go", S,,, = H sin 8, and, if 0 is small, S,,, = H e , where 0 is in radians. The equations for S , a t 0" and 90" are of fundamental importance in magnetic stabilization. From them we obtain the ratio = =

+

A common value for 0 is about 5 minutes, or 0.0015 radian, in which case the ratio S,,,/S,, = 1330. This ratio indicates clearly the tremendous advantage t o be gained in aligning or orienting the detector magnetometer parallel t o the earth magnetic field vector. When the magnetometer is oriented exactly parallel t o the earth's field, the equation for X,, may be used t o give directly the noise signal caused by imperfect stabilization. Figure 11 is a graph of noise sig,ial versus dynamic stabilization error angle for this case. The earth's field has been assumed t o have a typical value of 50,000 gammas. Although (4) has indicated the importance of orienting the magnetometer parallel t o the earth's field, i t does not show the accuracy with which the orientation should be made. From (3), however, we see t h a t if 0 is very small and 4 is small but not zero, S,

=

H

(g +

98)

(5)

Figure 12 is a graph of noise signal versus 4, the angle by which the magnetometer is misaligned from the earth's field, for a dynamic stabilization error angle of 0.0015 radian (5 minutes). The earth's field has again been assumed t o have the typical value of 50,000 gammas. From this graph we see that very precise orientation is required for this type

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W I N F I E L D E . FROMM

e = STABILIZATION

/ 0

2

4

6

/

ERROR, RADIANS

MAGNETOMETER ORIENTED PARALLEL TO EARTH FIELD

I

I

I

I

I

1

8

I0

12

14

16

la

DYNAMIC STABILIZATION ERROR IN MINUTES

FIG.11. Noise versus dynamic stabilization error. 05

r SN= H p * + H 8 0 H: 50,000 GAMMAS

8 = .0015 RADIAN ( 5 MINUTES)

0

I

I

I

I

I

I

I

I

I

MISALIGNMENT ANGLE 0 IN MINUTES

FIG.12.

Noise versus detector magnetometer misalignment angle.

of magnetometer if the noise signal is t o be kept small. For instance, in this example a misalignment of only 2.3 minutes doubles the noise from 0.05 gamma t o 0.1 gamma. It should be realized that the discussion thus far and Figs. 10, 11, and 12 apply only t o stabilization of the magnetometer in one plane, or in one

MAGNETIC AIRBORNE DETECTOR

283

degree of freedom. The detector magnetometer actually must be stabilized in two degrees of freedom. This is normally done by stabilizing a platform mounted in gimbals similar to those used in compass supports. The two perpendicular axes of rotation ordinarily are called the pitch and roll axes. Assuming that the stabilization error is the same in each degree of freedom and that the two errors are maximum a t the same time, the resultant and effective stabilization error angle is 1.4 times the error of each; This angle may then be used with Figs. 11 and 12 to give the resultant noise signal. One further point should be mentioned. It so happens that most of the energy in the noise due to stabilization errors occurs in the same restricted frequency spectrum as the energy of the submarine or geologic signal. The signal-to-noise ratio is therefore little affected by the frequency characteristics of the detector circuits, and the noise levels given by Figs. 11 and 12 are representative of those obtained in practice from stabilization and orientation errors. 2. Methods of -Magnetic Stabilization and Orientation

The saturable-core magnetometer is ideally suited to function as a stabilization control element because of its small size and high sensitivity. Furthermore, it was shown in See. IV that both the peak and even harmonic types of magnetometers supply amplitude and sense information when operated about the zero value of axial field. At this zero value the peak type magnetometer produces balanced output pulses of opposite polarity. If an axial field appears (such as might be caused by the magnetometer rotating out of a plane perpendicular to the earth’s field) the absolute difference of the pulse heights is proportional to the axial field. The polarity of the difference is determined directly by the polarity of the field. In a similar fashion, the even harmonic magnetometer produces an even harmonic output proportional to the axial field. The phase of each even harmonic reverses as the axial field reverses in polarity. The outputs of both magnetometers therefore possess the necessary characteristics of amplitude and sense for servo control. It is highly desirable to position the stabilizer magnetometers in the manner just described, because, as shown above, maximum useful output is obtained for a given stabilization error when the magnetometer is perpendicular ( 4 = 90’) to the earth’s magnetic field. In general, then, the detector magnetometer should be oriented parallel to the earth’s field to minimize noise due to stabilization errors. Conversely, stabilizer magnetometers should be mounted in a plane perpendicular to the earth’s field vector H to provide servo operation with maximum sensitivity.

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W I N F I E L D E. FROMM

Figure 13 is a schematic diagram of a magnetically stabilized magnetometer head employing the principles just outlined. The stabilized platform Carrying detector magnetometers D-D and stabilizer magnetometers 1-1 and 2-2 is mounted on a shaft driven by rotary drive 1. We may call the axis of this shaft the pitch axis. The pitch axis shaft is carried in bearings mounted in the roll gimbal which is driven by rotary drive 2 . The axes of rotary drives 1 and 2 are frequently called respectively the inner and outer axes. All the magnetometers are connected as pairs in bridge circuits for increased sensitivity. Magnetometers 1-1 control rotary drive 1.

MAGNETIC FIELD ROTARY DRIVE

FIG.13. Schematic diagram of a magnetically stabilized magnetometer head.

Whenever a component of H exists parallel to their lengths, a signal (pulses or even harmonics) is produced. This is directed to a servo amplifier that usually drives an electric motor (though it may control a gyroscopeg) connected t o rotary drive 1. The sense of the resulting rotation is such as to reduce the component of H along the magnetometers t o zero. Magnetometers 2-2 control rotary drive 2 in a similar fashion. Thus the magnetometers 1-1 and 2-2 maintain themselves and the stable platform perpendicular to H despite the movements of the aircraft in flight. The detector magnetometers D-D mounted normal to the stable platform are thus maintained parallel to H . In Fig. 14 is shown a photograph of one type of magnetometer head used extensively for submarine detection during World War 11. The various parts of this head are easily identified. Figure 15 is a photograph

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285

of the complete head and shows the driving motors a t the lower end of the head frame. The head and frame must be essentially nonmagnetic t o avoid unwanted magnetic fields a t the detector magnetometer. For this reason the slightly magnetic motors are mounted some distance away from the magnetometers.

FIG.14. Two-axis magnetometer head showing pitch and roll axes.

The possibility of using either peak or even harmonic magnetometers for stabilizer elements has been noted. Both types have been used in practical systems. The even harmonic system suffers the disadvantage of requiring substantial filtering t o accept the desired even harmonic and t o reject unwanted even and all odd harmonics. For instance, if the second harmonic is accepted, both the fundamental and third (as well

286

WINFIELD E. FROMM

as higher) harmonics must be rejected. The amplitudes of both of these harmonics always are much larger than the small second harmonic signal; therefore excellent filters (in this case, sharply tuned bandpass filters) are needed. However, the severe phase shifts introduced by such filters must be carefully considered from the standpoint of servo stability. Ordinarily, these phase shifts complicate considerably the design of high-performance servos. In general, peak magnetometer systems are less complicated, require fewer components, and give satisfactory performance. A combined schematic-block diagram of the electronic portion of a single stabilizer channel with peak magnetometers is shown in Fig. 16. Conventional portions of the circuit are shown in block form. The diagram shows that the output pulses of the magnetometer, occurring at a pulse repetition frequency of f cps, are amplified and passed through a diode charging circuit that includes the R-C network. This network acts both as a pulse stretcher and an antihunt circuit for the servo system. The balanced sawtooth voltages, 180" out of phase, are combined in the mixer circuit. When the sawtooth voltages are equal, the mixer output contains only a sawtooth voltage of frequency 2f. However, a slight unbalance of pulses due to stabilization error results in a fundamental component (f cps) a t the mixer output. The phase of the fundamental component depends upon the direction of the stabilization error. The fundamental component is filtered, amplified, and applied to the control field of a high-performance two-phase FIG. 15. Two-axis servo motor with a low-inertia rotor. The magnetometer head with system is so phased that the rotor turns in a servo motor assembly. direction that reduces the stabilization error. In analyzing the stabilizer servomechanism, two distinct aspects of the problem must be considered. The first is the static condition in which the aircraft is motionless. Here the system is an electromechanical closed loop and it may easily be unstable, in which case the supposedly stable platform will oscillate violently. Antihunt circuits in the system usually provide reasonable stability for this condition. The second

MAGNETIC AIRBORNE DETECTOR

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287

condition is the dynamic one, in which the aircraft imparts translatory and semi-rotary motion t o the magnetometer frame. Under these dynamic conditions, the platform must not rotate (with respect to the earth's field), except for very small stabilization errors. The forcing or input function is the displacement of the frame. The output function is the equivalent displacement of the motor shaft after a mechanical reduction. The difference of the input and output functions is exactly equal to the small displacement of the stable platform and is the stabilization error. It is important to realize that in the dynamic condition one is primarily interested in dynamic response, or minimum stabilization

I

I I I

I

I

a

FIG.16. Schematic-block diagram of stabilizer channel with peak type magnetometer bridge.

error, and that the inertia of the stable platform is directly coupled to the error shaft of the system. Thus, increasing the inertia of the stable platform and decreasing the friction of the bearings will effectively improve the dynamic response of the system. It is interesting to note the restrictions on the use of the two-axis gimbal system for stabilizing the detector magnetometer. There are actually three possible mountings for this system, and these may be defined with respect to the airplane as follows: (a) outer axis horizontal and in line with the direction of flight; ( b ) outer axis horizontal and perpendicular t o the direction of flight; (c) outer axis vertical and perpendicular t o the direction of flight. Mounting (a,) is that used in the head of Figs. 14 and 15. This mounting is especially useful in regions where the magnetic dip angle is greater than 45". For dip angles below this, and especially for small or zero dip angles near the magnetic equator, operation of the system will

288

WINFIELD E. FROMM

fail in a lateral turn of the aircraft. This is because a unique position of the gimbal system about the outer axis is not defined when the detector magnetometer is in line with the outer axis. This undefined position occurs for instance on a north or south heading a t the magnetic equator. I n such a case, the slightest deviation in heading from north or south immediately defines a unique position of the system about the outer axis, and very high gimbal velocities will be required t o stabilize the platform properly without introducing noise signals due t o stabilization errors. Practical systems are unable t o correct errors this rapidly, SO that "gimbal locking" must be avoided. This is done by operating mounting (a) only a t the higher dip angles. Mounting (b) has limitations similar t o those of (a,) and a n additional one. I n (b) gimbal locking also occurs when the detector magnetometer is in line with the outer axis. This alignment would occur a t the magnetic equator on a n east or west heading. However, this could also occur for the same headings in a region of 45" dip angle if the aircraft banked 45" in a direction such as t o cause the axes of the detector magnetometer and outer gimbal t o coincide. Because bank angles are higher than pitch angles [by which ( a ) is similarly affected] mounting ( b ) is less practical than ( a ) and operation with i t is limited t o dip angles above about 60". Mounting (c) is limited t o equatorial regions where the dip angle is small. With this mounting the complement of the dip angle must always exceed the angle of bank. Assuming a bank angle of 45" and a leeway of 15", the mounting is satisfactory only for regions with a dip angle of less than 30". A further disadvantage of ( c ) is that successive turns of the aircraft in one direction require continuous, unobstructed rotation about the vertical axis of the gimbal system. This bars the use of pigtail electrical connections and requires slip rings. One advantage of (c) is that only a 90" change in mounting converts an equatorial unit t o a polar unit. None of the mountings ( a , b, or c) is satisfactory in itself for all dip angles. From the preceding discussion it is evident that a ('universal" head that will function a t all dip angles can be made by adding a third gimbal t o the two gimbals already described. The three gimbals of such a head are shown in Fig. 17. The entire head is shown in Fig. 18. This head employs a two-axis gimbal system with mounting ( b ) , but with a n added third gimbal axis horizontal and in line with the direction of flight. Neither the first (inner) nor second (outer) is fixed with respect t o the aircraft; both may rotate about the third axis. The function of the third axis is t o defeat the tendency of the detector element t o come in line with the outer axis a t one particular heading. T o

MAGNETIC A I R B O R N E DETECTOR

289

accomplish this, motion of the gimbal system about the third axis is made a function of the movement about the first axis of the detector element from its neutral position (with respect to the outer axis). When motions

FIG.17. Three-axis magnetometer head showing pitch, roll, and third axes.

about the first and third axes are set for approximately one-to-one ratio, these two axes share equally the movement of the aircraft relative to the earth’s magnetic field, and alignment of the detector element and outer axis is impossible. The gimbal system of the universal head therefore functions satisfactorily a t all magnetic latitudes. In reality, the third axis provides a variable combination of mountings ( b ) and (c). The motion about the third axis need only be approxi-

290

WINFIELD E. FROMM

mately as fast as the average rate of aircraft turn or bank. Thus the third axis servo need not be one of high performance. Control for the third axis motion may be achieved in several ways. The head in Figs. 17 and 18 employs pick-up coils mounted on the second axis gimbal. The alternating magnetic field of the driving current in the detector magnetometer coil induces a voltage in the pick-up coils, and this voltage is used as part of the control signal for the third axis servo. Alternative methods of control include the use of low-friction switches or potentiometers mounted on the second axis gimbal, with the variable arm of the switch or potentiometer controlled by motion about the first axis. The control system is ustially complicated by the necessity of introducing for comparison an electrical signal representing the position of the third gimbal with respect to the head frame. 3. Special Methods

a. Three-Component Clnstabilized Tota.1 Field Magnetometer. In a three-component unstabilized total-field magnetometer there are three similar, mutually perpendicular magnetometer elements mounted rigidly in a framework that is unstabiliaed. The outputs of the three magnetometers are squared and added; the resultant is then proportional to the square of the total magnetic field. Such a system has been used to explore the earth's magnetic field at very high altitudes.'O Although the three-component system is simple, operation a t very low noise levels places stringent requirements on its electrical and mechanical FIG. 18. Three-axis characteristics. For instance, an error of 4 minm a g n e t o m e t er head utes in the perpendicularity of one magnetometer w i t h servo m o t o r can result in 0.1 gamma noise with an ambient assembly. field of 50,000 gammas. For the same noise, the allowable departure from perfect squaring for any single magnetometer output is only 0.001%. Requirements on linearity and summing are also very strict. Because of these practical difficulties, the three-component unstabilized magnetometer has been used only where relatively insensitive detection is adequate.

