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Electronics Calculations Data Handbook

Electronics Calculations Data Handbook

About the author Daniel McBrearty is a freelance electronics engineer specializing in audio systems. He was an RAF electronics technician for several years before studying for an HND at Luton College of Higher Education. Thereafter he worked for various companies including Soundcraft Electronics and Drake Electronics. He is currently involved in the redevelopment of the Royal Opera House, Covent Garden. His other interests include playing the saxophone.

Electron ics Ca Icu lations Data Handbook

Daniel McBrearty

Newnes

OXFORD BOSTON JOHANNESBURG MELBOURNE NEW DELHI SINGAPORE

Newnes An imprint of Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd " ~

A member of the Reed Elsevier plc group

First published 1998 9Daniel McBrearty 1998 All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Rd, London, England W1P 9HE. Applications for the copyright holder's written permission to reproduce any part of this publication should be addressed to the publishers.

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 07506 3744 7

Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress.

RELANT _ E A

FOR EVERYTITLE THATWE PUBLISH, B~ORTH-HBINEMANN WILL PAY FOR BTCVTO PLANT AND CAREFOR A

Typeset by Jayvee Computer Services and Exports Pvt. Ltd., India Printed and bound in Great Britain by Biddies Ltd., Guildford and Kings Lynn

Contents Preface Acknowledgements Part One

viii ix

Basic Concepts

Introduction to Part One Fundamentals To the beginner What is electricity? If we can't see electricity, how do we measure it? M M F a n d current E M F a n d voltage Circuits and components Conductors and insulators Resistance Ohms Law Circuits, diagrams and common expressions Resistors Are electrons psychic? Capacitance and capacitors Self-inductance and inductors Mutual-inductance and transformers

10 10 10 10 11 12 14 15 17 18

Direct current AC and DC signals Direct current Calculations on DC quantities Resistors in DC circuits Capacitors in DC circuits Inductors in DC circuits Power in DC circuits

20 20 20 21 22 22 22 23

Contents Alternating current The sine wave Calculations on AC quantities Resistors and sine waves Capacitors and sine waves Inductors and sine waves Why are sine waves so important? More AC waveforms AC waveforms with a DC level Power calculations with AC waveforms

26 26 30 31 31 32 33 35 35 36

5 A circuit analysis toolkit Introduction Basic topologies The series circuit and Kirchhoff's voltage law The parallel circuit and Kirchhoff's current law Arrow directions for voltages and currents More about voltage and current sources Th6venin's and Norton's equivalent circuits

39 39 39 39 41 42 44 45

Part Two

53

Resistive Circuits

Equivalent resistances Introduction Using the Tables for resistors Tolerance of components Using the Tables for capacitors and inductors Table 6.1 E6 equivalent resistances Table 6.2 El2 equivalent resistances Table 6.3 E24 equivalent resistances 7 Maximum powers for resistors Table 7.1 Maximum power for resistors up to 0.25W Table 7.2 Maximum power for resistors 033W to 1W Table 7.3 Maximum power for resistors 2W to 5W Table 7.4 Maximum power for resistors 6W to 10W Table 7.5 Maximum power for resistors llW to 25W Table 7.6 Maximum power for resistors 50W to 300W Voltage dividers Introduction Using Table 8.1 in cases where source and load impedances can be ignored

55 55 55 56 57 58 61 70 102 103 112 121 127 132 137 142 142 143

Contents When source and load impedances cannot be ignored Table 8.1 Voltage dividers

Part Three

Reactive Circuits

First-order CR and LR circuits Introduction Time response Frequency response Table 9.1 Time and frequency constants for frst-order CR circuits Table 9.2 Time and frequency constants for first-order LR circuits Table 9.3 Step response of first-order CR and LR circuits Table 9.4 Frequency and phase response of first-order CR and LR circuits

vii 143 146 203 205 205 205 212 216 220 221 222

10 LC circuits Introduction Series tuned circuit Parallel tuned circuits Table 10.1 Frequency constants for LC circuits

223 223 223 226 231

Part Four

257

Operational Amplifier Circuits

11 Amplifier gains Introduction Inverting op-amp Non-inverting op-amp Table 11.1 Inverting op-amp gain

259 259 259 261 264

Appendix Appendix Appendix Appendix

285 287 289 291

1 Units, symbols and suffixes 2 Colour codes 3 The decibel 4 Complex number analysis

Further reading Index

295 297

Preface This book began life as a selection of tables for electronics engineers. Dealing with such common requirements as setting op-amp gains, forming non-standard resistor values from standard pairs and setting CR time constants, it was my hope that such a book would find common favour. In writing explanatory notes to accompany these tables, I found myself constantly wondering how much knowledge to assume on the part of the reader. After all, the book should be as useful to a beginner as to a professional with 20 years of experience. The time came to make a decision, and Part One was born. In it I have attempted to go from first principles to the point where the reader can hope to understand the workings of the circuits discussed in Parts Two and Three with little prior knowledge. My intention has been to be non-mathematical, logical and concise. I have drawn a line at explaining the workings of electronic devices as there is not time or space, and this book only deals with them in the final chapter. An overview of the op-amp is given there. I hope that Part One provides a useful foundation for the beginner and a point of reference for the more experienced. How well all this works as a whole will not be seen until the book is subjected to the final test by its readership. It is my hope that it will prove a valuable aid to you, whatever your level of experience. I will be happy to receive comments, criticism or suggestions for future improvement (and also to hear about any places where my spellchecker replaced 'squarewave' with'scurvy' without my asking it to).

by mail: Dan McBrearty c/o Butterworth-Heinemann Linacre House Jordan Hill Oxford OX2 8DP UK or by email: dan@ danmcb.demon, co.uk

Daniel McBrearty December 1997

Acknowledgements Thanks are due to Jim and Sybil McBrearty, for love and support in this; Eric Pressley and John Charlton, from whom I have learnt a great deal; all the staff at Butterworth-Heinemann for making the book a reality; William L. Bahn for helping me to convice myself that tuned circuits really should do what they do; and Hilary and Fi for putting up with my moods while I wrote!

This Page Intentionally Left Blank

Part One Basic Concepts

This Page Intentionally Left Blank

Introduction to Part One In this part of the book we take a look at the founding principles of electronics, from voltage, current and O h m s Law to some basic ways to analyse circuits mathematically. If you know all of this then skip it, using it for reference as required. If not then read on. I have tried to arrange ideas so that you are introduced to them sequentially, but this is a bit impractical in places. So if you are a real newcomer to electronics I'd like to suggest two readings; the first to get an overview of each topic, the second to cross-refer between them and to begin to see how they relate to each other.

This Page Intentionally Left Blank

Fundamentals To the beginner Before gettinginto the technical stuff, we might wish to ask ourselves what el ectricity is. My first recollection of thinking about it (though I did not know that I was) is of being a child and dismantling a prized radio to find out that no one was inside; just a mind-boggling collection of small coloured objects which evidently were not sweets, though some looked like them. My first direct experience of electricity was more sudden; an electric shock from a bar fire while trying to melt some plastic on it. I knew it was hot, but hadn't expected that! Later I came across the manual for a record player and amplifier in the house, which was old-fashioned enough to come with a circuit diagram. I was fascinated by it. It meant something to someone, but these hieroglyphics were like no language that I could figure out. Later I took a technician's course, and a confusing set of concepts was presented to me as explanation for this unseen and magical force. Electricity, I had now realised, is used in a huge range of ways; recording sound, reproducing pictures, lighting our darkness and a lot else besides. All this was, they told me, due to unseen little balls which whiz around in some materials, creating equally unseen lines which can cause little balls in other places to whiz around as well. And this the mental territory of staid, rational looking people who would probably claim that they don't believe in magic. I have to confess that, some years later, I have still not seen the little balls or the lines which they fling about, and I'm not very sure that I really understand them. But I have managed a reasonable career as a technician and an engineer, and I believe that I would have a fair chance of fixing my cassette machine, T V or house wiring should they misfunction. On the whole, I have not thought about the antics of little balls very much (though I suppose that it helps to know that they are there). Electricity looks, in my mind, more like water, wires like pipes, resistors like very thin pipes, capacitors like pairs of half-filled balloons which squash against each other, and inductors l i k e - well something else. (I never said that the analogy was complete or accurate.) I say all this as, I hope, a source of comfort to the new student of the subject who may be suffering the same pangs of insecurity about atoms, electrons and so on that I went through. Unless you feel strongly to do otherwise, let them live their own strange lives. You can be a very competent and effective user of the principles of electricity and electronics without needing to know much about

6

Electronics Calculations Data Handbook

them (though the same might not be said of completing your college course). Leave it to the physicists. What helps a great deal is having a good and clear grasp of the laws of electricity, and being able, as much as is possible, to prove them to yourself.

W h a t is electricity? We are never concerned with the behaviour of an individual atom in electronics; but with their movement in vast numbers, as they fling themselves, lemminglike, around the wires of your circuit. And yet we hardly think of them at all. We think a great deal about 'voltage', 'current' and about the golden rule of electronics, Ohms Law. You will meet these soon. Actually it is not atoms that move, but mostly bits of them, even tinier particles called electrons which separate themselves somehow from the larger atom which is their usual home. These electrons are now called 'free electrons'. Though unimaginably small, they are pretty powerful. They carry something which is called a'negative charge' which is another way of saying that if, having been separated from the parent atom, they should ever encounter another with a vacancy then they will be in there like a shot and pretty difficult to move. And the feeling is mutual; once it has lost an electron the atom feels the loss and will try to bring close to it any waifs that it senses nearby. Being much bigger, it moves much less easily, or not at all. All of which physicists understate quite magnificently when they describe atoms which are an electron short as being 'holes'. Where a material has very few free electrons but many holes it is said to be 'positively charged'. The movement of charge is called 'electric current'.

If w e can't see electricity, h o w do w e m e a s u r e it? The answer is that we don't, directly. We measure voltage and current, we read the values written on the sides of components, and we work the rest out from there. But that's jumping the gun. Who built the meters that we use for measurement? What did they use? Electricity is unseen. It is only through its ability to affect things physically that we know anything about it, be that people a hundred and more years ago, watching thunderstorms and making the legs of dead frogs jump, or us with our loudspeakers and computer screens. There are two ways of converting electrical energy to mechanical energy that we are concerned with.

M M F and current M M F is most familiar to us as magnetism. The physical force that you feel between magnets is called MMF, or 'magnetomotive force'. A less familiar mani-

Fundamentals

7

festation occurs when two wires with electric current passing through them are placed near to each other. A physical force exists between them. (It's usually too small to feel but the effect is exploited in electric motors.) An M M F is a result of a magnetic field, and the study of magnetic fields is called electromagnetics, which we won't get involved in here. If we were to make the wires a given length and separate them by a given distance we could increase the current until we had some given measurable force. Then we would have a unit value of electrical current, the ampere or amp. The amp is abbreviated to A. The symbol which we use for electrical current in equations is I. This in turn gives rise to a unit of measurement for electric charge, the coulomb. The coulomb is defined as the amount of charge passing a point in a wire that carries one amp of current in one second. This gives us our first equation: I=

zxO At

(1.1)

where Iis current in amps, Q is charge in coulombs and t is time in seconds. (The symbol A means 'change in', so the term -AT aQ means 'change in charge divided by change in time'-or the amount of charge which passed the point divided by the time period that charge was measured for.) This tells us that a charge of one coulomb passing a point in one second equates to a current of one amp; two coulombs in a second, or half a coulomb in one second would be two amps; and so on. A coulomb is a lot of charge. Typically we deal in charges of thousandths of coulomb per second (mC/s), or mA. (The prefix 'm' denotes a thousandth. We will use these prefixes increasingly as we progress. They are described fully in Appendix 1.)

"Electron current" and "conventional current" There is something of a mixup which has taken place over history with regard to the direction of current flow, and no one has ever bothered to sort it out. You would think from what we've said above that, as the electrons do most or all of the running around in circuits, the current flow would be from the negative end of a battery to the positive end. It is, but we have a convention of always arrowing diagrams with the direction of current flow reversed. When people were discovering the laws of electricity they had some idea about things moving in wires but no way of seeing in which direction, so they had to guess. They guessed wrongly. Later this was discovered, but by this time people had been labelling currents on circuit diagrams for ages, quite happily and without any problem. The numbers all work out the same; its like deciding to rewrite your bank statement with the signs reversed. A minus sign means you are in credit or have deposited cash, and a plus that you took money out or are in debt. So long as you know what the symbols mean there is no problem. So it was with current flow, and they left it at that. It was too much hassle to change the labels on everything. If you hear talk about 'electron current' (which goes from negative to positive) and 'conventional current'

8

Electronics Calculations Data Handbook

(positive to negative) this is what it means. Most people, and this book, use conventional current.

EMF and voltage Electric charges of the same polarity repel and of opposite polarity attract. The attraction is the second physical force, called the 'electromotive force' or EME This is how electrons and holes know about each others' presence and are caused to move towards each other. EMF's are caused by electric fields. The study of electric fields is electrostatics and, like electromagnetics, we won't get into it here. EMF is often called'potential difference'or'voltage'. It is measured in volts, abbreviated toV. When we need a symbol for voltage in equations we will also use V. Voltage is a comparison between two places that are charged. We say that one place on a circuit is '10 V positive with respect to' another or that a potential difference of 10 Vexists. The important thing to remember is that the number is always a difference between two places, or it means nothing. Generally we take one point, the metal chassis of equipment, mains earth or perhaps a piece of wire connected to the power supply, and we call it '0 V' or 'earth'. This becomes our reference for other measurements, unless we state otherwise. The volt is defined by its ability to make charge do work (by pushing it more or less quickly through something and generating another form of energy, like heat or light). The amount of potential required to make one coulomb of charge do one joule of work is one volt: J V = --

0

(1.2)

where Vis voltage in volts, J is work in joules and Q is charge in coulombs. Ajoule is a measurement of energy or of work done which is derived from physical quantities. We will not actually use this but we will develop it into something more useful in Chapter 2. For now it is enough to know that a volt is a definite measurable quantity.

How fast does electricity move? When a current flows through a wire, the same electron doesn't go in one end and come out of the other; one bounces a little way along, until it is able to find a home, which it often does by dislodging another and sending it on its way down the wire. (In doing so it generates heat.) The average speed of electron movement in a wire is extremely low, fractions of millimetres per second, even for currents which are, by our standards, large. However, what we generally mean by this question is something very different; when we apply a voltage to one end of a wire, how long is it before the voltage is felt at the other end of the wire? The answer is that the impulse travels at the speed of light- instantly for all our purposes. An analogy is a string of marbles in a narrow tube. If you shove the end m a r n e very hard, the impulse (the voltage) travels along the tube like a wave and

Fundamentals

9

reaches the other end quickly, say one metre in a second. In that time, any one marble may have only moved 1 cm. So the average marble speed (the current) is 1 cm/s while the impulse speed is 1 m/s, 100 times greater. The average marble speed changes at the other end of the tube just as quickly- they start falling out of the tube at a rate of 1 cm/s, a second later. With electrons the effect is the same, but unimaginably more exaggerated. If that seems a bit confusing, please don't w o r r y - it is to most people. The important thing is that changes in voltage or current travel instantly but electrons have different physical speeds. (The second fact is only relevant ~if you want to understand how power is dissipated in components. Even if you don't, you can get by quite well just knowing that it is. We look at this in Chapter 3.)

2

Circuits and components

Conductors and insulators Why do some materials conduct electricity, while others don't? Some materials are populated by good and careful atoms which don't lose their electrons easily (and probably feel ashamed if they do). Hence the itinerant population is low. The few free electrons that exist tend to sit miserably in one place, having given up hope of ever finding a home. These are insulators, typically air, rubber or the fibreglass backing of a circuit board. In other materials atoms are positively feckless. There are many free electrons and should some charged material come near they move accordingly. How do they know? They feel the voltage. These are conductors. Most metals are conductors. We use copper a great deal, gold where corrosion could be a problem, and sometimes aluminium or other metals for housing equipment.

Resistance Some materials fall into a kind of grey area between being conductors and insulators. We can use these to make resistors. It's as if the material was a kind of mud; if we make the mud thicker electrons move less easily. The resistance of a given piece of a material depends on 'how thick the mud is' (the 'resistivity' of the material) and its geometry. Making it thinner increases, and doubling or tripling length doubles or triples, its resistance.

Ohms Law The unit for resistance is the ohm, or, and the symbol in equations is R. Now we come to the most important equation in electronics: V = IR

(2.1a)

with Vin volts,/in amps, R in ohms.This is Ohm's Law.We will use it so much that it bears being rewritten in its two other forms:

Circuits and components V I = -R

11

(2.1b)

and: V

R = -

I

(2. l c )

These are used so frequently that you need to know them by heart. O h m s Law tells us that placing a steady voltage across a material causes a proportional steady current to flow. Even insulators and conductors have resistance. Insulators have very high resistance; tens or hundreds of Mf~ or more, so that for the normal voltages that we use an unmeasurably small current flows. If the voltage is raised to sufficiently high levels, usually at least a kV, a condition called 'breakdown' occurs; electrons are blasted free from atoms within the structure of the material, and its essential nature is changed. You will know if this happens; there is a nasty burning smell, and things stop working. It is a condition which we try to avoid. Conductors are the opposite; their resistance is very low, small fractions of an ohm typically. The commonest conductor that we use is copper. We cannot normally measure the voltage across a piece of copper wire, unless it is long. We can find out, from catalogues and so on, the resistance per metre of any given type of wire; this depends on the wire, but figures of around 0.1 f~/m are typical. Occasionally we need to find this out and calculate the total resistance of a length of cable when our wires are very long, in a large system. T h e wire will also have a m a x i m u m current rating, which is what we can pass through it before the amount of heat generated in it becomes dangerous to its structure. The insulating material around it may melt, causing it to short to things that it shouldn't, or the conductor itself. We only need know that we should stay comfortably within the m a x i m u m rated current for a conductor. In essence, anything can be destroyed with too much voltage/current. To summarize, we have three distinct classes of material; conductors, insulators and resistors. Conductors connect our circuit up and have very low resistance. We assume that the voltage is the same at both ends of them unless they are very long or current is very high. They are just vessels to carry current. Insulators are the separating material between different points in a circuit that need to be kept apart and have very high resistance. Resistors are electrical components having a known resistance. We can predict the current through them for any given voltage, or vice versa, using the all-powerful Ohm's Law, V = IR.

Circuits, diagrams and common expressions A circuit is exactly what its name suggests; a loop around which electric current can flow. The loop is generally made up of conductors (bits of wire or

12

Electronics Calculations Data Handbook

otherwise), circuit elements or components (which we start to meet soon) and one or more sources of electrical e n e r g y - current or voltage. Circuit diagrams, sometimes called schematic diagrams, are symbolic representations of the way that the components of a circuit are interconnected. They are the starting point for most designs, and invaluable aid in servicing or faultfinding equipment that already exists. Each element of the circuit, from a battery or a tiny resistor to a complex microprocessor chip, is represented by a symbol, with each connection to it represented by a line joining to it. Interconnections between elements are shown by lines drawn between components. In reality, these could be any form of conductor; a wire soldered directly to a leg of the component (not recommended for a microprocessor!), a copper track on a PCB, or a test lead with a crocodile clip at either end of it. Sometimes a circuit diagram doesn't show all of the circuit, and you can't see all of the loop around which the current will flow. (For example, see Figure 2.2 later.) The inference here is that things start to happen when something else is connected to it, completing the c i r c u i t - in this case a DC voltage (as you will see). 'Block diagrams' are a special type of circuit diagram worthy of explanation. You generally find them with fairly complex electronic circuits which are either too large to see on one drawing, or more understandable by being broken into smaller parts. Each 'circuit block' is drawn as a box or some commonly understood symbol, with lines connecting the blocks. The lines represent 'signals' (in reality any means by which the individual circuits can communicate), generally one or more conductors carrying voltage or current. It is the job of the person drawing the block diagram to make it less vague than this definition! Two more very common t e r m s - 'short circuit'and 'open circuit'. A short circuit is what happens when you connect two points with a conductor. An open circuit between two points means that they are not connected at all (an insulator is between them).

Resistors

Figure 2.1 A resistor We buy resistors as discrete electrical components. They come in values ranging from fractions of an ohm to tens of megohms, and are found everywhere in electronic circuits. We will see values between about 10 f~ and 1 M fl most commonly in our circuits; values outside that do occur, but less commonly. They are identified

Circuits and components

13

by a series of coloured bands, each band signifying a number, or sometimes they just have the value written on. The colour code system is described in Appendix 2. The circuit symbol for a resistor is shown in Figure 2.1. W h e n we combine more than one resistor together in a circuit we can calculate an equivalent resistance for them, and treat them as a single component. There are two ways of doing this.

Resistors in series

R, I I

I |

I_

I

l I

i' I

"

i I

is equivalent to

R | [

1 i

-

R = RI+R2+R 3

Figure 2.2 Resistors in series Three resistors in series are shown in Figure 2.2. W h e n we have this situation, we just add the values of the resistors to get their equivalent. We can do this for any number of resistors: R = R1 + R2 -k- R~ + . . .

+ Rx

(2.2)

Example 2.1: Three resistors of lk, 4k7 and 680 f~ in series have an equivalent resistance of 6380 f~

Resistors in parallel Three resistors in parallel are shown in Figure 2.3. Here we must add the reciprocal of each to get the reciprocal of the equivalent resistance. Again this applies for any number of them: 1 . R

.

1

1 1 . = -. -=. . -t R1 ["/i~2-I--/~3 "~- " " "

1

RN

(2.3a)

A special case of this worth remembering is when we have just two. T h e n we can calculate the equivalent in one step by dividing the product by the sum:

14

Electronics Calculations Data Handbook R1

R2

R3 is

equivalent to

,I I

! I

I

I

R - R1 +~'2 +~3"3

Figure 2.3 Resistors in parallel

Example 2.2: W h a t is the equivalent parallel resistance of the three resistors from Example 2.1? 1

1

1

= 100---0+ ~

1

§ 6-~ = 2.68m

1 R = ~ = 373 f~ 2.68m

R=

R~.R2

(2.3b)

R1 + R2

We can always get some idea of equivalent resistance without calculating. Here are some rules of thumb: ]. For resistors in series the equivalent is always, obviously, larger than the largest resistor. 2. For resistors in parallel the equivalent is always smaller than the smallest. 3. Two same value resistors in parallel have a resistance which is half their value; three a third, and so on.

Are electrons psychic? There are two ways in which electrons seem to know about what others are doing and be caused to move. One effect is due to E M F and the other to M M E A full analysis requires excursions into the subjects of electrostatics and magnetics, but

Circuits and components

15

luckily we can get a good picture of these effects without all that. Both forces exist and have an application in electronics whether the charges are in the same conductor or two separate ones. 1. An EMF causes opposite charges to be attracted to each other, like ones to be repelled. If the two charges are in the same conductor this causes electrical current. If they are in two conductors separated by an insulator this gives rise to an effect known as capacitance. Capacitance is a property of a pair of isolated conductors which resists a change in the voltage between them. 2. Any electrical current creates a magnetic field, and any change in magnetic field creates a Voltage in a conductor in the field. These two effects combine to create an effect known as inductance. There are two types of inductance. Self-inductance is a property of a conductor which opposes change in current flow. Mutual inductance is a property of isolated conductors by which a current flowing in one causes voltage in the other.

Capacitance and capacitors When two conductors are separated by an insulator there is voltage between them if they have different amounts of charge. Changing that voltage requires charge to be moved, which requires energy. We can buy components specially made to have an appreciable amount of capacitance and use the effect in our circuits. Capacitors ('caps') consist of a pair of conductive plates separated by a special insulator called a 'dielectric', which magnifies the effect. When caps have no voltage across them we say that they are 'discharged' or, conversely, when they do that they are 'charged'. The capacitance between the plates gets greater when: 1. they are moved closer together 2. they have greater surface area 3. the dielectric has a higher 'dielectric constant'-which, in English, means it is better at magnifying. The unit of capacitance is the farad, or F, and the symbol used in equations is C. A farad is a lot of capacitance. A capacitor of one farad would have a potential of one volt across it when it had a charge of one volt on it: Q=CV

or C = --Q V

(2.4)

where Q is charge in coulombs, C is capacitance in farads and Vis voltage in volts. This is more useful if we write it in terms of current, using Eqn (1.1):

AQ

AV

I = A--~ = C A-~

(2.5)

16

Electronics Calculations Data Handbook

This tells us that the rate of change of voltage across a capacitor is proportional to the current through it. Capacitance exists everywhere, but is so small normally, say between two wires running side by side for a few feet, that we wouldn't bother much about it. (For cables containing more one conductor, separated by an insulator ('multicore cables') we can find out a value of 'typical capacitance between cores per metre', which we might take into account, if running signals through long cables, in the same way that we talked about for 'resistance/metre' earlier.) Capacitors range in value from a few pF to 100 000 #Fand more, with physical sizes getting larger with value. Figure 2.4 shows the circuit symbol for a capacitor.

Figure 2.4 A capacitor Capacitors come in a variety of types, with different characteristics. The most important of these are listed below: 1. Working voltage. If we put too much voltage across a capacitor, its dielectric, an insulator, will break down and current will flow from plate to plate, which it's not supposed to. The device will be destroyed. (They often, but not always, go short circuit.) The m a x i m u m working voltage tells us our safe limit. We try to design so that we never get too close to this. 2. Polarization. Large capacitors tend to be 'polarized' t y p e s - that is they use a special type of dielectric to squeeze more capacitance into a small volume, but the trade off is that you should only put voltage across them one way around. The most common type of polarized capacitor is the 'electrolytic'. They are marked with positive and negative terminals. If you disobey this by accident they go bang and bits of fluffy stuff come out of the top. Then you change them. 3. Tolerance. This varies greatly from type to type. Electrolytics have tolerances of something like-10%, +20%, because they are designed to be used in situations where you try to get as much capacitance into as small space as possible, and accuracy is not the prime consideration. At the other extreme, silvered mica types can be 1%, and give excellent stability. They are used in situations where the capacitor is used perhaps to set a time constant or a frequency (see Part Two) that must be accurately maintained. 4. Leakage current. Capacitors should be open circuit to a DC voltage. In practice you get a small current flowing, particularly for electrolytics. There are other specifications which can come into play, but these are the most important. The value of a capacitor is usually written in numbers, in pF or

Circuits and components

17

in #F if no unit is specified. Unfortunately it is not always clear which, but it is usually possible to guess from the physical size, once you become familiar with them.

Capacitors in series and parallel We can combine capacitors in series or parallel as we did with resistors. The law for caps in series is like that for resistors in parallel, and vice versa. Hence putting them in parallel creates a larger capacitor, and in series a smaller one. Here are the formulae: In parallel: c = c~ + c 2 + c 3 + .. . + CN

(2.6)

In series: 1

1

1

1

= c--; + E +

1 +"

(2.7/

Self-inductance and inductors Magnetic fields, when they move through a conductor, cause a voltage which can make electrons move. And electric current (or movement of electrons) causes a magnetic field. This adds up to an interaction of magnetic field, voltage and current, the net effect of which is this: if current flows in a wire there is a certain tendency for it to want to continue to do so, and not to change. (Sometimes we say this another way; when the current through an inductor changes, the inductor sets up a'back EMF' which opposes the change in current.) This effect is known as self-inductance (or just inductance). Like capacitance, it is not noticeable under normal circumstances. It can be made much stronger, however, if the wire is wound into a coil shape; the more turns the better. Inductance is also much increased by winding the coil on a core of some special material said to have a high'permeability'; that is, it has the effect of concentrating the magnetic field. Such a device is called an inductor. Figure 2.5 is the circuit symbol. T h e voltage across and current through an inductor are related as follows: AI

v = L zxt

(2.s)

where L is the inductance in its standard unit, the henry(H). This says that the voltage across an inductor is proportional to the rate of change of current through it. We can see that this is not unlike Eqn (2.5), for a capacitor. And, indeed, capacitors and inductors are in many ways the converse

18

Electronics Calculations Data Handbook

of each other. One resists change in voltage, the other change in current. As we look at these components again in the following chapters, we will see that in each circumstance they do opposite things to each other.