MAGNETIC A I R B O R N E D E T E C T O R

29 1

b. Three-Component Stabilized Total Field Magnetometer. The requirements on alignment, squaring, etc., of the three-component magnetometer are eased considerably if the system is stabilized with respect t o the earth's magnetic field in a manner somewhat similar to that described earlier. Two of the orthogonal elements are used as stabilizer elements and supply signals of such phase and amplitude that continuous control servos maintain the elements perpendicular to the ambient field. The third orthogonal element is thus maintained parallel to the ambient field exactly as in simpler stabilized magnetometers. However, each of the three elements is also a part of the detection system and the squared outputs of each are added t o give a quantity proportional t o H 2 . A magnetometer of this type was developed and used during World War I1 and has been employed since 1945 in geophysical surveying." The thrcc-component stabilized magnetometer has the advantage over the single-detector stabilized magnetometer in that stabilization requirements are eased somewhat if accurate squaring and proper alignment between elements can be achieved. We have seen t h a t the noise of the single-detector stabilized magnetometer is

8, where 0

=

H

(a +

$0)

(5)

dynamic stabilization error angle misaligiimciit angle of magnetometer with the earth field vector. The corresponding expression for the three-component stabilized magnetometer can be shown t o be (assuming perfect squaring, summing, and linearity) S , = H+O (6) =

+ = initial

Here 4 is defined as above with the understanding that it is a t the same time the misalignment angle of the third element with respect to a true perpendicular t o the two stabilizer elements. I n other words, the stabilizer elements are oriented exactly perpendicular to the earth's field. It should be noted a t this point that in the case of the single-detector stabilized magnetometer, can be made zcro or very small by the simple expedient of static electrical adjustments on either or both servomechanism channels (first and second axes). However, this cannot be done in the case of the three-component stabilized magnetometer where the magnitude of is determined solely by the mechanical misalignment of the magnetic axes of the magnetometers. I n practice this is usually at least several minutes of arc and may easily be much more.

+

292

=INFIELD

E. FROMM

Equations (5) and (6) are plotted as curves A and B respectively in Fig. 19. For simplicity, i t is assumed that the misalignment angle 4 is 2 minutes in both cases, but it should be remembered t h a t although this is easily achieved in the single-detector case, it is a very optimistic figure for the three-component case. I t is evident that the three-component system permits greater stabilization error for a given noise, particularly for relatively large noise levels. However, for small noise levels (below 0.1 gamma) there is little practical difference in the servo accuracy required in the tn-o systems. When the added requirements of accurate 07

06

.

t i = 50,000 GAMMAS 0 = MISALIGNMENT ANGLE = 2 MINUTES (ooO6 RADIAN) 8 = STABILIZATION ERROR, RADIANS

05 ul

5

04

0

G

#

0

03

02

STABILIZED SINGLE-DETECTOR

01

0 2

4

6

8

10

12

14

16

18

DYNAMIC STABILIZATION ERROR IN MINUTES

FIG. 19. Xoise versus dynamic stabilization error for stabilized single-detector and three-component niagnctomcters.

squaring, summing, etc., in the three-component magnetometer are considered, it appears that the advantages o f its use in very high-performance magnetic airborne detectors are not outstanding.

TI. ~ I A G X C .IIRI~ORSE TIC DETECTOR Swrm I n this section we shall consider the overall system of a universal magnetic airborne detect or employing a single-detector stabilized magnetometer. This is tlic type used most extensively up t o the end of M’orld War I1 for military uses and is of a kind employed today in geophysical prospecting. The block diagram for the single-detector magnetometer employing

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MAGNETIC AIRBORNE DETECTOR

three axes of stabilization is shown in Fig. 20. The equipment consists of four principal units: (1) universal head, ( 2 ) drive amplifiers, (3) servo amplifiers, and (4)detector. These will be considered briefly. 1. Universal Head This is the magnetically sensitive portion of the equipment. It is usually mounted on the aircraft in a region of low spurious magnetic fields and gradients. It may also be towed in a nonmagnetic housing behind the aircraft. The head contains the detector and stabilizer magnetometers, a n appropriate gimbal system with three axes, and a PRIMARY POWER-I

-

i I

REGULATED POWER WPPLY

I

PULSE OR EVEN I

AMPLIFIER

I II

STABILIZER

PHASE 2 0 MOTOR

DETECTOR

131 AXIS

MOTOR

PHA5E

wixlsz 0

THIRD A X I S SENSE COIL

MOTOR -

1

I _ _ _ _ _ _ _ _ _!?1IE_R_sLL?kXJ%LEE--_-___-1 L

FIG.20.

Block diagram of universal MAD system.

servo motor for each axis. The motors are mounted a t some distance from the magnetometer t o reduce undesired magnetic effects. The gimbal system of the universal head was described in Sec. V. The system is "universal" in that one mounting is adequate for all magnetic latitudes. 2. Drive Amplifiers This unit includes a stable audio oscillator operating with negligible harmonic distortion a t a compromise frequency satisfactory for both magnetometers and servo motors. The oscillator output is amplified in the three separate amplifier stages to drive respectively the detector magnetometers, the stabilizer magnetometers, and the fixed phases of the three servo motors. The detector magnetometer drive amplifier

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WINFIELD E. FROMM

must be carefully designed t o achieve the stability.and very low harmonic distortion essential for sensitive detection. 3. Xeroo Amplifiers

The universal MAD has three servo amplifiers. The first (inner) axis and second (outer) axis servo amplifiers are normally driven from peak magnetometers as shown in Fig. 16. These two amplifiers must be carefully designed t o make possible the servo accuracy of a few minutes of arc required for a high performance MAD. This servo accuracy must be maintained for all normal maneuvers of the aircraft. The third axis servo amplifier is normally driven from a pick-up coil sensitive in phase and amplitude t o the detector magnetometer driving flux. This servo amplifier is a relatively insensitive one because the response of the third axis servo system need only be approximately as rapid as the average maneuver rate of the aircraft.

4. Detector A magnetic airborne detector is in reality a magnetic anomaly detector. The MAD indicates the presence of a n anomaly in the earth’s magnetic field. Such a n anomaly (caused by a submarine) is illustrated in Fig. 1. An anomaly may also be caused by variations in the magnetic characteristics of the earth’s surface that cause fairly extensive effects on the main field of the earth. The extent of the anomaly may thus be localized, as in the case of the submarine, or it may cover a wide area, as in the case of geological effects. I n any event, the detector portion of the system must be designed t o detect signals from desired anomalies and reject signals from undesired anomalies. The manner of detecting a magnetic anomaly, as we have sren earlier, is to detect the component of the anomaly field parallel t o the earth’s field, and thus parallel t o the longitudinal axis of the detector magnetometer. The magnitude of this component affects directly the output of the magnetometer bridge. Modulation of the output appears as a difference in the pulse heights of a peak type detector, or as a difference in the even harmonic output of the magnetometer bridge. It should be noted here that in describing MAD systems, the term ‘ I detector magnetometer” is used t o include both single-coil magnetometers and magnetometer bridges, since both types are used in practical systems. Both peak and even harmonic types of detection have been employed. The block diagram of Fig. 20 indicates both. I n either case, the carrier (pulses with pulse repetition rate f , or a n even harmonic off) is amplitudemodulated a t a signal frequency determined by the extent of the anomaly

MAGNETIC AIRBORNE DETECTOR

295

and the altitude and speed of the aircraft. The amplitude-modulated carrier is amplified, then demodulated. The modulation or signal frequency may vary from essentially zero to a few cps. Consequently the following d-c or very low frequency amplifier incorporates a bandpass filter designed to accept desired signals and reject undesired ones. I n general, for anomalies of great extent such as are encountered in geophysical surveying, signal frequencies are lowest and d-c amplifiers with low-pass filters are used. For more localized anomalies, bandpass filters are employed. The very low-frequency signal is usually amplified sufficiently to drive a recorder producing a permanent inked trace. The time scale of the recorder is useful in mapping the magnetic contours.

VII. THENOISEPROBLEM The noise or interference th at appears as continual or intermittent fluctuation in the MAD output is important because it defines the smallest detectable signal. There are three classes of background interference: (1) instrumental noise, (2) aircraft noise, and (3) noise from sources external to the aircraft. 1 . Instrumental Noise

Instrumental noise originates within the MAD itself. It may be divided into four types. a. Electrical Noise. As in all high-gain systems, fluctuations in supply voltages or microphonics in vacuum tubes may cause noise. b. Magnetic Noise. Unless transformers, inductors, and vacuum tubes in low-level portions of the circuits are magnetically shielded, movement or tilt of the equipment in the earth’s magnetic field may cause noise. c . Stabilization Noise. This was discussed in detail in Sec. V. The noise t o be expected for a stabilized single-detector system is plotted in Figs. 11 and 12. d. Magnetometer Noise. The noise from the saturable-core magnetometer (or any other detecting device) is basic and represents the absolute minimum noise level for the system. I n a saturable-core magnetometer there is a small noise output due to thermal agitation effectsI2in the coil, but a more serious noise results from the Barkhausen effect.12,13,14 It is well-known that the process of magnetization is a discontinuous one because of the domain structure of ferromagnetic materials. It has also been demonstrated (Zoc. cit.) that a representative magnetization

296

WINFIELD E. FROMM

curve for these materials can be divided into three parts: (1) the initial portion where reversible domain boundary displacements occur, ( 2 ) the middle portion where irreversible boundary displacements occur discontinuously, and (3) the upper portion where reversible rotation of the domain magnetic moments occurs smoothly. Barkhausen discontinuities occur when the magnetization is changing along the steep, middle portion (2) of the magnetization curve. The discontinuities correspond t o the irregular fluctuations in the motion of the domain boundary (termed the Bloch wall) as the applied magnetic field is changed. The Barkhausen discontinuities are not repeated exactly from cycle t o cycle, so that the amplitude and phase of the harmonics generated by the nonlinearity of the magnetometer are altered from one cycle t o the next. The random variation in amplitude and phase of the harmonics appears as noise in the magnetometer output. Saturable-core magnetometers have been built with a n equivalent noise level of the order of 0.02 gamma for a bandwidth of 1 or 2 cps. 2. Aircraft Noise Aircraft (or carrier) noise is defined as that caused by a relative movement of the MAD head (carrying the detector magnetometer) with respect t o magnetic fields generated by ferromagnetic or conducting parts in the aircraft. The ferromagnetic parts (engines, landing gear struts, etc.) may have permanent or induced moments that produce strong fields a t the detector. Movements of the aircraft may cause the component of the resultant field parallel t o the magnetometer axis t o change considerably, thus causing noise. Conducting parts (wing surfaces, etc.) may support eddy currents caused by movements of the aircraft in the earth’s magnetic field, and the magnetic fields set up in turn by these eddy currents may cause serious noise signals. Aircraft noise in general may be reduced by locating the MAD head appropriately on the aircraft in a region of small spurious magnetic fields and gradients. Such a region may be found a t the wing tip or aft of the tail structure. The noise may be greatly decreased by towing the MAD head in a nonmagnetic streamlined housing well behind or below the aircraft. Both types of installation have been employed. I n aircraft installations where spurious fields are not small, noise signals may be reduced by applying a systematic compensation technique t o cancel all or most of the locally generated fields a t the detector magnetometer. Considerable success has been achieved with this procedure, hut it is not a simple one. Small permanent magnets must be oriented properly t o neutralize fields due t o permanently magnetized parts, strips

MAGNETIC AIRBORNE DETECTOR

297

of high permeability material are oriented t o neutralize fields due t o induced moments, and fields due t o eddy currents are neutralized by the magnetic field of a n output coil controlled by the amplified signal of a properly oriented pick-up coil. The compensation procedure must be repeated a t frequent intervals because of changes in the magnetic characteristics of the aircraft structure. 3. Noise f r o m Sources External to the Aircraft The noise is caused by time and space variations in the magnetic field of the earth. a. T i m e Variations in the Earth’s Fzeld. An exhaustive survey over the entire frequency spectrum of time variations in the earth’s field has not been made. The amplitude of such variations will depend t o a considerable extent on the geographical location. For instance, in high latitudes time fluctuations may be of very high amplitude, particularly in the zones of maximum occurrence of aurora, while in the temperate or equatorial zones the fluctuations may be quite small. b. Space Variations zn the Earth’s Field. Space variations may be divided into two types: uniform and nonuniform. Uniform variations are those due t o the normal vertical and north-south horizontal gradients of the earth’s field. Nonuniform variations are those caused by geological discontinuities in the earth’s crust with resultant variations in the earth’s magnetic field. I n geographical prospecting signals caused by such variations may or may not be regarded as noise. The vertical gradient of the earth’s field lies between 0.005 gamma per foot a t the magnetic equator and 0.01 gamma per foot a t the poles. Altitude fluctuations of 10 ft can therefore produce noise signals of about 0.1 gamma. The north-south horizontal gradient is about 0.0015 gamma per foot, and fast maneuvers may produce some noise from this source. The signals due t o variations in geologic structure may be very large. For instance, over shallow water or land where magnetic rocks are very close t o the surface, the magnetic anomalies may have amplitudes of hundreds of gammas. Small signals are usually completely masked in such regions. On the other hand, over deep water or in regions where the magnetic rocks are a t great depth, the geologic anomaly may not be measurable. I n geological surveys, of course, space variations in the earth’s field are of vital importance. By using MAD systems with direct-coupled detectors it is possible t o plot fairly accurate magnetic contour maps of a region. From these maps certain areas can be pinpointed for more detailed ground surveys. I n such work, naturally, signals due t o the space variations are the desired signals, and all other signals are regarded as noise.

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W I N F I E L D E. FROMM

VIII. CONCLUSION I t is evident from our consideration of the characteristics of magnetic fields from ferromagnetic bodies, and the spurious magnetic fields which may result from various noise sources, that the magnetic airborne detector is essentially a low-range device. The actual range of detection depends of course on the magnitude of the magnetic moment causing the anomaly in the earth’s field. The magnetic airborne detector will undoubtedly find increased use in future geophysical prospecting. It is often possible (though not always) t o save considerable time and money in examining vast areas, particularly when covered by water, if aerial magnetic surveys are made rather than by using the older ground methods of prospecting. The usefulness of the magnetic method depends however upon the existence of a recognizable relationship between the magnetic anomalies and the geological structure being sought, and also upon the random space variations in magnetic field (noise) due to superficial rocks and soil over the terrain being surveyed. The extreme sensitivity of the saturable-core magnetometer has been described. Applications will be found for laboratory and industrial instruments using this device in the detection and measurement of extremely small magnetic fields and direct currents. Detection of fields as low as 0.015 gamma with toroidal magnetometers has been reported12 by the British, and several laboratories in this country have achieved similar results. Direct currents of below 7 x 1O-lo amp, corresponding t o about lo-’’ watt, have also been measured using these instruments.

ACKNOWLEDGMENTS During World War I1 many individuals, both in the United States and Great Britain, contributed greatly to the development of the magnetic airborne detector. Their achievements should be recognized despite the fact that most of their wartime reports must remain unpublished. The author is indebted to Dr. J. W. Joyce, formerly of the Bureau of Aeronautics, Department of the Navy, and presently with the State Department, Washington, for his helpful suggestions regarding this article. R. F. Simons, I. Kasindorf, and F. Rockett of Airborne Instruments Laboratory, Inc., have made valuable critical comments. Special thanks are due Dr. E. G. Fubini of the same laboratory for the material of Sec. IV and for his continuous help and encouragement. REFERENCES 1. Chapman, S., and Bartels, J. Geomagnetism; Vol. I. Oxford University Press, London, 1940. 2. Heiland, C. A. Geophysical Exploration. Prentice-Hall, Inc., New York, 1940.

MAGNETIC AIRBORNE DETECTOR

3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

299

Thomas, H. P. U. S. Patent No. 2,016,977 (1931). Vacquier, V. V. U. S. Patent No. 2,406,870 (1946). Squier, R. T. Electronics, 20, 121 (1947). Wurm, 51. Z. angew. Physik, [2] 6, 210 (1950). Wyckoff, R. D. Geophysics, 13, 182 (1948). Bemrose, J., Heggblom, J. C., Holt, T. C., Richards, T. C., and Watson, R. J. Geophgsics, 16, 102 (1950). Vacquicr, V., Simons, R. F., and Hull, A. W. Rev. Sci. Instruments, 18,483 (1947). Maple, E., Bowen, W. A., and Singer, S. F. J . Geophys. Research, 66, 115 (1950). Felch, E. P., Means, W. J., Slonczewski, T., Parratt, L. G., Rumbaugh, L. H., and Tickner, A. J. Elec. Eng., 66, 680 (1947). Wil!iams, F. C., and Noble, S. W. J . Inst. Elec. Engrs. (London), 97, Pt 11, 445 (1950). Bozorth, R. M. Revs. Modern Phys., 19, 29 (1947). Kittel, C. Revs. Modern Phys., 21, 541 (1949).

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Multichannel Radio Telemetering M. G. PAWLEY

AND

W. E. T R I E S T

National Bureau of Standards, Corona, California, and International Business Machines Corporation, Poughkeepsie, New York CONTENTS

Page 301 11. Evolution of Radio Telemetering.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 1. Television Telemetering .... . . . . . . . . . . . . . . . . . 303 ........................ 2. Instrument Telemeterin 3. Oscillogram Telemetering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. Basic Systems of Radio Telemetering ........ . . . . . . . . . . . . 304 1. Frequency-Division Telemetering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 2. Time-Division Telemetering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 a. Pulse Position Modulation and Demodulation. . . . . . . . . . . . . . 306 b. Pulse Interval Modulation and Demodulation. . . . . . . . . . . . . . 309 3. Factors Determining Choice of Telemetering System.. . . . . . . . . . . . . . . . . 311 IV. Typical Telemetering Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 1. Early Telemetering Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 2. Example of Frequency-Division Telemetering System. 3. Examples of Time-Division Telemetering System. . . . . . . . . . . . . . . . . . . . . 316 a. Typical Pulse Position-Modulated Telemet,ering System. . . . . . . . . . . . 31 6 b. Typical Pulse Interval-Modulated Telemetering System. . . . . . . . . . . . 320 c. Typical Mechanically Commutated Telemetering System. . . . . . . . . . . 325 V. Future Trends in Telemetering., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I. INTRODUCTION A telemeter is defined b y Websterl as an electrical instrument for measuring a quantity, transmitting the result t o a distant station, and there indicating or recording the quantity measured. This definition was satisfactory in the days when single-channel telemetering was the vogue, but now, with the advent of multichannel telemetering, the definition should be revised to include the measurement of one or more quantities. It is the purpose of this review t o describe briefly some advances in the art of radio telemetering which have been made since the period just prior t o World War 11. The multichannel radio telemetering systems t o be described were developed largely for military applications and hence have been illustrated chiefly for application t o the flight testing of pilot30 1

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M. G . PATVLEY AND W. E. TRIEST

less aircraft. It is likely that in the future, there will be more and more applications of telemetering to industry, where a telemeter would provide means for transmitting over a single mire (or radio) link a number of varying measurements for remote indication or recording. E'sually important are the applications of telemetering techniques to remote control, where many separate control signals may be transmitted simultaneously over a single wire (or radio) link. The material in this review is largely descriptive and reference should be made to other publications for theory related t o t e l e m e t e r k ~ g . ~ ~ ~

11. EVOLUTION OF RADIOTELEMETER~NG Prior to World War 11,the principal applications of telemetering were industrial and usually involved single-channel telemetering.* The Radio Sonde15which was developed at the National Bureau of Standards early in 1937 for meteorological applications, was a simple form of multichannel radio telemeter. However, a need for more adequate multichannel radio telemetering grew out of the rapid growth of the airplane industry where, with the increased speed and cost of airplanes, the taking of data during flight tests of models became increasingly important. The target drone, or radio-controlled target aircraft, and a number of guided missiles were developed during World War 11. Since these vehicles carried no pilot, some new means had to be devised t o obtain flight test data. I n the first flight tests, the pilot, with pad and pencil, made notes from meter observations. Later, with the introduction of pilotless vehicles, photo-panels mere installed in which recording cameras photographed a panel of test instruments dwing flight. Photo-panel recording necessitated recovery of the test vehicle, or at least recovery of the record magazine, in order to obtain the record of flight test data. Experience showed, however, that vehicle recovery was the exception rather than the rule. Loss of a model, representing a considerable expenditure of time, effort, and money, meant the loss of expensive recording equipment and often the loss of the record indicating the causes of failure of the tests. Multichannel radio telemetering equipment that was relatively compact, inexpensive, and expendable might well mean the difference between total loss of flight test data and a successful test, since the data obtained during flight tests are essential for future design and development. For the above reasons we find that the greatest advances in the art of multichannel telemetering have been associated with the flight testing of military aircraft, particularly in the United States where the great need has been supported by the appropriation of large sums of money for research and development. It is not possible in this review to give just

MULTICHANNEL RADIO TELEMETERING

303

credit to agencies in Europe and elsewhere who contributed to the development of multichannel radio telemetering, although it is recognized that t.he contributions of scientists throughout the world have been vital in this development. Wartime liaison between American and British scientists resulted in fruitful exchange of ideas which contributed to the success of telemetering in both countries. 1 . Television Telemetering

As an outgrowth of the first test flights wherein the pilot, with pad and pencil, made notes from meter observations, and of the later ones when photo-panels were used, the use of television for flight test observations came naturally. Compact narrow-band airborne television equipment was produced in large quantities during World War I1 for purposes other than telemetering. Some of this equipment was adapted for telemetering so that the camera viewed several test meters, modified with special high-contrast indicator dials. In some applications, a bank of oscillograph elements was also viewed by the camera, and this, together with a view of the test meters, was televised to a remote ground station during flights. The television telemetering system proved to be unsatisfactory for a number of reasons. The method was unnecessarily complex because of double conversion of electrical signals to optical signals. An unnecessarily wide bandwidth was imposed by the television link. The equipment was bulky and very expensive, particularly as an expendable item. For these reasons, we find that television telemetering lost favor. 6. Instrument Telemetering

The first radio telemetering systems, developed specifically for flight testing of pilotless aircraft during the early part of World War 11, or just prior to it, were instrument telemetering systems wherein the indications of flight instruments were transmitted by radio to a remote location. This was another logical extension of the test pilot pad and pencil method. In these so-called instrument telemetering systems, existing flight test instruments were modified by such devices as the coupling of lightweight phase-transformer rotors or microtorque potentiometers to the shafts of needle instruments, or by the use of small magnets, differential coils, or photocell pickoffs. Corresponding remote indicating dials were observed visually and notes were made from them during flights. 3. Oscillogram Telemetering

Many of the early telemetering systems were extremely complex, costly, unstable, and not practicable for multichannel operation. The

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M. G. PAWLEY AND W. E. TRIEST

accuracy of these telemeters suffered from the loading of the meters, which themselves were not very accurate. The accuracy fell far short of that required for securing research test and evaluation data. I n many cases, the frequency response of the system was inadequate to transmit the desired information. I n the early flight tests, when only a few channels were required and tests were usually of short duration] little attention was paid to the manner in which the data were recorded. As the need arose for the transmission of many data channels during a test, it became apparent that data recording and data analysis could not be adequately accomplished by manual recording methods. There arose a need for automatic recording of channel signals as continuous functions of time, together with reference time signals. With this new requirement, we find that the more recent telemetering systems, developed during the war, used multi-element recording oscillographs, such as had been developed for use in the seismic method of geophysical prospecting. The growing need for accommodating more channels of information a t increased frequency response and for improving accuracy in the transmission of flight test data led to the development of improved telemetering sensory elements or pickups, and to the development of more adequate telemetering systems. A number of systems were built by the Naval Aircraft Experiment Station, the Princeton Laboratories, the National Defense Research Committee, the Naval Research Laboratory] the Applied Physics Laboratory of Johns Hopkins University, several aircraft companies] and by numerous other organizations.

111. BASICSYSTEMS OF RADIOTELEMETERING Two basic systems for multichannel telemetering grew out of this period of development. The first is known as frequency-division or subcarrier telemetering, and the second is known as time-division or commutation telemetering.

I. Frequency-Division Telemetering h frequency-division or subcarrier system of telemetering is defined as one in which a number of information channels to be transmitted are synthesized or multiplexed by combining a number of subcarrier frequency signals, each carrying a particular information channel, into a composite electrical signal. Each measurement, utilizing one channel, modulates a subcarrier oscillator. A number of these subcarriers, differing in frequency] are mixed, and the resulting signal modulates the radio frequency carrier. It is possible, and customary, to choose the sub-

MULTICHANNEL RADIO TELEMETERING

305

carrier frequencies in such a manner as to minimize cross-modulation effects. Subcarrier telemeters differ in the manner in which the subcarriers are modulated by the input signals, which vary in accordance with the information to be transmitted and in the manner in which the radio frequency carrier is modulated by the composite signal. For example, in a typical subcarrier telemeter to be described later, the subcarriers are frequency-modulated by the corresponding channel signals, and the radio frequency carrier is frequency-modulated by the composite signal which is the sum of the frequency-modulated subcarriers. Such a telemetering system is commonly referred to as an FM-FM subcarrier telemetering

FIQ. 1. Block diagram for a typical N-channel frequency-division telemetering system.

system. At the receiving station, the output of a radio receiver passes to band-pass filters which separate the frequency-modulated subcarriers. These channel signals separately pass to conventional FM discriminators and thence to corresponding recording elements in the recording oscillograph. The practical limit to the number of subcarriers which can be transmitted by a single radio frequency carrier a t the present time is between 10 and 14. With more subcarriers than this, cross-modulation effects and noise become serious obstacles, principally because it is not possible to build a transmission system that is perfectly linear in response. With any number of subcarriers, each channel modulation must be limited so that the composite signal does not overmodulate the radio frequency carrier. The restricted number of channels is a disadvantage of the subcarrier system of telemetering. An advantage of the subcarrier

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M. G . PAWLEY AND W.

E.

TRIEST

system, however, is that it can transmit a relatively high frequency continuously in each channel. Also, with certain types of pickups as described later, the telemetering transmitter unit can be made quite simple and compact, particularly if the radiated power is low. Figure 1 shows a block diagram for a typical N-channel frequencydivision telemetering system. A more detailed description of a system of this type is given in a later section of this review. 2. Time-Division Telemetering

A time-division or commutation system of telemetering is defined as one in which the transmission of a number of information channels is divided in time. The channels are rapidly switched or commutated in a fixed sequence. Each channel modulates the carrier fully during that part of the commutation cycle assigned to that particular channel. The time-division or commutation system of telemetering can transmit a much larger number of channels than a subcarrier system before cross-modulation becomes a serious limiting factor. The channel frequency response, however, depends upon the commutation speed and upon the number of channels transmitted, and electronic methods of commutation must be employed if many channels of high frequency response are required. Since pulse techniques are used in the electronically commutated time-division telemetering systems, high peak power may be obtained with relatively compact radio transmitters. In some applications where long ranges are required, this is an advantage over the continuous wave transmitters used in the subcarrier telemeters. A disadvantage of the pulse system in some applications is the relatively wide bandwidth required to adequately pass the short pulses. Figures 2 to 5 show block diagrams for typical N-channel time-division telemetering systems. More detailed descriptions of systems of these types will be given in a later section of this review, only the principles of operation being outlined here. a. Pulse Position Modulation and Demodulation. Figure 2 shows one type of multichannel time-division telemetering transmitter utilizing pulse position modulation, in which the sampling rate is established by a sine wave master oscillator. For an N-channel system, the phase splitter gives N sine wave outputs equally distributed in phase or time, thereby setting the zero-modulation phase for each of the N channels. The phase modulator shown in each channel shifts the phase in accordance with the information from the corresponding pickup or sensory element. The sine wave output from the phase modulator passes to a pulse generator which develops a short pulse locked in phase with the

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MULTICHANNEL RADIO TELEMETERING

signal from the phase modulator. I n a separate path, the master oscillator signal passes t o a frame synchronizing pulse generator which develops a coded signal, usually two or three pulses in close time sequence. This coded signal identifies the initiation of the sequence of channel pulses in the frame. The frame synchronizing signal and the separate channel pulses pass to a mixer, and the composite signal from the mixer modulates the radio transmitter. The signal transmitted consists of a repeating sequence or frame of N-channel pulses, marked by a coded synchronizing signal. Each channel pulse is displaced in time from its zero-modulation

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position in accordance with the signal from the corresponding telemetering pickup. The type of modulation illustrated here is referred to as pulse position modulation, sometimes abbreviated as PPM. Figure 3 shows a block diagram of another N-channel time-division telemetering transmitter utilizing pulse position modulation. The type of signal transmitted is identical with that transmitted by the system illustrated in Fig. 2; However, in this case, the frame sampIing rate is established by a ring counter chain which is triggered by a master pulse generator. The pulses from the generator cause successive tubes in the chain to conduct in sequence and to generate pulses distributed uniformly in time. The pulse from one of the counter chain tubes is coded and is

M. G. PAWLEY AND W. E. TRIEST

308

used as a frame synchronizing signal. Each channel pulse produced in the counter chain passes to a corresponding pulse interval modulator which generates a pulse delayed with respect to the pulse from the counter chain, the delay being proportional to the information signal from a corresponding telemetering pickup. The N pulses from the pulse interval modulators, together with the coded frame synchronizing signal, pass to a mixer, and thence to the modulator of the radio transmitter as in the system illustrated in Fig. 2.

I FIG.3. Block diagram for a typical N-channel time-division telemetering transmitter utilizing pulse position modulation and a master pulse generator.

Figure 4 shows a block diagram for a typical W-channel time-division telemetering receiver and recorder for pulse position modulated signals as generated by the telemetering transmitters shown in Figs. 2 and 3. The multichannel sequence of pulses from the radio receiver passes to a channel synchronizing pulse generator which electronically separates the coded frame synchronizing pulse from the incoming pulse train and develops a sequence of channel synchronizing pulses which mark the reference time or phase for the separate channels. Each of these channel synchronizing pulses triggers a variable pulse width generator in which the pulse width is initiated by the channel synchronizing pulse and terminated by the corresponding channel signal pulse which is also fed into the pulse width generator. Thus, for each channel, a pulse is generated whose width varies in accordance with the modulation produced

309

MULTICHANNEL RADIO TELEMETERING

by the corresponding sensory element or pickup in the telemetering transmitter. These variable-width chanpel pulses, recurring a t the sampling rate generated at the transmitter, pass to suitable metering circuits and to corresponding elements in the recording oscillograph. Alternately, the receiving system illustrated in Fig. 4 may be modified to utilize a cathode-ray oscillograph with recording film. This will be illustrated in more detail in the description of a typical pulse positionmodulated telemeter, t o be given later in this review.