Figure 2.5 An inductor Inductors are available with values from about 0.01/M to 100 m H and more. Like capacitors, they get physically larger with value. As large value inductors consist of very many turns of wire on a heavy iron former, they also tend to get very heavy, one reason why they are not as popular as capacitors. They also tend to have a significant amount of resistance, which can be a disadvantage. The main specifications for an inductor are: 1. Internal resistance. This is caused by the large number of turns of wire, which can also be quite thin, to minimize the volume. 2. Maximum DC current. If too much DC current is passed through the wire of which the coil is made, it can overheat and melt, damaging or destroying the component. Even if the amount of DC is not so much as that, the core can 'saturate' - meaning that it doesn't work as well. Despite their problems, they are quite common in some applications, and sometimes nothing else will do.

Inductors in series and parallel Again, we can combine the inductance of series or parallel inductors and treat them as a single component. The laws are the same as those for resistors, and the inverse of those for capacitors. In series: L = LI + L2 + L3 -k- . . . 4- LN

(2.9)

In parallel: 1

1 1 1 = L1 + ~22 + ~3 + " "

1 + LN

(2.10)

Mutual-inductance and transformers Magnetic fields also cause electrons in unconnected conductors to influence each other. This effect is called mutual inductance. To make the effect strong, coils of wire are wound together on a core (which again has the effect of concentrating the magnetic field). This is a transformer. The symbol is shown in Figure 2.6.

Circuits and components

19

A

I! ),,C.

~

Figure 2.6 A transformer The coil of a transformer into which you put current is called the'primary'. The coil(s) from which you take current are the 'secondary(s)'. The 'turns ratio' of a transformer is the ratio of the number of turns on the primary to those on the secondary. When we apply AC voltage to the primary, we get AC from the secondary. And, conveniently: Tp=Vp

(2.11)

Ts where Tp and Ts are the number of turns on primary and secondary, respectively, and Vp and Vs the voltages. Transformers are very useful in certain situations, the most common being the passing of a signal from one part of a circuit to another while keeping the two electrically isolated. Virtually all equipment connected to the AC mains supply is done so via a transformer. For safety reasons this is a special type, designed to have good electrical isolation. We n e v e r use anything but a proper mains transformer for this! Transformers are also very useful in many other circuits, and many other special types exist.

3

Direct cu rrent

AC and DC signals We often hear electrical signals classified as ~ C ' or 'DC'. These abbreviations stand for the terms 'alternating current' and 'direct current', but they are applied as much to voltages as to currents. In this chapter we will talk about DC. Given that we understand O h m s Law, stated in Chapter 2, we have actually covered most of what ground there is. We will also introduce the term 'power' and consider its implications, which are important.

Direct current A DC current is one which flows in one direction only. If we were to connect a resistor between the two terminals of a battery a DC current would result. For conventional current, it would flow from the positive terminal to the negative and have a magnitude, determined by O h m s Law, of I = V/R. Similarly, we would refer to the voltage across that battery as a ' D C voltage'. One application of DC is supplying power to an electronic circuit. T h e output from a power supply is often called the 'power rail' or just 'the rail'. The supply could be a separate circuit, operating from AC mains, or batteries. Virtually all circuits require one or more DC voltages to operate. A very common arrangement is to supply two rails with equal and opposite voltages, perhaps one of + 15 V and one of-15 V. T h e n there will be three power rails; 0 V, used as a reference point for the whole circuit, and +/-15 V, used to supply power. Computer circuits often use a single rail of +5 V, perhaps with one or more other voltages used by the circuits which interface the computer to the outside world. Circuit symbols for DC voltages and currents come in many flavours. Figure 3.1 shows some. You may just get lines, as in (a), with an indication of what the voltage or current is. (In a block diagram, like this example, the arrow may not follow the direction of current flow; it can just show that the supply is an 'input' to the circuit.) The symbol for a battery is shown at (b). The two general symbols for a voltage and current source are shown in (c). These would both indicate an unspecified device or circuit block; the intent is to indicate that a source exists at that point in the circuit, to help you see what is going on without actually telling you what physical devices to expect.

Directcurrent

21

+15V

A circuit

0V

-15V

(a)

+terminal

i

I I I

9V =

-terminal

(b)

12V

)

mA

(c) Figure 3.1 DC source symbols

Calculations on DC quantities Addition, subtraction, multiplication and division can be performed on DC voltages and currents simply by performing the relevant operation on the numbers, paying due regard to their signs.

22

Electronics Calculations Data Handbook

Resistors in DO circuits There is hardly anything to say about this; they obey Ohms Law, as already described. Also you should make sure that the rated power dissipation is not exceeded, as we discuss later.

Capacitors in DC circuits If we put a DC voltage across a capacitor an instantaneous ('transient') current flows while it charges to the voltage. Thereafter no current flows as long as the voltage remains steady, with the exception of the leakage current that was discussed in Chapter 2. Capacitors are often used to isolate one part of a circuit from another to DC, while allowing AC signals to pass (as a'DC block'). If we make a steady DC current flow into a capacitor (from a current source) the result is a ramp voltage across it. From Eqn (2.5), the ramp has a slope of:

xv_I At-

(3

C

A__VVis the slope of the ramp in volts per second, I is the current in amps and C the At capacitance in farads. This is a common method of making ramp generator circuits. Example 3.1: A steady DC current of 1 mA is fed into a 680 pF capacitor; what is the slope of the voltage across its terminal~ How long does it take to change by 10 V? I lm = = 1.47 V/#s slope ~ 680p 10 Time taken to change 10 V is ~ = 6.8 #s

Inductors in DC circuits An ideal inductor would be a short to DC. A real one appears to be a resistor with the value of the internal resistance of the inductor (hopefully very low). When DC current is passed through the inductor we get a transient voltage (the back EMF mentioned in Chapter 2). Thereafter the voltage will be small. Because of this, inductors are sometimes used to block AC but pass DC (as a 'choke'). Placing a steady DC voltage across an inductor causes the current waveform to be a ramp (in the same way that a DC current in a capacitor causes a ramp voltage). The slope of the current waveform is, from Eqn (2.8):

Direct current AI_V At-- L

23 (3.2)

(Did you notice how capacitors and inductors tend to do similar but opposite things to AC and DC voltages and currents?)

Power in DC circuits Why do w e w o r r y a b o u t p o w e r dissipation? As we saw in Chapter 2, connecting a voltage across a resistor causes a current to flow. The amount of the current depends on the value of the resistor; the lower the more current. In physical terms, this means that the average electron speed through the resistor is higher. Thus an electron making its way through strikes atoms in its path harder, and creates more heat. (We never have to worry about the electron speed, just the value of current; this is just a reminder of the physical process taking place.) The heat will be lost to the air, hopefully. How quickly the heat can dissipate depends mostly on physical structure of the resistor. If it cannot get away more quickly than it is generated, then the temperature will rise until it reaches a point where it destroys the component. Resistors go brown at this point, start to smell, and eventually go open circuit (sometimes catching fire in the process). Then you change them. Watching miniature resistors (1/8 W or 1/4 W types) catch fire isn't too bad, may even be mildly entertaining. (I have known heavy smoking engineers to use the trick to get a light in the middle of the night when the garage is shut, though I don't recommend the chemical content for your health.) Anything larger than that should definitely be avoided. So that we can avoid this situation, resistors always have a 'maximum power rating'. Power is measured in watts(W). The power rating of a resistor might be anything from less than 0.1 W, for very small surface-mounted devices, to 100 W or more, for large, heavy devices intended to be bolted to'heatsinks' (pieces of metal designed to radiate and make heat dissipate more quickly). On opening up pieces of electronic equipment we may sometimes see resistors which have obviously been overheating; the painted exterior may be brown and cracked. This may be the cause of the fault that we are investigating or an indication that some other fault is causing excessive current to flow. Sometimes it is an indication that the designer of the equipment wasn't as meticulous as he might have been. A resistor run continually at its m a x i m u m power may show signs of burning without misfunctioning, but the long-term reliability is likely to be reduced. I have tried to follow a'rule-of-thumb' which I learnt from an experienced engineer early in my career; to try not to run components continually at more than about one-third to one-half of their rated power. Running them at m a x i m u m for a short duration is generally OK; the device has time to cool off. If in doubt, prototype and use common sense. If it goes brown, you are being a bit ambitious.

24

Electronics Calculations Data Handbook

Power calculation in DC circuits How do we calculate the power dissipation in a resistor? Power is defined as the rate of energy dissipation, or: P - J t

(3.3a)

where P is the power in watts, J is the energy in joules and t is the time in seconds. From Eqn (1.2): or

J--VQ

Substituting into Eqn(3.3), we get: P-

V --Q t

(3.3b)

From Eqn (1.1):

I=_Q t So: (3.4a)

P = VI

Like Ohm's Law, this gets used a lot, and you need to know it. (The derivation is just for interest's sake.) The result is important enough to be restated, and learnt, in its two other forms: I = - ~P

(3.4b)

and:

v=sI Example 3.1: A resistor of 10 Ft has a voltage of 3 V across it. How much power does it consume? Using Ohms Law V I=~=0.3A and using Eqn(3.4a): P = VI = 3 x 0.3-

0.9W

Often we use two equations which we can get from Ohm,s Law and Eqn (3.4a) by a little algebraic substitution:

Direct current V2

25

P = -~-

(3.4d)

P=I2R

(3.4e)

and

These enable us to answer questions like that posed in Example 3.1 in one step. Using Eqn (3.4d): 32 P=--=0.9W l0 The business of using components within their maximum power rating quickly becomes fairly intuitive. For a circuit working from low voltages, say + / - 15 V DC, the maximum available voltage is 30 V. Our workshop resistor kit may contain miniature resistors all rated at 1/8 W. This enables us to calculate a value of resistor above which we cannot, no matter how we try, exceed the rated power. ,,

i

i

,

,

,

i,

Example 3.2: For the circumstances which we just described, what is the 'minimum' value, following the 'half-rated-power' rule-of-thumb? V2 P=~

V2 so

R

R=~

P

P is half of 1/8: 0.125

= 0.0625 W

V-30V Our threshold value of resistance is: 302 0.0625

= 14400 f~

- or say 15 kfL ,

,

This does not mean, of course, that we won't use any components of less than this value; but that above this value we can dot them around without worrying about power rating. At values around 15 k f~, we only need worry if they spend a lot of time strapped across the power rails, which very few will. Even for low values, we will tend only to get the calculator out when we know that the resistor has a large voltage across it.

4

Alternating current

An AC voltage or current is any which is changing. It will very often be one which changes at a known rate. Where a DC voltage or current is easily described by its magnitude and sign ('3 V DC' or '-16.2 V DC' says it all, as long as we know where 0 V is), AC signals are a bit more complicated.We are going to start by considering the simplest type of AC signal. Then we will look at more complex ones. The most ubiquitous AC signal is the sine wave. We will understand so much electronics in terms of how circuits respond to sine waves that it is worth our while spending some time describing and thinking about them.

T h e sine w a v e If you haven't known about sine waves before, the word 'sine' probably brings back dimly remembered memories of school maths lessons, trigonometry, and all that goes with it. The sine is a mathematical function which describes the ratio of two sides of a right angled triangle in relation to one of the other angles, and a sine wave is a graph of the ratio against the angle. That's putting it mathematically. To many technicians and engineers, who try to do as much practical work as possible with the minimum use of mathematics, a sine wave is a very useful 'wiggle' which appears on the screens of an oscilloscope (a device which cleverly shows a graph of voltage against time) when they are working on equipment. We describe a great number of the essential properties of circuits in terms of what comes out when the input is a sine wave. The reasons for this are discussed later. Figure 4.1 shows a sine wave. It is 2 V peak to peak (pk-pk or p-p) with a frequency of 1 Hz. (We'll define these terms soon.) The voltage begins at a level of 0 V, rises smoothly up to a level of 1 V, back down through 0 V to-1 V, and up to 0 Vagain. Each transition, 0 V to 1V, 1V to 0 V, 0 V to-1 V a n d - 1 V to 0 V, takes the same amount of time, 0.25 s. The whole process is referred to as 'one cycle'. We don't often come across sine waves which exist for one cycle only and then stop, however; usually the voltage oscillates continually while the circuit generating it is on. This may be for many hours. We call this a'continuous signal'. There are two things that we need to describe a sine wave unambiguously; how big it is, and how long it takes to complete one cycle. These two quantities we normally call 'amplitude' and either 'period' or 'frequency'.

Alternating current +lV

.

.

.

.

27

.

V

0

/

ls

-1

Figure 4.1 A sine wave

Amplitude There are three ways of defining the amplitude of a sine wave: 1. Peak to peak amplitude is the difference between the positive and the negative peaks. Figure 4.1 is a sine wave of 2 V pk-pk. Pk-pk amplitude can be used to describe signals which are not sine waves as well. 2. Peak amplitude is the difference between the mid-point of the signal and the positive peak. Figure 4.1 is a sine wave of (1-0) = 1 V pk. We can say that: pk amplitude = pk - pk amplitude 2

(4.1)

3. Root mean square (RMS) amplitude is the level ofa DC signal which has the same energy content as the AC signal. This odd way of specifying amplitude exists because it is needed for power calculations (on which more later in this chapter). For a sine wave: R M S amplitude -- pk amplitude or: R M S amplitude -- pk amplitude x 0.707

(4.2a)

pk amplitude = R M S amplitude x 1.414

(4.2b)

or again:

28

Electronics Calculations Data Handbook

Which of these three we use depends on the situation, and we often need to convert between them. For instance, we might see a sine wave displayed on the screen of our oscilloscope, and wish to calculate the power which it causes to be dissipated in a certain component. Here we might read the pk-pk amplitude from the display, divide by two to get pk amplitude and then multiply by 0.707 to get the R M S amplitude. Then we can make a power calculation. Conversely, we might measure the amplitude of a sine wave using an RMS multimeter. If we needed for some reason to have a rough idea of the pk-pk value of the voltage, we could divide by 0.7 (multiply by 1.4) and then multiply by 2 in our heads-multiply by 2.8.

Period and frequency The period of a sine wave is the time which it takes to complete one cycle. Its symbol in equations is T, and its unit is that of time, the second (s). For Figure 4.1, T is one second. It is more usual to refer to the 'frequency' of a sine wave. The symbol for frequency in equations is f, and its unit is the hertz, abbreviated to Hz, meaning cycles per second. The frequency is the number of cycles completed in one second. Converting from frequency to period is very easy: f=-~

1

or

T=~

1

(4.3)

with f i n Hz and T in s. So our signal of Figure 4.1 has a frequency of 1 Hz. Amplitude and frequency are independent of each other; a sine wave of 3 kHz will oscillate 3000 times per second whether it has a level of 1#Vor 10 V. One of 10 V R M S will still be at 10 V RMS, and have the same heating effect through a given resistor whether it is at 10 Hz or 1 MHz. (An interesting aside to this second case; if the frequency were 0.01Hz, a period of 100 s, would this still be true? No; remember, from Chapter 3, the mechanism of heating and cooling of resistive components. In this case, the frequency is so low that we would do better to consider it as a slowly varying DC voltage. For a quarter of the period, 25 s, the resistor will have a voltage across it of 20 V or greater! This time is obviously long enough to destroy the resistor if it is not adequately rated. In our power calculations, we should budget for the pk amplitude of about 14 V. This is a very extreme example, and such slow moving signals are not often encountered. The statement in the above paragraph holds true for frequencies of a few Hz and above.)

Phase We can describe a single sine wave completely by specifying its amplitude and frequency. When we are talking about two such signals the important question of phase arises.

Alternating current

29

Figure 4.2 shows the sine wave of Figure 4.1 again, labelled V1, and a second nearly identical sine wave which starts its cycle at a later time t, labelled V2. We say that there is a phase difference between V1 and V2. +IV

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

_~ tim,e

.

.

.

V,

%

os

ov-

V1 -1V

.

V2

0.1S --

,

Figure 4.2 Illustration of phase Phase is an angular quantity, and its units are degrees or radians. We use degrees in this book. There are two important points to bear in mind when talking about phase: 1. We only generally make phase comparisons between waveforms of the same frequency. 2. Phase, like voltage, is a relative quantity. It is meaningless to say that, for instance,'the voltage has a phase angle of 30 ~ unless we specify that that 30 ~ refers to some other waveform. A reference must be specified. To calculate the phase difference between two waveforms, we use the following expression: ~b =

360t T

(4.4a)

We can, of course, calculate t from q5and T: t --

TO 360

(4.4b)

30

Electronics Calculations Data Handbook

where ~b is the phase in degrees, t is the time difference in seconds and T is the period in seconds. For example, if t in Figure 3.2 is 100 ms, then ~b= 36 ~ V2 starts 100 ms after V1, so we can either say that V2 lags V1 by 36 ~ or that V1leads V2 by 36 ~. The two statements mean the same thing. We might, if we were being awkward, say that V2 leads V1 by (360-36)o or 324 ~ This statement means that V2 starts its cycle 324 ~ or 900 ms, before V1 - j u s t as true if they are continuous, but not the easiest way to say it. Normally we specify phase using the smallest possible angle, which is always less than 180 ~. Sometimes calculations give us numbers larger than this, and we convert them to a more sensible form. Waveforms which are 90 ~ out of phase are said to be in quadrature, while ones which are 180 ~ out of phase are said to be in antiphase. Putting a waveform in antiphase is 'inverting' it. Waveforms which have no phase difference are simply 'in phase'.

Calculations on AC quantities We can do calculations on AC quantities of the same frequency to analyse the behaviour of a circuit at that frequency. Every quantity that we use will have two components; magnitude (amplitude) and phase. Mathematical operations on waveforms of any phase are slightly tricky and require the use of something called 'phasor mathematics'. Ideally, a mathematical technique called 'complex algebra' is used which makes use of a notional quantity called j, equal to V / ( - 1 ) to denote a phase shift of 90 ~ This technique allows not only voltages and currents but also combinations of reactances, resistances and even amplification to be treated under one umbrella. The behaviour of circuits can then be predicted at a fixed frequency. The algebra involved is actually not much more difficult than the more conventional techniques which the next chapter uses, but a complete explanation of it is somewhat beyond the scope of this book. Should you already be familiar with it then Appendix 4 gives a quick restatement of its principle techniques. Even if you are not (or don't want to bother with it) its not really a problem. There are some simple rules and special cases of phasor mathematics which are presented below. In Part Three we will consider what some basic circuits do under these conditions and hence get a lot of insight into their workings. You could take these ideas on board now, or refer back to this point when you get there. Anyway, here goes: Phase Rule 1: For waveforms in phase, magnitudes of quantities can be used in calculations directly. The phase of the result is the same as that of the 'inputs' to the calculation. Phase Rule 2: A positive value of phase means 'leading', a negative one 'lagging'. Phase Rule 3: A negative value of magnitude means an inversion of the quantity

Alternatingcurrent

31

(i.e. it is in antiphase). So subtraction is addition with one waveform inverted. We could say t h a t - V is Vat an angle of 180~ Phase Rule 4: Adding two equal waveforms in antiphase gives a result of zero. This is called 'phase cancellation'. Phase Rule 5: Multiplication of any pair of waveforms. The magnitudes are multiplied and the phase angles added together. Phase Rule 6: Division of any pair of waveforms. The magnitudes are divided and the phase of the denominator subtracted from the phase of the numerator.

Resistors and sine waves The terms pk, pk-pk and RMS can be used to refer to both voltages and currents. Provided that we are consistent we can do Ohm's Law calculations on resistors with any of them. So, for example: 1. A pk voltage of 10 V across a lk resistor causes a pk current o f ~

-- 10 mA to

flow.

2. A p k - p k current of 3 mA through a 4k7 resistor causes a p k - p k voltage of 3 x 4k7 - 14.1Vacross it. 3. An R M S voltage of 150 V across a 1M resistor causes an R M S current of 11M-5___~0_ 150 #A to flow. Current and voltage through a resistor are always in phase. In fact, the current waveform is always an exact replica of the voltage waveform, its magnitude at every point being determined by Ohm's Law.

Capacitors and sine waves A capacitor with a sinusoidal voltage of frequency f across it will have a sinusoidal current flowing through it. The ratio of the voltage to the current is known as the'reactance'of the capacitor at frequencyf. The situation is analogous to that with a resistor, and the unit of reactance is again ohms. And Ohm's Law again applies: Vc = I c Xc

(4.5)

where Xc is capacitive reactance, Vc is the voltage across the capacitor and I c is the current through it. As with resistors, amplitudes of voltage and current can be specified using pk, pk-pk or RMS conventions, so long as the same is used for both. We can calculate the reactance of a capacitor at any particular frequency using the expression:

32

Electronics Calculations Data Handbook Xe =

1

27rfC

(4.6)

where C is the capacitance in farads a n d f i s the frequency. We can see from this that the magnitude of the reactance of a capacitor decreases proportionally with frequency. But hold on! Capacitors are more than 'frequency-dependent resistors'. They do something important to AC signals. The current through a capacitor always leads the voltage across it by 90 ~ This is the difference between a capacitor and a resistance with the same value as its reactance at that frequency. We can often get a very good idea of what a circuit does by thinking of caps as 'frequency-dependent resistors', but we can't do calculations to solve C R networks (using techniques from Chapter 5) without taking account of phase. (A C R network is any consisting of capacitors and resistors- we'll meet CR, L R and L C R networks in Part Two.) For calculation purposes, we consider that capacitive reactance has a phase angle o f - 9 0 ~ as passing a current with a phase angle of 0 ~ through it results in a voltage of 90 ~ lagging. (See Phase Rules 5 and 6 earlier in this chapter.) (It is this idea of assigning phase to reactance that makes otherwise incomprehensible complex numbers work.) Now that we've met the terms resistance and reactance, this seems like the moment to mention the word'impedance', which is used a lot. Strictly speaking, resistors have resistance, capacitors (and inductors) have reactance. Circuits have some combination of the two. If you want to be non-committal about which you mean, say 'impedance' - it can be either. And everyone should understand.

Inductors and sine w a v e s Like capacitors, the sinusoidal voltage across and current through an inductor are proportional at any given frequency. The ratio is again known as the reactance of the inductor, and here's Ohms Law again: VL - -

IL X L

(4.7)

with XL as inductive reactance, VL voltage across the inductor and IL current through it. Again we may use pk, pk-pk or RMS amplitudes but must be consistent. For an inductor voltage leads current by 90 ~, so we consider that the reactance has a phase angle of 90 ~ The inductive reactance can be calculated using the expression:

XL = 27rfL

(4.8)

where L is the inductance in henries and f is the frequency in hertz. From this, inductive reactance increases proportionally with frequency. (Again we see capacitors and inductors doing nice complementary things to

Alternating current

33

each other, while resistors form a nice 'neutral background' against which to view it all.)

W h y are sine waves so important? In other words, why do we do so much of our analysis of AC circuits in terms of what they do when you put a sine wave through them? All AC waveforms can be considered as being the sum of sine waves of various frequencies. T h e mathematical technique behind this is known as Fourier analysis. We are not going to get into the mathematics here, but we will consider the implications. W h a t the maths says is that we can treat any continuous periodic waveform (such as all the ones in Figure 4.3) as the sum of a n u m b e r of sine waves of various frequencies. T h e frequencies will all be whole n u m b e r multiples of the frequency of the repeating periodic waveform. So a 1 kHz triangle wave can be considered to be the sum of sine waves of 1 kHz, 2 kHz, 3 k H z . . , and so on. T h e amplitudes and phases of the sine waves will vary, generally getting less with frequency, but we could, if we knew them, and had the means to do it, reconstitute the waveform, like baking a cake to a recipe. For instance, the 'recipe' for a square wave of lkHz is: 1 kHz sine wave, at 1 V R M S , plus ... 3 kHz sine wave, at 89V RMS, plus ... 5 kHz sine wave, at ] V RMS, plus ... 7 kHz sine wave, at -~ V RMS, plus ... n k H z sine wave, at n1 VRMs. 'n' can be any whole n u m b e r as high as you care to keep going. T h e higher in frequency you continue, the better the shape of the resulting wave - that is the closer to the ideal, with the voltage changing from one voltage to the other almost instantaneously. Real square waves are not ideal, having a finite 'risetime' - the time taken to get from 10 to 9 0 % of the value of the step. You will notice in our square wave 'recipe' (known more properly as a Fourier series) that we only have the odd n u m b e r multiples of 1 kHz. T h e 1 kHz waveform is known as t h e ' f u n d a m e n t a l ' o f the series (i.e. the sine wave at the same frequency as the periodic waveform being analysed). T h e sine waves at 2 kHz, 3 kHz, and so on, are known as the 'harmonics'of the fundamental. 2 kHz would be the 2nd harmonic, 3 kHz the third, and so on. So we can say that 'a square wave consists only of the fundamental plus odd harmonics'. It contains no even harmonics. T h e exact amplitude of the result can be foretold, but we are not often worried about it.

34

Electronics Calculations Data Handbook N

/\

/

(a) square wave

/

r

\

(b) rectangle wave

/

\

T=~,T2

9

/"

(c) ramp

(d) sawtooth

(e) triangle

Figure 4.3 More AC waveforms You can get tables showing the equations to write various waveforms in terms of their harmonics, but we rarely need them. Quite a lot can be done intuitively. Where a waveform has a sharp transition between two levels, that's where you get the high harmonics. The 'frequency response' of a circuit is the way that its output, relative to the input, varies with frequency. If a circuit, such as a lowpass filter (of which more in Part Two) tends to attenuate high frequencies then it will affect the edges of a square w a v e - they will be slower. If we know the frequency at which the filter begins to 'cut', then we can get an idea of how serious this is - for example if our square wave is at 1 kHz, and the filter starts to 'roll off' from 2 kHz, the effect will be quite noticeable. If the filter rolls off from 20 kHz, much less so. Conversely, the low frequencies of a waveform contribute most to the portions where it changes slowly, or not at all; the top and bottom of a square wave will tend to 'sag'. The time responses of 1st order circuits, which we look at in Chapter 9 are in fact extreme examples of this.

Alternating current

35

More AC waveforms Figure 4.3 shows some types of AC signal which are commonly encountered. There is not too much to know about them, except to recognize their shapes and their names. With rectangle waves we sometimes hear talk of mark-to-space ratio. This is the ratio of duration of the more positive part to the more n e g a t i v e T1 : T2 on the diagram. These waveforms are best specified, amplitude-wise, in terms of pk-pk level, again the difference between the positive and the negative voltage. Time-wise, we obviously refer to them by either their frequency or their period, w i t h f = 1/ T once again.

AC waveforms with a DC level It often happens that we come across signals which are a combination of AC and DC. Then we say that the waveform has a'DC level'. The DC level of an AC waveform is just its average level. Hence if it has an equal area below 0 V as above it has a DC level of zero. Sine waves, square waves, ramps, sawtooths and triangles have a DC level of zero if they move between equal positive and negative voltages. Rectangle waves with uneven mark-to-space ratios (if they didn't have they'd be square waves) will go more positive than negative (ratio less than 1:1) or more negative than positive (more than 1:1) to have no DC level. In fact changing their mark-to-space ratio changes their DC level too, assuming that they stay between the same two voltages. Figure 4.4 shows some examples. The triangle wave goes between 1 and 9 Vand so it has a DC level of 5 V. This is the case regardless of the duration of its ramps. (Sketch one of any shape on squared paper and then draw a line horizontally through its mid point. You should see that its area above the line is the same as that below. This is true for sines, squares, sawtooths and ramps as well.) So the DC level of any sine, square, ramp, sawtooth or triangle is: VDC =

v++v_ 2

(4.9)

For the triangle in Figure 4.4, VDC = (9 + 1)/2 = 5 V. The rectangle wave goes between +5 V a n d - 5 V. But it has a mark-to-space ratio of 3:1, and so has a positive DC level, as the area above 0 V is greater than that below. The DC level is given by: Ts VDC ----TTM VM "~-T VS

(4.10)

TM is the duration of the mark, VM its voltage, Ts and Vs the same for the space. T is the period, TM + Ts. So for our example: VDC = 0.75 X 5 - - 0 . 2 5 x 5 = 2.5V

36

Electronics Calculations Data Handbook +9V

-

-

-

-

+lV

+5V

. . . .

--SV

Figure 4.4 AC waveforms with D C level

Power calculations with AC waveforms For power calculations involving AC waveforms, we must use the R M S value of the signal. R M S stands for 'root-mean-square'. It is what we get when we take the average of the square of the amplitude of a waveform over its cycle, and then take the square root of that. If that sounds like a rigmarole, it is, but we never actually have to do it.

Sine waves

We already know how to find the R M S value of a sine wave from our discussions on amplitude earlier in this chapter. W h e n calculating the power that a sinu-

Alternating current

37

soidal signal develops in a load we must also take account of the phase angle between voltage across and current through that load. The power dissipated by a circuit element which is passing a sinusoidal current (with no DC) is defined a s : P = VI

eosq~

(4.11)

where P is the power in watts, Vis the R M S voltage across the component in volts, I is the R M S current in amps and q~ is the phase angle between voltage and current. The cos 4) term varies between 1 when r = 0 ~ and 0 when r = 90 ~ (or-90~ Hence for resistors, for which ~ = 0 ~ always, we simply use the same power equations that were given for DC circuits in Chapter 3, of course using R M S values. Equally we can say that ideal capacitors and inductors, for which r = 90 ~ (or -90~ don't dissipate power. When we use circuits made up of combinations of these components, and ~ is between 0 and 90 ~ the power will be somewhere between zero and 'volts-times-amps'. But all of that power will be dissipated in the resistive components of the circuit. (An aside: the term'peak power' is sometimes heard, but has no relationship to 'pk amplitude'. It is used in such things as sound amplification systems to describe the the m a x i m u m amount of electrical power delivered to a loudspeaker at any given moment. There is no such thing as p k - pk power. Thought I'd mention it.)

R M S values of other waveforms Its not often that we have to calculate these, but if we do it's nice to know how. If you're a beginner you may well prefer to skip this. I just couldn't resist putting them in. For any triangle, ramp or sawtooth wave with no DC level, and a positive excursion, VpK:

VpK

RMStriangle = ~

--

0.577 VPK

(4.12)

For any rectangle wave (of which a square wave is just a special case), if TM is the duration of the mark, VM its voltage, Ts the duration of the space, Vs its voltage and T the period ( TM + Ts): R m S rectangle --

V2 T

~" V2 - -

/

(4.13)

with VM the voltage of the mark and Vs that of the space. This takes into account the DC level.

38

Electronics Calculations Data Handbook

For a signal with AC and DC components:

RMSAc+Dc

(V~c + VRMSAC)

(4.14)

And finally, for a'piecewise' signal with known RMS values over different parts of its period tl t2 T) RMgtotal--~ ( V12RMS-~ + V22RMS-~ + ... + gn2MS

(4.15)

We can see that Eqn (4.13) is just a special case of this. By way of illustration: Example 4.1: The triangle wave of Figure 4.4 has an AC component that goes between +4 V a n d - 4 V. Its RMS value is therefore 0.577 x 4 = 2.31 V. It has a DC component of 5 V, so the true R M S value is: RMStriangle -- 4 ( 5 2 + 2.312) = 5.5 V

Example 4.2: A signal consists of a high frequency sine wave of 5 V pk for 400 ms with no DC, followed by a DC voltage of 2 V for 300 ms. What is the RMS value? RMS value of the sine wave is 5 x 0.707 = 3.54V RMStotal --

3 22) = 2.98 V

• 3.542 + ~ x

5

A circuit analysis toolkit

Introduction This chapter is intended as a quick guide to the basic techniques of network analysis. The mathematical requirements are minimal; you need to be able to transpose equations and solve simultaneous equations by substitution. We also get to consider some characteristics of real voltage and current sources, which ties in nicely with some of the analysis tools presented. We will take DC circuits for all of our examples, as this is the easiest way of demonstrating the techniques. Everything said applies equally to AC circuits as well, but you generally need to use complex numbers (see Chapter 4 and Appendix 4) to take account of phase if there are capacitors and inductors present, or sources at different phases.

Basic topologies There are two basic shapes that electric and electronic circuits come in; series and parallel. Each has associated with it one of two electrical laws which tell us how to go about calculating the voltages and currents in that circuit.

The series circuit and Kirchhoff's voltage law A series circuit is represented in Figure 5.1. The components are an input voltage, V,l0 V DC, and three resistors: R1, lk; R2, 2k2; and R3, 4k7. We have also labelled on the drawing, for our convenience, the voltages across each resistor, Vz, V2 and $/3. The voltages are labelled with arrows. With DC voltages we follow a convention of putting the head of the arrow to the more positive end of the component. The key to analysing a series circuit is to remember that the current is identical through each component in the loop. (We can also say that connecting the components in a different order will not affect that current.) Hence the current in the loop is labelled just once, this time with an arrow on the loop, with the legend I next to it to identify it. The head of the arrow shows the direction of current flow.

40

Electronics Calculations Data Handbook V=lO v /

+

R3

R2

4k7

-"-!" !

R1

2k2

1' \ v3 /

lk

1,_

'!

t

P--

N

v2

/

\

Vl

/

Figure 5.1 Series circuit

E x a m p l e 5.1: Suppose that we wish to calculate V1, V2 a n d V3. H o w do we do it? We need to find the value of current, I. T h e n we will be able to calculate each voltage using Ohm's Law. We can find the total resistance as described in C h a p t e r 2. In our case: R s = l k + 2k2 + 4k7 = 7900 9t Now we can say that: 10 I = ~ = 1.27mA 7900 Now we can use Ohm's L a w to find V1, V2 a n d V3: Vl=l.27mAx

lk=l.27V

V2 = 1.27 m A x 2k2 = 2.78 V V3 = 1.27 m A x 4k7 = 5.95 V Kirchhoff's voltage law states that, in any loop of voltages on a circuit, their sum will be zero if we take the clockwise ones as being positive, the anticlockwise ones as negative (or vice versa). Put a n o t h e r way, the clockwise ones equal the anticlockwise ones. This enables us to check our calculations: 1.27 + 2.78 + 5.95 - 1 0 V - w e did it right. In any m a t h e m a t i c a l analysis of a circuit, its always good to have a way to check our result, and using voltage loops is one way. ,

,

,

A circuit analysis toolkit 41 The parallel circuit and Kirchhoff's current law i

i

Example 5.2: Figure 5.2 shows a basic parallel circuit made with the same components. With parallel circuits the rule is that the voltage across all the branches is identical. Hence there is only one voltage to be labelled, the source voltage. But there are four currents:/, the current leaving the voltage source, and I1,/2 and/3, the currents through the resistors.We would like to calculate them. We can see that the voltage across each resistor is the same; the 10 V source voltage. Therefore we can apply O h m s Law directly to each branch of the circuit to find 11, 12 and 13: 10 I1 = -i-~ = l O m A 10 12 = ~ -- 4.55 m A 2k2 10 /3 = = 2.13 m A 4k7 Kirchhoff's current law states that the total of currents entering and leaving any'node' (a node is any place where two or more conductors join) is zero. This enables us to calculate the current I: I - I1 + / 2 + / 3 = (10 + 4.55 + 2.13)mA = 16.68 m A We know that the resistance between any two points is the ratio of the voltage across them and the current passing between them. So in this case the resistance is: 10 R p = 16.68 m A - 600 f~ We could have calculated the parallel resistance directly, by using the formula from Chapter 2: 1 Rp

1 1 1 lk +~ +4-~

1.67m

So: 1 R p - 1.67 m-------~- 600 9t Again we have cross-checked our result, and it's fine.

42

Electronics Calculations Data Handbook

> t~

V--'0V C'>

R1 lk

2k2

4k7

Figure 5.2 Parallel circuit

Arrow directions for voltages and currents It is worth taking a moment to think about the rules that we apply when adding voltages and currents in using Kirchhoff's two theorems, as it can be surprisingly easy to confuse ourselves. Here's the rules. If we follow these, things work: 1. The arrows for voltage across and current through a voltage or current source must point in the same direction. 2. The arrows for voltage across and current through a resistance must point in opposite directions. 3. For a voltage loop, the sum of arrows going clockwise equals the sum of arrows going anti-clockwise. 4. For a node, the sum of currents entering a node equals the sum of currents leaving the node, as denoted by the arrows' directions. In the above examples, it was obvious which end of the resistors would be more positive and in which direction currents would be flowing. Hence drawing the arrows was easy. In other instances it will not be obvious, when labelling currents and voltages at the start of the analysis, which end of the component is the more positive. Such a situation is shown in Figure 5.3.We wish to know the voltage 1/2, but this voltage is affected by both voltage and current sources which have a tendency to create voltages of opposite polarity across R2. The way to approach this sort of problem is not to worry about the polarity of the voltage; if we label it in the wrong direction, the voltage will come out as negative in solving the equations. We

A circuit analysis toolkit

43

simply get on with labelling the voltages and currents (following rules 1 and 2), then we can write equations for voltage loops (using rule 3, the voltage law) or nodes (with rule 4, the current law). Example 5.3: Solve Figure 5.3. For node A, we can write: 11 -- I2 + 1 0 m A /2 = / 1 - 1 0 m A (call t h i s E q n (A)) For the loop on the left we can write:

VIN = V~ + 8 9 89 = V I N - v1 (but 171 = I1.R1 -- 10 k.I1 a n d V2 = I2.R2 = 2k2.I2) SO:

2 k2.I2 = 5 - 10 k.I1 /2 = (5-10k.I~ 2k2

12 -- 2.27 m A

]

- 4.55./1

W e can substitute this back into E q n (A), giving: 2.27 m A - 4.55./1 = 11 - 10 m A I~(1 + 4.55) = 2 . 2 7 m A -{- 1 0 m A 11 "-" 12.275.55mA----2.21 m A So, again from Equation A: 12 -- 2.21 m A

- 10 m A

= -7.79 m A

and therefore

V2 = I2.R2 = - 1 7 . 1 V and V1 - 2.21 m A x 10k = 22.1 V Our solution is: V1 - 22.1 V, /1 -- 2.21 mA, V2 - - 1 7 . 1 V, /2 - - 7 . 7 9 mA. We can now redraw the circuit, reversing the direction of the arrows where our solution gave a minus sign (Figure 5.4). A few seconds of calculator-punching demonstrates that nothing went wrong with the number crunching, and the solution obeys the voltage and current laws. There are quicker ways to get to this result, but as a'swiss army knife' technique, this is a good one to have. Soon we get some better ones still.

44 Electronics Calculations Data Handbook R1

I Ok

l \

t

11

Node

>

~

vl

10 m A

\

/

12

210.

Figure 5.3 Example 5.3 R1

1Ok -

/ N

2.21 mA

10 mA

,.

/

/

22.1V \ 7.79 mA

(

v 17.1 V

2k2

Figure 5.4 Solution to Example 5.3

M o r e about voltage and current sources The voltage and current sources that we considered above were 'ideal' - that is, we consider that they will supply their correct voltage or current, regardless of what load is placed on them. (As such, they have no real existence.) For the ideal voltage source, we could say that the change in voltage across it is zero for any

A circuit analysis toolkit

45

change in output current. This means that a notional quantity which we call its 'internal resistance' is also zero, by O h m s Law. For the current source we could say that the change in output current is zero for any change in output voltage. Hence its internal resistance is infinite. Real voltage and current sources are not ideal, and we have a way to represent this in our circuits (see Figure 5.5). We give our ideal voltage source a series resistor, R s. The closer this resistor is to a short circuit the closer the source is to ideal. If we connect a real voltage source to too low a load resistance the voltage across the load will drop (and the source could be damaged). The current source is given a parallel resistor, Rp; the closer this is to an open circuit, the better the source. If we connect a real current source to too high a load resistance the current through the load will drop.

/

] .......

R,

Figure 5.5 Representation of non-ideal sources These circuit representations of real voltage and current sources are invaluable for circuit analysis, as we will now see. It is possible for any network of voltage sources, current sources and resistances to be replaced by either a single ideal voltage source with a series resistor, or a single ideal current source with a parallel resistor.

Th6venin's and Norton's equivalent circuits The techniques that we used in the last example of circuit analysis are fine for instances where we can get a solution for the circuit by writing two or three

46

Electronics Calculations Data Handbook

simultaneous equations and solving them. If the network gets much more complicated than that, however, the amount ofmaths involved can get pretty tedious, and it can get time consuming to arrive at the correct result without making a numerical error. Also, we have only solved the network for one value of load resistance; if we want to see what happens with a different value, we must do the calculations again. This is where replacing whole lumps of circuit with an equivalent non-ideal current or voltage source is great. Here's how we go about finding the right values for our equivalent circuit: Replace with a voltage source (Th+venin's equivalent circuit): 1. Cut the network at two places to isolate the section to be replaced. 2. Calculate the voltage at the load terminals with no load connected (called the 'open circuit voltage' or VTH). 3. Calculate the equivalent resistance looking into the load terminals when any voltage sources are replaced with a short circuit and any current sources with an open circuit (called the 'output resistance' or R wn).

Example 5.4: What is the voltage across RL in Figure 5.6? First we separate out the 12 Vand the 3 mA source, and combine then into a single voltage s o u r c e ( - Figure 5.7). The points where we cut are labelled A and B. Replacing the 12 V source with a short and the 3 mA one with an open, we get RTH = 1 k + l k = 2k (Figure 5.8).When we calculate the open circuit voltage, we get 3 m A x lk - 3 V across Rz, and nothing across R3, which has no current flowing in it. Hence VTH is 12 - 3 - 9 V. The equivalent circuit is replaced into the original in Figure 5.9. Things are getting easier! Now we can cut and replace at the load terminals themselves, L1 and L2. This time we'll replace with a current source. Looking into L1 and L2 with both sources replaced by a short, we get 2k in parallel with 2k, so RN is lk. (Figure 5.10). To calculate short circuit current, we replace RL with a short, and then calculate the current through the two resistors; 2.5 mA and 4.5 mA as shown on the drawing, taking care to label directions correctly. I n is then clearly the difference between the two (by Kirchhoff's current law), 2 mA. So Figure 5.11 shows the equivalent circuit with R1 now connected. If R1 is I kf~, parallel resistance with R N is 500 f~, and voltage across RI is 1 V, terminal L1 being most positive. Naturally we want to check, and the easiest way to do this is to redraw the original circuit, labelling in voltages and currents, using Ohms Law and voltage and current laws, and working backwards from R1. If there is a problem it will become apparent. We find we are O K (see Figure 5.12). We now could find the current through any other load using our existing solut i o n - no need to do all that number-crunching again.

A circuit analysis toolkit

47

T h e network can now be replaced with an ideal voltage source equivalent to VTH, in series with a resistor equivalent to RTH. Replace with a current source (Norton's equivalent circuit): 1. Cut the network at two places to isolate the section to be replaced. 2. Calculate the c u r r e n t at the load terminals w h e n they are short circuited (called the 'short circuit current' or In). 3. Calculate the equivalent resistance looking into the load terminals when any voltage sources are replaced with a short circuit and any current sources with an open circuit (called the 'output resistance' or R N). T h e network can now be replaced with an ideal current equivalent to IN, in parallel with a resistor equivalent to R N. R1

2k

-I-

lk

~'**'~l3 mA

"I"

12V (

Ik

Figure 5.6 Example 5.4

lk

48

Electronics Calculations Data Handbook R1

f

2k

!

5V

R~ lk

"

L

12V

~, 3mA I

lk " ~

J lk /

Figure 5.7 Figure 5.6 redrawn before simplifying

A circuit analysis toolkit O A

R~ lk

/ \

_

R==2k

R~ lk

~B

Ve,=9V 3 mA lk

9

3v

lk

. /

>

ov

Figure 5.8 Finding Rth and Vth

49

50

Electronics Calculations Data Handbook R1

/

2k

1

5V

R~ lk ,

! |

v

+

~h)

9V

Rth 2k I

|

"

Figure 5.9 Vth and Rth replaced

A circuit analysis toolkit

v,.

Rth 2k

!

(

,2)5

l

/

\

9V

4.5 mA

IN=2 mA

L1

A V

/

2.5 mA R1

i 2k I+ C , j~ 5V

LI C

RN-lk -

\

/"

/-20,,

'

I

RI

Rt. 2k

2k

!-

Figure 5.10 Finding IN and RN

51

52 Electronics Calculations Data Handbook

( m

lk

lk 2 mA

Figure 5.11 Equivalent circuit to Figure 5.6

R1

2k

1

~, I,i' ~

6v

1V

~ / 3mA L2 1~

L1

/4

3 mA

7 mA

RI~

t

! - \ i

7V

1\

i

/

4V

Figure 5.12 Solution of Figure 5.6

/

mA

Part Two

Resistive Circuits

This Page Intentionally Left Blank

6

Equivalen t resistances

Introduction Resistors can be bought in certain standard values. The ranges of values are commonly called the E6, the El2 and the E24 series, the numbers denoting the quantity of values per decade of resistance. For building or repairing low voltage electronic circuits most workshops will stock a full range of E12 or E24 miniature resistors (i.e. 1/8 W o r 1/4 W power rating), usually 1 or 2% tolerance, plus a selection of resistors rated at higher powers, which are available in combinations of E6 and El2 values. An additional range, E96, is also available, but these are more expensive, 0.1% tolerance, and few workshops will stock them as standard due to the large number of values. Also they are hard to obtain below 100 f~ or over about 250k. The standard values are almost always fine, but once in a while you need a value that lies between two of them. This can be achieved by combining two components in series or parallel, their values being chosen so that the overall equivalent is near enough. It is evident that choosing the best pair of resistors for this purpose might involve a fair amount of trial and error with a calculator, and that several near solutions might exist. For this purpose, three 'Tables of equivalent resistance' are provided in the rest of this chapter. Table 6.1 is for E6, Table 6.2 for El2, and Table 6.3 for E24.You should use the appropriate one for the range of components which you intend to use.

Using the Tables for resistors Each table shows all achievable values between lk and 10k with two resistors, s denotes series connection and p denotes parallel. The tables are sorted in order of ascending equivalent resistance.

56

Electronics Calculations Data Handbook ,

,

,

,

,

,

Example 6.1: Choose a pair of E24 resistors to give an equivalent resistance of 7k7. From Table 6.1: RE R1 7700 200R 7700 lk5 7700 3k

s/p s s s

R2 7k5 6k2 4k7

PREL 1.03 1.24 1.64

,,

There are plenty of others that would be close enough too. To get a value of less than lk, or greater than 10k, you should scale all values by factors of ten as necessary. Example 6.2: Choose a pair of E24 resistors to form a resistance of 125k. RE 1250

R1 lk5

s/p p

R2 7k5

PREL 1.2

125k is 1250 multiplied by 100, so resistors of 150k (lk5 times 100) and 750k (7k5 times 100), connected in parallel, form a resistance of 125k. ,

Maximum power rating of the pair Each line of the table gives a value of PREL-Where each resistor of the pair is of the same power rating, this can be used to find the overall power rating of the pair. It is always a number between 1 and 2. For example, if a pair of 1/4 W resistors are used and PREL has a value of 1.2 then the power rating of the pair is equal to: 0.25 x 1 . 2 - 0.3 W In this way, the pair of resistors can be lumped and considered as a single circuit element.

Tolerance of components If two components of the same tolerance are used the tolerance of the equivalent resistance is the same.

Equivalent resistances 57

Using theTables for capacitors and inductors Both inductors and capacitors are normally bought in combinations of the standard E6 and El2 ranges. Like resistors, they can be combined in series or parallel to obtain non-standard values. As was discussed in Chapter 2, inductors in series and parallel obey the same rules as resistors, while capacitors in series behave like resistors in parallel, and vice-versa. Hence, the tables can be used to find equivalent capacitance or inductance. For capacitors, you should read p for s and s for p. ,i

,

,

,

,,,

,

,

Example 6.3: To form a capacitor of 3nl using a range of 1%, El2 capacitors: RE 3090 3095 3116

R1 390R 3k9 3k3

s/p s p p

R2 2k7 15k 56k

PREL 1.14 1.26 1.06

This gives three alternatives: 2n7 p 390p, 3n9 s 15n and 3n3 s 56n. All three form a capacitor of 3nl, 1%. However, as capacitors (and inductors) tend to increase in physical size with increasing value the first might be preferable. ,