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0. Pulse Interval Modulation and Demodulation. Figure 5 shows a block diagram for a typical N-channel time-division telemetering system which utilizes pulse interval modulation. The upper part of the diagram shows the transmitter. The sampling rate is established by a master, free-running multivibrator, the pulse output of which triggers channel 1 monostable multivibrator, whose pulse width is determined by the instantaneous DC voltage from the channel 1 sensory element or pickup. The trailing edge of the pulse from the channel 1 multivibrator triggers the channel 2 multivibrator, which functions in a similar fashion t o that of channel 1. Thus, the channel multivibrators are triggered in sequence and the width of the pulse generated by any channel monostable multivibrator varies in accordance with the instantaneous voltage from the corresponding telemetering pickup. The trailing edges of the synchroniz-

3 10

M. G . PAWLEY AND W . E. TRIEST

ing pulse and of the channel pulses are differentiated t o give short pulses t o mark accurately the channel pulse intervals. These pulses are mixed and pass t o the radio transmitter. Note t h a t the composite signal in this system is different from t h a t generated in the pulse position-modulated telemeter. I n this pulse interval-modulated system, the information t o be transmitted in any channel varies the interval between the corresponding channel pulse and the preceding channel pulse. As any one channel is modulated, all succeeding channels are shifted equally in time by the modulation, but the interval is changed only for the channel being modulated.

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A t the receiving station, illustrated in the lower part of the block diagram of Fig. 5, the pulse sequence from the radio receiver passes to a synchronizing pulse separator where the synchronizing pulse is recognized by virtue of the relatively long time interval between the X t h channel pulse and the synchronizing pulse. The separated synchronizing pulse triggers ON the channel 1 monostable decoder multivihrator, which in turn is triggered OFF by the incoming channel 1 pulse. Similarly, and in time sequence, each channel decoder multivihrator is triggered O N by the trailing edge of the preceding channel decoder pulse, and triggered O F F by the corresponding channel pulse. Each channel monostable decoder multivibrator, therefore, generates a pulse whose width varies with the corresponding channel signal. By means of

MULTICHANNEL RADIO TELEMETERING

31 1

suitable metering circuits in the channel decoder, the sequence of variable width pulses in each channel is converted to a varying DC voltage which is recorded on the multi-element oscillograph. The pulse interval modulated telemeter, requiring only one tube envelope per channel in the transmitter coding unit is simpler than other multichannel pulse telemeters. This is important where space is at a premium and where simplicity is desired. Such a system will be described in more detail later in this review. 3. Factors Determining Choice of Telemetering System

Many telemetering systems have been built combining features of the basic systems described above. Because of added complexity in these hybrid systems, the current tendency is to use one or the other of the basic systems; the subcarrier system when fewer than ten channels are required, and a time-division telemetering system when ten or more channels are required. However, as described later, it is common practice to subcommutate with motor-driven multicontact switches, one or more subcarriers in a frequency-division system. It is thus possible to accommodate many additional channels of information a t the expense of the lowered sampling rate of the mechanical switch and with greatly increased difficulty in reduction of data. This subcommutated frequency-division system is not as complex as some of the hybrid systems which have been built. Factors which determine the choice of a telemetering system in a particular application include required accuracy, desired channel frequency response, information handling ability, size, weight, cost, stability, durability, effectiveness under specified operating conditions, and availability of transmitting, receiving, decoding, and recording apparatus. Availability is an important factor because relatively few telemetering systems can be purchased on the market today. There have been many specialized military needs for telemetering equipment, and there has been considerable duplication of effort, with but little standardization. Only recently has there been a concerted effort toward standardization of telemetering equipment. This effort of the Research and Development Board in the United States is currently in progress. In general the best overall accuracy which can be expected with existing telemetering equipment is approximately 2 per cent. The channel frequency response in subcarrier telemetering systems is of the order of 100 or 200 cps and is limited by the recording galvanometer frequency response and by the particular channel subcarrier frequency involved.2 If higher frequency response is required, a correspondingly

312

M. G . PAWLEY AND W. E. TRIEST

high subcarrier frequency is used, and the recording generally is made with a cathode-ray oscillograph and camera. The channel frequency response in time-division (commut,at.ion) telemetering is of the order of one-fifth the channel sampling rate, although this response may also be further limited by recording galvanometer response. The channel frequency response may be increased by suitable integrating methods to a value approaching one-half the channel sampling rate.2 The choice between a subcarrier type of telemetJer or a commutat.ion type may depend upon a number of factors, perhaps the most important of which is the number of channels desired. Since, at present, ten t,o fourteen channels (not counting subcommutated channels) are the most, that can be used in subcarrier telemetering without excessive cross-talk, a commutation type telemeter might be chosen if it were essential that more channels be provided. I n some applications, the high peak power available in the commutation (pulse type) system is a distinct advantage, particularly where space for telemetering equipment is at, a premium, and long ranges of transmission are involved. Considerably more effort has been expended in the development of subcarrier telemetering systems than in the development of electronic commutation systems. Therefore we find more equipment of the subcarrier type available on the market, and we can look for earlier standardization of this type of equipment. Extensive development of timedivision systems is currently in progress, but it is likely that several years will elapse before these latter syst,ems can be adequately tested and standardized.

IV. TYPICAL TELEMETERING SYSTEMS 1. Early Il'elemetering Systems

The Naval Aircraft Experimental Station Telemetering System, which was one of the first usable systems, used six amplitude-modulated subcarriers which in turn frequency-modulated the radio frequency carrier. This is an example of an AM-FM subcarrier telemetering system. The Vultee Telemetering System,s which was one of the first commutation systems, used .a mechanical commutator to connect the signals from seventy-two channels to an amplitude-modulated transmitter. The information in each channel varied the frequency of an oscillator, and this frequency was transmitted over a radio link. One of the first telemetering sets to use high-speed electxonic commutation with a relatively high channel frequency response was developed by Princeton University under sponsorship of the National Defense Research Committee (NDRC).'

MUT,TICH.4NNE:T, RADIO TELEMETERING

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A compact four-channel subcarrier type telemeter was also developed (luring World War I1 by Princeton University under NDRC contract. Although these early telemetering systems served a useful purpose, they proved t o be inadequate with increasing flight test requirements. However, they did serve as a pattern for extensive development which has continued ever since. More than fifty telemetering syhtems were in existence at the end of World War 11, and new systems are currently being developed. It is beyond the scope of this review t o tlesc*ribe many of these in detail. Rather, me are concerned in pointing out thc trend in advancement of the art of multichannel radio telrmetering. I n the detailed descriptions t o follow, typical telemetering systems of the two basic types are described, the choice having been made from among systems which are currently being used successfully in flight testing and which, in the authors’ opinion, represent good engineering design. Other telemetering systems are heing used successfully, but in general no new principles are involved in their operation beyond thow dcscaribed in the following typical examples. 2. Example of Frequency-Division Tclpmctcring System During World War 11, Princeton University developed a subcarrier telemetering system utilizing four audio subcarriers frequency-modulated 5 7 . 5 per cent of center frequency by the intelligence t o be transmitted. The Applied Physics Laboratory of the .Johns Hopkins University (APL/ JHU) developed a similar system with different subcarrier frequencies. The designation AN/AKT-5 was applied to a system employing the APL/JHU frequencies and four voltage-controlled multivibrator type subcarrier oscillators. This system was used by several of the military services. When the Telemetering Group a t APL/JI-IU was consolidated, i t was decided that the Princeton subcarrier frequencies would be used in the APLIJHU Telemetering System. As this work progressed, i t became evident that greater intelligence carrying capacity was required. TWO subcarriers were added, making a six-band system. One version of this system, with a fixed scheme of sulwommutation, was designated the AN/DKT-3. Later, the need for a channel with higher frequency response was satisfied by the addition of one more subcarrier, making a scven-band system. The suhcarrier oscillators of the APT,/JHU seven-band system are frequency-modulnt ctl by the intelligence to be transmitted. These subcarriers are mixed a t the proper levels in linear circuits, and the composite signal applied to the input of a frequency-modulated radio fre-

314

M. G . PAWLEY AND W. E. TRIEST

quency transmitter. The combined information is transmitted through a radio frequency link t o the ground station. Here it is received and the R F carrier demodulated by conventional F M circuitry. The composite audio subcarrier output of the receiver is applied to the proper number of band-pass filters and audio subcarrier discriminators. The output of each subcarrier discriminator is a voltage representing the original quantity measured. Here i t is passed through a low-pass filter whose cut-off frequency depends upon the frequency response of that particular band. A number of different recording schemes may be applied a t the output of the low-pass filters, depending upon the type of information and data display desired. The band-pass filters provide the subcarrier selection for each individual discriminator. These filters have an attenuation of not more than 3 d b within the rt7.5 per cent subcarrier deviation. The skirts of the response curve are down 20 db a t f l l per cent of the center frequency and 40 db a t +13 per cent and beyond. The audio discriminators have sufficient linearity and stability so that only three frequency points need be used t o determine the calibration curve. The low-pass filters decrease the high frequency noise above the intelligence band. The output impedance of the low-pass filters is 330 ohms. The low impedance of the recording galvanometer elements is increased by series resistance in order to match the output of the filters. This type of impedance matching network has adequate efficiency t o drive the elements to full output, since they are essentially current-operated elements. The sensitivity of the discriminator is such that its output provides a current of & 10 ma for full subcarrier deviation. Recordings are made on standard electromagnetic recording oscillographs with 12-in. photographic paper running a t 6 in. per second. A camera and cathode-ray oscillograph are used t o record the information from the high frequency subcarrier. A ten-channel FM-FM telemetering system, recently developed a t APL/JHU, uses an improved radio receiver and improved audio frequency discriminators in order t o increase the overall telemetering accuracy. Three types of audio frequency subcarrier oscillators are commonly used in the APL/JHU telemetering system. The first is a n 1,C type in which conventional Hartley resistance-stabilized oscillators are used. The frequency variation is accomplished by variation of inductance. The second type of oscillator is used for the measurement of voltage and utilizes a n RC phase shift netmoik t o determine the frequency. The

MULTICHANNEL RADIO TELEMETERING

315

plate resistance of a modulator tube is varied with the applied intelligence voltage, which thereby shifts the oscillator frequency. A third type of oscillator is used t o transmit intelligence having a frequency of several thousand cycles per second. This oscillator is a multivibrator frequencymodulated by the input voltage. The following sensory elements or pickups of the variable-inductance type have been used extensively with the APL/JHU and other subcarrier systems. Accelerometer. An oil-damped accelerometer is made by attaching a mu-metal slug t o a thin, corrugated beryllium copper diaphragm. The mass of the slug moves the diaphragm toward or away from the air gap of an inductance coil, thereby varying its inductance. The resonant frequency of the diaphragm is 50 t o 75 cps. Pressure Gages. Absolute and differential pressure gages use two chambers with a corrugated heryllium copper diaphragm hetween them. A high-mu pad, which varies the air gap of an inductance, is attached to the diaphragm. I n the differential gage, the chamhers are each connected t o a pressure source. I n the absolute pressure gage, one of the chambers is sealed a t fixed pressure. Motion Meter. With the motion meter, the rotation of a control surface through 10" or 15" is mechanically amplified by means of gears to cause a 180" or 360" rotation on a threaded shaft. When the shaft advances, the air gap of an inductance coil is varied. Tachometer. The tachometer consists of a disk which rotates in front of an inductance coil air gap. The disk consists of mu-metal which is mounted eccentrically, thereby varying the inductance of the air gap with each revolution and causing a frequency change of the associated subcarrier oscillator with each revolution. The speed of the shaft can be determined by counting the number of cycles per second of oscillator frequency shift. Gyro Position Indicator. A wedge-shaped piece of mu-metal is attached t o a gyroscope cage so that rotation of the cage causes a thicher or thinner portion of the wedge to be across the air gap of an inductance coil. I n addition t o the above variable-inductance type pickups, microtorque or other potentiometers are usrd frequently t o vary the voltage input t o voltage-controlled oscillators. These potentiometers may be used t,o telemeter angular shaft displacement or linear displacement when properly geared t o the moving part. Thermocouples are used t o measure temperature by allowing the output of the couples t o saturate a reactor, thereby varying its inductance and the frequency of the associated subcarrier oscillator.

316

M . G. PAWLEY AND W. E. TRIEST

3. E.uniples

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u. l‘gpicul Pulse Position-ill oduluted l’elemctering System. ‘l’hc pulse position-modulated (PPM) telemeter t o be described was developed by the Rocket Sonde Research Branch of the Naval Research Laboratory (YRL) shortly after World War 11. It is referred t o by N l t L as the Matrix Telemetering System. The transmitting unit is designated the XN/DKT-2. The system has been used successfully in telemetering

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from a number of V-2 rockets launched a t the White Sands Proving Grounds for upper atmosphere research. The matrix telemetering system utilizes pulse position modulation t o convey thirty channels of input information. Data in the form of varying DC voltages is supplied t o the equipment from the various instrument pickups. The data channels are sampled successively and the whole process is repeated at a 312.5-cycle rate. A coded triple pulse identifies the start of each group and establishes a time reference framework, or matrix, of thirty-two intervals of 100 microseconds each. Within thirty of these intervals, single data pulses occur, the position of the pulse within its interval indicating the voltage being measured on the channel. This

MULTICHANNEL RADIO TELEMETERIXG

317

chain of pulses is used to modulate an RF transmitter operating a t a frequency of 1025 megacycles per second with an average power in the pulse of about 4 km. Figure 6 shows a block diagram of the matrix telemeter transmitting unit. This diagram shows the 10-kc oscillator t o be the independent initiating part of the circuit. The sine wave output of this oscillator is fed to a multivibrator which serves to shape it t o derive a series of pulses accurately spaced a t 100-microsecond intervals. These 'pulses are fed through a cathode follower to a bus feeding each of the thirty-two tubes of the electronic commutator. These tubes are arranged as a chain so connected that only one tube can conduct a t a time. As any one of these thyratron tubes fires, it readies the next tube in the chain. Upon the appearance of the next pulse on thc triggering bus, conduction shifts to the next succeeding tube, and so on down through the whole chain of thirty-two tubes, and the process is repeated when the last tube readies the first tube for conduction. As each of the first thirty of the chain tubes fires in turn, it generates a sawtoothed wave form which is added electrically to the input voltage of a channel pick-off thyratron. When the sum of these two voltages reaches a predetermined level (as it will sometime during the 100 microsecond interval), it will cause its corresponding pick-off thyratron to fire, producing a time-modulated output pulse. The greater the input voltage, the sooner the sum of the input voltage and sawtooth will reach the firing voltage. The output pulses from the various channels are collected on a common bus. For synchronization of the time base generators a t the ground station, a coded pulse group consisting of three pulses each separated by 7.9 microseconds is generated in a multivibrator circuit triggered by channel 32. This multivibrator has an LC ringing circuit with a 7.9-microsecond period in the plate of the normally ON tube, with associated limiting and differentiating circuits. This output is combined with the channel video pulses on the common bus. The output of the common bus triggers a blocking oscillator to form a 0.9-microsecond pulse which is used to key ON a coaxial L band VHF cavity by means of a pair of 3E29 modulators. The output of this cavity feeds a 50-ohm line with an average pulse power of 4 kw a t a frequency of about 1025 megacydes per second. For calibration, each input channel is connected to its data input via a single-pole double-throw microswitch operated by a synchronized motor-driven cam unit. For about 2 per cent of the time, data input is removed from the input channel and a calibrating voltage, consisting of 1 volt steps from 0 to + 5 volts, is substituted. This step voltage is repeated on each channel in sequence every 10 seconds during flight. For