i

,

,,

i

Table 6.1 E6 equivalent resistances RE

R1

s/p

R2

PREL

RE

1010

10R

1010 1015

330R 15R

s

lk

1.01

1662

s s

680R lk

1.49 1.02

1680 1720

1022

22R

1031 1033 1047 1068

lk5 33R 47R 68R

s

lk

1.02

1803

p s s s

3k3 lk lk lk

1.45 1.03 1.05 1.07

1830 1919 1939 1970

R1

s/p

R2

PREL

2k2

p

6k8

1.32

680R 220R

s s

lk lk5

1.68 1.15

2k2

p

10k

1.22

330R 2k2 3k3 470R

s p p s

lk5 15k 4k7 lk5

1.22 1.15 1.7 1.31

1100

100R

s

lk

1.1

2000

lk

s

lk

2

1100 1137 1150

2k2 lk5 150R

p p s

2k2 4k7 lk

2 1.32 1.15

2000 2063 2102

2k2 2k2 2k2

p p p

22k 33k 47k

1.1 1.07 1.05

1150 i 470R

s

680R

1.69

2131

2k2

p

68k

1.03

1220 1229 1304 1320 1330 1360 1364 1404 1435 1454

220R lk5 lk5 2k2 330R 680R lk5 lk5 lk5 lk5

s p p p s s p p p p

lk 6k8 10k 3k3 lk 680R 15k 22k 33k 47k

1.22 1.22 1.15 1.67 1.33 2 1.1 1.07 1.05 1.03

2153 2168 2178 2180 2222 2222 2233 2247 2268 2300

2k2 2k2 2k2 680R 22R 3k3 33R 47R 68R 100R

p p p s s p s s s s

100k 150k 220k lk5 2k2 6k8 2k2 2k2 2k2 2k2

1.02 1.01 1.01 1.45 1.01 1.49 1.02 1.02 1.03 1.05

1468 1470 1478 1485

lk5 470R lk5 lk5

p s p p

68k lk 100k 150k

1.02 1.47 1.02 1.01

2350 2350 2420 2481

150R 4k7 220R 3k3

s p s p

2k2 4k7 2k2 10k

1.07 2 1.1 1.33

1499

2k2

p

4k7

1.47

2500

lk

s

lk5

1.67

1515 1522

15R 22R

s s

lk5 lk5

1.01 1.01

2530 2670

330R 470R

s s

2k2 2k2

1.15 1.21

1533 1547

33R 47R

s s

lk5 lk5

1.02 1.03

2705 2779

3k3 4k7

p p

15k 6k8

1.22 1.69

1568

68R

s

lk5

1.05

2870

3k3

p

22k

1.15

1600

100R

s

lk5

1.07

2880

680R

s

2k2

1.31

1650 1650

150R 3k3

s p

lk5 3k3

1.1 2

3000 3000

lk5 3k3

s p

lk5 33k

2 1.1

Table 6. 1 E6 equivalent resistances

59

RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

PREL

3083

3k3

p

47k

1.07

4850

150R

s

4k7

1.03

3147

3k3

p

68k

1.05

4920

220R

s

4k7

1.05

3195

3k3

p

100k

1.03

5000

10k

p

10k

2

3197

4k7

p

10k

1.47

5030

330R

s

4k7

1.07

3200

lk

s

2k2

1.45

5170

470R

s

4k7

1.1

3229

3k3

p

150k

1.02

5194

6k8

p

22k

1.31

3251

3k3

p

220k

1.02

5380

680R

s

4k7

1.14

3267 3333 3347 3368

3k3 33R 47R 68R

p s s s

330k 3k3 3k3 3k3

1.01 1.01 1.01 1.02

5500 5638 5700 5941

2k2 6k8 lk 6k8

s p s p

3k3 33k 4k7 47k

1.67 1.21 1.21 1.14

3400

100R

s

3k3

1.03

6000

10k

p

15k

1.67

3400 3450

6k8 150R

p s

6k8 3k3

2 1.05

6182 6200

6k8 lk5

p s

68k 4k7

1.1 1.32

3520

220R

s

3k3

1.07

6367

6k8

p

100k

1.07

3579

4k7

p

15k

1.31

6505

6k8

p

150k

1.05

3630 3700 3770 3873 3980 4048 4114 4273 4300 4396 4400 4489 4557 4602 4634 4653

330R lk5 470R 4k7 680R 6k8 4k7 4k7 lk 4k7

s s s p s p p p s p

3k3 2k2 3k3 22k 3k3 10k 33k 47k 3k3 68k

1.1 1.68 1.14 1.21 1.21 1.68 1.14 1.1 1.3 1.07

6596 6600 6663 6703 6733 6868 6875 6900 6900 6950

6k8 3k3 6k8 6k8 6k8 68R 10k 100R 2k2 150R

p s p p p s p s s s

220k 3k3 330k 470k 680k 6k8 22k 6k8 4k7 6k8

1.03 2 1.02 1.01 1.01 1.01 1.45 1.01 1.47 1.02

2k2 4k7 4k7 4k7 4k7 4k7

s p p p p p

2k2 100k 150k 220k 330k 470k

2 1.05 1.03 1.02 1.01 1.01

7020 7130 7270 7480 7500

220R 330R 470R 680R 15k

s s s s p

6k8 6k8 6k8 6k8 15k

1.03 1.05 1.07 1.1 2

7674

10k

p

33k

1.3

p s

15k 4k7

1.45

7800

lk

s

6k8

1.15

4747

6k8 47R

1.01

8000

3k3

s

4k7

1.7

4768

68R

s

4k7

1.01

8246

10k

p

47k

1.21

4800

100R

s

4k7

1.02

8300

lk5

s

6k8

1.22

4800

lk5

s

3k3

1.45

8718

10k

p

68k

1.15

4679

60

Electronics Calculations Data Handbook

RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

PREL

8919 9000 9091 9375 9400

15k 2k2 10k 10k 4k7

p s p p s

22k 6k8 100k 150k 4k7

1.68 1.32 1.1 1.07 2

9565 9706 9792 9855 9901

10k 10k 10k 10k 10k

p p p p p

220k 330k 470k 680k 1M

1.05 1.03 1.02 1.01 1.01

Table 6.2 E12 equivalent resistances

RE

PREI

RE

R1

s/p

lk

1.01 1.49

1158 1164

lk2

680R

1165

lk2 lk8

1170

1.18

1175 1179

lk lk 560R 3k3 lk lk

1.02 k0~3 1.84 1.45 1.03 1.04

1180 1183 1183 1186 1188 1210

s s

820R lk

1.27 1.05

lk2

p

8k2

1212 1212 1215

1056 1068

56R 68R

s s

lk lk

! 1.06 1.07

1070 1071 1080 1082 1083 1090 1091 1100

390R lk2 lk8 82R lk5 270R lk2 100R

s p p s p s p s

680R 10k 2k7 lk 3k9 820R 12k lk

1.57 1.12 1.67 1.08 1.38 1.33 1.1 1.1

1100 1111 1120 1120 1125

2k2 lk2 120R 560R lk2

p p s s p

2k2 15k lk 560R 18k

2 1.08 1.12 2 1.07

R1

s/p

R2

1010

10R

s

1010

330R

s

1012

12R

s

lk

1.01

1015

15R

s

lk

1.02

1018

18R

s

lk

1.02

1020

lk2

p

6k8

1022 1027 1030 1031 1033 1039

22R 27R 470R lk5 33R 39R

s s s p s s

1040 1047

220R 47R

1047

i

1.15

R2

Pm~L

p

33k

1.04

p p

39k 3k3

1.03

lk2

p

47k

1.03

lk2 lk2 180R lk2 lk5

p p s p p

56k

1.02 1.02 1.18 1.01

lk2 lk2 390R

p p s

12R

s

2k2 15R

p s

1218

18R

s

1220

220R

s

1222 1227 1229 1232 1233 1239 1240 1247 1256 1268 1268 1270

22R 27R lk5 lk8 33R 39R 560R 47R 56R 68R lk5

s s p p s s s s s s p

270R 82R 470R 100R lk8

s s s s p

820R lk2 4k7

68k lk 82k 5k6 100k 120k 820R lk2 2k7

1.55

1.27 1.01 1.01 1.48 1.01 1.81

lk2

1.01

lk2 lk

1.02

lk2 lk2 6k8 3k9 lk2 lk2 680R lk2 lk2 lk2 8k2 lk

1.22 1.02 1.02 1.22 1.46 1.03 1.03 1.82 1.04 1.05 1.06 1.18 1.27 1.07 1.57

1137

lk5

p

4k7

1.32

1138 1149

lk2 lk2

p p

22k 27k

1.05 1.04

1282 1290 1300 1302

1150

150R

s

lk

1.15

1304

lk5

p

10k

1.15

1150

330R

s

820R

1.4

1320

120R

s

lk2

1.1

1150

470R

s

680R

1.69

1320

2k2

p

3k3

1.67

lk2

1.08 1.38

62

Electronics Calculations Data Handbook

RE

R1

s/p

R2

PREL

RE

Ra

s/p

R2

PREL

1330 1333

330R lk5

s p

lk 12k

1.33 1.13

1533 1539

33R 39R

s s

lk5 lk5

1.02 1.03

1350

150R

s

lk2

1.13

1547

47R

s

lk5

1.03

1350

2k7

p

2k7

2

1556

56R

s

lk5

1.04

1360 1362 1364

680R lk8 lk5

s p p

680R 5k6 15k

2 1.32 1.1

1560 1565 1568

560R lk8 68R

s p s

lk 12k lk5

1.56 1.15 1.05

1380 1380 1385

180R 560R lk5

s s p

lk2 820R 18k

1.15 1.68 1.08

1579 1582 1590

2k2 82R 390R

p s s

5k6 lk5 lk2

1.39 1.05 1.33

1390 1404

390R lk5

s p

lk 22k

1.39 1.07

1595 1600

2k7 100R

p s

3k9 lk5

1.69 1.07

1407

2k2

p

3k9

1.56

1607

lk8

p

15k

1.12

1420 1421 1423 1435 1444

220R lk5 lk8 lk5 lk5

s p p p p

lk2 27k 6k8 33k 39k

1.18 1.06 1.26 1.05 1.04

1620 1636 1640 1650 1650

120R lk8 820R 150R 3k3

s p s s p

lk5 18k 820R lk5 3k3

1.08 1.1 2 1.1 2

1454 1461 1468 1470 1470 1473 1476 1478 1481 1485 1485

lk5 lk5 lk5 270R 470R lk5 lk8 lk5 lk5 lk5 2k7

p p p s s p p p p p p

47k 56k 68k lk2 lk 82k 8k2 100k 120k 150k 3k3

1.03 1.03 1.02 1.23 1.47 1.02 1.22 1.02 1.01 1.01 1.82

1662 1664 1670 1680 1680 1688 1707 1715 1720 1721 1734

2k2 lk8 470R 180R 680R lk8 lk8 2k7 220R lk8 lk8

p p s s s p p p s p p

6k8 22k lk2 lk5 lk 27k 33k 4k7 lk5 39k 47k

1.32 1.08 1.39 1.12 1.68 1.07 1.05 1.57 1.15 1.05 1.04

1499 1500

2k2 680R

p s

4k7 820R

1.47 1.83

1735 1744

2k2 lk8

p p

8k2 56k

1.27 1.03

1515

15R

s

lk5

1.01

1754

lk8

p

68k

1.03

1518

18R

s

lk5

1.01

1760

560R

s

lk2

1.47

1522 1525

22R lk8

s p

lk5 10k

1.01 1.18

1761 1768

lk8 lk8

p p

82k 100k

1.02 1.02

1527

27R

s

lk5

1.02

1770

270R

s

lk5

1.18

1530

330R

s

lk2

1.28

1773

lk8

p

120k

1.02

Table 6.2 E12 equivalent resistances

63

RE i R1

s/p

R2

Par

RE

R1

s/p

R2

PREt

1779 1782

lk8 lk8

p p

150k 180k

1.01 1.01

2070 2076

270R 3k3

s p

lk8 5k6

1.15 1.59

1788

3k3

p

3k9

1.85

2083

2k2

p

39k

1.06

1803 1818

2k2 18R

p s

10k lk8

1.22 1.01

2102

2k2

p

47k

1.05

2117

2k2

p

56k

1.04

1820

820R

s

lk

1.82

2126

2k7

p

10k

1822 1822

22R 2k7

s p

lk8 5k6

1.01 1.48

1827 1830 1833 1839 1847 1856

27R 330R 33R 39R 47R 56R

s s s s s s

lk8 lk5 lk8 lk8 lk8 lk8

1.02 1.22 1.02 1.02 1.03 1.03

1859 1868

2k2 68R

p s

12k lk8

1880

680R

s

1882 1890 1900 1919 1920

82R 390R 100R 2k2 120R

1933 1939 1950 1950 1960 1970 1980 2000

2130

330R

s

lk8

1.27 1.18

2131 2131

2k2 3k9

p p

68k 4k7

1.03 1.83

2k2 2k2 2k2 2k2 2k2 2k2 680R

p p p p p p s

82k 100k

180k

1.03 1.02 1.02 1.01 1.01

1.18 1.04

2143 2153 2160 2168 2173 2178 2180

220k lk5

1.01 1.45

lk2

1.57

2190

390R

s

lk8

s s s p s

lk8 lk5 lk8 15k lk8

1.05 1.26 1.06 1.15 1.07

2200

lk

s

lk2

1.22 1.83

6k8 4k7 lk8 3k9 18k lk5 lk8 lk

1.4 1.7 1.08 2 1.12 1.31 1.1 2

2000

2k2

p

22k

1.1

2k2 2k2 2k2 2k2 2k2 lk8 2k2 15k 5k6

1.02 1.02 1.02 1.03 1.03 1.26 1.04 1.18 1.7

2020 2020

220R 820R

s s

lk8 lk2

1.12 1.68

p s p s s s s s s s s p p s

1.23 1.01 1.49 1.01

p p s p p s s s

2k7 22R 3k3 27R 33R 39R 47R 56R 68R 470R 82R 2k7 3k9 100R

12k 2k2 6k8 2k2

2k7 3k3 150R 3k9 2k2 470R 180R lk

2204 2222 2222 2227 2233 2239 2247 2256 2268 2270 2282 2288 2299 2300 2320

120R

s

1.05 1.05

2031 2034 2060

2k7 2k2 560R

p p s

8k2 27k lk5

1.33 1.08 1.37

2320 2348

s p s

1.55 1.15

2350

820R 2k7 150R

2k2 2k2 lk5 18k

2063

2k2

p

33k

1.07

2350

4k7

p

2k2 4k7

2

120k 150k

1.07

64

Electronics Calculations Data Handbook

RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

PREL

2353 2360

3k3 560R

p s

8k2 lk8

1.4 1.31

2756 2760

2380 2400 2405 2420 2455 2470 2479 2480 2481 2496 2500 2525 2530 2553 2555 2576 2588 2590 2597 2614 2620 2629 2641 2643 2652 2660 2667 2670 2673 2700 2705

180R lk2 2k7 220R 2k7 270R 3k9 680R 3k3 2k7 lk 2k7 330R 2k7 4k7 2k7 3k3 390R 2k7 2k7 820R 2k7 2k7 3k9 2k7 2k7 2k7 470R 2k7 lk2 3k3

s s p s p s p s p p s p s p p p p s p p s p p p p p p s p s p

2k2 lk2 22k 2k2 27k 2k2 6k8 lk8 10k 33k lk5 39k 2k2 47k 5k6 56k 12k 2k2 68k 82k lk8 100k 120k 8k2 150k 180k 220k 2k2 270k lk5 15k

1.08 2 1.12 1.1 1.1 1.12 1.57 1.38 1.33 1.08 1.67 1.07 1.15 1.06 1.84 1.05 1.28 1.18 1.04 1.03 1.46 1.03 1.02 1.48 1.02 1.02 1.01 1.21 1.01 1.8 1.22

2768 2779 2782 2789 2800 2800 2800 2806 2820 2850 2870 288O 288O 2920 2941 2943 2970 2988 3000 3000 3000 3020 3030 3043 3071 3083 3090 3095 3116 3147 3170

27R 33R 39R 47R

s s s s

2k7 2k7 2k7 2k7

1.01 1.01 1.01 1.02

3172 3195 3197 3200

s s s p s p s s p p s s p s s s p p s p s s p s s p p p s p p p s p p p s

2k7 2k2 2k7 6k8 2k7 18k 2k7 lk8 5k6 10k 2k7 2k7 22k 2k7 2k2 2k7 27k 12k 2k7 8k2 lk8 lk5 33k 2k2 2k7 39k 6k8 47k 2k7 15k 56k 68k 2k7 82k 100k 10k 2k2

1.02 1.25 1.03 1.69 1.03 1.18 1.04 1.56 2 1.39 1.04 1.06 1.15 1.07 1.31 1.08 1.12 1.33 1.1 1.57 1.67

2727 2733 2739 2747

56R 560R 68R 4k7 82R 3k3 100R lk 5k6 3k9 120R 150R 3k3 180R 680R 220R 3k3 3k9 270R 4k7 lk2 lk5 3k3 820R 330R 3k3 5k6 3k3 390R 3k9 3k3 3k3 470R 3k3 3k3 4k7 lk

2 1.1 1.37 1.12 1.08 1.82 1.07 1.14 1.26 1.06 1.05 1.17 1.04 1.03 1.47 1.45

Table 6.2 E12 equivalent resistances

65

RE

R1

s/p

R2

PREL

RE

R1

s/p

R~

PREL

3205 3212

3k9 3k3

p p

18k 120k

3229 3241

3k3 3k3

p p

150k 180k

1.22 1.03 1.02 1.02

3688 3690 3700 3700

3k9 390R lk lk5

p s s s

68k 3k3 2k7 2k2

1.06 1.12 1.37 1.68

3251

3k3

p

220k

1.02

3717

6k8

p

8k2

1.83

3260

560R

s

2k7

3k3 3k3 lk5

p p s

270k 330k lk8

3723 3727

3k9 4k7

p p

82k 18k

1.05

3260 3267 3300 3313

1.21 1.01 1.01 1.83

3754 3770

3k9 470R

p s

100k 3k3

1.26 1.04 1.14

p p s s s s s p s

22k 8k2 3k3 3k3 3k3 3k3 3k3 12k 2k7

1.18 1.68 1.01 1.01

3777 3801 3817 3818

3k9 3k9 3k9 5k6

p p p p

120k 150k 180k 12k

1.03 1.03 1.02 1.47

3356 3368 3377 3380

3k9 5k6 33R 39R 47R 56R 68R 4k7 680R

1.01 1.02 1.02 1.39 1.25

3832 3844 3854 3860 3861

3k9 3k9 3k9 560R 3k9

p p p s p

220k 270k 330k 3k3 390k

1.02 1.01 1.01

3382 3400

82R 100R

s s

3k3 3k3

3400 3400 3408 3420 3450 3480 3488

lk2 6k8 3k9 120R 150R 180R 3k9 220R 820R 3k9 270R

s p p s s s p s s p s

2k2 6k8 27k 3k3 3k3 3k3 33k 3k3 2k7 39k 3k3

1.02 1.03 1.55 2 1.14 1.04 1.05 1.05 1.12 1.07 1.3

3873 3900 3939 3947 3956 3968 3980 3982 4000 4000 4003

4k7 lk2 39R 47R 56R 68R 680R 82R 100R lk8 4k7

p s s s s s s s s s p

22k 2k7 3k9 3k9 3k9 3k9 3k3 3k9 3k9 2k2 27k

1.01 1.01 1.01 1.02 1.21 1.02 1.03 1.82 1.17

1.1 1.08

4020 4048

120R 6k8

s p

3k9 10k

1.03 1.68

4k7 5k6

p p

15k 10k

1.31 1.56

4050 4078

150R 5k6

s p

3k9 15k

1.04

3590 3600 3601

lk8 3k9

s p

lk8 47k

3630 3646

330R

s

3k3

2 1.08 1.1

4080 4100 4114

180R 8k2 4k7

s p p

3k9 8k2 33k

2 1.14

3k9

p

56k

1.07

4120

220R

s

3k9

1.06

3328 3333 3339 3347

3520 3520 3545 3570 3579

1.17 1.01 1.21 1.44

1.37 1.05

66

Electronics Calculations Data Handbook

RE

R1

s/p

R2

4120 4170

820R 270R

s s

4195

4k7

4200

lk5

4230 4271 4273

PREL

RE

R1

s/p

R2

PREL

3k3 3k9

4788

5k6

4800

100R

p

33k

1.17

s

4k7

1.02

p

39k

4800

lk5

s

2k7

330R 5k6 4k7

s p p

3k9 18k 47k

4820 4850

120R 150R

s

3k3

1.45

s s

4k7 4k7

1.03 1.03

4871 4880

8k2 180R

p s

12k 4k7

1.68 1.04

4290 4300 4336 4340 4370

390R lk 4k7 6k8 470R

s s p p s

3k9 3k3 56k 12k 3k9

4897 4900 4900 4920 4935 4970 5000 5004 5030

5k6 lk 2k2 220R 6k8 270R 10k 5k6 330R

p s s s p s p p s

39k 3k9 2k7 4k7 18k 4k7 10k 47k 4k7

1.14 1.26 1.81 1.05 1.38 1.06 2 1.12 1.07

4396 4400 4445

4k7 2k2 4k7

p s p

68k 2k2 82k

4460

560R

s

3k9

4464 4489 4500 4500 4505 4523 4557 4580 4580

5k6 4k7 lk2 lk8 8k2 4k7 4k7 680R 4k7

p p s s p p p s p

22k 100k 3k3 2k7 10k 120k 150k 3k9 180k

5090 5091 5100 5100 5170 5174 5194 5242 5260 5302 5303

390R s 5k6 p lk2 s lk8 s 470R s 5k6 p 6k8 p 5k6 p 560R s 8k2 p 5k6 p

4k7 56k 3k9 3k3 4k7 68k 22k 82k 4k7 15k 100k

1.08 1.1 1.31 1.55 1.1 1.08 1.31 1.07 1.12 1.55 1.06

4602 4620 4634

4k7 4k7 4k7

p p p

220k 270k 330k

4638

5k6

p

27k

5350 5380

5k6 680R

p s

120k 4k7

1.05 1.14

4644 4653

4k7 4k7

p p

390k 470k

5398 5400

5k6 lk5

p s

150k 3k9

1.04 1.38

4679

6k8

p

15k

4720 4747

820R 47R

s s

3k9 4k7

5400 5431

2k7 5k6

s p

2k7 180k

2 1.03

56R

s

4k7

5432 5455

6k8 10k

p p

27k 12k

1.25

4756 4768

68R

s

4k7

5461

5k6

p

220k

1.03

4782

82R

s

4k7

5486

5k6

p

270k

1.02

1.83

Table 6.2 E12 equivalent resistances

67

RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

PREI

5500 5507 5520 5521 5534 5545 5634 5638 5656 5668 5682 5700 5700 5700 5720 5750 5780 5790 5820 5870 5900 5930 5941 5974 5990 6000 6000 6000 6064 6070 6100 6160 6182 6200 6279 6280 6290

2k2 5k6 820R 5k6 5k6 5k6 8k2 6k8 56R 68R 82R 100R lk lk8 120R 150R 180R 6k8

S

3k3 330k 4k7 390k 470k 560k 18k 33k 5k6 5k6 5k6 5k6 4k7 3k9 5k6 5k6 5k6 39k 5k6 5k6 4k7 5k6 47k 22k 5k6 3k3 15k 12k 56k 5k6 3k9 5k6 68k 4k7 82k 5k6 27k

1.67 1.02 1.17 1.01 1.01 1.01 1.46 1.21 1.01 1.01 1.01 1.02 1.21 1.46 1.02 1.03 1.03 1.17 1.04 1.05 1.26 1.06 1.14 1.37 1.07 1.82 1.67 2 1.12 1.08 1.56 1.1 1.1 1.32 1.08 1.12 1.3

6367 6420 6429 6435 6500 6505 6552 6568 6596 6600 6600 6600 6633 6663 6667 6683 6703 6718 6733 6775 6800 6868 6875 6882 6900 6900 6920 6950 6980 6982 7020 7070 7100 7130 7153 7190 7200

6k8 820R 10k 6k8 lk8 6k8 6k8 8k2 6k8 lk 2k7 3k3 6k8 6k8 12k 6k8 6k8 6k8 6k8 8k2 lk2 68R 10k 82R 100R 2k2 120R 150R 180R 8k2 220R 270R lk5 330R 8k2 390R 3k3

p s p p s p p p p s s s p p p p p p p p s s p s s s s s s p s s s s p s s

100k 5k6 18k 120k 4k7 150k 180k 33k 220k 5k6 3k9 3k3 270k 330k 15k 390k 470k 560k 680k 39k 5k6 6k8 22k 6k8 6k8 4k7 6k8 6k8 6k8 47k 6k8 6k8 5k6 6k8 56k 6k8 3k9

1.07 1.15 1.56 1.06 1.38 1.05 1.04 1.25 1.03 1.18 1.69 2 1.03 1.02 1.8 1.02 1.01 1.01 1.01 1.21 1.21 1.01 1.45 1.01 1.01 1.47 1.02 1.02 1.03 1.17 1.03 1.04 1.27 1.05 1.15 1.06 1.85

220R 270R lk2 330R 6k8 8k2 390R 2k7 10k 12k 6k8 470R 2k2 560R 6k8 lk5 6k8 680R 8k2

P S

P P P P P S $ S S S $ S S S

P S S S $

P P S s

P P P S S S

P S

P S

P

68 RE

Electronics Calculations Data Handbook R1

s/p

R2

PREL

RE

R1

s/p

R2

PREL

12k 470R

p s

18k 6k8

1.67 1.07

8308

p s

27k 8k2

1.44 1.01

10k 8k2 560R lk8 2k7 8k2 680R 15k 8k2 820R 10k

p p s s s p s p p s p

27k 68k 6k8 5k6 4k7 82k 6k8 15k 100k 6k8 33k

1.37 1.12 1.08 1.32 1.57 1.1 1.1 2 1.08 1.12 1.3

8320 8350 8380 8420 8470 8485 8530 8590 8600 8600 8670 8718

12k 120R 150R

s

8k2

180R

s

8k2

220R 270R 10k 330R 390R lk8 3k9 470R 10k

s s p s s s s s p

8k2 8k2 56k 8k2 8k2 6k8 4k7 8k2 68k

1.02 1.02 1.03 1.03 1.18 1.04 1.05 1.26 1.83 1.06 1.15

8k2 12k 8k2 lk 2k2 3k9 8k2 8k2 8k2 10k lk2 3k3 8k2 8k2 8k2 8k2 8k2 8k2 15k 10k 82R 100R

p p p s s s p p p p s s p p p p p p p p s s

120k 22k 150k 6k8 5k6 3k9 180k 220k 270k 39k 6k8 4k7 330k 390k 470k 560k 680k 820k 18k 47k 8k2 8k2

1.07 1.55 1.05 1.15 1.39 2 1.05 1.04 1.03 1.26 1.18 1.7 1.02 1.02 1.02 1.01 1.01 1.01 1.83 1.21 1.01 1.01

8760 8800 8880 8900 8913 8919 9000 9000 9020 9091 9176 9200 9231 9375 9400 9400 9474 9500 9500 9559 9565 9643

560R 12k 680R 3k3 10k 15k 2k2 18k 820R 10k 12k lk 10k 10k lk2 4k7 10k 2k7 3k9 12k 10k 10k

s p s s p p s p s p p s p p s s p s s p p p

8k2 33k 8k2 5k6 82k 22k 6k8 18k 8k2 100k 39k 8k2 120k 150k 8k2 4k7 180k 6k8 5k6 47k 220k 270k

1.07 1.36 1.08 1.59 1.12 1.68 1.32 2 1.1 1.1 1.31 1.12 1.08 1.07 1.15 2 1.06 1.4 1.7 1.26 1.05 1.04

lk5 2k7

s s

6k8 5k6

1.22 1.48

9643 9700

15k lk5

p s

27k 8k2

1.56 1.18

Table 6.2 E12 equivalent resistances RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

9706 9750 9792 9825 9855

lOk lOk lOk lOk lOk

p p p p p

330k 390k 470k 560k 680k

1.03 1.03 1.02 1.02 1.01

9880 9882 9900 9901

lOk 12k 18k lOk

p p p p

820k 56k 22k 1M

69

Pl~L 1.01 1.21 1.82 1.01

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

1001 1005 1005 1008 1010 1010 1010 1010 1011 1012 1013 1014

91R lk2 lk6 lkl 10R 100R 330R 390R llR 12R 13R lkl

s p p p s s s s s s s p

910R 6k2 2k7 12k lk 910R 680R 620R lk lk lk 13k

15R 16R 18R lk3 20R ll0R 200R 270R 510R lk2 22R 24R lkl 27R lkl lk8 30R 120R 470R lk5 33R lk2 36R lk3

s s s p s s s s s p s s p s p p s s s p s p s p

lk lk lk 4k7 lk 910R 820R 750R 510R 6k8 lk lk 15k lk 16k 2k4 lk 910R 560R 3k3 lk 7k5 lk 5kl

I

1015 1016 1018 1018 1020 1020 1020 1020 1020 1020 1022 1024 1025 1027 1029 1029 1030 1030 1030 1031 1033 1034 1036 1036

RE

R1

s/p

R2

1.1 1.19 1.59 1.09 1.01 1.11 1.49 1.63 1.01 1.01 1.01 1.08

1037 1039 1040 1040 1040 1043 1043 1043 1047 1047 1048 1048

lkl 39R 130R 220R 360R 43R lkl lk6 47R lk2 lkl

P

18k lk 910R 820R 680R lk

1.02 1.02 1.02 1.28 1.02 1.12 1.24 1.36 2 1.18 1.02 1.02 1.07 1.03 1.07 1.75 1.03 1.13 1.84 1.45 1.03 1.16 1.04 1.25

1050 1050 1051 1052 1055 1056 1057 1059 1060 1060 1060 1061 1062 1065 1067 1068 1070 1070 1070 1070 1071 1073 1075 1075

PREL

2k 300R 430R 51R lkl lk3 56R lkl lk5 150R 240R lk2 lkl 62R lkl lkl 68R 160R 390R 510R lkl lk2 lkl 75R lkl

S S S s S

P P S

P P P S S S

P P S

P P s s

P P S

P P S S S S

P P P S

P

20k 3k lk 8k2 22k 2k2 750R 620R lk 24k 5k6 lk 27k 3k6 910R 820R 9kl 30k lk 33k 36k lk 910R 680R 560R 39k 10k 43k lk 47k

PREL

1.06 1.04 1.14 1.27 1.53 1.04 1.06 1.53 1.05 1.15 1.05 1.91 1.4 1.69 1.05 1.05 1.23 1.06 1.04 1.42 1.16 1.29 1.13 1.04 1.06 1.03 1.03 1.07 1.18 1.57 1.91 1.03 1.12 1.03 1.08 1.02

Table 6.3 E24 equivalent resistances

71

RE

R1

s/p

R2

P~L

1.21 1.02

1115 1116

15R 16R

s s

lkl lkl

1.01 1.01

3k3 56k 750R

1.48 1.02 1.44

1116 1118 1120

lk2 18R 20R

p s s

16k lkl lkl

p p s

2k7 62k lk

1.67 1.02 1.08

1120 1120 1120

120R 300R 560R

s s s

lk 820R 560R

1.08 1.02 1.02 1.12 1.37 2 1.02 1.16 1.02 1.07 1.6 1.02 1.03 1.13 1.24 1.82 1.06 1.03 1.41 1.03 1.32 1.05 1.14 1.04 1.52 1.04 1.05 1.04 1.92 1.04 1.74 1.15 1.26 1.4 1.69

RE

R1

s/p

R2

PREL

1075 1077

lk3 lkl

p p

6k2 51k

1078 1079 1080

lk6 lkl 330R

p p s

1080 1081 1082

lk8 lkl 82R

1082

lkl

p

68k

1.02

1122

22R

s

lkl

1082

lk2

p

llk

1.11

1122

lk3

p

8k2

1083

lk5

p

3k9

1.38

1124

24R

s

lkl

1084

lkl

p

75k

1.01

1125

lk2

p

18k

1085

lkl

p

82k

1.01

1125

lk8

p

3k

1087

lkl

p

91k

1.01

1127

27R

s

lkl

1088 1089

lkl lkl

p p

100k ll0k

1.01 1.01

1130 1130

30R 130R

s s

lkl lk

1090 1090

180R 270R

s s

910R 820R

1.2 1.33

1130 1130

220R 510R

s s

910R 620R

1090 1091 1091 1091 1091 1099 1100 1100 1108 1108 1110 1110

470R 91R lk2 lk3 2k lk2 100R 2k2 lk3 lk6 ll0R 200R

s s p p p p s p p p s s

620R lk 12k 6k8 2k4 13k lk 2k2 7k5 3k6 lk 910R

1.76 1.09 1.1 1.19 1.83 1.09 1.1 2 1.17 1.44 1.11 1.22

1132 1133 1135 1136 1137 1138 1138 1139 1140 1143 1143 1147

lk2 33R lk6 36R lk5 lk2 lk3 39R 390R 43R lk2 47R

p s p s p p p s s s p s

20k lkl 3k9 lkl 4k7 22k 9kl lkl 750R lkl 24k lkl

1110

360R

s

750R

1.48

1148

2k2

p

2k4

1110

430R

s

680R

1.63

1149

lk2

p

27k

1111

llR

s

lkl

1.01

1149

2k

p

2k7

1111

lk2

p

15k

1.08

1150

150R

s

lk

1112

12R

s

lkl

1.01

1150

240R

s

910R

1112

lk5

p

4k3

1.35

1150

330R

s

820R

1113

13R

s

lkl

1.01 I

1150

470R

s

680R

72

Electronics Calculations Data Handbook

RE 1150 1151 1154 1156 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1170 1172 1173 1175 1175 1177 1179 1180 1180 1180 1180 1180 1181 1182 1182 1183 1183 1184 1186 1187 1188 1190

: R1 lk3 51R lk2 56R lk2 lk5 160R lk2 62R lk3 lk2 lk8 lk6 lk2 68R lk2 lk2 lk3 75R lk2 lk2 lk2 180R 270R 360R 430R 560R lk2 82R lk3 lk2 lk5 lk2 lk2 lk2 lk2 510R

s/p

R2

p s p s p p s p s p p p p p s p p p s p p p s s s s s p s p p p p p p p s

10k lkl 30k lkl 33k 5kl lk 36k lkl llk 39k 3k3 4k3 43k lkl 47k 51k 12k lkl 56k 62k 68k lk 910R 820R 750R 620R 75k lkl 13k 82k 5k6 91k 100k ll0k 120k 680R

PREL 1.13 1.05 1.04 1.05 1.04 1.29 1.16 1.03 1.06 1.12 1.03 1.55 1.37 1.03 1.06 1.03 1.02 1.11 1.07 1.02 1.02 1.02 1.18 1.3 1.44 1.57 1.9 1.02 1.07 1.1 1.01 1.27 1.01 1.01 1.01 1.01 1.75

RE

R1

1191 1194 1196 1200 1200 1200 1200 1200 1202 1208 1210 1210 1210 1212 1212 1212 1213 1215 1216 1218 1218 1220 1220 1220 1220 1221 1222 1224 1227 1227 1229 1230 1230 1232 1233 1233 1236

91R lk6 lk3 100R 200R lk8 2k 2k4 lk3 lk5 ll0R 300R 390R 12R lk3 2k2 13R 15R 16R 18R lk6 20R 120R 220R 470R lk3 22R 24R 27R lk3 lk5 30R 130R lk8 33R lk3 36R

s/p

R2

PREL

lkl 4k7 15k lkl lk 3k6 3k 2k4 16k 6k2 lkl 910R 820R lk2 18k 2k7 lk2 lk2 lk2 lk2 5kl lk2 lkl lk 750R 20k lk2 lk2 lk2 22k 6k8 lk2 lkl 3k9 lk2 24k lk2

1.08 1.34 1.09 1.09 1.2 1.5 1.67 2 1.08 1.24 1.1 1.33 1.48 1.01 1.07 1.81 1.01 1.01 1.01 1.02 1.31 1.02 1.11 1.22 1.63 1.07 1.02 1.02 1.02 1.06 1.22 1.03 1.12 1.46 1.03 1.05 1.03

Table 6.3 E24 equivalent resistances 73 RE

R1

s/p

R2

1239 1240 1240

39R 240R 330R

s s s

lk2 lk 910R

1240 1240

560R 620R

s s

680R 620R

1240 1243 1244

lk3 43R lk6

p s p

27k lk2 5k6

1245 1246 1247

2k lk3 47R

p p s

3k3 30k lk2

1250

150R

s

lkl

1250

430R

s

820R

1250

lk5

p

7k5

1251 1251

51R lk3

s p

lk2 33k

1255

lk3

p

1256 1258 1260 1260 1262 1262 1265 1268 1268 1268 1269 1269 1270 1270

56R lk3 160R 510R 62R lk3 lk3 68R lk3 lk5 lk8 2k2 270R 360R

RE

R1

s/p

R2

PRE

1.03 1.24 1.36

1278 128C 128C

lk3 180R

p s

75k lkl

lk3

p

82k

1.0~ 1.16 1.0~

1.82

1282 1282 1283 1285 128(5

82R lk3

s p

lk2 91k

1.0~ 1.01

lk3 lk3 lk3

p p p

100k ll0k 120k

1.01 1.01 1.01

1286 1287 1288

2k lk3 lk5

p p p

3k6 130k 9kl

1.5s 1.01

129C

470R

s

820R

1.52

1291

91R

s

lk2

1.57 1.0~

1.2

lk6

p

6k8

1.24

1.04 1.04

1295 130(1

100R

s

lk2

13013

200R

s

lkl

1.0~ 1.18

36k

1.04

13013

s p s s s p p s p p p p s s

lk2 39k lkl 750R lk2 43k 47k lk2 51k 8k2 4k3 3k lk 910R

1.05 1.03 1.15 1.68 1.05 1.03 1.03 1.06 1.03 1.18 1.42 1.73 1.27 1.4

13013 13013 1302 1304 1310 1310 1313 1315 1316 1318 1319 1320 1320

300R 390R

s s

lk 910R

1.3 1.4~

620R lk8 lk5 ll0R 560R 13R 15R 16R 18R lk6 20R 120R 220R lk5

s p p s s s s s s p s s s p

680R 4k7 10k lk2 750R lk3 lk3 lk3 lk3 7k5 lk3 lk2 lkl llk

1.91 1.3~ 1.15 1.0c

PREL

2 1.05 1.04 1.29 1.61 1.04 1.04 1.14

1.16

1.75 1.01 1.01 1.01 1.01 1.21 1.02 1.1

1271

lk3

p

56k

1.02

1320 1320

1271

2k4

p

2k7

1.89

1320

2k2

p

3k3

1.67

1272

lk6

p

6k2

1.26

1322

22R

s

lk3

1273

lk3

p

62k

1.02

1275

75R

s

lk2

1.06

1322 1324

2k 24R

p s

3k9 lk3

1.02 1.51

1276

lk3

p

68k

1.02

1327

27R

s

lk3

L

1.2 1.14

1.02 1.02

74

Electronics Calculations Data Handbook RE

R1

s/p

R2

1380

560R

s

820R

1.68

1382 1385 1389 1390 1391 1395 1395

82R lk5 2k4 390R 91R

s p p s s

lk3 18k 3k3 lk lk3

1.06 1.08

lk5 lk8 lk6

p p p

20k 6k2 llk

RE

R1

s/p

R2

PREL

1330

30R

s

lk3

1330 1330 1330 1330 1333

130R 330R 510R lk8 33R

s s s p s

lk2 lk 820R 5kl lk3

1.02 1.11 1.33

1333 1333

lk5 2k4

p p

12k 3k

1.62 1.35 1.03 1.13 1.8

1336

36R

s

lk3

1.03

1339

39R

s

lk3

1.03

1397 1400

1339

lk6

p

8k2

1.2

1400

1340

240R

s

lkl

1340

430R

s

910R

1343 1345 1347 1350 1350 1351 1356 1360 1360 1360 1361 1362 1362 1364

43R lk5 47R 150R 2k7 51R 56R 160R 360R 680R lk6 62R lk8 lk5

s p s s p s s s s s p s p p

lk3 13k lk3 lk2 2k7 lk3 lk3 lk2 lk 680R 9kl lk3 5k6 15k

1365

2k

p

4k3

1366 1368

2k2 68R

p s

3k6 lk3

1.61 1.05

1370

270R

s

lkl

1430 1435

1370

620R

s

750R

1.25 1.83

1371

lk5

p

16k

1.09

1375

75R

s

lk3

1.379 1380 1380

lk6 180R 470R

p s s

10k lk2 910R

PREL

1.73 1.39 1.07 1.08 1.29 1.15

100R

s

lk3

1.08

1.22 1.47

s s

lk2 lkl

1.17

1400

200R 300R

1403

2k

p

4k7

1.03

1404

lk5

p

22k

1.12 1.04 1.13

1407 1410 1412 1412 1420 1420 1420 1421 1421 1423 1425 1429 1430

2k2 ll0R lk5 lk6 120R

p s p p s

3k9 lk3 24k 12k lk3

220R 510R lk5 2k7 lk8 lk6 lk5 130R

s s p p p p p s

lk2 910R 27k 3k 6k8 13k 30k lk3

1430

330R

s

lkl

1430

430R 680R

s s

lk 750R

lk5

p

33k

1.05

1437

2k

p

5kl

1.39

1440

240R

s

lk2

1.06

1440

620R

s

820R

1.2 1.76

1.16

1440 1440 1444

lk5 2k4 lk5

p p p

36k 3k6 39k

2 1.04 1.04 1.13 1.36 2 1.18 1.05 1.32 1.1 1.47

1.15 1.52

1.27 1.43 1.07

1.56 1.08 1.06 1.13 1.09 1.18 1.56 1.06 1.9 1.26 1.12 1.05 1.1 1.3 1.43 1.91

1.04 1.67 1.04

Table 6.3 E24 equivalent resistances

RE

R1

1446 1449 1450 1452 1454

lk6 lk5 150R lk8 lk5 lk6

1455 1455 1457 1460 1460 1461 1465 1468 1469 1470 1470 1470 1471 1473 1474 1476 1476 1478 1480 1480 1481 1481 1483 1485 1485 1486 1490 1492 1499 1500 1500 1500

2k2 lk5 160R 360R lk5 lk5 lk5 lk6 270R 470R 560R lk5 lk5 2k lk5 lk8 lk5 180R lk5 lk5 lk6 lk5 lk5 2k7 2k4 390R lk6 2k2 200R 300R 680R

s/p

R2

PREL

15k 43k lk3 7k5 47k 16k 4k3 51k lk3 lkl 56k 62k 68k 18k lk2 lk 910R 75k 82k 5k6 91k 8k2 100k lk3 ll0k 120k 20k 130k 150k 3k3 3k9 lkl 22k 4k7 lk3 lk2 820R

75

RE

R1

s/p

R2

PREL

1.11 1.03 1.12 1.24 1.03 1.1 1.51 1.03 1.12 1.33

1500 1500 1500 1503 1510 1510 1512 1515 1516 1518

750R lk6 3k lk8 510R lk6 2k 15R 16R 18R

s p p p s p p s s s

750R 24k 3k 9kl lk 27k 6k2 lk5 lk5 lk5

2 1.07 2 1.2 1.51 1.06 1.32 1.01 1.01 1.01

1.03 1.02 1.02 1.09 1.23 1.47 1.62 1.02 1.02 1.36 1.02 1.22 1.02 1.14 1.01 1.01 1.08 1.01 1.01 1.82 1.62 1.35 1.07 1.47 1.15 1.25 1.83

1519 1520 1520 1522 1524 1525 1526 1527 1530 1530 1530 1530 1532 1533 1536 1537 1537 1539 1540 1540 1543 1543 1543 1545 1547 1547 1547

lk6 20R 220R 22R 24R lk8 lk6 27R 30R 330R 430R 620R lk6 33R 36R lk6 2k2 39R 240R 2k4 43R lk6 2k7 2k 47R lk6 lk8

p s s s s p p s s s s s p s s p p s s p s p p p s p p

30k lk5 lk3 lk5 lk5 10k 33k lk5 lk5 lk2 lkl 910R 36k lk5 lk5 39k 5kl lk5 lk3 4k3 lk5 43k 3k6 6k8 lk5 47k llk

1.05 1.01 1.17 1.01 1.02 1.18 1.05 1.02 1.02 1.28 1.39 1.68 1.04 1.02 1.02 1.04 1.43 1.03 1.18 1.56 1.03 1.04 1.75 1.29 1.03 1.03 1.16

76

Electronics Calculations Data Handbook RE

R1

s/p

R2

PREL

1.03 1.03

1608 1610

2k ll0R

p s

8k2 lk5

1.24 1.07

lk5

1.04

1610

510R

s

lkl

1.46

56k

1.03

1616

1.3

1618

s p

lk 62k

1.56 1.03

1618 1620

s s p

lk6 lk6 16k

1.01

lk2

16R 18R lk8 20R

s

lk6

62R lk6 lk8

s p p

lk5 68k 12k

1.04 1.02 1.15

1620 1620 1622

lk6 68R

p s

75k lk5

1.02 1.05

1624 1624

120R 620R 22R 24R

s s s s

lk5 lk lk6 lk6

1569

lk6

p

82k

1.02

1627

2k2 27R

p s

6k2 lk6

1570

270R

s

lk3

1.21

1630

30R

s

lk6

1570

470R

s

lkl

1.43

1630

1570 1571 1572 1575 1575 1577 1579 1579 1579 1581 1581 1582

750R 3k lk6 75R lk6 lk6 lk6 2k 2k2 lk6 lk8 82R

s p p s p p p p p p p s

820R 3k3 91k lk5 100k ll0k 120k 7k5 5k6 130k 13k lk5

1.91 1.91 1.02 1.05 1.02 1.01 1.01 1.27 1.39 1.01 1.14 1.05

1630 1630 1632 1633 1636 1636 1636 1639 1640 1640 1643 1647

130R 330R 430R 2k4 33R 36R lk8 3k 39R 820R 2k 43R

s s s p s s p p s s p s

lk5 lk3 lk2 5kl lk6 lk6 18k 3k6 lk6 820R 9kl lk6

47R

s

lk6

1583 1584

lk6 lk6

p p

150k 160k

1.01 1.01

1650 1650

1589

2k4

p

4k7

1.51

1651

150R 3k3 51R

s p s

lk5 3k3 lk6

2 1.03

1590

390R

s

lk2

1.33

1651

lk8

p

20k

1.09

1590

680R

s

910R

1.75

1656

1591 1595

91R 2k7

s p

lk5 3k9

1.06 1.69

1659 1660

56R 2k7 160R

s p s

lk6 4k3 lk5

1.03 1.63 1.11

1600

100R

s

lk5

1.07

1660

360R

s

lk3

1.28

1600i i 300R 1607 I lk8

s

lk3

1.23

1660

560R

s

lkl

1.51

p

15k

1.12

1660

750R

s

910R

1.82

RE

R1

s/p

R2

PREL

1551 1551

51R lk6

s p

lk5 51k

1556

56R

s

1556

lk6

p

1560

360R

s

1560 1560

560R lk6

1562 1563 1565 1567 1568

1.01 1.11 1.01 1.08 1.62 1.01 1.02 1.35 1.02 1.02 1.09 1.25 1.36 1.47 1.02 1.02 1.1 1.83 1.02 2 1.22 1.03 1.03 1.1

Table 6.3 E24 equivalent resistances R1 62R 2k2 lk8 2k 68R 470R lk8 75R 180R 680R 2k4 82R lk8 390R 91R 2k 3k lk8 100R 200R 2k2 lk8 ll0R 510R lk8 2k 2k7 120R 220R 620R lk8 3k3 lk8 130R 430R 820R 2k4

s/p

R2

}REL

lk6 6k8 22k 10k lk6 lk2 24k lk6 lk5 lk 5k6 lk6 27k lk3 lk6 llk 3k9 30k lk6 lk5 7k5 33k lk6 lk2 36k 12k 4k7 lk6 lk5 lkl 39k 3k6 43k lk6 lk3 910R 6k2

1.04 1.32 1.08 1.2 1.04 1.39 1.08 1.05 1.12 1.68 1.43 1.05 1.07 1.3 1.06 1.18 1.77 1.06 1.06 1.13 1.29 1.05 1.07 1.43 1.05 1.17 1.57 1.0~ 1.15 1.5~ 1.05 1.92 1.04 1.08 1.33 1.9 1.39

RE

R1

s/p

R2

2k lk8 2k2 lk8 240R lk8 lk8 150R 750R lk8 lk8 160R 560R lk8 lk8 2k 2k7 3k lk8 270R 470R lk8 2k2 lk8 2k4 lk8 2k lk8 180R 680R lk8 lk8 3k3 200R 300R 2k 3k6

p p p p s p p s s p p s s p p p p p p s s p p p p p p p s s p p p s s p p

13k 47k 8k2 51k lk5 56k 62k lk6 lk 68k 75k lk6 lk2 82k 91k 15k 5kl 4k3 100k ik5 lk3 ll0k 9kl 120k 6k8 130k 16k 150k lk6 lkl 160k 180k 3k9 lk6 lk5 18k 3k6

77

PREL 1.15 1.04 1.27 1.04 1.16 1.03 1.03 1.09 1.75 1.03 1.02 1.1 1.47 1.02 1.02 1.13 1.53 1.7 1.02 1.18 1.36 1.02 1.24 1.02 1.35 1.01 1.13 1.01 1.11 1.62 1.01 1.01 1.85 1.13 1.2 1.11 2

78

Electronics Calculations Data Handbook R1

s/p

R2

PREL

1870 1872 1875 1875

270R 3k6 75R

s p s

lk6 3k9 lk8

1.17 1.92 1.04

2k

p

30k

1.07

1.32

1880

680R

s

lk2

1.57

lk8

1.01

1881

2k7

6k2

1.44

lk6 lk2 lk 910R

1.14 1.52 1.82 2

1882 1882 1886 1889

82R 2k2 2k 3k

lk8 13k 33k 5kl

1.05 1.17 1.06 1.59

s p s s s

lk8 5k6 lk8 lk8 lk8

1.01 1.48 1.01 1.02 1.02

1890 1891 1895 1899 1900

390R 91R 2k 2k4 100R

s s p p s

lk5 lk8 36k 9kl lk8

1.26 1.05 1.06 1.26 1.06

s

lk5 4k7 lk8 22k

1.22 1.64 1.02 1.09

1900 1902 1910 1910

300R 2k ll0R

s p s

lk6 39k lk8

1.19 1.05 1.06

s s p s s

llk lk8 lk8 lk6 lk8 24k lk8 lkl

1.2 1.02 1.02 1.15 1.02 1.08 1.03 1.68

1911 1918 1919 1920 1920 1920 1925 1930

910R 2k 2k 2k2 120R 620R 820R 2k 130R

s p p p s s s p s

lk 43k 47k 15k lk8 lk3 lkl 51k lk8

1.91 1.05 1.04 1.15 1.07 1.48 1.75 1.04 1.07

51R

s

lk8

1.03

1930

330R

s

lk6

1.21

1856

56R

s

lk8

1.03

1930

430R

s

lk5

1.29

1857

2k4

p

8k2

1.29

i 1931

2k

p

56k

1.04

1859 1860

2k2 360R

p s

12k lk5

1.18 1.24

1933 1934

2k7

p

6k8

1.4

2k2

p

16k

1.14

1860

560R

s

lk3

1.43

1935

1862 1862 1867

62R 2k 3k3

s p p

lk8 27k 4k3

1.03 i 1.07 1.77

1938 1939 1943

2k4 2k 3k3

p p p

10k 62k 4k7

1.24 1.03 1.7

2k

p

68k

1.03

1868

68R

s

lk8

1.04

1948

2k

p

75k

1.03

RE

R1

s/p

R2

PREL

1803 1810 1818 1818

2k2 510R 18R 2k

p s s p

10k lk3 lk8 20k

1.22 1.39 1.01 1.1

1818

2k4

p

7k5

1820

20R

s

1820 1820 1820 1820

220R 620R 820R, 910R

s s s s

1822 1822 1824 1827 1830

22R 2k7 24R 27R 30R

1830 1831 1833 1833

330R 3k 33R 2k

1833 1836 1839 1840 1843 1846 1847 1850

2k2 36R 39R 240R 43R 2k 47R 750R

1851

, RE

Table 6.3 E24 equivalent resistances RE

R1

1950 1950 1950 1952 1953 1957 1959 1960 1960 1960 1961 1964 1967 1970 1970 1970 1974 1975 1978 1980 1980 1980 1982 1985 1990 2OOO 2000 2000 2OOO 2004 2010 2010 2015 2020 2020 2020 2022

150R 750R 3k9 2k 3k 2k 3k6 160R 360R 2k2 2k 2k 2k 470R 2k 2k4 2k 2k 2k 180R 680R 2k 2k2 2k7 390R 200R lk 2k2 2k4 3k3 510R 910R 2k2 20R 220R 820R 22R

s/p

79

R2

PREL

!RE

R1

s/p

R2

PREL

lk8 lk2 3k9 82k 5k6 91k 4k3 lk8 lk6 18k 100k ll0k 120k lk5 130k llk 150k 160k 180k lk8 lk3 200k 20k 7k5 lk6 lk8 lk 22k 12k 5kl lk5 lkl 24k 2k lk8 lk2 2k

1.08 1.63 2 1.02 1.54 1.02 1.84 1.09 1.23 1.12 1.02 1.02 1.02 1.31 1.02 1.22 1.01 1.01 1.01 1.1 1.52 1.01 1.11 1.36 1.24 1.11 2 1.1 1.2 1.65 1.34 1.83 1.09 1.01 1.12 1.68 1.01

2022 2024 2026 2027 2030 2030 2031 2033 2034 2036 2039 2039 2040 2043 2045 2047 2050 2050 2051 2056 2060 2062 2063 2068 2069 2070 2070 2073 2075 2076 2082 2082 2082 2083 2087 2091 12093

3k 24R 2k4 27R 30R 430R 2k7 33R 2k2 36R 39R 3k6 240R 43R 3k9 47R 750R 2k2 51R 56R 560R 62R 2k2 68R 2k4 270R 470R 2k2 75R 3k3 82R 2k7 3k 2k2 2k4 91R 2k2

p s p s s s p s p s s p s s p s s p s s s s p s p s s p s p s p p p p s p

6k2 2k 13k 2k 2k lk6 8k2 2k 27k 2k 2k 4k7 lk8 2k 4k3 2k lk3 30k 2k 2k lk5 2k 33k 2k 15k lk8 lk6 36k 2k 5k6 2k 9kl 6k8 39k 16k 2k 43k

1.48 1.01 1.18 1.01 1.02 1.27 1.33 1.02 1.08 1.02 1.02 1.77 1.13 1.02 1.91 1.02 1.58 1.07 1.03 1.03 1.37 1.03 1.07 1.03 1.16 1.15 1.29 1.06 1.04 1.59 1.04 1.3 1.44 1.06 1.15 1.05 1.05

80 RE

Electronics Calculations Data Handbook R1

2100 100R 2100 300R 2100 lk 2102 2k2 2109 2k2 2110 ll0R 2110 510R 2110 910R 2110 3k6 2117 2k2 2118 2k4 2120 120R 2120 620R 2120 820R 2125 2k2 2126 2k7 2130 130R 2130 330R 2131 2k2 2131 3k9 2137 2k2 2143 2k2 2143 2k4 2143 3k 2 1 4 8 2k2 2150 ~ 150R 2150 4k3 2153 2k2 2154 3k3 2157 2k2 2160 160R 2160 360R 2160 560R 2160 2k2 2163 2k2 2164 2k4 2168 I 2k2

s/p

R2

s s s p p s s s p p p s s s p p s s p p p p p p p s p p p p s s s p p p p

2k lk8 lkl 47k 51k 2k lk6 lk2 5kl 56k 18k 2k lk5 lk3 62k 10k 2k lk8 68k 4k7 75k 82k 20k 7k5 91k 2k 4k3 100k 6k2 ll0k 2k lk8 lk6 120k 130k 22k 150k

PREL 1.05 1.17 1.91 1.05 1.04 1.06 1.32 1.76 1.71 1.04 1.13 1.06 1.41 1.63 1.04 1.27 1.07 1.18 1.03 1.83 1.03 1.03 1.12 1.4 1.02 1.08 2 1.02 1.53 1.02 1.08 1.2 1.35 1.02 1.02 1.11 1.01

RE

R1

s/p

R2

2168 2170 2173 2176 2178

2k7 2k2 2k2 2k2 2k2 180R 680R 2k4 390R 3k6 3k 200R lk lkl

p p p p p s s p s p p s s s

llk 160k 180k 200k 220k 2k lk5 24k lk8 5k6 8k2 2k lk2 lkl

2k4 2k7 910R 3k9

p p s p

27k 12k lk3 5kl

220R 620R 22R 2k4 3k3 24R 27R 30R 430R 33R

s s s p p s s s s s

2k lk6 2k2 30k 6k8 2k2 2k2 2k2 lk8 2k2

36R 2k7 2k4 39R 240R 43R 4k3 47R 750R

s p p s s s p s s

2k2 13k 33k 2k2 2k 2k2 4k7 2k2 lk5

2180 2180 2182 2190 2191 2196 2200 2200 2200 2204 2204 2210 2210 2220 2220 2222 2222 2222 2224 2227 2230 2230 2233 2236 2236 2237 2239 2240 2243 2246 2247 2250

PREL 1.25 1.01 1.01 1.01 1.01 1.09 1.45 1.1 1.22 1.64 1.37 1.1 1.83 2 1.09 1.23 1.7 1.76 1.11 1.39 1.01 1.08 1.49 1.01 1.01 1.01 1.24 1.02 1.02 1.21 1.07 1.02 1.12 1.02 1.91 1.02 1.5

Table 6.3 E24 equivalent resistances RE

R1

2250 2251 2256 2256 2261 2262 2268 2270 2270 2273 2275 2278 2280 2282 2283 2288 2291 2292 2292 2299 2300 2300 2300 2300 2301 2308 2310 2310 2310 2311 2318

2k4 51R 56R 3k 2k4 62R 68R 270R 470R 2k4 75R 3k6 680R 82R 2k4 2k7 91R 2k4 3k3 3k9 100R 300R lk lkl 2k4 3k ll0R 510R 2k7 2k4 2k4 120R 820R 2k4 130R 330R 2k4

2320 2320 2326 2330 2330 2332

s/p

R2

PREL

P

36k 2k2 2k2 9kl 39k 2k2 2k2 2k lk8 43k 2k2 6k2 lk6 2k2 47k 15k 2k2 51k 7k5 5k6 2k2 2k lk3 lk2 56k 10k 2k2 lk8 16k 62k 68k

1.07 1.02 1.03 1.33 1.06 1.03 1.03 1.14 1.26 1.06 1.03 1.58 1.43 1.04 1.05 1.18 1.04 1.05 1.44 1.7 1.05 1.15 1.77 1.92 1.04 1.3 1.05 1.28 1.17 1.04 1.04 1.05 1.55 1.03 1.06 1.17 1.03

s S

P P s S S S

P S

P s s

P P S

P P P S S s s

P P s s

P P P S S

P S S

P

2k2 lk5 75k 2k2 2k 82k

RE

2333 2338 2344 2348 2349 2350 2350 2350 2353 2353 2354 2356 2357 2360 2360 2360 2362 2365 2368 2372 2374 2376 2379 2380 2390 2394 2400 2400 2400 2400 2405 2410 2420 2420 2420 2422 2424

81

R1

s/p

R2

PREI

4k3 2k4 2k4 2k7 2k4 150R 750R 4k7 2k4 3k3 3k6 2k4 3k 160R 360R 560R 2k4 2k4 2k4 2k4 2k4 2k4 2k7 180R 390R 3k9 200R lkl lk2 3k 2k7 910R

p p p p p s s p p p p p p s s s p p p p p p p s s p s s s p p s

5kl 91k 100k 18k ll0k 2k2 lk6 4k7 120k 8k2 6k8 130k llk 2k2 2k lk8 150k 160k 180k 200k 220k 240k 20k 2k2 2k 6k2 2k2 lk3 lk2 12k 22k lk5

1.84 1.03 1.02 1.15 1.02 1.07 1.47 2 1.02 1.4 1.53 1.02 1.27 1.07 1.18 1.31 1.02 1.02 1.01 1.01 1.01 1.01 1.14 1.08 1.2 1.63 1.09 1.85 2 1.25 1.12 1.61

220R 620R 820R 3k3 24R

s s s p s

2k2 lk8 lk6 9kl 2k4

1.1 1.34 1.51 1.36 1.01

82

Electronics Calculations Data Handbook

RE

R1

s/p

R2

2427 2427 2430 2430 2432 2432 2433 2436 2438 2439 2440 2443 2446

27R 2k7 30R 430R 3k6

s p s s p

2k4 24k 2k4 2k 7k5

I PRELI 1.01 ! 1.11 1.01 1.22 1.48

RE

RI

s/p

R2

PREL

2510 2512 2520 2525 2526

910R 2k7 120R 2k7 3k

s p s p p

lk6 36k 2k4 39k 16k

4k3

p

5k6

1.77

2530

130R

s

2k4

33R 36R

s s

2k4 2k4

1.01 1.02

2530 2538

330R 3k3

s p

2k2 llk

1.57 1.08 1.05 1.07 1.19 1.05 1.15 1.3

2447 2451 2455 2456 2462 2468 2470 2470 2475 2477 2479 2480 2481 2482 2491

3k 39R 240R 43R 4k7 47R 51R 2k7 56R 62R 68R 270R 470R 75R 2k7 3k9 680R 3k3 82R 91R

p s s s p s s p s s s s s s p p s p s s

13k 2k4 2k2 2k4 5kl 2k4 2k4 27k 2k4 2k4 2k4 2k2 2k 2k4 30k 6k8 lk8 10k 2k4 2k4

1.23 1.02 1.11 1.02 1.92 1.02 1.02 1.1 1.02 1.03 1.03 1.12 1.24 1.03 1.09 1.57 1.38 1.33 1.03 1.04

2539 2540 2550 2550 2550 2553 2555 2560 2560 2560 2564 2566 2571 2576 2580 2580 2587 2588 2590 2597

4k3 2k7 150R 750R 5kl 2k7 4k7 160R 360R 560R 2k7 3k9 3k 2k7 180R 3k6 2k7 3k3 390R 2k7

p p s s p p p s s s p p p p s p p p s p

6k2 43k 2k4 lk8 5kl 47k 5k6 2k4 2k2 2k 51k 7k5 18k 56k 2k4 9kl 62k 12k 2k2 68k

1.69 1.06 1.06 1.42 2 1.06 1.84 1.07 1.16 1.28 1.05 1.52 1.17 1.05 1.08 1.4 1.04 1.28 1.18 1.04

2496 2500 2500 2500 2500 2500 2502 2510 2510

2k7 100R 300R lk lk2 3k 3k6 ll0R 510R

p s s s s p p s s

33k 2k4 2k2 lk5 lk3 15k 8k2 2k4 2k

1.08 1.04 1.14 1.67 1.92 1.2 1.44 1.05 1.26

2600 2600 2600 2600 2606 2609 2614 2620 2620

200R lk lkl lk3 2k7 3k 2k7 220R 620R

s s s s p p p s s

2k4 lk6 lk5 lk3 75k 20k 82k 2k4 2k

1.08 1.63 1.73 2 1.04 1.15 1.03 1.09 1.31

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

820R 2k7 2k7 430R 3k3 4k3 2k7 240R 3k 2k7

s p p s p p p s p p

lk8 91k 100k 2k2 13k 6k8 ll0k 2k4 22k 120k

3k9 2k7 3k6 2k7 2k7 2k7 2k7 2k7 3k 5kl 270R 470R 2k7 2k7 4k7 680R 300R lkl lk2 3k 3k3 510R 910R 3k6

p p p p p p p p p p s s p p p s s s s p p s s p

8k2 130k 10k 150k 160k 180k 200k 220k 24k 5k6 2k4 2k2 240k 270k 6k2 2k 2k4 lk6 lk5 27k 15k 2k2 lk8 llk