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M . G. PAWLEY AND W. E. TRIEST

any channel requiring continuous input data recording, this calibration can be removed. For ease of disassembly of the unit from the rocket, aircraft type quick-disconnect straps are used for mounting, with a vee-ring pressure seal using similar quick-disconnect toggle snaps to seal the pressurized transmitter case to its top bulkhead. The total weight of the telemeter transmitter set, with batteries suitable for thirty-minute operation, is about 130 lb. Two 28-volt plastic-cased storage batteries are used in conjunction with a vibrator type converter unit to provide the various plate voltage and bias supplies, and four 2-volt plastic-cased storage batteries for the filament supplies. Total power requirements for the system are 15 amperes at 28 volts and 20 amperes at 8 volts. Matrix Ground Station. Each ground station comprises four racks, the monitor rack containing receiving and decoding apparatus as well as a monitoring oscilloscope, and three identical recording racks. The ground station receives the recurrent train of pulses from the remote transmitter in a suitable receiver. The triple pulse is recognized by a discriminator and is used to generate a 10-kc matrix in exact phase with the matrix in the transmitter. From this, signals are obtained at any particular time in the matrix which are used to generate the sweep voltages for the cathode-ray tubes on which the data are presented as intensity modulation. Pulses generated a t the beginning of each matrix interval are also applied to the display and the scopes are photographed on a continuous film camera. There results a graph of the variation of the input voltage with time, with reference lines (which do not vary in position) between each of the data lines. Each ground display has six cathode-ray tubes upon which the thirty data channels can be applied in any combination. Sweeps of appropriate duration and timing in respect to the triple pulse are so arranged that one tube after another is swept in succession until all channels are recorded. Additional information is also supplied on the record by the application of signals to the cathode-ray tube to indicate time from a standard source. Referring to the block diagram for the matrix system ground station, Fig. 7, main signal paths are indicated by arrows. The receiver delivers the video signal on two lines, one to the recording racks, and another into the synchronizing pulse discriminator where the triple pulse is recognized and supplies a pulse which is used to phase and frequency lock the 10-kc matrix oscillator to the airborne oscillator. The output of the oscillator is shaped and fed into the scale-of-32 binary counter. This counter operates in synchronism with the chain counter in the airborne unit. It is reset by the synchronizing pulse, when necessary, so that particular

MULTICHANNEL RADIO TELEMETERING

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states correspond in both units. By means of resistor networks from different stages of the counter, the state selector delivers a timed series of 100-microsecond pulses to a patchboard on the panel of the unit. Suitable connections are made to the trigger and gate unit to form gates for controlling the sweep circuits in the recorder racks. There are several auxiliary units in the monitor rack. The frequency monitor determines whether the matrix oscillator is operating on the proper harmonic of the 312.5-cycle synchronizing signal and indicates the

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proper frequency by means of lights on the face of the unit. The monitor oscilloscope is used for adjustment of the units and for monitoring the signal during operation. It is swept from associated generators which are synchronized from 312.5-cycle and 10-kc pulse sources. Appropriate power supplies are included in the unit, as are switches to control the operation of the recording racks. Each of the three recorder racks contains a double recording unit consisting of tivo type 5 R P l l cathode-ray tubes and a continuous 9x-in. film camera. Appropriately timed gates from the monitor rack allow sweep generators to operate one after another and, at the same time, unblank the cathode-ray tube so that the video pulses from the receiver

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M. G . PAWLEY AND W. E. TRIEST

in the monitor rack can be presented as intensity modulation on the tube. Necessary video amplifiers are included in this unit, as are circuits for mixing the video with timing signals and with the reference pulses generated by the 10-kc matrix oscillator on the ground. There are also controls for positioning and focusing the cathode-ray tubes, as well as necessary power supplies. The image on the face of the cathode-ray tubes is focused on a slit on the front plate of the unit by means of two lenses, placed side by side. A film magazine is placed so that the image from both tubes is recorded on it as the film is drawn continuously past. The ground station operates on 110 volts, 60 cycles AC with a power consumption of about 3000 watts. Voltage regulation of the primary power for these units is obtained from constant voltage transformers. All plate supplies under 600 volts are electronically regulated against load variations. The high voltage supplies required for the cathode-ray tubes are - 2000 volts obtained from a conventional transformer-rectifier circuit, unregulated, and +10,000 volts obtained from an R F power supply operated from an electronically regulated 300-volt power supply. Owing to the complexity of the ground station circuits and the number of tubes involved; two complete and separate ground stations are utilized for every flight. In normal flights, six 9X-inch film records of about 120 ft. in length are produced, corresponding to about 450 seconds of flight. These films give a complete graph of voltage versus time for all thirty channels and are reproduced in the form of black line paper prints. b. Typical Pulse Interval-Modulated Telemeterhg System. The pulse interval-modulated (PIM) telemeter to be described was originally developed in a twenty-three-channel form by the Rocket Sonde Research Branch of the Naval Research Laboratory near the end of World War 11. The transmitter unit was later repackaged in a ten-channel form which carries the designation AN/AKT-1 A. This model of the transmitter unit, which was designed by the Control and Report Links Branch, R.D. 3, of the Naval Research Laboratory, has been successfully used in about sixty-five flight tests. The operation of the AN/AKT-1A telemetering transmitter unit may be explained by reference to Figs. 8 and 9. Referring to Figure 8, the sampling rate of the pulse interval modulator is controlled by the master multivibrator 2-101, which is of the “freerunning ” type, preset to give approximately 400-cycle-per-second square wave pulses a t point (A). The output is coupled to: (a) Channel No. 1 monostable multivibrator (2-102) through a differentiating circuit consisting of C-103 and the grid to ground impedance of V-104 and (b) to the

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MULTICHANNEL RADIO TELEMETERING

mixer (Z-112) through a differentiating circuit consisting of C-104 and R-106. The positive surge from 2-101 a t point (A) does not affect Channel No. 1 (2-102) because V-104 is already conducting due t o the grid's being returned to a positive potential by R-109, and the surge does not pass t o the mixer because i t is blocked by the crystal diode, CR-101. At the end of a pulse from 2-101, a negative surge is impressed on the grid of V-104 and is also passed through CR-101 t o the mixer (Z-112). The IMELLWNCE INPUT

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potential across the common cathode resistors, R-111 and R-112, drops until V-103 begins t o conduct. Conduction of V-103 produces a negative surge a t its plate which is coupled t o the grid of V-104 through capacitor C-105 and drives the grid of V-104 further negative. The channel remains in this temporary or unstable condition until the grid potential of V-104, rising a t a n exponential rate determined by the discharge of c-105 through R-109 (see Fig. 9b), reaches a sufficiently positive value for conduction to begin again in V-104. The cathode potential again rises and a positive surge occurs a t the plate of V-103 which applies a further positive surge t o the grid of V-104, returning thc channel t o its stable condition. During this time, a positive pulse is generated

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M. G. PAWLEY AND W. E. TRIEST

a t point (B), in Fig. 8, which is coupled to (a) Channel No. 2 monostable multivibrator (2-103) through a differentiating circuit consisting of C-107 and the grid to ground impedance of V-106 and (b) to the mixer (2-112) through a differentiating circuit consisting of C-106 and R-113 initiating in Channel No. 2 the same action that occurred in Channel No. 1. At the same time, a negative surge resulting from the negative swing of the positive pulse a t point (B) is passed through the crystal diode CR-102 to the mixer (2-112).

FIQ.9. Waveforms in the AN/AKT-1A telemetering transmitter.

This action continues from channel to channel, the return of one channel to the stable state triggering the next channel into its unstable condition and simultaneously delivering a negative pulse to the mixer. When the action in the last channel is completed, the circuit is quiescent until the next pulse from the master multivibrator 2-101 triggers 2-102 again. The input of each channel, which is the grid of the non-conducting tube when the channel is in the stable condition, is connected to a sensory element or pickup which supplies a variable voltage from 0 to +4 volts. When this positive voltage is applied to the input of a channel such as 2-102, V-103 will conduct more heavily than it would if this voltage were zero when the channel is triggered. A large negative surge is impressed

MULTICHANNEL RADIO TELEMETERING

323

on the grid of V-104 and therefore a longer time is required for it to leak off through R-109. (See Fig. 9b.) This produces a positive pulse a t the plate of V-104 whose width is linearly proportional to the DC voltage applied to the grid of V-103. (See Fig. 9c.) Consequently, time T (see Fig. 9d) is governed by the intelligence voltage applied to Channel No. 1 and varies from a minimum of t l to a maximum of T . In the same manner, the time that Channel No. 2 (2-103) is in its temporary state is governed by the intelligence voltage applied t o the input of Channel No. 2, and so on for the succeeding channels. The intelligence in any particular channel is independent of that in any of the other channels. The crystal diodes, CR-101 through CR-111, allow the negative surges from the master multivibrator and from the channel multivibrators to pass t o the mixer, and in addition, prevent feedback between channels. In this manner, each sampling of ten channels of intelligence which appears at the input of the mixer, V-123 (point D, Fig. 8) is represented by a group of negative pulses, equal t o the number of channels, plus a frame synchronizing pulse. (See Fig. ge.) The number of these sampling groups per second is equal to the pulse frequency of the master multivibrator, approximately 400 cps. The frame time, or interval between successive Synchronizing pulses, therefore remains constant and is equal to the reciprocal of the sampling frequency or approximately 2500 microseconds. (See Fig. 9e.) At point D, the negative pulses decrease the small positive bias maintained by R-114 on the amplifier or mixer, V-123. This grid change causes amplified positive surges or pulses on the plate of V-123 which are passed through the cathode follower, V-124, t o key the blocking oscillator, V-125. (See Fig. 8.) The time relationship between the pulses is the same as it was at the input t o the mixer-cathode follower, 2-112. The pulse group from the output of 2-112 is made up of pulses approximately 15 microseconds long. In order t o keep the average power consumption in the radio frequency oscillator as small as possible, each pulse is reshaped in the blocking oscillator, V-125, to be approximately 2 microseconds long and 180 volts in amplitude. Capacitor C-111 and resistor R-120 in the cathode of V-125 determine the duration of the output pulse. Resistor R-121, a t the output grid of V-125, is a damping resistor and prevents the blocking oscillator from delivering more than one output pulse for each input pulse. The driver tube, V-126, is a cathode follower providing a low impedance driving source directly coupled to the grid of the radio frequency oscillator, V-127. The oscillator is biased by applying a fixed positive voltage t o the cathode of V-127. The oscillator consists of a “lighthouse” high frequency triode, V-127,

324

M . G. PAWLEY AND W. E. TRIES”

xvhich excites an “ L ” band cavity (2-113) shown in Fig. 8. The cavity is capable of being tuned from 500 t o 580 me per second but is normally tuned to approximately 525 mc per second. At this frequency, the transmitter delivers approximately 400 watts peak power a t the cavity. The radio frequency energy is removed from the cavity by the inductive coupling loop on 5-104. This energy is fed to receptacle J-105 on the front panel through a short coaxial cable. The quarter-wave antenna is connected with coxial cable to the receptacle 5-105. The batteries, which include the 2000-volt supply for the oscillator, weigh 21 lb. and occupy a volume of 350 cu. in. They are housed in a cylindrical metal enclosure and are held in the container with shockabsorbent padding. The transmitter unit and power supply are enclosed in a cylindrical metal housing 944 in. in diameter by 2648 in. long, and the assembly weighs 78 lb. The Telemetering Group a t the National Bureau of Standards has recently completed repackaging of the AN/AE(T-l A Telemetering Transmitter. For flexibility, the equipment was broken down into smaller units. The overall weight and space occupied by this repackaged version is approximately one-half its former weight and volume. As a result of experience with the former version, minor but important circuit changes were incorporated in the newer version, which is designated the AN/AKT-lA(XN-2). The ground station receiving equipment used with this pulse interval modulated (PIM) system is the same as originally developed a t the Naval Research Laboratory. Its principle of operation was described earlier in this review in connection with the block diagram for the PIM telemetering system shown in Fig. 5. The pulse interval modulated telemeter described above requires approximately 0 to + 4 volts input to the channels. The sensory elements or pickups must therefore, either directly or indirectly, supply this varying DC voltage t o each channel. For this reason, we find microtorque potentiometer type pickups commonly used, or ordinary potentiometers when the mechanical load on the sensory element is not excessive. A small battery across a number of these potentiometers supplies the excitation for the corresponding channels. Microtorque potentiometer type accelerometers, pressure gages, and vane type instruments are available on the market. Considerable ingenuity is frequently required in adapting the many and varied test measurements involving telemetering to the 0- to 4-volt DC channel voltage input requirement.

MULTICH.INNEL

325

R.IDIO T E L E M E T E R I S G

c. Typical Mechanically Commiitated Telemeteriny S y s t e m . The system* to be described in this section was developed by the General Electric Company to meet requirements of a large number of information channels and rigid limitations on space and weight. Basically, this is a time-division system, and it has the inherent limitation of a lo\\. frequency response due t o the low (mechanical) switching rate. The recorded data appears in a form difficult t o reduce. These disadvantages may, in some applications, be outweighed by the relatively high number of channels and compactness of the system.

w PICKUP

0 3

OMITTED FOR FRAME SYNCHRONIZATION

T

FIQ.10. Block diagram of mechanically commutated telemetering system.

The entire transmitter is packaged in two pressure-tight cylindrical cans, each 4 in. in diameter and of lengths 15 in. and 16 in. The total weight is 23 Ib., and the total space is 0.2 cu. ft. for this equipment. One cylindrical can contains a high voltage dynamotor, which also drives the commutator used for sequencing the channels (to be described below) ; the second cylinder contains the transmitter and other electronic equipment. As shown in Fig. 10, the mechanical commutator sequentially connects voltages from the instrument pickups t o the transmitter unit. The commutator is driven a t 2000 rpm, through reduction gearing t o the dynamotor, which operates a t GO00 rpm, speed-regulated t o 2 per cent over a 20 per cent change in voltage. The commutator has sixty segments, of which alternate contacts are used t o give break-before-make

326

M. G . P A W L E Y AND

W.

E. TRIEST

action. Two contacts are used for synchronization of the ground (receiving) station, leaving twenty-eight useful channels. The transmitter unit receives a series of pulses of amplitude 0 to 5 volts from the commutator, and the premodulator chassis converts these t o variable width pulses, 100 microseconds corresponding to 0 volts and 700 microseconds to 5 volts. This conversion is done with a monostable multivibrator, giving an output pulse width linear with input amplitude. An antibounce circuit uses a capacitor to maintain the input voltage on the premodulator input despite any commutator bounce and discharges this condenser, between successive channels, to - 15 volts. Any pickup can be used which gives a variable DC output of 0 to 5 volts. However, it was found desirable t o include a variable transformer gage, a moving core being used to vary the coupling between primary and secondary windings, in this system. For this purpose, a 10-kc audio oscillator was included in the telemeter and is shown as the pickup exciter in Fig. 10. The output of the oscillator is applied t o two sets of variable transformer windings connected in a bridge so that movement of the core simultaneously increases the coupling in one set and decreases the coupling in the other. The output of the bridge is rectified and filtered to produce the required 0 to 5 volts DC. The variable pulse width output of the premodulator is applied to a 6AK5 reactance tube which frequency-modulates a 6C4 oscillator. A 2326 power amplifier then delivers 7 watts at 150 mc per second with 21 100 kc per second frequency deviation. The ground system, shown in block diagram in Fig. 11, uses a modified communications receiver with a band width of 300 kc per second in the IF amplifiers and discriminator. The output of the receiver is a reproduction of the width-modulated pulses generated in the transmitter. These pulses are passed through a clipper and differentiated t o obtain pulses at the leading edges and at the trailing edges of the channel pulses. The frame synchronizing pulse separator generates a frame synchronizing pulse, using the large interval preceding the synchronizing pulse t o charge a condenser t o a higher level than it can be charged during the intervals between channel pulses. These pulses are used to generate waveforms necessary t o produce three different types of recording on 35-mm film. For all types of film record, a 5 R P l l cathode-ray tube is used; this tube has high sensitivity, good resolution, and an optically flat face. The P I 1 phosphor is especially adaptable t o oscilloscope photography. Film in the 35-mm camera is moved vertically across the cathode-ray tube during the flight with camera shutter continuously open. In the ground station, separate tubes and cameras are used for the three methods of recording which will be described.