27R 3k 30R

s p s

2k7 30k 2k7

PREL 1.46 1.03 1.03 1.2 1.25 1.63 1.02 1.1 1.14 1.02 1.48 1.02 1.36 1.02 1.02 1.02 1.01 1.01 1.13 1.91 1.11 1.21 1.01 1.01 1.76 1.34 1.13 1.69 1.8 1.11 1.22 1.23 1.51 1.33 1.01 1.1 1.01

RE

R1

s/p

R2

2730 2730 2733 2733 2736 2736 2739 2743 2747 2750 2750 2751 2756 2760 2760 2762 2768 2769 2769 2775 2779 2782 2786 2789 2790 2791 2798 2800 2800 2800 2800 2800 2804 2806 2810 2819 2820

330R 3k9 33R 4k3 36R 3k3 39R 43R 47R 750R 3k 51R 56R 360R 560R 62R 68R 3k 3k6 75R 4k7 82R 3k 3k3 390R 91R 5kl 100R lk lk2 lk3 5k6 3k 3k9 ll0R 3k6 120R

s p s p s p s s s s p s s s s s s

2k4 9kl 2k7 7k5 2k7 16k 2k7 2k7 2k7 2k 33k 2k7 2k7 2k4 2k2 2k7 2k7 36k 12k 2k7 6k8 2k7 39k 18k 2k4 2k7 6k2 2k7 lk8 lk6 lk5 5k6 43k 10k 2k7 13k 2k7

s s p s s s s p p p s p s

83

PREL 1.14 1.43 1.01 1.57 1.01 1.21 1.01 1.02 1.02 1.38 1.09 1.02 1.02 1.15 1.25 1.02 1.03 1.08 1.3 1.03 1.69 1.03 1.08 1.18 1.16 1.03 1.82 1.04 1.56 1.75 1.87 2 1.07 1.39 1.04 1.28 1.04

84

Electronics Calculations Data Handbook

RE

R1

s/p

R2

2820 2820 2820 2821 2830 2830 2833 2833 2847 2850 2860 2862 2870 2870 2873 2879 2880 2880 2885 2889 2894 2900 2900 2900 2901 2903 2904 2910 2910 2913 2914 2920 2920 2920 2927 2932 2939

620R 820R 3k 4k3 130R 430R 3k 3k3 3k 150R 160R 3k 470R 3k3 3k 3k9 180R 680R 3k 4k7 3k 200R lkl lk3 3k3 3k6 3k 510R 910R 3k 5kl 220R 3k 4k3 3k 3k 3k6

s s p p s s p p p s s p s p p p s s p p p s s s p p p s s p p s p p p p p

2k2 2k 47k 8k2 2k7 2k4 51k 20k 56k 2k7 2k7 62k 2k4 22k 68k llk 2k7 2k2 75k 7k5 82k 2k7 lk8 lk6 24k 15k 91k 2k4 2k 100k 6k8 2k7 ll0k 9kl 120k 130k 16k

PREL 1.28 1.41 1.06 1.52 1.05 1.18 1.06 1.17 1.05 1.06 1.06 1.05 1.2 1.15 1.04 1.35 1.07 1.31 1.04 1.63 1.04 1.07 1.61 1.81 1.14 1.24 1.03 1.21 1.46 1.03 1.75 1.08 1.03 1.47 1.03 1.02 1.23

RE

R1

s/p

R2

2940 2941 2941 2942 2943 2945 2950 2951 2956 2960 2960 2963 2967 2970 2970 2973 298~ 300C, 3000 3000 3000 3000 3000 3000 3007 3020 3020 3023 3030 3030 3033 3036 3036 3039 3043 3043 3047

240R 3k 3k3 5k6 3k9 3k 750R 3k 3k 560R 3k 3k 3k 270R 3k 3k3 4k7 300R lk lk2 lk5 3k3 3k6 3k9 4k3 620R 820R 3k3 30R 330R 33R 36R 5kl 39R 43R 3k3 47R

S

2k7 150k 27k 6k2 12k 160k 2k2 180k 200k 2k4 220k 240k 270k 2k7 300k 30k 8k2 2k7 2k lk8 lk5 33k 18k 13k 10k 2k4 2k2 36k 3k 2k7 3k 3k 7k5 3k 3k 39k 3k

P P P P P S

P P S

P P P s

P P P S S s S

P P P P s S

P S S S S

P S S

P S

PREL

1.09 1.02 1.12 1.9 1.33 1.02 1.34 1.02 1.02 1.23 1.01 1.01 1.01 1.1 1.01 1.11 1.57 1.11 1.5 1.67 2 1.1 1.2 1.3 1.43 1.26 1.37 1.09 1.01 1.12 1.01 1.01 1.68 1.01 1.01 1.08 1.02

Table 6.3 E24 equivalent resistances

85

RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

Pm~L

s p s s s p s p s s s p s s p p p p p s s s s p s s p s s s p p p p p s s

3k 20k 3k 2k7 3k 43k 3k 6k8 3k 2k4 3k 47k 2k7 3k llk 22k 15k 51k 9kl 3k 2k lk8 lk6 6k2 3k 2k2 56k 3k 3k 2k7 24k 62k 16k 8k2 68k 3k 2k4

1.02 1.18 1.02 1.13 1.02 1.08 1.02 1.82 1.03 1.28 1.03 1.07 1.14 1.03 1.39 1.16 1.26 1.06 1.52 1.03 1.55 1.72 1.94 2 1.04 1.41 1.06 1.04 1.04 1.16 1.15 1.05 1.24 1.62 1.05 1.05 1.31

3160 3161 3166 3170 3172 3176 3180 3185 3195 3197 3200 3200 3200 3200 3204 3205 3206 3210 3212 3214 3218 3220 3220 3229 3231 3233 3240 3241 3243 3246 3246 3251 3255 3260 3260 3264 3264

160R 3k3 4k3 470R 3k3 3k6 180R 3k3 3k3 4k7

s p p s p p s p p p

3k 75k 12k 2k7 82k 27k 3k 91k 100k 10k

1.05 1.04 1.36 1.17 1.04 1.13 1.06 1.04 1.03 1.47

200R lk lk2 lk6 3k3 3k9 5k6 510R 3k3 3k6 3k3 220R 820R 3k3 4k3 3k3 240R 3k3 6k2 3k3 3k6 3k3 3k3 560R

s s s s p p p s p p p s s p p p s p p p p p p s

3k 2k2 2k lk6 ll0k 18k 7k5 2k7 120k 30k 130k 3k 2k4 150k 13k 160k 3k 180k 6k8 200k 33k 220k 240k 2k7

1.07 1.45 1.6 2 1.03 1.22 1.75 1.19 1.03 1.12 1.03 1.07 1.34 1.02 1.33 1.02 1.08 1.02 1.91 1.02 1.11

3136 3144 3147 3150 3150

51R 3k6 56R 360R 62R 3k3 68R 5k6 75R 680R 82R 3k3 390R 91R 4k3 3k6 3k9 3k3 4k7 100R lkl lk3 lk5 6k2 ll0R 910R 3k3 120R 130R 430R 3k6 3k3 3k9 5kl 3k3 150R 750R

3k3 3k3 3k9

p p p

270k 300k 20k

1.02 1.01 1.21 1.01 1.01 1.2

86

Electronics Calculations Data Handbook RE

R1

s/p

R2

PREL

1.01

3390

390R

s

3k

1.13

9kl 3k 36k llk

1.56 1.09 1.1 1.43

3391 3394 3400 3400

91R

s

3k3

1.03

6k2 100R

p s

7k5 3k3

1.83 1.03

lk

s

2k4

1.42

p s

39k 3k

1.09 1.1

3400 3400

lk2 lk6

s s

2k2 lk8

1.55 1.89

lkl

s

2k2

1.5

3400

6k8

p

6k8

2

3300 3300

lk3 lk5

s s

2k lk8

1.65 1.83

3402 3408

3k6 3k9

p p

62k 27k

1.06 1.14

3310 3313

910R 3k9

s p

2k4 22k

1.38 1.18

3410 3419

ll0R 3k6

s p

3k3 68k

1.03 1.05

3320 3322 3328 3330 3333 3336 3339 3342 3343 3344 3347 3351 3355 3356 3360

620R 3k6 5k6 330R 33R 36R 39R 4k3 43R 3k6 47R 51R 3k9 56R 360R

s p p s s s s p s p s s p s s

2k7 43k 8k2 3k 3k3 3k3 3k3 15k 3k3 47k 3k3 3k3 24k 3k3 3k

1.23 1.08 1.68 1.11 1.01 1.01 1.01 1.29 1.01 1.08 1.01 1.02 1.16 1.02 1.12

3420 3430 3430 3435 3449 3450 3450 3451 3452 3460 3463 3467 3470 3471 3475

120R 130R 430R 3k6 3k6 150R 750R 3k9 4k7 160R 3k6 5k6 470R 4k3 3k6

s s s p p s s p p s p p s p p

3k3 3k3 3k 75k 82k 3k3 2k7 30k 13k 3k3 91k 9kl 3k 18k 100k

1.04 1.04 1.14 1.05 1.04 1.05 1.28 1.13 1.36 1.05 1.04 1.62 1.16 1.24 1.04

3362

62R

s

3k3

1.02

3480

180R

s

3k3

1.05

RE

R1

s/p

R2'

3267

3k3

p

330k

3268 3270 3273 3293

5kl 270R 3k6 4k7

p s p p

3296 3300

3k6 300R

3300

PREL

3363

3k6

p

51k

1.07

3484

5kl

p

llk

1.46

3368

68R

s

3k3

1.02

3486

3k6

p

ll0k

1.03

3375

75R

s

3k3

1.02

3488

3k9

p

33k

1.12

3377

4k7

p

12k

1.39

3495

3k6

p

120k

1.03

3377

5kl

p

10k

1.51

3500

200R

s

3k3

1.06

3380

680R

s

2k7

1.25

3500

lkl

s

2k4

1.46

3382 3383

82R 3k6

s p

3k3 56k

1.02 1.06

3500 3500

lk3 lk5

s s

2k2 2k

1.59 1.75

3389

4k3

p

16k

1.27

3503

3k6

p

130k

1.03

Table 6.3 E24 equivalent resistances RE

I R1

s/p

R2

PREL

RE

R1

s/p

R2

PREL

3639 3643

39R 43R

s s

3k6 3k6

1.01 1.01

3646

3k9

p

56k

47R 4k3

s p

3k6 24k

1.07 1.01 1.18 1.01 1.02 1.11 1.02 1.39 1.02 1.06 1.02 1.23 1.02 1.06 1.68 1.12 1.03 1.03 1.37 1.54 1.68 1.05 1.16 1.03 1.51 1.83 1.03 1.05 1.26 1.04 1.13 1.04 1.04 1.25 2

3510 3516 3519

510R

s

3k

1.17

3k6 3k9

p p

150k 36k

1.02 1.11

3520

220R 820R 3k6 3k6

s s p p

3k3

1.07

2k7 160k 180k

1.3

3647 3647

6k2 3k6 4k3

p p p

1.02 1.02 1.76

3651 3656 3660

51R 56R 360R

s s s

3k6 3k6 3k3

1.02

3662 3663

62R 5kl

s p

3k6 13k

240R 3k6

s p

3668

68R

s

3k6

3669

3k9

p

62k

3547

3k9 3k6

p p

3553 3557 3560 3561 3564

3k6 3k6 560R 3k6 3k6

p p s p p

3566 3570

6k8 270R 3k9 4k7 5kl 5k6 4k3 300R lk2 lk6 lk8

p s p p p p p s s s s

3520 3521 3529 3531 3536 3539 3540 3542 3545

3576 3579 93579 3590 3597 3600 3600 3600 3600

8k2 200k 20k 3k3

1.22 1.07

220k 39k

1.02 1.1

240k

1.02 1.01 1.01 1.19 1.01 1.01 1.91 1.08

270k 300k 3k 330k 360k 7k5 3k3 43k 15k 12k 10k 22k 3k3 2k4 2k lk8

1.09 1.31 1.43 1.56 1.2 1.09 1.5 1.8 2 1.08 1.34

87

3675

75R

s

3k6

3680

680R

s

3k

3682 3688 3688 3690 3691 3700 3700

82R 3k9 6k2 390R 91R 100R lk

s p p s s s s

3k6 68k 9kl 3k3 3k6 3k6 2k7

3700 3700 3707 3709 3710 3711 3717 3720 3723

lk3 lk5 3k9 4k3 ll0R 5k6 6k8 120R 3k9

s s p p s p p s p

2k4 2k2 75k 27k 3k6 llk 8k2 3k6 82k

3727 3730

4k7 130R

p s

18k 3k6

3601 3610

3k9

p

47k

910R

s

3620

620R

s

2k7 3k

430R

s

3k3

3k9

p

51k

1.21 1.08

3730

3623

3740

3k9

p

91k

3630

330R

s

3k3

1.1

3750

150R

s

3k6

3633

4k7

p

16k

3750

750R

s

3k

3636

36R

s

3k6

1.29 1.01

3750

7k5

p

7k5

88

Electronics Calculations Data Handbook

RE

R1

3k9 160R 4k3 3k9 470R 3k9 180R 3k9 3800 200R 3800 lkl 3800 lk6 3800 lk8 3801 3k9 3804 4k3 3806 4k7 3806 5kl 3807 3k9 3810 510R 3817 3k9 3818 5k6 3820 220R 3820 820R 3825 3k9 3827 6k2 3832 3k9 3838 3k9 38413 240R 3841 4k3 3844 3k9 3850 3k9 3854 3k9 3858 3k9 3860 560R 3861 3k9 3867 5kl 3870 270R 3873 4k3 3754 3760 3761 3766 3770 3777 3780 3786

s/p

R2

RE

R1

s/p

R2

p s p p s p s p s s s s p p p p p s p p s s p p p p s p p p p p s p p s p

100k 3k6 30k ll0k 3k3 120k 3k6 130k 3k6 2k7

3873

4k7 6k8 300R lk2 lk5 4k3 910R 5k6 7k5 620R 330R 4k7 39R 4k3 43R 47R 51R 56R 360R 62R 6k2 4k3 68R 5kl 75R 680R 82R 390R 91R 4k3 100R lk lk3 lk6 lk8 2k 4k7

P P

22k 9kl 3k6 2k7 2k4 43k 3k 13k

2k2 2k 150k 33k 20k 15k 160k 3k3 180k 12k 3k6 3k 200k 10k 220k 240k 3k6 36k 270k 300k 330k 360k 3k3 390k 16k 3k6 39k

3892 3900 3900 3900 3909 3910 3914

1.01 1.3,~ 1.01 1.11

3917 3920 3930 3930 3939 3940 3943 3947 3951 3956 3960 3962 3965 3966 3968 3974 3975 3980 3982 3990 3991 3993 4000 4000 4000 4000 4000 4O00 4003

s S S

P S

P P S S

P S

s s

P P s

P s s s s s

P S S S S s S

P

8k2 3k3 3k6 24k 3k9 47k 3k9 3k9 3k9 3k9 3k6 3k9 llk 51k 3k9 18k 3k9 3k3 3k9 3k6 3k9 56k 3k9 3k 2k7 2k4 2k2 2k 27k

PREL

1.21 1.75 1.08 1.44 1.63 1.1 1.3 1.43 1.91 1.19 1.09 1.2 1.01 1.09 1.01 1.01 1.01 1.01 1.1 1.02 1.56 1.08 1.02 1.28 1.02 1.21 1.02 1.11 1.02 1.08 1.03 1.33 1.48 1.67 1.82 2 1.17

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

PRELI

4010 4020

ll0R 120R

s s

3k9 3k9

1.03 1.03

4021

4k3

p

62k

4030 4030

130R 430R

s s

3k9 3k6

4044 4048 4050 4050 4060 4063

4k3 6k8 150R 750R 160R 4k7

p p s s s p

4064

5kl

4067 4070

89

RE

R1

s/p

R2

PREL

4180 4187

4k3 4k3

p p

150k 160k

1.03 1.03

1.07

4195

4k7

p

39k

1.12

1.03 1.12

4198 4200

6k2 300R

p s

13k 3k9

1.48 1.08

68k 10k 3k9 3k3 3k9 30k

1.06 1.68 1.04 1.23 1.04 1.16

4200 4200 4200 4200 4200 4202

lk2 lk5 lk8 2k 4k3 6k8

s s s s p p

3k 2k7 2k4 2k2 180k llk

1.4 1.56 1.75 1.91 1.02 1.62

p

20k

1.26

4206

5kl

p

24k

1.21

4k3 470R

p s

75k 3k6

1.06 1.13

4209 4210

4k3 910R

p s

200k 3k3

1.02 1.28

4078

5k6

p

15k

1.37

4218

4k3

p

220k

1.02

4080 4086 4088 4100 4100 4100

180R 4k3 6k2 200R lkl 8k2

s p p s s p

3k9 82k 12k 3k9 3k 8k2

1.05 1.05 1.52 1.05 1.37 2

4220 4224 4230 4233 4237 4239

620R 4k3 330R 4k3 4k7 4k3

s p s p p p

3k6 240k 3k9 270k 43k 300k

1.17 1.02 1.08 1.02 1.11 1.01

4106 4110 4111 4114

4k3 510R 7k5 4k7

p s p p

91k 3k6 9kl 33k

1.05 1.14 1.82 1.14

4245 4249 4253 4257

4k3 4k3 4k3 4k3

p p p p

330k 360k 390k 430k

1.01 1.01 1.01 1.01

4120 4120 4123 4138 4140

220R 820R 4k3 4k3 240R

s s p p s

3k9 3k3 100k ll0k 3k9

1.06 1.25 1.04 1.04 1.06

4260 4271 4273 4280 4286

360R 5k6 4k7 680R 7k5

s p p s p

3k9 18k 47k 3k6 10k

1.09 1.31 1.1 1.19 1.75

4140 4148

5kl 5k6

p p

22k 16k

1.23 1.35

4290 4290

390R 5kl

s p

3k9 27k

1.1 1.19

4151

4k3

p

120k

1.04

4300

lk

s

3k3

1.3

4157

4k7

p

36k

1.13

4300

lk3

s

3k

1.43

4160

560R

s

3k6

1.16

4300

lk6

s

2k7

1.59

4162

4k3

p

130k

1.03

4303

4k7

p

51k

1.09

4170

270R

s

3k9

1.07

4313

8k2

p

9kl

1.9

90

Electronics Calculations Data Handbook

RE

R1

s/p

R2

PREL

4330

430R

s

3k9

1.11

4336 4340 4343 4347 4350 4351

4k7 6k8 43R 47R 750R 51R

p p s s s s

56k 12k 4k3 4k3 3k6 4k3

4356

56R

s

4359 4362 4368

5kl 62R 68R

4369

R1

s/p

R2

PREL

4467

5kl

p

36k

1.14

1.08 1.57 1.01 1.01 1.21 1.01

4468 4469 4480 4489 4500 4500

6k2 4k7 180R 4k7 200R lk2

p p s p s s

16k 91k 4k3 100k 4k3 3k3

1.39 1.05 1.04 1.05 1.05 1.36

4k3

1.01

4500

lk5

s

3k

1.5

p s s

30k 4k3 4k3

1.17 1.01 1.02

4500 4505 4507

lk8 8k2 4k7

s p p

2k7 10k ll0k

1.67 1.82 1.04

4k7

p

62k

1.08

4510

910R

s

3k6

1.25

4370 4375 4375 4382 4387 4391 4396 4400 4400

470R 75R 5k6 82R 6k2 91R 4k7 100R lkl

s s p s p s p s s

3k9 4k3 20k 4k3 15k 4k3 68k 4k3 3k3

1.12 1.02 1.28 1.02 1.41 1.02 1.07 1.02 1.33

4510 4520 4520 4523 4536 4540 4541 4550 4557

5kl 220R 620R 4k7 4k7 240R 5k6 9kl 4k7

p s s p p s p p p

39k 4k3 3k9 120k 130k 4k3 24k 9kl 150k

1.13 1.05 1.16 1.04 1.04 1.06 1.23 2 1.03

4400 4400 4410 4410 4417 4420

2k 2k2 ll0R 510R 5kl 120R

s s s s p s

2k4 2k2 4k3 3k9 33k 4k3

1.83 2 1.03 1.13 1.15 1.03

4559 4566 4570 4580 4580 4592

5kl 4k7 270R 680R 4k7 4k7

p p s s p p

43k 160k 4k3 3k9 180k 200k

1.12 1.03 1.06 1.17 1.03 1.02

4420 4423

820R 4k7

s p

3k6 75k

i 1.23 1.06

4600 4600

300R lk

s s

4k3 3k6

1.07 1.28

4430

130R

s

4k3

1.03

4600

lk3

s

3k3

1.39

4445

4k7

p

82k

1.06

4600

lk6

s

3k

1.53

4450

150R

s

4k3

1.03

4600

2k2

s

2k4

1.92

4459

7k5

p

llk

1.68

4601

5kl

p

47k

1.11

4460 4460 4464

160R 560R 5k6

s s p

4k3 3k9 22k

1.04 1.14 1.25

4602 4610 4612

4k7 4k7 6k2

p p p

220k 240k 18k

1.02 1.02 1.34

4465

6k8

p

13k

1.52

4615

7k5

p

12k

1.63

!

~ RE

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

PREL

4791 4800

91R 100R

s s

4k7 4k7

1.02 1.02

4k3

1.02 1.02 1.08

4800

lk2

s

3k6

1.33

330k 51k

1.01 1.1

4800 4800

lk5 lk8

s s

3k3 3k

1.45 1.6

p p

27k 360k

4800 4801

4k7 750R 4k7

p p s p

390k 430k 3k9 470k

4660

360R

s

4k3

1.21 1.01 1.01 1.01 1.19 1.01 1.08

2k4 5kl ll0R 510R 910R 120R 5kl

s p s s s s p

2k4 82k 4k7 4k3 3k9 4k7 91k

2 1.06 1.02 1.12 1.23 1.03 1.06

4674 4679

5kl 6k8

p p

56k 15k

4690

390R 8k2 lkl

4k3 llk

4830 4837 4846

4698 4700

s p

1.09 1.45 1.09 1.75

4850

4700 4712 4719

2k 5kl 5k6

4720 4730 4733 4744 4747

820R 430R

s s p p s

3k6 2k7 62k 30k 3k9

4853 4860 4860 4871 4874

s

4k3

1.31 1.74 1.08 1.19 1.21 1.1

p p s

20k 68k 4k7

56R 7k5 62R 9kl

s s p s p

4k7 4k7 13k 4k7 10k

4770

68R 470R

s s

4k7 4k3

4772 4775

6k8 75R

p s

16k 4k7

4775

5kl

p

75k

1.02 1.07

4782 4788

82R 5k6

s

4k7

1.02

p

33k

1.17

RE

R1

s/p

R2

4620 4628

4k7 4k7

p p

270k 300k

4630

330R

s

4634 4636

4k7 5kl

p p

4638 4639 4644

5k6 4k7 4k7

4649 4650 4653

4751 4756 4756 4762 4764 4768

6k2 5kl 47R 51R

PREL

91

4810 4810 4810 4820 4829

130R

s

4k7

1.03

6k2 5k6 150R

p p s

22k 36k 4k7

1.28 1.16 1.03

5kl 160R 560R

p s s

100k 4k7 4k3

1.05 1.03 1.13

8k2 5kl

p p

12k ll0k

1.68 1.05

4880 4892 4897 4900

180R 5kl 5k6 200R

s p p s

4k7 120k 39k 4k7

1.04 1.04 1.14 1.04

4900 4900 4900 4900 4907

lk lk3 lk6 2k2 5kl

s s s s p

3k9 3k6 3k3 2k7 130k

1.26 1.36 1.48 1.81 1.04

1.01

4920

1.11 1.43

4920 4927 4932

220R 620R

s s

4k7 4k3

1.05 1.14

6k2 5kl

p p

24k 150k

1.26 1.03

6k8

p

18k

1.38

4940

240R

s

4k7

1.05

4942

5kl

p

160k

1.03

1.31 1.08 1.01 1.01 1.01 1.58 1.01 1.91

4935

92

Electronics Calculations Data Handbook

RE

R1

s/p

R2

4955 4959 4970 4973 4980 4980 4984 4994 5000 5000 5000 5000 5000 5004 5005 5015 5022 5O28 5029 5O30 5034 5040 5042 5045 5046 5050 5050 5060 5075 5090 5091 5100 5100 5100 5100 5106 5120

5k6 5kl 270R 5kl 680R 9kl 5kl 5kl 300R lkl 2k 7k5 10k 5k6 5kl 5kl 5kl 8k2 5kl 330R 5kl 5kl 6k2 5kl 5k6 750R 5kl 360R 6k8 390R 5k6 lk2 lk5 lk8 2k4 7k5 820R

p p s p s p p p s s s p p p p p p p p s p p p p p s p s p s p s s s s p s

43k 180k 4k7 200k 4k3 llk 220k 240k 4k7 3k9 3k 15k 10k 47k 270k 300k 330k 13k 360k 4k7 390k 430k 27k 470k 51k 4k3 510k 4k7 20k 4k7 56k 3k9 3k6 3k3 2k7 16k 4k3

PREL

1.13 1.03 1.06 1.03 1.16 1.83 1.02 1.02 1.06 1.28 1.67 1.5 2 1.12 1.02 1.02 1.02 1.63 1.01 1.07 1.01 1.01 1.23 1.01 1.11 1.17 1.01 1.08 1.34 1.08 1.1 1.31 1.42 1.55 1.89 1.47 1.19

RE

R1

s/p

R2

5130 5136 5138 5151 5156 5162 5168 5170 5174 5175 5175 5182 5191 5194 52OO 5200 520O 52OO 5210 5210 5210 5211 5219 5220 5230 5238 5242 5250 5260 5260 5275 5280 5289 5294 5299 5300 5300

430R 5k6 6k2 51R 56R 62R 68R 470R 5k6 75R 9kl 82R 91R 6k8 100R lk3 lk6 2k2 ll0R 510R 910R 5k6 6k2 120R 130R 10k 5k6 150R 160R 560R 5k6 180R

S

4k7 62k 30k 5kl 5kl 5kl 5kl 4k7 68k 5kl 12k 5kl 5kl 22k 5kl 3k9 3k6 3k 5kl 4k7 4k3 75k 33k 5kl 5kl llk 82k 5kl 5kl 4k7 91k 5kl 36k 18k 24k 5kl 4k3

6k2 7k5 6k8 200R lk

P P S S s s S

P S

P s s

P s s S S s s s

P P s s

P P S s S

P S

P P P S S

PREL

1.09 1.09 1.21 1.01 1.01 1.01 1.01 1.1 1.08 1.01 1.76 1.02 1.02 1.31 1.02 1.33 1.44 1.73 1.02 1.11 1.21 1.07 1.19 1.02 1.03 1.91 1.07 1.03 1.03 1.12 1.06 1.04 1.17 1.42 1.28 1.04 1.23

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

PREL

1.61 1.55 1.06

5500 5500 5500

lk2 lk6

s s

4k3 3k9

1.28 1.41

5kl

1.04

5500

2k2 Ilk

s p

3k3 Ilk

s p

4k7 ll0k

1.13 1.05

5507 5514 5520

RE

R1

s/p

R2

5300 5302 5303

2k 8k2 5k6

s p p

3k3 15k 100k

5320

220R

s

5320

620R 5k6

5329 5340

PREL

93

1.67

5k6

p

330k

2 1.02

5k6 820R 5k6

p s p

360k 4k7 390k

1.02 1.17 1.01

5350 5350 5353 5369 5370

240R 5k6

s p

5kl 120k

1.05 1.05

6k2 9kl 5k6 270R

p p p s

39k 13k 130k 5kl

1.16 1.7 1.04 1.05

5521 5528 5528 5530 5534

5k6

p

430k

1.01

6k2 430R 5k6

p s p

51k 5kl 470k

1.12 1.08 1.01

5380 5398 5400 5400

680R 5k6 300R lkl

s p s s

4k7 150k 5kl 4k3

1.14 1.04 1.06 1.26

5539 5543 5545 5570

5k6 6k8 5k6 470R

p p p s

510k 30k 560k 5kl

1.01 1.23 1.01 1.09

5400

lk5

s

3k9

1.38

5582

6k2

p

56k

1.11

5400 5400

lk8 2k4

s s

3k6 3k

1.5 1.8

5593 5600

7k5 lk3

p s

22k 4k3

1.34 1.3

5400 5411 5419

2k7 5k6 6k2

s p p

2k7 160k 43k

2 1.03 1.14

5600 5610 5610

2k 510R 910R

s s s

3k6 5kl 4k7

1.56 1.1 1.19

5421 5430 5431 5432 5447 5450 5455 5455

8k2 330R 5k6 6k8 5k6 750R 7k5 10k

p s p p p s p p

16k 5kl 180k 27k 200k 4k7 20k 12k

1.51 1.06 1.03 1.25 1.03 1.16 1.38 1.83

5634 5636 5638 5652 5656 5660 5662 5664

8k2 6k2 6k8 10k 56R 560R 62R 9kl

p p p p s s s p

18k 62k 33k 13k 5k6 5kl 5k6 15k

1.46 1.1 1.21 1.77 1.01 1.11 1.01 1.61

5460

360R

s

5kl

1.07

5668

68R

s

5k6

1.01

5461

5k6

p

220k

1.03

5675

75R

s

5k6

1.01

5472 5477

5k6 6k2

p p

240k 47k

1.02 1.13

5682 5682

82R 6k2

s p

5k6 68k

1.01 1.09

5486

5k6

p

270k

1.02

5691

91R

s

5k6

1.02

5490

390R

s

5kl

1.08

5700

100R

s

5k6

1.02

5497

5k6

p

300k

1.02

5700

lk

s

4k7

1.21

94

Electronics Calculations Data Handbook

RE

R1

s/p

R2

PREL

5700

lk8

s

3k9

1.46

RE

RI

s/p

5918

6k2

p

130k

s s

5kl 5k6 47k

5700 5700 5710

2k4 2k7 ll0R

s s s

3k3 3k 5k6

1.73 1.9 1.02

5920 5930 5941

820R 330R 6k8

p

5714

7k5

p

24k

1.31

5954

5720 5720 5720 5727

120R 620R 6k8 6k2

s s p p

5k6 5kl 36k 75k

1.02 1.12 1.19 1.08

5958 5960 5969 5974

5730 5739 5750

130R llk 150R

s p s

5k6 12k 5k6

1.02 1.92 1.03

5990 5994 6000

6k2 llk 360R 6k2 8k2 390R

p p s p p s

6k2 lk3

p s s

R2

150k 13k 5k6 160k 22k 5k6 180k 4k7

PREL 1.05 1.16 1.06 1.14 1.04 1.85 1.06 1.04 1.37 1.07 1.03

1.28

3k6 3k3

1.67

3k 51k 30k 15k 12k 5kl 200k 5k6 220k 240k 18k

2 1.13

5760

160R

s

5k6

1.03

6000

2k4

5764

6k2

p

82k

1.08

6000

5780 5780 5790 5800 5800

180R 680R 6k8 200R lkl

s s p s s

5k6 5kl 39k 5k6 4k7

1.03 1.13 1.17 1.04 1.23

6000 6000 6000 6000 6000

5800 5800 5801 5805 5816 5820 5838 5840 5850 5869

lk5 2k2 9kl 6k2 8k2 220R 6k2 240R 750R 6k2

s s p p p s p s s p

4k3 3k6 16k 91k 20k 5k6 100k 5k6 5kl ll0k

1.35 1.61 1.57 1.07 1.41 1.04 1.06 1.04 1.15 1.06

6010 6014 6030 6030 6044 6044 6061 6064 6070 16074

2k7 3k 6k8 7k5 10k 12k 910R 6k2 430R 6k2 6k2 9kl

s s p p p p s p s p p p

6k2 6k8 470R

p p s

270k 56k 5k6

1.02 1.12 1.08

s p p

5k6 27k 43k

1.05 1.28 1.16

6086 6095 6100

p p p s

1.02

270R 7k5 6k8

96k2 6k2 6k2 lk

300k

5870 5870 5871

330k 360k

1.02

5kl

1.2

5895

6k2

p

120k

1.05

6100

lk8

s

4k3

1.42

5900

300R

s

5k6

1.05

6100

2k2

s

3k9

1.56

p s

390k 5k6

1.02 1.09

p

33k

1.23

5900 5900

lk2 lk6

s s

4k7 4k3

1.26 1.37

6103 6110

6k2 510R

5900

2k

s

3k9

1.51

6111

7k5

1.82

1.25 1.67 2 1.18 1.03 1.08 1.03 1.03 1.51

1.02

Table 6.3 E24 equivalent resistances RE

R1

6112 6112 6119 6126 6128 6132 6139 6154 6160 6182 6200 6200 6207 6220 6235 6240 6254 6262 6268 6275 6279 6280 6282 6290 6290 6291 6300 6300 6300 6300 6300 6300 6300 6310 6320 6327 6330

6k2 8k2 6k2 6k2 6k8 6k2 6k2 10k 560R 6k8 lkl lk5 7k5 620R 6k8 12k 9kl 62R 68R 75R 6k8 680R 82R 7k5 8k2 91R 100R lk2 lk6 2k 2k4 2k7 3k ll0R 120R 6k8 130R

s/p

R2 430k 24k 470k 510k 62k 560k 620k 16k 5k6 68k 5kl 4k7 36k 5k6 75k 13k 20k 6k2 6k2 6k2 82k 5k6 6k2 39k 27k 6k2 6k2 5kl 4k7 4k3 3k9 3k6 3k3 6k2 6k2 91k 6k2

PREL 1.01 1.34 1.01 1.01 1.11 1.01 1.01 1.63 1.1 1.1 1.22 1.32 1.21 1.11 1.09 1.92 1.46 1.01 1.01 1.01 1.08 1.12 1.01 1.19 1.3 1.01 1.02 1.24 1.34 1.47 1.62 1.75 1.91 1.02 1.02 1.07 1.02

RE

R1

s/p

R2

llk 150R 750R 160R 6k8 180R 7k5 200R lk3 6k8 220R 820R 10k 6k8 9kl 240R 8k2 6k8 7k5 270R 300R lk8 2k2 13k 6k8 910R llk 6k8 330R 7k5 6k8 360R 8k2 6k8 390R 6k8 9kl

p s s s p s p s s p s s p p p s p p p s s s s p p s p p s p p s p p s p p

15k 6k2 5k6 6k2 100k 6k2 43k 6k2 5kl ll0k 6k2 5k6 18k 120k 22k 6k2 30k 130k 47k 6k2 6k2 4k7 4k3 13k 150k 5k6 16k 160k 6k2 51k 180k 6k2 33k 200k 6k2 220k 24k

95

PREL 1.73 1.02 1.13 1.03 1.07 1.03 1.17 1.03 1.25 1.06 1.04 1.15 1.56 1.06 1.41 1.04 1.27 1.05 1.16 1.04 1.05 1.38 1.51 2 1.05 1.16 1.69 1.04 1.05 1.15 1.04 1.06 1.25 1.03 1.06 1.03 1.38

96

Electronics Calculations Data Handbook

[RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

lk

s

5k6

1.18

6857

12k

p

16k

6600

lk5

s

6600

2k7

s

5kl

1.29

68681 68R

s

6k8

3k9

1.69

6872

7k5

p

6600

3k

82k

s

3k6

1.83

6875

75R

s

6600 6613 6614 6630 6633 6649

6k8

3k3 6k8 7k5 430R 6k8 6k8

s p p s p p

3k3 240k 56k 6k2 270k 300k

2 1.03 1.13 1.07 1.03 1.02

6875 6880 6882 6887 6891 6900

10k 680R 82R 8k2 91R 100R

p s s p s s

22k 6k2 6k8 43k 6k8 6k8

6663 6667 6667

6k8 10k 12k

p p p

330k 20k 15k

1.02 1.5 1.8

6900 6900 6900

lk3 lk8 2k2

s s s

5k6 5kl 4k7

6670

470R

s

6k2

1.08

6900

3k

s

3k9

6674

6k8

p

360k

1.02

6900

3k3

s

3k6

6679 6683 6691 6694 6700 6700 6700 6700 6703 6710 6711 6718

8k2 6k8 7k5 6k8 lkl lk6 2k 2k4 6k8 510R 6k8 6k8

p p p p s s s s p s p p

36k 390k 62k 430k 5k6 5kl 4k7 4k3 470k 6k2 510k 560k

1.23 1.02 1.12 1.02 1.2 1.31 1.43 1.56 1.01 1.08 1.01 1.01

6910 6920 6929 6930 6950 6950 6960 6964 6977 6980 6982 6982

ll0R 120R 7k5 130R 150R 750R 160R 13k 7k5 180R 8k2 9kl

s s p s s s s p p s p p

6k8 6k8 91k 6k8 6k8 6k2 6k8 15k 100k 6k8 47k 30k

6726

6k8

p

620k

1.01

7000

200R

s

6k8

6733

6k8

p

680k

1.01

7000

2k7

s

4k3

6755

7k5

p

68k

1.11

7020

220R

s

6k8

6760 6775 6800

560R 8k2 lk2

s p s

6k2 39k 5k6

1.09 1.21 1.21

7020 7021 7040

820R 7k5 240R

s p s

6k2 ll0k 6k8

6806

9kl

p

27k

1.34

7059

7k5

p

120k

6818

7k5

p

75k

1.1

7059

10k

p

24k

6820 6828

620R llk

s p

6k2 18k

1.1 1.61

7064 8k2 7070i 270R

p s

51k 6k8

6600

J

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

7091 7097 7100 7100

7k5 llk 300R lk5

p p s s

130k 20k 6k8 5k6

7100

2k

s

5kl

97

[ PREL

RE

R1

s/p

R2

1.06 1.55 1.04

7333 7347 7358

llk 7k5 7k5

p p p

22k 360k 390k

7360 7371

560R 7k5

s p

6k8 430k

7378

9kl

p

39k

1.23

PREL

1.5 1.02 1.02 1.08

7100

2k4

s

4k7

1.27 1.39 1.51

7110 7130

910R 330R

s s

6k2 6k8

1.15 1.05

7382 7391

7k5 7k5

p p

470k 510k

1.02 1.01

7133 7143 7153 7160 7164

9kl 7k5

p p

33k 150k

p s p p

56k 6k8 160k 16k

7392 7400 7400 7400 7401

8k2 lk2 lk8 2k7 7k5

p s s s p

75k 6k2 5k6 4k7 560k

1.11

8k2 360R 7k5 13k

7200 7200 7200

390R lk lk6 3k3

s s s s

6k8 6k2 5k6 3k9

1.28 1.05 1.15 1.05 1.05 1.81 1.06 1.16

7410 7418 7420 7426

7k5 7k5 620R 7k5

p p s p

620k 680k 6k8 750k

1.32 1.57 1.01 1.01 1.01 1.09 1.01

7200

3k6

s

3k6

7455 7480

8k2 680R

p s

82k 6k8

1.1 1.1

7200 7200 7229 7230 7242 7253 7264 7270 7273 7297 7297

7k5 12k 7k5

p p p

180k 18k 200k

2 1.04 1.67 1.04

7500 7500 7500

lk3 2k4 3k6

s s s

6k2 5kl 3k9

1.21 1.47

430R 8k2 7k5 9kl 470R 7k5 7k5 10k

s p p p s p p p

6k8 62k 220k 36k 6k8 240k 270k 27k

1.06 1.13 1.03 1.25 1.07 1.03 1.03 1.37

7500 7500 7500 7511 7522 7543 7548 7550

10k 12k 15k 9kl 8k2 llk 13k 750R

p p p p p p p s

30k 20k 15k 43k 91k 24k 18k 6k8

2 1.21 1.09 1.46 1.72 1.11

7300

lkl

s

6k2

1.18

7575

75R

s

7k5

1.01

7300

2k2

s

5kl

1.43

7579

8k2

p

100k

1.08

7300 7310

3k

s

4k3

1.7

s p

6k8 300k

1.08 1.03

8k2

p

68k

1.12

7582 7591 7600 7600

82R 91R 100R 2k

s s s s

7k5 7k5 7k5 5k6

1.01

510R 7k5 7k5

p

330k

1.02

7600

3k3

s

4k3

1.77

7172 7190

7317 7318 7333

1.29 1.85

1.02

1.19

1.92 1.33 1.6

1.01 1.01 1.36

98

Electronics Calculations Data Handbook

RE

R1

s/p

R2

PREL

RE

R1

s/p

R2

PREL

....

7610 762O 7620 7624 7630 7631 7650 7660 7674 7676 7680 7700 7700 7700 7710 7713 7720 7722 7740 7742 7765 7770 7775 7800 7800 7800 7800 7800 7800 7800 7816 7826 7828 7830 7843 7860 7877

ll0R 120R 820R 9kl 130R 8k2 150R 160R 10k 8k2 180R 200R lk5 3k 910R 8k2

s s s p s p s s p p s s s s s p

7k5 7k5 6k8 47k 7k5 ll0k 7k5 7k5 33k 120k 7k5 7k5 6k2 4k7 6k8 130k

1.01 1.02 1.12 1.19 1.02 1.07 1.02 1.02 1.3 1.07 1.02 1.03 1.24 1.64 1.13 1.06

7879 7890 7900 7900 7905 7929 7930 7935 7958 7959 7970 7982 8000 8000 8000 8000

13k 390R lkl 3k6 8k2 8k2 430R 9kl 8k2 10k 470R 8k2 lk2 lk8 2k4 3k3

20k 7k5 6k8 4k3 220k 240k 7k5 62k 270k 39k 7k5 300k 6k8 6k2 5k6 4k7

220R 9kl 240R 15k 12k 270R 8k2 300R lk lk6 2k2 2k7 3k9 8k2 llk 10k 9kl 330R 8k2 360R 8k2

s p s p p s p s s s s s s p p p p s p s p

7k5 51k 7k5 16k 22k 7k5 150k 7k5 6k8 6k2 5k6 5kl 3k9 160k 27k 36k 56k 7k5 180k 7k5 200k

1.03 1.18 1.03 1.94 1.55 1.04 1.05 1.04 1.15 1.26 1.39 1.53 2 1.05 1.41 1.28 1.16 1.04 1.05 1.05 1.04

8000 8000 8001 8010 8017 8026 8031 8047 8049 8059 8060 8070 8082 8093 8100 8100 8102 8111 8113 8115 8119

12k 16k 8k2 510R 8k2 9kl 8k2 8k2 llk 8k2 560R 8k2 8k2 8k2 lk3 3k 8k2 8k2 10k 9kl 8k2

24k 16k 330k 7k5 360k 68k 390k 430k 30k 470k 7k5 510k 560k 620k 6k8 5kl 680k 750k 43k 75k 820k ,

1.65 1.05 1.16 1.84 1.04 1.03 1.06 1.15 1.03 1.26 1.06 1.03 1.18 1.29 1.43 1.7 1.5 2 1.02 1.07 1.02 1.13 1.02 1.02 1.37 1.02 1.07 1.02 1.01 1.01 1.19 1.59 1.01 1.01 1.23 1.12 1.01

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

PREL

8120 8171 8180

620R 13k 680R

s p s

7k5 22k 7k5

8182

15k

p

8191

9kl

8200 8200

2k 3k9

8246

99

RE

R1

s/p

R2

PREL

1.08 1.59 1.09

8459 8470 8471

9kl 270R 16k

p s p

120k 8k2 18k

1.08 1.03 1.89

18k

1.83

8485

10k

p

56k

1.18

p

82k

1.11

8500

300R

s

8k2

1.04

s s

6k2 4k3

1.32 1.91

8500 8505

lk 9kl

s p

7k5 130k

1.13 1.07

10k

p

47k

1.21

8530

330R

s

8k2

1.04

8250 8250

750R llk

s p

7k5 33k

1.1 1.33

8560 8571

360R 12k

s p

8k2 30k

1.04 1.4

8273 8282

9kl 82R

p s

91k 8k2

1.1 1.01

8571 8580

15k 9kl

p p

20k 150k

1.75 1.06

8291 8300

91R 100R

s s

8k2 8k2

1.01 1.01

8580 8590

llk 390R

p s

39k 8k2

1.28 1.05

8300

lk5

s

6k8

1.22

8600

lkl

s

7k5

1.15

8300

2k7

s

5k6

1.48

8600

lk8

s

6k8

1.26

8300

3k6

s

4k7

1.77

8600

2k4

s

6k2

1.39

8308 8310

12k ll0R

p s

27k 8k2

1.44 1.01

8600 8600

3k 3k9

s s

5k6 4k7

1.54 1.83

8320 8320

120R 820R

s s

8k2 7k5

1.01 1.11

8600 8610

4k3 9kl

s p

4k3 160k

2 1.06

8330 8341 8350 8360 8361 8380 8400 8400 8400

130R 9kl 150R 160R 10k 180R 200R lk6 2k2

s p s s p s s s s

8k2 100k 8k2 8k2 51k 8k2 8k2 6k8 6k2

1.02 1.09 1.02 1.02 1.2 1.02 1.02 1.24 1.35

8611 8630 8662 8670 8700 8700 8704 8710 8718

10k 430R 9kl 470R lk2 3k6 9kl 510R 10k

p s p s s s p s p

62k 8k2 180k 8k2 7k5 5kl 200k 8k2 68k

1.16 1.05 1.05 1.06 1.16 1.71 1.05 1.06 1.15

8400

3k3

s

5kl

1.65

8739

9kl

p

220k

1.04

8405

9kl

p

ll0k

1.08

8759

llk

p

43k

1.26

8410 8420

910R 220R

s s

7k5 8k2

1.12 1.03

8760 8768

560R 9kl

s p

8k2 240k

1.07 1.04

8426 8432

llk 13k

p p

36k 24k

1.31 1.54

8775 8800

13k lk3

p s

27k 7k5

1.48 1.17

8440

240R

s

8k2

1.03

8800

2k

s

6k8

1.29

100

Electronics Calculations Data Handbook RE

R1

s/p

R2

PREL

1.36

9110

910R

s

8k2

1.11

270k

1.03

9167

10k

p

ll0k

8k2 75k 300k 330k 360k 8k2 20k 390k 6k2 5k6 430k 82k

1.08 1.13 1.03 1.03 1.03 1.08 1.8 1.02 1.44 1.59 1.02 1.12

9176 9191 9194 9200 9200 9200 9200 9200 9210 9220 9230 9231

12k 91R llk 100R lk 2k4 3k 3k6 ll0R 120R 130R 10k

p s p s s s s s s s s p

39k 9kl 56k 9kl 8k2 6k8 6k2 5k6 9kl 9kl 9kl 120k

1.09 1.31 1.01

p p p p s p p p p s s s s p p p

47k 22k 470k 510k 8k2 560k 620k 680k 750k 7k5 6k8 5kl 4k7 820k 36k 18k

1.23 1.68 1.02 1.02 1.09 1.02 1.01 1.01 1.01 1.2 1.32 1.76 1.91 1.01 1.33 2

9kl 10k

p p

910k 91k

1.01 1.11

820R llk 13k 10k lk6

s p p p s

8k2 51k 30k 100k 7k5

1.1 1.22 1.43 1.1 1.21

9231 9250 9260 9263 9280 9286 9300 9300 9300 9320 9326 9340 9342 9370 9375 9382 9400 9400 9400 9400 9412 9430 9460

15k 150R 160R 16k 180R 10k 200R lkl lk8 220R 13k 240R llk 270R 10k 12k 300R lk2 4k3 4k7 10k 330R 360R

p s s p s p s s s s p s p s p p s s s s p s s

24k 9kl 9kl 22k 9kl 130k 9kl 8k2 7k5 9kl 33k 9kl 62k 9kl 150k 43k 9kl 8k2 5kl 4k7 160k 9kl 9kl

RE

R1

s/p

R2

I PREL

8800

12k

p

33k

8803

9kl

p

8820 8824 8832 8856 8876 8880 8889 8893 8900 8900 8911 8913

620R 10k 9kl 9kl 9kl 680R 16k 9kl 2k7 3k3 9kl 10k

s p p p p s p p s s p p

8914 8919 8927 ! 8940 8950 8954 8968 8980 8991 9000 9000 9000 9000! 9000 9000 9000

llk 15k 9kl 9kl 750R 9kl 9kl 9kl 9kl lk5 2k2 3k9 4k3 9kl 12k 18k

9010 9010 9020 9048 9070 9091 9100

1.2 1.01 1.12 1.35 1.48 1.64 1.01 1.01 1.01 1.08 1.63 1.02 1.02 1.73 1.02 1.08 1.02 1.13 1.24 1.02 1.39 1.03 1.18 1.03 1.07 1.28 1.03 1.15 1.84 2 1.06 1.04 1.04

Table 6.3 E24 equivalent resistances RE

R1

s/p

R2

9468 9474 9474 9490

llk 10k 18k

p p p

68k 180k 20k

390R lk3

s s

9kl 8k2

2k 2k7 3k3 3k9 10k 430R 13k 12k 10k 470R llk 10k 16k 510R 10k 15k 560R 10k llk lk5 2k2 10k 12k

s s s s p s p p p s p p p s p p s p p s s p p

7k5 6k8 6k2 5k6 200k 9kl 36k 47k 220k 9kl 75k 240k 24k 9kl 270k 27k 9kl 300k 82k 8k2 7k5 330k 51k

9500 9500 9500 9500 9500 9524 9530 9551 9559 9565 9570 9593 9600 9600 9610 9643 9643 9660 9677 9699 9700 9700 9706 9714

PREL

101

RE

R1

s/p

R2

PREL

1.16 1.06 1.9 1.04 1.16 1.27 1.4 1.53 1.7 1.05 1.05 1.36 1.26 1.05

9720 9730 9750 9750 9773 9780 9792 9800 9800 9800 9800 9808 9814 9825

620R 10k 10k 13k 10k 680R 10k lk6 3k 3k6 4k7 10k llk 10k

s p p p p s p s s s s p p p

9kl 360k 390k 39k 430k 9kl 470k 8k2 6k8 6k2 5kl 510k 91k 560k

1.07 1.03 1.03 1.33 1.02 1.07 1.02 1.2 1.44 1.58 1.92 1.02 1.12 1.02

1.05 1.15 1.04 1.67 1.06 1.04 1.56 1.06 1.03 1.13 1.18 1.29 1.03 1.24

9841 9850 9855 9868 9880 9882 9891 9900 9900 9900 9901 9910 9920 9982

10k 750R 10k 10k 10k 12k 10k 2k4 4k3 18k 10k llk 820R 13k

p s p p p p p s s p p p s p

620k 9kl 680k 750k 820k 56k 910k 7k5 5k6 22k 1M 100k 9kl 43k

1.02 1.08 1.01 1.01 1.01 1.21 1.01 1.32 1.77 1.82 1.01 1.11 1.09 1.3

7

Maximum powers for resistors

Tables 7.1-7.6 show the voltage across or current through standard value resistors which are equivalent to a selection of common rated maximum powers. As discussed in Chapter 3, it is wise to avoid running components continuously at full rated power. A good rule of thumb is not to exceed half of rated power; that is roughly 0.7 times the value of voltage or current presented here.

Table 7.1 Maximum power for resistors up to 0.25 W R

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

0R10

79.4m 794m 86.9m 725m 97.2m 648m 106m 592m l18m 535m 130m 483m 144m 437m 157m 402m 172m 366m 188m 335m 207m 304m 227m 277m 251m 251m 263m 239m 275m 229m 286m 220m 307m 205m 317m 198m

100m 1.00 ll0m 913m 122m 816m 134m 745m 148m 674m 164m 609m 182m 550m 197m 506m 217m 461m 237m 423m 261m 383m 286m 349m 316m 316m 332m 302m 346m 289m 361m 277m 387m 258m 400m 250m

l12m 1.12 122m 1.02 137m 913m 150m 833m 166m 754m 184m 680m 203m 615m 221m 566m 242m 516m 265m 472m 292m 429m 320m 390m 354m 354m 371m 337m 387m 323m 403m 310m 433m 289m 447m 280m

124m 1.24 136m 1.14 152m 1.02 167m 928m 185m 839m 205m 758m 226m 685m 246m 630m 270m 574m 295m 526m 325m 477m 357m 435m 394m 394m 413m 375m 431m 359m 449m 345m 482m 321m 498m 311m

158m 1.58 173m 1.44 194m 1.29 212m 1.18 235m 1.07 260m 962m 287m 870m 312m 801m 343m 729m 374m 668m 412m 606m 453m 552m 500m 500m 524m 477m 548m 456m 570m 439m 612m 408m 632m 395m

0R12 0R15 0R18 0R22 0R27 0R33 0R39 0R47 0R56 0R68 0R82 1R 1R1 1R2 1R3 1R5 1R6

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Electronics Calculations Data Handbook

104 R

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

1R8

337m 187m 355m 177m 372m 169m 389m 162m 412m 153m 435m 145m 456m 138m 476m 132m 496m 127m 520m 121m 544m l16m 567m lllm 594m 106m 625m 101m 655m 96.3m 687m 91.7m 719m 87.7m 757m 83.2m 794m 79.4m

424m 236m 447m 224m 469m 213m 490m 204m 520m 192m 548m 183m 574m 174m 600m 167m 624m 160m 656m 152m 686m 146m 714m 140m 748m 134m 787m 127m 825m 121m 866m l15m 906m ll0m 954m 105m 1.00 100m

474m 264m 500m 250m 524m 238m 548m 228m 581m 215m 612m 204m 642m 195m 671m 186m 698m 179m 733m 170m 766m 163m 798m 157m 837m 149m 880m 142m 922m 136m 968m 129m 1.01 123m 1.07 l17m 1.12 l12m

528m 293m 557m 278m 584m 265m 610m 254m 647m 240m 682m 227m 715m 217m 747m 207m 777m 199m 816m 190m 854m 182m 889m 174m 932m 166m 980m 158m 1.03 151m 1.08 144m 1.13 137m 1.19 131m 1.24 124m

671m 373m 707m 354m 742m 337m 775m 323m 822m 304m 866m 289m 908m 275m 949m 264m 987m 253m 1.04 241m 1.08 231m 1.13 221m 1.18 211m 1.24 201m 1.30 192m 1.37 183m 1.43 175m 1.51 166m 1.58 158m

2R 2R2 2R4 2R7 3R 3R3 3R6 3R9 4R3 4R 7 5R1 5R6 6R2 6R8 7R5 8R2 9R1 10R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.1 Maximum power for resistors up to 0.25 W R

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

llR

832m 75.7m 869m 72.5m 905m 69.6m 972m 64.8m 1.00 62.7m 1.06 59.2m 1.12 56.1m 1.18 53.5m 1.23 51.2m 1.30 48.3m 1.37 45.8m 1.44 43.7m 1.51 41.8m 1.57 40.2m 1.65 38.3m 1.72 36.6m 1.79 35.1m 1.88 33.5m 1.98 31.9m

1.05 95.3m 1.10 91.3m 1.14 87.7m 1.22 81.6m 1.26 79.1m 1.34 74.5m 1.41 70.7m 1.48 67.4m 1.55 64.5m 1.64 60.9m 1.73 57.7m 1.82 55.0m 1.90 52.7m 1.97 50.6m 2.07 48.2m 2.17 46.1m 2.26 44.3m 2.37 42.3m 2.49 40.2m

1.17 107m 1.22 102m 1.27 98.1m 1.37 91.3m 1.41 88.4m 1.50 83.3m 1.58 79.1m 1.66 75.4m 1.73 72.2m 1.84 68.0m 1.94 64.5m 2.03 61.5m 2.12 58.9m 2.21 56.6m 2.32 53.9m 2.42 51.6m 2.52 49.5m 2.65 47.2m 2.78 44.9m