327

MULTICHANNEL RADIO TELEMETERING

Figure l l b shows the type of record obtained with a ('lines" presentation. Successive channels appear as parallel bright lines, each of length proportional to the quantity measured by the corresponding channel in the missile. Each frame gives one reading on each channel, and it can be seen that the omission of two contacts in the commutator of the transmitter separates the groups of lines so that each frame is

I

I DIFFEREN-

FN RADIO

TIATOR & CLIPPER

RECEIVER

1 f A J BLOCK

+ONE

J

~-~.{-l INDICATOI1-4J

'IpMERA

DIAGRAM OF GROUND STATION

FRAME4

--

CXRLCTION OF FILM NOTION

f B ) " L l N E " TYPE OF 3 S M M FILM RECORD

FIG.11. Block diagram of ground station for mechanically commutated telemeter and a typical record.

recognized. Small marker pips are put on the channel signals at 50-microsecond intervals to facilitate direct reading of the recording. A film motion of 15 in. per second is used for this recording, to make successive pulses appear as lines. In the "dash" type of presentation, the ground station generates a twenty-eight-step sweep, which successively '(jumps" the cathode-ray beam horizontally for each channel and allows the channel modulation

328

M. G.

P A W L E Y AND W. E. TRIEST

to vary the level of its step. Thus, as the 35-mm film moves vertically across the face of the cathode-ray tube, twenty-eight plots of channel modulation versus time are obtained in the form of dashes, each of width proportional t o channel modulation. The twenty-eight plots are spaced across the width of the 35-mm film. For this presentation, a film speed of about 55 in. per second is used. The accuracy is reduced because each channel is displayed on one twenty-eighth of the film width, but the record is compact and useful for initial examination and inclusion in reports. The third type of presentation is by LLdots.’’Each channel is recorded as a time variation of the quantity measured, successive samples of a quantity taken a t 445-second intervals appearing as adjacent dots which permit easy tracing of the time variation of the channel. It is not feasible t o put twenty-eight channels on one film without confusion; in this system, the twenty-eight channels are divided into four groups, and seven channels are recorded on one film. T o prevent possible confusion with seven channels crossing and recrossing, (‘sequential intensification ” is used. The dots are intensified in a fixed sequence and, in the data analysis, this helps to eliminate ambiguity in separation of the channel traces. A film speed of $6 in. per second is used. This method of presentation is more compact than the “lines” method and has equal accuracy since the full width of the film is used t o record one channel. The principal difficulty with this method, however, is that identification of the channels is sometimes not easy, especially if several channels operate a t about the same level of modulation.

V. FUTURE TRENDS IN TELEMETERING Increasing demands of telemetering user-groups are for more channels and higher frequency response, compactness and ruggedness, and increased overall accuracy, stability, and flexibility. Because of the labor required for data reduction from multichannel telemeter records, the cost may run as high as a dollar per second of flight per channel. Hence, there is a n increasing demand for automatic, or semiautomatic equipment for aiding in the reduction of data. Such equipment should include automatic means for applying instrument calibration corrections and for plotting of corrected data in a form suitable for inclusion in reports. New recording methods should be investigated with a view t o eliminating the time delay required for photographic processing. I n this connection i t seems likely that magnetic recording techniques mill become increasingly important. New measurement problems are continuing t o arise for which new

M U L T I C H A N N E L RADIO T E L E M E T E R I N G

329

sensory elements or pickups must be developed. Existing pickups must be improved t o give better accuracy. It is likely t h a t continued studies in information theory and continued progress in digital computer development will lead to advancements in the a r t of telemetering. I n this connection, pulse code modulation (PCM) methods may become important in telemetering, since they possess relatively high signal-to-noise ratio capabilities and involve binary pulse coding which matches with digital computer techniques and may lead t o better integrated overall telemetering, recording, and data reduction performance. REFERENCES 1. Webstcr's New International Dictionary, 2d ed., G. and C. lferriani, Springfield Mass., 1949. 2. Nichols, M. H., and Raiich, L. L. Rev. Sci. Instruments, 22, 1-29 January, 1951. 3. Leifer, M., and Schreihcr, 11'. F. Advances in Electronics, 3, 306-343 (1951). 4. Borden, P. A., and Thyncll, G. M. Principles and hfethods of Tclcmctering, Reinhold, New York, 1948. 5. Diamond, €I., Hinman, JV. S., Jr., and Dunmore, F. W. J . Aeronaut. Sci., 4, 241-248 (1 937). 6. Giffen, Harvey D. Ae1,onaut. Eng. Rev., 2, 9-21 (1943). 7. Rauch, L. L. Electronics, 20, 241-248 (1947). 8. Neelands, I . J., and Hausz, W. Radio-Electronic Eng., 10, 3-6 (1948).

This Page Intentionally Left Blank

Author Index Numbers in parentheses are reference numbers. They are included to assist in locating references in which the authors' names are not mentioned in the text. Numbers in italics refer to the page on which the reference is listed in the bibliography a t the end of each article. 131 (20), , 153, indicates t h a t this author's article is reference 20 Example: Bakker, C. J.. . on page 131 and is listed on page 153.

..

A Acheson, L. K., 13, 68

B

...

Brown, G. W., 239 (33), 256 Bruining, P., 16, 67 Buechner, W. W., 10 (18), 12 (181, 67 Bullard, E. C., 7, 67 Burgess, R., 118, 153 Burhop, E. H. S., 10 (17), 28, 67 Burrill, E. A., 10 (18), 12 (18), 67 Bush, R. R., 152 (44), 154, 201 (8), 211 (20), 215 (20), 254, 255 Bush, V., 4, 66 Butler, S. T., 33 (47), 68

Bakker, C. J., 118, 122, 131 (20), 133, 134, 15s Ballantine, S.,124, 153 Bardeen, J., 65, 66, 68 Barnes, R. B., 110 ( l l ) , 163 Bartels, J., 259 (l), 298 L Bartlett, J. H., 11, 67 Batten, H. W., 209 (18), 255 Caldwell, S. H., 4, 66 Begovich, N. A., 126 (23), 153 cerenkov, P., 54, 68 Behrend, W. L., 239 (33), 256 Bell, P. R., 88 (14), 91 (14), 99 (19), Chandrasekhar, S., 110 (12), 153 Chao, K. T., 55, 68 100 (19), 107 Chapman, S., 259 ( l ) , 298 Bell, R. L., 131, 132 (22), 15s Christensen, C. J., 140 (28), 153 Bemrose, J., 268 (8), 299 Clark, J. C., 28 (36), 67 Bernamont, J., 117, 118, 119 (24), 155 Cochrane, L., 3 (2), 66 Bethe, H., 25, 33 (44), 44, 47, 48, 67 Black, J. R., 202 (10, 12), 205 (15, 16), Collins, G. B., 190 (3), 192 (3), 193 (3), 209 (12), 210 (12), 254, 255 254 Coltman, J. W., 69, 106 Bleuler, E., 56, 57, 58, 68 Conwell, E., 65, 68 Blewett, J. P., 204, 254 Corson, D. R., 43, 68 Bloch, F., 50, 68 Crane, H. R., 55, 68 Bogle, H., 140 (25), 143, 144 (25), 153 Cuccia, C. L., 201 (8), 219 (23, 24), 221, Bohr, A., 49 (60), 52, 68 254, 255 Bond, D. S., 234 (32), 239, 256 Cutler, C. C., 130 (28a), 131, 153 Borden, P. A., 302 (4), 329 Borries, B. von, 8 ( l l ) , 67 D Bothe, W., 48, 68 Bowen, W. A., 290 (lo), 299 David, E. E., Jr., 225, 232, 233, 255 Bozorth, R. M., 295 (13), 299 Brewer, J. R., 202 (10, 12), 205 (15, 16), Davydov, B., 117, 140 (29), 154 De Benedetti, 105, 107 209 (12), 210 (12), 254, 255 Debye, P., 8, 67 Brillouin, L., 140 (26), 153 331

.-.

332

AUTHOR INDES

Diamond, H., 302 (5), 329 Dienier, G., 122. 151, 154 Donal. J. S., Jr., 201 (8), 211 (20), 215 (20), 219 (24), 234 (31), 234 (32), 2s4, 25s Dresel. I, A. C., 124 (50), 125 (50), 129 (SO), f54 Dunmore, F. &’., 302 (5), 529 I h r a l l , G. 15.) 116 (32), 124, 125, 164 Duveneck, F. B., 28 (36), 67 Dgsoti, J. P., 88 (9), 106

E I*:lliott, J. O., 88 (17), 107 Illton. L. It. B., 12, 67 Engstrom, R. IV.,71 (5), 106

F Farnsworth, €I. E., 16, 31, 67 Frazel, C. E., 88 (l5), 107 Felch, I<. P., 291 ( l l ) , 299 Fernli, E., 3, 50 (el), 54, 66, 68 Ferris, W.R., 152 (44),154 Frshlmch, EX., 10 (18). 12, 67 Fisk, J. B., 189 ( l ) , 190 ( l ) , 192 ( I ) , 254 Fleischmann, R., 48 (57), 68 Fo\vlcr, IT. A., 57, 58, 68 Frank, I., 54, 68 F r a n z , Xi., 147 (33), 154 Freeman, J . J., 116 (34), 126, 154 Friis, H. T., 14i ( 3 5 ) , 164 Furth, It., 120, 154 G

Gadsdcn, C. l’., 151 (91a), 155 Garrison, J. 13., 118 ( 3 7 ) , 154 Grttings, II. T., 88 (16), 107 Giffen, Harvey D., 312 ( G ) , 329 Cillette, R. H., 88 (12), 91 (12), 106 Crimpel. I., 16, 67 Gisolf, J. l I . , 117, 140 ( 3 8 ) , 164 Glendennin, 1,. E., 56, 68 Goldman, S., 110 (2), 153 Goldschmidt-Clermont, G.. 13 ( 5 3 ) , 68 Coldstein, L., 136, f 5 J Goudsmit, S., 36, 12, 68 Graves, J . D., 88 (9). 106 Griesen, K., 45 (55), 68

Gurevich, B., 117, 140 (29), 154 Gutton, H., 253, 256

H Haantjes, J., 138 (39), 154 Haeff, A,, 214, 256 Hagstrum, H. D., 189 ( I ) , 190 (l), 192 (11, 254 Hall, H., 54, 68 Halpern, O., 54, 68 Hamilton, D. R., 125 (3), 126 (3), 129 (3), 150 (3), 152 (3), 165 IIansen, W.JF-., 28 (36), 67 Hanson, A. D., 39, 68 Hanson, A. O., 13, 67 Hartman, D. L., 189 (l), 190 (l), 192 (l), 254 Hartree, D. R., 4 (6), 67 Hatton, J., 124 (50), 125 (50), 129 (50)) 164 Hausz, JV., 325 (8), 529 Hayner, I,. J., 134 (40),154 Hayward, E., 29 (37), 67 Haworth, K., 28 (36), 67 Hegbar, H. R., 201 (8), 254 Heggblom, J. C., 268 (8), 299 Heiland, C. A., 263 (2), 298 Heisenberg, W., 22, 67 Hellcr, G., 118, 153 Herbstreit, J. W., 147 (13), 153 Hereford, F. L., 55, 57, 58, 68 Herold, E. \V., 137 (41, 42, 42a), 138, 139 (43), 147 (42), 152 (44),164 Herzog, G. B., 140, 145, 154 IIinman, It-.S., Jr., 302 ( 5 ) , 529 Hofstadter, It., 88 (11, 17), 90 ( l l ) , 101 (20), 102, 103, 104 (21), 106 Hok, G., 202 (lo), 205 (15), 254 Holt, T. C., 268 (8), 299 Hull, A. W., 284 (Y), 299

J Johnson, H., 124, 154 Johnson, J. B., 117, 140 (45), 154 Jones, H., 60 (78), 61 (80), 63 (80), 64 (83), 68 Jordan, W. H., 99 (19), 100 (19), 107

333

AUTHOR INDEX

K Kallmann, H., 69, 106 Kilgore, G. R., 201 (7), 254 King, D. T., 43 (53), 68 Kircher, R. J., 146 (69), 155 Kirkpatrick, P., 28 (36), 67 Kittel, C., 295 (14), 299 Kleen, W., 132, 133, 144 @a), 151 (49), 154

Knipp, J. K., 125 (3), 126 (3), 129 (3), 150 (3), 152 (3), 155 Knol, K. S., 122, 151, 154 Kompfner, R., 124, 125 (50), 129, 154 Koppe, I€.,23, 67 Kramers. H. A., 52, 68 Kronenberger, K., 144 (55a), 154 Kulchitsky, L. A., 42, 68 Kuper, J. B. H., 125 (3), 126 (3), 129 (3), 150 (3), 152 (3), 155 Kurrelmeyer, B., 134 (40), 154 Kurshan, J., 201 (7), 254

L Lamb, R'. E., Jr., 204, 25.5 Lanzl, L. H., 39, 68 Latyschev, G. D., 42, 68 Lauritsen, C. C., 57, 58, 68 Lauritsen, T., 57, 58, 68 Lawson, A. W., 118 (37), 154 Lawson, J. L., 155 Lebenbaum, M. L., 150 (50b), 154 Leibson, S. H., 88 (17), 107 Leifer, M., 302 (3), 529 Lewis, H. W., 33 (46), 68 Llewellyn, F. B., 127 (64), 132, 138 (64), 154

Lyman, M., 13, 39, 67

M MacColl, L. A., 16, 67 MacDonald, D. K. C., 120, 154 MacFarlane, G. G., 141 (52), 143, 154 MacIntyre, W. J., 88 (13), 91 (13), 101 (20), 102, 104 (21), 107 McKay, K. G., 2 ( l ) ,66 McKinley, W., 12, 67 MacNee, A. B., 151 (91a). 155 Malter, I,., 71 (3), 106, 137 (42), 154

Maple, E., 290 (lo), 299 Marshall, F. H., 69, 106 Marton, L., 8, 23, 25, 67, 210 (19a), 255 Massey, H. S. W., 5 (7), 7, 8 (12), 9 (14), 10 (16, 17), 12, 27 (34), 67 Means, W. J., 291 (11), $99 Melman, I. J., 149 (54a), 154 Messel, H., 29, 67 hleyer, E., 140 (53), 154 Milatz, J. M. W., 119, 154 Miller, P. H., Jr., 114 (55), 140 (55), 143, 146 (55), 154 Mitchell, J. A., 84 (7), 106 Mohr, C. B. O . , 12, 67 Moliere, G., 8 (52), 36 (50), 39, 40 (50), 42 (52), 43, 68 Montgomery, H. C., 141 (56), 144,145,154 Mooers, H. T., 146, 154 Moore, D. G., 234 (32), 239, 256 Morrison, W. C., 239 (33), 256 Morton, G. A., 71 (3, 6), 73 (6), 84 (6, 7), 105 (22), 106, 101 Mott, N. F., 5 (7), 8 (12), 9 (14), 10 (16), 11 (19), 12, 27 (34), 60 (78), 61 (80), 63 (80), 64, 66 (82), 61, 68 Moullin, E. B., 117 (5), 118 ( 5 ) , 120 (5), 153

Moxon, L. A,, 147 (6), 150 (6), 155 hluirhead, H., 43 (53), 68 Mumford, W. W., 136 (57), 149 (57), 154

N Needle, J. S., 202 (12), 209 (12), 210 (12), 254

Neelands, L. J., 325 (8),329 Nichols, M. H., 302 (2), 311 (2), 312 (2), 329

Noble, S. W., 295 (12), 298 (12), 299 North, D. O., 122, 123 (58), 131 (60), 133, 134 (59), 136, 154 Nyquist, H., 115, 117, 118, 154, 240, 256 0

Olescn, N. L., 55, 68 Ortusi, J. A., 253, 256

P Parker, W. N., 214, 255 Parratt, L. G., 291 (11), 299

334

AUTHOR INDEX

Parzen, G., 13, 67, 136, 154 Paul, W., 55, 68 Pearson, G. L., 65, 66, 68, 140 (28), 163 Percival, W. S., 119, 154 Peters, P. H., Jr., 207, 208, 255 Peterson, L. S . , 127 (64, 65), 130 (65), 132, 138 (64), 154, 155 Peterson, W., 202 (12), 209 (12, 18), 210 (12), 254, 265 Phillips, M., 204, 255 Pierce, J. R., 130, 152 (7), 153 Pitts, J. C., 229, 255 Pockman, L. T., 28 (36), 67 Pound, R. V., 138 (8), 147 (8), 149 (8), 152 (S), 165

S

Saunderson, J. L., 36, 42, 6'8 Schiff, L. I., 8, 9 (15), 23, 25, 6: Schneider, E. E., 124 (50), 125 (50), 129 (5O), 154 Schneider, W. P., 232, 233, 256 Schottky, W., 115, 120, 122, 133, 139 (75), 141, 142 (71), 143 (72), 155 Schreiber, W. F., 302 (3), 329 Scott, M. B., 13, 39, 67 Scot,t, W. T., 33 (45), 43, 45 (56), 68 Seitz, F., 60 (79), 61 (81), 63 @ I ) , 68 Sherr, R., 88 (8), 106 Shockley, W., 141 (56), 144, 145, 154 Shulman, Carl, 194 (5, 6), 196, 201 (6), 201 (7), 254 Q Silverman, S., 110 ( l l ) , 153 Quate, C. F., 130 (28a), 153 Simons, R. F., 284 (9), 299 Singer, S. F., 290 (lo), 299 R Slater, J. C., 31, 67, 190, 192 (2), 229, 254, 255 Rack, A. J., 122, 127, 128, 155 Slonczewski, T., 291 (ll),299 Rajchman, J. A., 71 (4), 106 Smick, A. E., 28 (36), 67 Ramo, S., 204, 254 Smith, C. D., 88 (15), 107 Rauch, L. L., 302 (2), 311 (2), 312 (2, 7), Smith, L. P., 33 (44), 44, 47, 48, 68 329 Smith, Lloyd P., 194 (5, 6), 196, 201 (6), Reddeck, J. G., 239 (33), 256 254 Reich, H., 55, 68 Smyth, C. N., 126 (76), 155 Reich, H. J., 191 (4), 254 Snyder, H. S., 33 (45), 43, 68 Reichertz, P. P., 31 (42), 67 Snyder, R. L., 71 (4), 106 Reverdin, D. L., 210 (19a, 19b), 255 Spenke, E., 118, 122, 155 Reynolds, G. T., 107 Sperduto, A., 10 (IS), 12 (18), 67 Rice, S. O., 110 (15)' 153 Sproull, R. L., 143, 155 Squier, R. T., 299 Richards, T. C., 268 (8), 299 Steenbeeck, M., 116, 15.3 Richardson, O., 16, 67 Richardson, R. J., 113 (68), 141 (68), 142, Strutt, M. J. O., 119, 132, 133, 147 (80), 155 151 (80, 81), 255 Swann, C. P., 57, 58, 68 Ritson, D. M., 29, 67 Swann, W. F. G., 54, 68 Ritson, R. M., 43 (53), 68 Robinson, K. W., 105 (22), 107 T Rogers, D. C., 149 (83), 155 Rose, M. E., 12, 33 (44), 44, 47, 48, 67, 68 Tamm, Ig., 54, 68 Ross, M., 55, 68 Tcllegen, B. D. H., 138 (39), f 5 4 Rossi, B., 45 (55), 68 Thiede, H., 140 (53), 164 Rothe, H., 144 @a), 153 Thomas, H. P., 264 (3), 299 Rudberg, E., 30, 31, 32, 67 Thomas, L. H., 3, 66 Rumbaugh, L. H., 291 ( l l ) , 299 Thompson, B. J., 136, 155 Ruthberg, S., 209 (18), 255 Thomson, G. P., 3 (2), 66 Ruthemann, G., 31, 32, 67 Thynell, G. M., 302 (4), 329 Ryder, R. M., 146 (69), 255

335

AUTHOR INDEX

Tickner, A. J., 291 ( l l ) , 299 Torrey, H. C., 140 (9), 145, 146 is), 152 (91, 153 Turnbull, J. C., 31, 67

U Uhlenbeck, G. E., 110 (16), 163 Ullrich, E. H., 149 (83), 166

V Vacquier, V. V., 264 (4), 268, 284 (9), 299 Valley, G. E., 149 (lo), 147 (lo), 150 (lo), 153 van der Graaff, R. J., 10 (18), 12, 67 van der Ziel, A., 118, 119, 125 (86), 126 (89), 131 (86), 132, 133, 140, 143 (go), 145, 147 (80), 149 (85), 150 (87), 151 (80, 81, 87), 156 van Wijngaarden, J. G., 144 ( ~ O C ) , 155 van Zolingen, J. J., 119, 142 (go), 156 Veisnel, A,, 125 (86), 126, 131 (861, 155 von Engel, A,, 116, 163 von Weiszoker, C. F., 52, 68

W Wallman, H., 149 (lo), 147 (lo), 150 (lo), 151 (Sla), 163

Wang, M. C., 110 (IS), 153 Watson, G . N., 37 (49), 68 Watson, R. J., 268 (8),299 Webster, D. L., 28 (36), 67 Weisskopf, V. F., 65, 68 Welch, H. W., Jr., 202 (9, 10, 11, 12), 205 (15, 16), 209 (12, 18),210 (12), 26.4, 255 Welton, T. A., 11, 67 Whitmar, C. H., 140 (9), 145, 146 (9), 152 (91, 153 Whittaker, E. T., 37 (49), 68 Wicks, W. F., 229, 255 Wilbur, D. A., 207, 208, 255 Williams, E. J., 49 (59), 68 Williams, F. C., 119, 166, 295 (12), 298 (12), 299 Wurm, M., 268 (6), 299 Wyckoff, R. D., 268 (7), 299

z Zajac, B., 55, 68 Zernike, F., 110 (17), 111 (17), 115 (17), 153 Ziegler, M., 134 (93), 135, 155 Ziinti, W., 56, 57, 58, 68 Zworykin, V. K., 71 (3), 106

Subject Index A

C

Cadmium tungstate, phosphor, 91ff Calcium fluoride, phosphor, 91 Capacity, storage, electronic computers, 160ff Cathode “active specks,” 141, 142, 143 diode, 122 flicker effect, oxide coated, 143 temperature, 121, 122, 123 Cathode ray tube, storage in electronic computers, 164, 166, 167 Circuits AN/AKT-l A telemetering transmitter, 32 1 antihunt, 286, 287 Eccles-Jordan trigger, 159 electronic computer, 171 flip-flop, 171ff, 184 gating, arithmetic organs, 171 injection-locking, 231 magnetometer bridge, 271 magnetron plate modulator, 236 noise figures, 149, 150, 151, 152 phase control, 239 pulse stretcher, 28G, 287 I t F , absorption modulation, 213, 214 scintillation counters in coincidence, 104, 105, 106 SEAC, 183, 184 single coil magnetometer, 265 B stabilizer channel, 287 time-pulser, 175, 176 Barkhausen discontinuities, 296 Whirlwind, 176, 177 Beta ray Code, Whirlwind order, 179 detection, 91, 96 Compton collisions, 1 O l f f measurement, 99ff Computer, electronic digital, 157ff Binary number system, 159, 174 arithmetic organs, 171, 172, 173, 175, Bloch wall, 296 178, 180 Born’s approximation, 5, 9, 10, 11, 12, EDSAC, 163 18, 19, 20, 21, 28, 65, 66 EIIVAC, 163 functions, 158, 159 Boron, phosphor, 93 336

A-c circuit analysis, noise, 112ff Accelerometer, 315 Acoustic delay line, 162, 163, 164 (See Storage, computer) “Active specks,” cathode, 141, 142, 143 Alpha particles, detection, 94 Amplifier, scintillation counter, 72 Amplitude modulation, magnetron absorption, spiral electron beam, 211ff, 253 bandwidth, 237, 238 electron coupler, 219ff, 253 out-phase, 232, 253 plate, simultaneous frequency control, 234ff production, 191, 192, 198, 264 Anthracene, phosphor beta particle penetration, 96 preparation, 91, 92 structure, 91 Arithmetic organs, electronic computers registers, 171, 172, 173, 175 Khirlwind, 178 SEAC, 180 Atomic diamagnetic susceptibility, 23 Atomic field, 4 Atomic nucleus, 3 Audio oscillator, 293

337

SUBJECT INDEX

input, 158ff, 181 output, 1586, 181 SEAC, 150, 163, 171, 172, 173 type designation, 159 UNIVAC, 163, 185 Whirlwind, 158, 164, 165, 166, 171ff, 185 word representation, 181 Conductivity electrometer triode, 122, 123 pure metal, 61, 62 total emission, 126 Control organs, electronic computers, 173 Convection noise currents (See Noise) Correlation, fluctuating quantities, 110, 111; coefficient, 110, 111 Cosmic rays, detection, 93 Counters Geiger, 70, 71, 94, 95 scintillation, 69ff Cross-modulation, telemetering, 305 Crystal, diode, 140 flicker effect, 141 noise, 145, 146, 147 Crystal rectifiers, 144 Current fluctuations, 118 Cyclotron resonance, 204

D

DC amplifier, 239 “Dark current,” 140 Data transmission, computers, 159 Debye approximation, scattering, 8 Deflection mixers (Herold), noise, 138, 139 Detectors high energy radiations, 69ff magnetic anomaly, 263ff Dielectric constant, magnetrons, 204 Digital computer techniques, telemetering, 329 Diode characteristics, 119 complex impedance, 128 conductivity, 122 cylindrical, 124 high frequency, 127 noise, high and low frequencies, 120, 121, 124 shot noise, 119ff

space-charge limited, 126, 127, 128, 143 iV cathode, 144 Diode matrix, computers, 173 Diode mixers, 138, 152 Diode rectifiers, 239 Diplexer, 239 Dirac’s equations, 9, 11 Disk-seal triode, 151 Dummy antenna, 147, 148, 149 Dynodes, 70ff

E Earth’s magnetic field, 281 characteristics, 259 gradients, 259 induction, magnetic moments in ferromagnetic bodies, 260 intensity, 259 magnetic detector problems, 259, 260 time variations, 259 Elastic scattering, electrons, 3ff atomic binding forces, 15 atomic interaction effects: range in aluminum, 58; effective range and actual range in a solid absorber, 56, 57; mean ranges, 56ff; Bohr’s argument, 51ff Born’s relativistic formula, llff cross sections, 8 energy loss, passage through solids, 48ff large angle, 10 perturbation, valence electrons, 13, 14, 15 reflection from metal surfaces, 16, 17 relativistic correction, 8ff small angle, 10 solid binding, 13ff total elastic cross section, 5 (See Scattering, electrons; and Electron) Electrometer, equivalent noise temperature, 119, 122, 123 Electron eerenkov radiation, 54 diffraction, 2 diffusion, solid scatterer, 3 low velocity, 123 motion, diodes, 127

338

SUBJECT INDEX

multiple scattering, 10 natural frequencies, 28 polarization, double scattering, 2, 4 range determination, 2 scattering, Iff, 118 secondary, 29 spin-orbit coupling effects, 9 transit time, 111, 116 velocity, 4, 202ff (See Scattering, electrons; and Electron mobility) Electron coupler, 219ff Electron gas, oscillation frequency, 50, 51 Electron gun, 164, 165, 199, 201, 234,239 Electron microscope, 2 Electron mobility drift velocity, metals, alloys, and semiconductors, 58, 59 energy states, 60 resistance, semi-conductors, 64ff; alloys, 63ff; pure metals, 61ff Electron multiplier tubes, 2 “Electron temperature,” 136 Emission limitation, 249 Energy spectrometry photomultiplier, 79 scintillation counter, 97 Equipartition law, 114, 118 Equivalent noise resistance, 123, 124 Equivalent noise temperature, 119ff

F Feedback, noise suppression, 146 Fermi-Dirac statistics, 4 Fermi-Thomas atom model, 50 field, 8 statistics, 22, 64 Flicker noise crystal diodes, 146, 147 semi-conductors and cathodes, 140ff Fluctuation quantities, 109ff calculation, 112ff Fokker-Planck equation, 45 Fourier spectrum, 113, 114, 115, 116 Frequency modulation, magnetrons electron clouds, 201, 202 methods, 189, 193, 194, 197, 202, 205, 211, 235 spiral electron beams, 253

tube structure, 206, 207 Frequency modulation, telemetering subcarriers, 305 Friis’ formula, 148 G

Gamma rays detection, 91, 95 energy spectrum measurements, 100ff quantum energy, 48 Gas-ionization detector (See Detectors, high energy radiations) Geiger counter alpha-particle detection, 94 integration time, TO, 71 resolving time, 71 (See Detectors’ high energy radiations) Geophysical surveying and prospecting, 263, 268, 291, 292, 298 Germanium crystals, 144, 146 Gradiometers 263ff (See Magnetometers) Green’s theorem, 5 Guided missiles, 302 Gyro Position Indicator, 315

H Hartree voltage, 249, 250 Hartree-Fock self-consistent field, 4, 8 Health hazards, alpha emitters, 94 Hexode, partition noise, 133, 134 Hexode mixers, 137

I Indium, phosphor, 93 Induced grid noise, pentodes and hcxodes, 134 Inelastic scattering, electrons, 17ff angular distribution, 21, 22, 23 cross sections, 23, 24, 25, 26 energy distribution, 30, 32 inner shell ionization, 23, 24, 25, 26, 27 interaction within the material, 29 low-energy loss collisions, 30ff quantities, 23ff relativistic modifications, 26ff solid binding influence, 28, 29 total ionization, 23, 24, 25, 26 (See Electron; and Scattering, electrons)

SUBJECT INDEX

Injection magnetron, 194, 247ff (See Magnetrons, continuous wave) Interdigital magnetron, 202, 205, 206, 208 (See Magnetrons, continuous wave) Ion feedback, photomultipliers, 73 Isomers, decay, 105, 106

K Klystron, 252 out-phase modulated, 232, 233 phase locking, static conditions, 226 reflection coefficient plane, 227

L Llewellyn-Peterson equations, 127, 129, 130, 132

M MAD (See Magnetic airborne detector) Magnetic airborne detector, 257ff components, 293 drive amplifiers, 293, 294 history, 258ff magnetic stabilization and orientation, 279ff noise, 295ff system, 292ff universal head, 293ff (See Magnetometer; and Submarine, detector) Magnetic airborne detector, Japanese, 264, 267, 268 Magnetic amplifier, 268, 269 Magnetic anomaly detector (See Magnetic airborne detector) Magnetic contour maps, 297 Magnetic drum, 162, 163 Magnetic equator, 287, 288 Magnetic field, earth, 259, 281 (See Earth's magnetic field) Magnetic stabilization and orientation i% earth's field, 282ff Magnetometer, 263ff coil inductor, 264 earth inductor, 264 electron beam, 266 even-harmonic, 283, 285

339

noise, 291 peak type, 283, 285, 286, 294 saturable-core, 258, 264, 265, 268ff, 280, 283 Schmidt, 263, 264 single coil, 269, 270, 271, 273ff single coil, second harmonic output, 265 single detector, stabilized, 292 stabilizer mounting, 283, 287, 288 theory, 269ff three component, 290, 291, 292 variable-resistance, 266 Magnetometer bridge, 271ff balanced bridge output, large external field, 273 even-harmonic, 272, 273 peak type, 273 Magnetometer head detector, 283, 285 magnetically stabilized, 284 three-axis, 289, 290 two-axis, 285, 286 Magnetrons, continuous wave, 187ff absorption: methods, 191; spiral beam efficiency, 213; system, 213ff absorption tube, 216 absorption-beam cathode, 212, 213 admittance, 189, 196, 197, 211, 229 amplitude modulation (See Amplitude modulation, magnetrons) anode voltage range, hot-resonance studies, 202, 203 carrier frequency, 199, 201, 202, 211; voltage, 233 circuit: efficiency, 192, 197, 211ff; finite bandwidth, 244; infinite bandwidth, 247 conductance, 190, 192, 193, 211 cyclotron frequency, 211 directional coupler, 231 efficiency, 188, 191, 207, 211, 214, 219 electron coupler, 193 energy, electron, 213 equivalent circuit, 189 experimental applications and results, 205, 206, 208ff feedback loop: circuit of finite bandwidth, 244; circuit of infinite bandwidth, 241ff; phase control system, 240

340

SUBJECT INDEX

frequency-control, 197, 201, 230ff, 245ff, 253 frequency deviation, 201 frequency modulation (See Frequency modulation, magnetrons) gain, 241, 243 Haeff’s factor, 198 hot-resonance studies, 202, 203, 205 injection locking, 225, 226ff, 231ff, 253 load variation, 200 locking: contours, 229; power, 230; range, 228ff, 239 longitudinal magnetic field, 195ff longitudinal magnetic tube, 219 Michigan studies, 209ff miniature, 208, 209 modulation (See Modulation, magnetrons) multicavity, 202 oscillating structures, 205, 206 phase-control, 2396 I phase-locking, 226, 227 power, 190, 207, 208 practical loop performance, 243 prediction of characteristics, 190, 191 preemphasis, 233, 234 “pushing,” 203, 207, 209, 234, 238, 253 “Q,” 194, 209, 211 reactance-section tuning, 253 space charge (See Space charge, magnetrons) spiral beams, 199, 200 stabilization, 232, 234, 235, 240ff susceptance relations, 190, 197 uncontrolled, 246 variation of Aw, 199ff voltage tuning, 207, 208, 209, 210, 253 l f a r k I, 157 >.lark 11, 157 Mark 111, 185 Maxwell distribution, 65 Measurement gain and sensitivity, photomultipliers, 79 time, scintillation counters, 103ff ‘(Memory,”electronic (See Storage, computers) Mercury line storage, 180, 181 Microwave noise standards, 136 Microwave tubes, 225

Modulation, magnetrons characteristics, 187ff, 191, 215, 216, 237 efficiency, 253 factor, 235, 236 incidental frequency, 194 linearity, 236ff methods, 189 outphase, 193, 232ff phase, 231 plate, 234, 235, 236, 253 power, 190, 191, 201, 207, 208 pulse, 253 spurious frequency, 234 transit time, 223 velocity, 227 voltage, 191, 237 (See Magnetrons, continuous \\ ave ; Amplitude modulation, magnet r o n s ; Frequency modulation, magnetrons) Motion meter, 315 Multichannel radio telemetering, 301ff (See Telemetering) Multiple scattering, electrons, 32ff absorption, electrons in plates, 43ff angular distribution, 34ff axially symmetric, 46 back diffusion coefficient, 28 Boltzmann equation, 33ff collisions (P), 36ff diffusion, 33, 46ff distribution, 40ff electron energy and density, 46, 47 energy distribution, 48 energy loss, 41ff Fokker-Planck approximation to the Boltzmann equation, 35, 44 functions, scattering formulae, 41 gaussian distribution, 36, 39, 44, 45 half-widths, distributions, 42 isotropic distribution, 46 K , 35ff mean free path, 35, 36 mean values, 41 momentum loss cross section, 35ff photographic emulsions and foils, 42, 43 Rutherford distribution, 39 small angle, 33, 36, 37, 38, 30, 40 (See Scattering, electrons; and Electrons)

34 1

SUBJECT INDEX

N Naphthalene, phosphor, 92 Neutrons detection, 93, 96 diffraction, 2 thermal, 93 Noise, 295ff aircraft (carrier), 296 average value, 110 beam deflection mixer tube, 138, 139 “bursts,” 141 calculations, l l O f f , 129 calibration, 125 crystal diodes, 145, 146, 147 diode, 123ff diode mixers, 138 effective noise figure, 147, 148, 149 electrometer triode imput circuit, 123 electron beam, 130, 131 figure, 147, 148, 149, 150 flicker effect, 140ff gas discharge tubes, 135, 136, 137 generators, thermal, 117ff high frequency, 126, 127, 128 instrumental, 282, 295 magnitude, 131 measurement, 110 measuring equipment, 141 mixer tubes, 137, 138, 139, 140 partition, 133, 134 pentodes and hexodes, 133, 134 photocells and photomultipliers, 139, 140 power, 117, 119, 131, 136 problems, I l O f f , 127 radio tubes, 115, 116 ratio, 119, 136, 148, 149, 152 receiver, 147, 148, 149 resistor, 118 secondary emission, 134, 135 shot, 110 (See Shot noise) sidebands, 152 space variations in earth’s field, 297 suppression, 121, 129, 135 telemetering, 305 “Temperature,” 136 thermal, 110 time variations in earth’s field, 297 total emission, 125, 126 transistor, 146

triode, 123ff uncorrelated, 132, 133 (See Shot noise) Nuclear radiation, detection, 94 Nuclear reactors, monitoring, 94 Number representation, computers, 159, 160 Nyquist theorem, 114, 115, 117, 122, 136

0 Oscillator, crystal controlled, 239; uncontrolled, 226

P Partition noise (See Noise, partition) Pauli’s principle, 31 Pentode, noise, 133, 134, 150, 151 Pentode mixers, 137 Phosphor, 88, 89, 90, 91, 92, 93, 167 Photocathode cesium-antimony, 73 fatigue effect, 77 quantum efficiency, 75, 76 spectral response, 75 thermionic emission, 76 Photocell, 139, 140 Photoelectron: collection efficiency, 79; emission, 139; pulse height distribution, 80 Photoemitters: internal (See Photocathode) ; surface, 73 Photographic emulsions, 29 Photomultipliers, 71ff commercially available, 73, 74, 77, 78, 82, 84 components, 71 electron trajectories, 72, 73 electron transit time, 86ff electrostatically focused, 72 energy spectrometry, 79 gain, 71, 79, 83, 84 initial velocity effects, 86 ion feedback prevention, 73 magnetically focused, 72 noise, 139, 140 operation, 71 performance characteristics, 78 resolving time, 85, 86 sensitivity measurement, 79

342

SUBJECT INDEX

space charge effects, 86 spurious pulse output, 84 thermionic emission, 76, 84, 85 tube temperature, 85 unfocused, 73 “Pickups” (See Telemetering) Polarization, E vector, 204 P P M (See Telemetering, Pulse position modulation) Pressure gage, 315 Pulsed injection magnetrons, 252 (See Magnetrons, continuous wave)

R Radar receiver, noise figure, 149 Radiation, ultraviolet, 89 Radio Sonde, 302 Radio telemetering (See Telemetering) Radioactive contamination, surveying, 94 Receivers, available power gain, 148; noise, 147, 148, 149 Reflection coefficient, magnetrons and klystrons, 226, 227 Rutherford scattering, 22, 49. 65 S

Scattered amplitude, electron scattering, 6 Scattering, electrons, Iff aluminum scatterer, 10 atomic binding forces, 156 beryllium scatterer, 10 cross sections, 7, 9 differential elastic scattering crosssection, 5 elastic (See Elastic scattering electrons) elastic reflection of electrons from metal surfaces. 16ff fermi energy, 16 foils, thin, 10 fourier analysis, perturbing force, 16ff gold scatterer, 11 “image force,” 16 inelastic (See Inelastic scattering, electrons) ionization, inner shell, 28 light nuclei scatterers, 11 limitingangles,solidcarbonandgold, 15

mean excitation energy, 27, 28, 29, 55 mercury scatterer, 11 multiple (See Multiple scattering, electrons) number scattered, solid angle, 5 perturbation of valence electrons, 13ff reflection coefficients, 17 Rutherford scattering, 6, 7 screening of field, 11 small angle scattering, 7 solid binding influence, 13ff, 28ff spin-orbit, 10, 11 time, collisions, 15 (See Electron; Elastic scattering, electrons; Inelastic scattering, electrons, and Multiple scattering, electrons) Schottky’s formula, flicker effect, 142 Schrodinger equation, 4, 5, 9, 18 Scintillation counters, 69ff applications, 946 circuits in coincidence, 104, 105 components, 69, 70 efficiency, 70 energy analyzer, 70, 97 history, 69 multiplication statistics, 80 operation, 70 resolving time, 71 (See Photomultipliers) Screen, fluorescent, 94 SEAC, 180ff; arithmetic organ, 184 (See Computer, SEAC) Secondary electrons, 125 Secondary emission, 2 multiplication statistics, photomultiplier, 808,97 Poisson’s law, 81, 82 time, 86 Secondary emission multiplication (See Photomultipliers) Secondary emission noise, 134, 135 Selectron storage tube, 158, 164, 168, 169, 170, 171 Semi-conductors, 2, 58, 59, 64ff, 116, 117, 140 Servomechanisms, 283, 284, 286, 290, 294 (See Magnetic airborne detector) Shot effect, 115,120, 121

SUBJECT INDEX

Shot noise, 136 diodes and triodes, 119ff semi-conductors, 116, 117, 140 space charge suppression, 145 Silicon, 64, 65 Slater wave functions, 23 Sodium Iodide, phosphor, 90, 91, 102 Sonic delay line (See Acoustic delay line) Space charge, 145 diodes, 119ff photomultipliers, 86 Space charge, magnetron, 198, 223 bulk effects, 203, 204, 205 cloud, 202, 205, 206 spokes, 202, 203, 209 studies, 210 Spectrometry, scintillation counter, 966 Spinthariscope (Set Detectors, high energy radiation) Split-anode magnetrons, “pushing,” 207, 208 (See Magnetrons, continuous wave) Stability, Nyquist criterion, 240 Storage, computers devices, 159ff electronic digital, 158ff internal, 161ff magnetic drum, 162, 163 mercury line, 164, 180, 181 “Williams” type, 166, 167, 168, 180 Storage tube, 162, 164 Subcarriers (See Telemetering) Submarine degaussing, 260 detection, 258, 259, 262ff, 284 equivalent magnetic moment, 260 magnetic dipole field, 260, 261, 262 permanent magnetic moment, 260 (See Magnetic airborne detector)

T Tachometer, 315 Target drone, 302 Telemeter, 301 (See Telemetering) Telemetering accelerometer, 315 AN/AKT-lA, 320, 321, 322 AN/AKT-lA(XN-2). 324 AN/AKT-5, 313 ANIDKT-2, 316

343

AN/DKT-3, 313 APL/JHU, 313, 314, 315 basic systems, 304ff choosing a system, considerations, 311, 312 evolution, 302, 303, 304 FM-FM subcarrier, 304, 305, 314 frequency division (sub-carrier), 304, 313, 314, 315, 316 frequency division, N-channel system, 305 gyro position indicator, 315 instrument, 303 matrix system, 316, 317, 318, 319 mechanically commutated system, 325, 326, 327, 328 motion meter, 315 oscillogram, 303, 304 “pickups,” 328, 329 pressure gages, 315 pulse code modulation, 306, 329 pulse interval modulation, 310 pulse position modulation, 306, 307, 308, 309, 316 sensory elements, 315, 328, 329 single channel, 301 subcarrier, 304, 305 tachometer, 315 television, 303 time division, 304, 306, 307, 308, 309, 310, 311 time division, N-channel system, 307, 308, 309, 310 Vultee system, 312 Temperature cathode, magnetron, 210 equivalent noise, 119 photomultiplier tube, 85 Tetrodes, 188 Thallium, activator, 90,91 Thermionic emission photocathodes, 76 photomultipliers, 84, 85 Total emission conductivity, 126, 129 Total emission noise triodes, 125, 126, 129 Tracer materials, observation, 94 Trajectories, electron, 72, 73 photomultipliers, 86 Trajectron (diode magnetron) 210 (See Magnetrons, continuous wave)

344

SUBJECT INDEX

Transistor N type, 146 N-P-N junction, 147 noise, 145, 146, 147 Trans-stilbene, phosphor, 85, 92 Triode, 212 characteristics, 123 energy absorbed per electron, 213 induced grid noise, 131, 132 noise, 124, 129ff, 150, 151 output power, 188 RF circuit, 213, 214 shot noise, 119ff transconductance, 123 Triode mixers, 137 Tropotron, voltage tuning, 208 (See Magnetrons, continuous wave)

U Units, Roentgens, 95, 96 UNIVAC, 185 (See Computer, UNIVAC)

v Vacuum tube electronics, noise, 112ff Valence electrons, charge distribution, 8

W “Williams Storage,” 180 Whirlwind, computer (See Computer, Whirlwind) Work function, cathode, 122

X X-ray diffraction, 2 generation, 24 scattering, atom form factor, 6