1.31 l19m 1.36 l14m 1.42 109m 1.52 102m 1.57 98.4m 1.67 92.8m 1.76 88.0m 1.85 83.9m 1.93 80.4m 2.05 75.8m 2.16 71.9m 2.26 68.5m 2.36 65.6m 2.46 63.0m 2.58 60.0m 2.70 57.4m 2.81 55.1m 2.95 52.6m 3.10 50.0m

1.66 151m 1.73 144m 1.80 139m 1.94 129m 2.00 125m 2.12 l18m 2.24 l12m 2.35 107m 2.45 102m 2.60 96.2m 2.74 91.3m 2.87 87.0m 3.00 83.3m 3.12 80.1m 3.28 76.2m 3.43 72.9m 3.57 70.0m 3.74 66.8m 3.94 63.5m

12R 13R 15R 16R 18R 20R 22R 24R 27R 30R 33R 36R 39R 43R 47R 51R 56R 62R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

105

Electronics Calculations Data Handbook

106 R

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

68R

2.07 30.4m 2.17 29.0m 2.27 27.7m 2.39 26.3m 2.51 25.1m 2.63 23.9m 2.75 22.9m 2.86 22.0m 3.07 20.5m 3.17 19.8m 3.37 18.7m 3.55 17.7m 3.72 16.9m 3.89 16.2m 4.12 15.3m 4.35 14.5m 4.56 13.8m 4.76 13.2m 4.96 12.7m

2.61 38.3m 2.74 36.5m 2.86 34.9m 3.02 33.1m 3.16 31.6m 3.32 30.2m 3.46 28.9m 3.61 27.7m 3.87 25.8m 4.00 25.0m 4.24 23.6m 4.47 22.4m 4.69 21.3m 4.90 20.4m 5.20 19.2m 5.48 18.3m 5.74 17.4m 6.00 16.7m 6.24 16.0m

2.92 42.9m 3.06 40.8m 3.20 39.0m 3.37 37.1m 3.54 35.4m 3.71 33.7m 3.87 32.3m 4.03 31.0m 4.33 28.9m 4.47 28.0m 4.74 26.4m 5.00 25.0m 5.24 23.8m 5.48 22.8m 5.81 21.5m 6.12 20.4m 6.42 19.5m 6.71 18.6m 6.98 17.9m

3.25 47.7m 3.41 45.5m 3.57 43.5m 3.76 41.3m 3.94 39.4m 4.13 37.5m 4.31 35.9m 4.49 34.5m 4.82 32.1m 4.98 31.1m 5.28 29.3m 5.57 27.8m 5.84 26.5m 6.10 25.4m 6.47 24.0m 6.82 22.7m 7.15 21.7m 7.47 20.7m 7.77 19.9m

4.12 60.6m 4.33 57.7m 4.53 55.2m 4.77 52.4m 5.00 50.0m 5.24 47.7m 5.48 45.6m 5.70 43.9m 6.12 40.8m 6.32 39.5m 6.71 37.3m 7.07 35.4m 7.42 33.7m 7.75 32.3m 8.22 30.4m 8.66 28.9m 9.08 27.5m 9.49 26.4m 9.87 25.3m

75R 82R 91R 100R ll0R 120R 130R 150R 160R 180R 200R 220R 240R 270R 300R 330R 360R 390R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.1 Maximum power for resistors up to 0.25 W R

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

430R

5.20 12.1m 5.44 ll.6m 5.67 ll.lm 5.94 10.6m 6.25 10.1m 6.55 9.63m 6.87 9.17m 7.19 8.77m 7.57 8.32m 7.94 7.94m 8.32 7.57m 8.69 7.25m 9.05 6.96m 9.72 6.48m 10.0 6.27m 10.6 5.92m 11.2 5.61m 11.8 5.35m 12.3 5.12m

6.56 15.2m 6.86 14.6m 7.14 14.0m 7.48 13.4m 7.87 12.7m 8.25 12.1m 8.66 ll.5m 9.06 ll.0m 9.54 10.5m 10.0 10.0m 10.5 9.53m 11.0 9.13m 11.4 8.77 m 12.2 8.16m 12.6 7.91m 13.4 7.45m 14.1 7.07m 14.8 6.74m 15.5 6.45m

7.33 17.0m 7.66 16.3m 7.98 15.7m 8.37 14.9m 8.80 14.2m 9.22 13.6m 9.68 12.9m 10.1 12.3m 10.7 ll.7m 11.2 11.2m 11.7 10.7m 12.2 10.2m 12.7 9.81m 13.7 9.13m 14.1 8.84m 15.0 8.33m 15.8 7.91m 16.6 7.54m 17.3 7.22m

8.16 19.0m 8.54 18.2m 8.89 17.4m 9.32 16.6m 9.80 15.8m 10.3 15.1m 10.8 14.4m 11.3 13.7m 11.9 13.1m 12.4 12.4m 13.1 ll.9m 13.6 ll.4m 14.2 10.9m 15.2 10.2m 15.7 9.84m 16.7 9.28m 17.6 8.80m 18.5 8.39m 19.3 8.04m

10.4 24.1m 10.8 23.1m 11.3 22.1m 11.8 21.1m 12.4 20.1m 13.0 19.2m 13.7 18.3m 14.3 17.5m 15.1 16.6m 15.8 15.8m 16.6 15.1m 17.3 14.4m 18.0 13.9m 19.4 12.9m 20.0 12.5m 21.2 ll.8m 22.4 ll.2m 23.5 10.7m 24.5 10.2m

470R 510R 560R 620R 680R 750R 820R 910R lk lkl lk2 lk3 lk5 lk6 lk8 2k 2k2 2k4

V A V A V A V A V A V A V A V A V A V A V A V A V A V A iV A V A V A V A V A

107

Electronics Calculations Data Handbook

108 R

0.063 W

0.1 W

0.1.25 W

0.155W

0.25 W

2k7

13.0 4.83m 13.7 4.58m 14.4 4.37m 15.1 4.18m 15.7 4.02m 16.5 3.83m 17.2 3.66m 17.9 3.51m 18.8 3.35m 19.8 3.19m 20.7 3.04m 21.7 2.90m 22.7 2.77m 23.9 2.63m 25.1 2.51m 26.3 2.39m 27.5 2.29m 28.6 2.20m 30.7 2.05m

16.4 6.09m 17.3 5.77m 18.2 5.50m 19.0 5.27m 19.7 5.06m 20.7 4.82m 21.7 4.61m 22.6 4.43m 23.7 4.23m 24.9 4.02m 26.1 3.83m 27.4 3.65m 28.6 3.49m 30.2 3.31m 31.6 3.16m 33.2 3.02m 34.6 2.89m 36.1 2.77m 38.7 2.58m

18.4 6.80m 19.4 6.45m 20.3 6.15m 21.2 5.89m 22.1 5.66m 23.2 5.39m 24.2 5.16m 25.2 4.95m 26.5 4.72m 27.8 4.49m 29.2 4.29m 30.6 4.08m 32.0 3.90m 33.7 3.71m 35.4 3.54m 37.1 3.37m 38.7 3.23m 40.3 3.10m 43.3 2.89m

20.5 7.58m 21.6 7.19m 22.6 6.85m 23.6 6.56m 24.6 6.30m 25.8 6.00m 27.0 5.74m 28.1 5.51m 29.5 5.26m 31.0 5.00m 32.5 4.77m 34.1 4.55m 35.7 4.35m 37.6 4.13m 39.4 3.94m 41.3 3.75m 43.1 3.59m 44.9 3.45m 48.2 3.21m

26.0 9.62m 27.4 9.13m 28.7 8.70m 30.0 8.33m 31.2 8.01m 32.8 7.62m 34.3 7.29m 35.7 7.00m 37.4 6.68m 39.4 6.35m 41.2 6.06m 43.3 5.77m 45.3 5.52m 47.7 5.24m 50.0 5.00m 52.4 4.77m 54.8 4.56m 57.0 4.39m 61.2 4.08m

3k 3k3 3k6 3k9 4k3 4k7 5kl 5k6 6k2 6k8 7k5 8k2 9kl 10k llk 12k 13k 15k

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7. I Maximum power for resistors up to 0.25 W

16k 18k 20k 22k 24k 27k 30k 33k 36k 39k 43k 47k 51k 56k 62k 68k 75k 82k 91k

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

31.7 1.98m 33.7 1.87m 35.5 1.77m 37.2 1.69m 38.9 1.62m 41.2 1.53m 43.5 1.45m 45.6 1.38m 47.6 1.32m 49.6 1.27m 52.0 1.21m 54.4 1.16m 56.7 1.11m 59.4 1.06m 62.5 1.01m 65.5 963u 68.7 917u 71.9 877u 75.7 832u

40.0 2.50m 42.4 2.36m 44.7 2.24m 46.9 2.13m 49.0 2.04m 52.0 1.92m 54.8 1.83m 57.4 1.74m 60.0 1.67m 62.4 1.60m 65.6 1.52m 68.6 1.46m 71.4 1.40m 74.8 1.34m 78.7 1.27m 82.5 1.21m 86.6 1.15m 90.6 1.10m 95.4 1.05m

44.7 2.80m 47.4 2.64m 50.0 2.50m 52.4 2.38m 54.8 2.28m 58.1 2.15m 61.2 2.04m 64.2 1.95m 67.1 1.86m 69.8 1.79m 73.3 1.70m 76.6 1.63m 79.8 1.57m 83.7 1.49m 88.0 1.42m 92.2 1.36m 96.8 1.29m 101 1.23m 107 1.17m

49.8 3.11m 52.8 2.93m 55.7 2.78m 58.4 2.65m 61.0 2.54m 64.7 2.40m 68.2 2.27m 71.5 2.17m 74.7 2.07m 77.7 1.99m 81.6 1.90m 85.4 1.82m 88.9 1.74m 93.2 1.66m 98.0 1.58m 103 1.51m 108 1.44m 113 1.37m 119 1.31m

63.2 3.95m 67.1 3.73m 70.7 3.54m 74.2 3.37m 77.5 3.23m 82.2 3.04m 86.6 2.89m 90.8 2.75m 94.9 2.64m 98.7 2.53 m 104 2.41m 108 2.31m 113 2.21m 118 2.11m 124 2.01m 130 1.92m 137 1.83m 143 1.75m 151 1.66m

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

109

110

Electronics Calculations Data Handbook R

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

100k

79.4 794u 83.2 757u 86.9 725u 90.5 696u 97.2 648u 100 627u 106 592u 112 561u 118 535u 123 512u 130 483u 137 458u 144 437u 151 418u 157 402u 165 383u 172 366u 179 351u 188 335u

100 1.00m 105 953u 110 913u 114 877u 122 816u 126 791u 134 745u 141 707u 148 674u 155 645u 164 609u 173 577u 182 550u 190 527u 197 506u 207 482u 217 461u 226 443u 237 423u

112 1.12m 117 1.07m 122 1.02m 127 981u 137 913u 141 884u 150 833u 158 791u 166 754u 173 722u 184 680u 194 645u 203 615u 212 589u 221 566u 232 539u 242 516u 252 495u 265 472u

124 1.24m 131 1.19m 136 1.14m 142 1.09m 152 1.02m 157 984u 167 928u 176 880u 185 839u 193 804u 205 758u 216 719u 226 685u 236 656u 246 630u 258 600u 270 574u 281 551u 295 526u

158 1.58m 166 1.51m 173 1.44m 180 1.39m 194 1.29m 200 1.25m 212 1.18m 224 1.12m 235 1.07m 245 1.02m 260 962u 274 913u 287 870u 300 833u 312 801u 328 762u 343 729u 357 700u 374 668u

ll0k 120k 130k 150k 160k 180k 200k 220k 240k 270k 300k 330k 360k 390k 430k 470k 510k 560k

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.1 Maximum power for resistors up to 0.25 W

620k 680k 750k 820k 910k 1M 1M2 1M5 1M8 2M2 2M7 3M3 3M9 4M7 5M6 6M8 8M2 10M

0.063 W

0.1 W

0.125 W

0.155W

0.25 W

198 319u 207 304u 217 290u 227 277u 239 263u 251 251u 275 229u 307 205u 337 187u 372 169u 412 153u 456 138u 496 127u 544 l16u 594 106u 655 96.3u 719 87.7u 794 79.4u

249 402u 261 383u 274 365u 286 349u 302 331u 316 316u 346 289u 387 258u 424 236u 469 213u 520 192u 574 174u 624 160u 686 146u 748 134u 825 121u 906 ll0u 1.00k 100u

278 449u 292 429u 306 408u 320 390u 337 371u 354 354u 387 323u 433 289u 474 264u 524 238u 581 215u 642 195u 698 179u 766 163u 837 149u 922 136u 1.01k 123u 1.12k l12u

310 500u 325 477u 341 455u 357 435u 376 413u 394 394u 431 359u 482 321u 528 293u 584 265u 647 240u 715 217u 777 199u 854 182u 932 166u 1.03k 151u 1.13k 137u 1.24k 124u

394 635u 412 606u 433 577u 453 552u 477 524u 500 500u 548 456u 612 408u 671 373u 742 337u 822 304u 908 275u 987 253u 1.08k 231u 1.18k 211u 1.30k 192u 1.43k 175u 1.58k 158u

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

111

Table 7.2 Maximum power for resistors between 0.33 and 1 W R 0R10 0R12 0R15 0R18 0R22 0R27 0R33 0R39 0R47 0R56 0R68 0R82 1R 1R1 1R2 1R3 1R5 1R6

0.33 W

0.4 W

0.5 W

0.66 W

1W

182m 1.82 199m 1.66 222rn 1.48 244m 1.35 269m 1.22 298m 1.11 330m 1.00 359m 920m 394m 838m 430m 768m 474m 697m 520m 634m 574m 574m 602m 548m 629m 524m 655m 504m i 704m 469m 727m 454m

200m 2.00 219m 1.83 245m 1.63 268m 1.49 297m 1.35 329m 1.22 363m 1.10 395m 1.01 434m 923m 473m 845m 522m 767m 573m 698m 632m 632m 663m 603m 693m 577m 721m 555m 775m 516m 800m 500m

224m 2.24 245m 2.04 274m 1.83 300m 1.67 332m 1.51 367m 1.36 406m 1.23 442m 1.13 485m 1.03 529m 945m 583m 857m 640m 781m 707m 707m 742m 674m 775m 645m 806m 620m 866m 577m 894m 559m

257m 2.57 281m 2.35 315m 2.10 345m 1.91 381m 1.73 422m 1.56 467m 1.41 507m 1.30 557m 1.19 608m 1.09 670m 985m 736m 897m 812m 812m 852m 775m 890m 742m 926m 713m 995m 663m 1.03 642m

316m 3.16 346m 2.89 387m 2.58 424m 2.36 469m 2.13 520m 1.92 574m 1.74 624m 1.60 686m 1.46 748m 1.34 825m 1.21 906m 1.10 1.00 1.00 1.05 953m 1.10 913m 1.14 877m 1.22 816m 1.26 791m

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.2 Maximum power for resistors between 0.33 and 1 W R

0.33 W

0.4 W

0.5 W

0.66 W

1W

1R8

771m 428m 812m 406m 852m 387m 890m 371m 944m 350m 995m 332m 1.04 316m 1.09 303m 1.13 291m 1.19 277m 1.25 265m 1.30 254m 1.36 243m 1.43 231m 1.50 220m 1.57 210m 1.64 201m 1.73 190m 1.82 182m

849m 471m 894m 447m 938m 426m 980m 408m 1.04 385m 1.10 365m 1.15 348m 1.20 333m 1.25 320m 1.31 305m 1.37 292m 1.43 280m 1.50 267m 1.57 254m 1.65 243m 1.73 231m 1.81 221m 1.91 210m 2.00 200m

949m 527m 1.00 500m 1.05 477m 1.10 456m 1.16 430m 1.22 408m 1.28 389m 1.34 373m 1.40 358m 1.47 341m 1.53 326m 1.60 313m 1.67 299m 1.76 284m 1.84 271m 1.94 258m 2.02 247m 2.13 234m 2.24 224m

1.09 606m 1.15 574m 1.20 548m 1.26 524m 1.33 494m 1.41 469m 1.48 447m 1.54 428m 1.60 411m 1.68 392m 1.76 375m 1.83 360m 1.92 343m 2.02 326m 2.12 312m 2.22 297m 2.33 284m 2.45 269m 2.57 257m

1.34 745m 1.41 707m 1.48 674m 1.55 645m 1.64 609m 1.73 577m 1.82 550m 1.90 527m 1.97 506m 2.07 482m 2.17 461m 2.26 443m 2.37 423m 2.49 402m 2.61 383m 2.74 365m 2.86 349m 3.02 331m 3.16 316m

2R 2R2 2R4 2R7 3R 3R3 3R6 3R9 4R3 4R7 5R1 5R6 6R2 6R8 7R5 8R2 9R1 10R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

113

Electronics Calculations Data Handbook

114 R

llR 12R 13R 15R 16R 18R 20R 22R 24R 27R 30R 33R 36R 39R 43R 47R 51R 56R 62R

0.33 W

0.4 W

0.5 W

0.66 W

1W

1.91 173m 1.99 166m 2.07 159m 2.22 148m 2.30 144m 2.44 135m 2.57 128m 2.69 122m 2.81 l17m 2.98 lllm 3.15 105m 3.30 100m 3.45 95.7m 3.59 92.0m 3.77 I 87.6m

2.10 191m 2.19 183m 2.28 175m 2.45 163m 2.53 158m 2.68 149m 2.83 141m 2.97 135m 3.10 129m 3.29 122m 3.46 l15m 3.63 ll0m 3.79 105m 3.95 101m 4.15 96.4m

2.35 213m 2.45 204m 2.55 196m 2.74 183m 2.83 177m 3.00 167m 3.16 158m 3.32 151m 3.46 144m 3.67 136m 3.87 129m 4.06 123m 4.24 l18m 4.42 l13m 4.64 108m

2.69 245m 2.81 235m 2.93 225m 3.15 210m 3.25 203m 3.45 191m 3.63 182m 3.81 173m 3.98 166m 4.22 156m 4.45 148m 4.67 141m 4.87 135m 5.07 130m 5.33 124m

3.32 302m 3.46 289m 3.61 277m 3.87 258m 4.00 250m 4.24 236m 4.47 224m 4.69 213m 4.90 204m 5.20 192m 5.48 183m 5.74 174m 6.00 167m 6.24 160m 6.56 152m

3.94 83.8m 4.10 80.4m 4.30 76.8m 4.52 73.0m

4.34 92.3m 4.52 88.6m 4.73 84.5m 4.98 80.3m

4.85 103m 5.05 99.0m 5.29 94.5m 5.57 89.8m

5.57 l19m 5.80 114m 6.08 109m 6.40 103m

6.86 146m 7.14 140m 7.48 134m 7.87 127m

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.2 Maximum power for resistors between 0.33 and 1 W R

0.33 W

0.4 W

0.5 W

0.66 W

1W

68R

4.74 69.7m 4.97 66.3m 5.20 63.4m 5.48 60.2m 5.74 57.4m 6.02 54.8m 6.29 52.4m 6.55 50.4m 7.04 46.9m 7.27 45.4m 7.71 42.8m 8.12 40.6m 8.52 38.7m 8.90 37.1m 9.44 35.0m 9.95 33.2m 10.4 31.6m 10.9 30.3m 11.3 29.1m

5.22 76.7m 5.48 73.0m 5.73 69.8m 6.03 66.3m 6.32 63.2m 6.63 60.3m 6.93 57.7m 7.21 55.5m 7.75 51.6m 8.00 50.0m 8.49 47.1m 8.94 44.7m 9.38 42.6m 9.80 40.8m 10.4 38.5m 11.0 36.5m 11.5 34.8m 12.0 33.3m 12.5 32.0m

5.83 85.7m 6.12 81.6m 6.40 78.1m 6.75 74.1m 7.07 70.7m 7.42 67.4m 7.75 64.5m 8.06 62.0m 8.66 57.7m 8.94 55.9m 9.49 52.7m 10.0 50.0m 10.5 47.7m 11.0 45.6m 11.6 43.0m 12.2 40.8m 12.8 38.9m 13.4 37.3m 14.0 35.8m

6.70 98.5m 7.04 93.8m 7.36 89.7m 7.75 85.2m 8.12 81.2m 8.52 77.5m 8.90 74.2m 9.26 71.3m 9.95 66.3m 10.3 64.2m 10.9 60.6m 11.5 57.4m 12.0 54.8m 12.6 52.4m 13.3 49.4m 14.1 46.9m 14.8 44.7m 15.4 42.8m 16.0 41.1m

8.25 121m 8.66 l15m 9.06 ll0m 9.54 105m 10.0 100m 10.5 95.3m 11.0 91.3m 11.4 87.7m 12.2 81.6m 12.6 79.1m 13.4 74.5m 14.1 70.7m 14.8 67.4m 15.5 64.5m 16.4 60.9m 17.3 57.7m 18.2 55.0m 19.0 52.7m 19.7 50.6m

75R 82R 91R 100R ll0R 120R 130R 150R 160R 180R 200R 220R 240R 270R 300R 330R 360R 390R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

115

Electronics Calculations Data Handbook

116 R

0.33 W

0.4 W

0.5 W

0.66 W

1W

430R

11.9 27.7m 12.5 26.5m 13.0 25.4m 13.6 24.3m 14.3 23.1m 15.0 22.0m 15.7 21.0m 16.4 20.1m 17.3 19.0m 18.2 18.2m 19.1 17.3m 19.9 16.6m 20.7 15.9m 22.2 14.8m 23.0 14.4m 24.4 13.5m 25.7 12.8m 26.9 12.2m 28.1 ll.7m

13.1 30.5m 13.7 29.2m 14.3 28.0m 15.0 26.7m 15.7 25.4m 16.5 24.3m 17.3 23.1m 18.1 22.1m 19.1 21.0m 20.0 20.0m 21.0 19.1m 21.9 18.3m 22.8 17.5m 24.5 16.3m 25.3 15.8m 26.8 14.9m 28.3 14.1m 29.7 13.5m 31.0 12.9m

14.7 34.1m 15.3 32.6m 16.0 31.3m 16.7 29.9m 17.6 28.4m 18.4 27.1m 19.4 25.8m 20.2 24.7m 21.3 23.4m 22.4 22.4m 23.5 21.3m 24.5 20.4m 25.5 19.6m 27.4 18.3m 28.3 17.7m 30.0 16.7m 31.6 15.8m 33.2 15.1m 34.6 14.4m

16.8 39.2m 17.6 37.5m 18.3 36.0m 19.2 34.3m 20.2 32.6m 21.2 31.2m 22.2 29.7m 23.3 28.4m 24.5 26.9m 25.7 25.7m 26.9 24.5m 28.1 23.5m 29.3 22.5m 31.5 21.0m 32.5 20.3m 34.5 19.1m 36.3 18.2m 38.1 17.3m 39.8 16.6m

20.7 48.2m 21.7 46.1m 22.6 44.3m 23.7 42.3m 24.9 40.2m 26.1 38.3m 27.4 36.5m 28.6 34.9m 30.2 33.1m 31.6 31.6m 33.2 30.2m 34.6 28.9m 36.1 27.7m 38.7 25.8m 40.0 25.0m 42.4 23.6m 44.7 22.4m 46.9 21.3m 49.0 20.4m

470R 510R 560R 620R 680R 750R 820R 910R lk lkl lk2 lk3 lk5 lk6 lk8 2k 2k2 2k4

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.2 Maximum power for resistors between 0.33 and 1 W R

0.33 W

0.4 W

0.5 W

0.66 W

1W

2k7

29.8 ll.lm 31.5 10.5m 33.0 10.0m 34.5 9.57m 35.9 9.20m 37.7 8.76m 39.4 8.38m 41.0 8.04m 43.0 7.68m 45.2 7.30m 47.4 6.97m 49.7 6.63m 52.0 6.34m 54.8 6.02m 57.4 5.74m 60.2 5.48m 62.9 5.24m 65.5 5.04m 70.4 4.69m

32.9 12.2m 34.6 ll.5m 36.3 ll.0m 37.9 10.5m 39.5 10.1m 41.5 9.64m 43.4 9.23m 45.2 8.86m 47.3 8.45m 49.8 8.03m 52.2 7.67m 54.8 7.30m 57.3 6.98m 60.3 6.63m 63.2 6.32m 66.3 6.03m 69.3 5.77m 72.1 5.55m 77.5, 5.16m

36.7 13.6m 38.7 12.9m 40.6 12.3m 42.4 ll.8m 44.2 ll.3m 46.4 10.8m 48.5 10.3m 50.5 9.90m 52.9 9.45m 55.7 8.98m 58.3 8.57m 61.2 8.16m 64.0 7.81m 67.5 7.41m 70.7 7.07m 74.2 6.74m 77.5 6.45m 80.6 6.20m 86.6 5.77m

42.2 15.6m 44.5 14.8m 46.7 14.1m 48.7 13.5m 50.7 13.0m 53.3 12.4m 55.7 ll.9m 58.0 ll.4m 60.8 10.9m 64.0 10.3m 67.0 9.85m 70.4 9.38m 73.6 8.97m 77.5 8.52m 81.2 8.12m 85.2 7.75m 89.0 7.42m 92.6 7.13m 99.5 6.63m

52.0 19.2m 54.8 18.3m 57.4 17.4m 60.0 16.7m 62.4 16.0m 65.6 15.2m 68.6 14.6m 71.4 14.0m 74.8 13.4m 78.7 12.7m 82.5 12.1m 86.6 ll.5m 90.6 ll.0m 95.4 10.5m 100 10.0m 105 9.53m 110 9.13m 114 8.77m 122 8.16m

3k 3k3 3k6 3k9 4k3 4k7 5kl 5k6 6k2 6k8 7k5 8k2 9kl 10k llk 12k 13k 15k

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

117

118

Electronics Calculations Data Handbook R

0.33 W

0.4 W

0.5 W

0.66 W

1W

16k

72.7 4.54m 77.1 4.28m 81.2 4.06m 85.2 3.87m 89.0 3.71m 94.4 3.50m 99.5 3.32m 104 3.16m 109 3.03m 113 2.91m 119 2.77m 125 2.65m 130 2.54m 136 2.43m 143 2.31m 150 2.20m 157 2.10m 164 2.01m 173 1.90m

80.0 5.00m 84.9 4.71m 89.4 4.47m 93.8 4.26m 98.0 4.08m 104 3.85m 110 3.65m 115 3.48m 120 3.33m 125 3.20m 131 3.05m 137 2.92m 143 2.80m 150 2.67m 157 2.54m 165 2.43m 173 2.31m 181 2.21m 191 2.10m

89.4 5.59m 94.9 5.27m 100 5.00m 105 4.77m 110 4.56m 116 4.30m 122 4.08m 128 3.89m 134 3.73m 140 3.58m 147 3.41m 153 3.26m 160 3.13m 167 2.99m 176 2.84m 184 2.71m 194 2.58m 202 2.47m 213 2.34m

103 6.42m 109 6.06m 115 5.74m 120 5.48m 126 5.24m 133 4.94m 141 4.69m 148 4.47m 154 4.28m 160 4.11m 168 3.92m 176 3.75m 183 3.60m 192 3.43m 202 3.26m 212 3.12m 222 2.97m 233 2.84m 245 2.69m

126 7.91m 134 7.45m 141 7.07m 148 6.74m 155 6.45m 164 6.09m 173 5.77m 182 5.50m 190 5.27m 197 5.06m 207 4.82m 217 4.61m 226 4.43m 237 4.23m 249 4.02m 261 3.83m 274 3.65m 286 3.49m 302 3.31m

18k 20k 22k 24k 27k 30k 33k 36k 39k 43k 47k 51k 56k 62k 68k 75k 82k 91k

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.2 Maximum power for resistors between 0.33 and 1 W R 100k ll0k 120k 130k 150k 160k 180k 200k 220k 240k 270k 300k 330k 360k 390k 430k 470k 510k 560k

0.33 W 182 1.82m 191 1.73m 199 1.66m 207 1.59m 222 1.48m 230 1.44m 244 1.35m 257 1.28m 269 1.22m 281 1.17m 298 1.11m 315 1.05m 330 1.00m 345 957u 359 920u 377 876u i 394 838u 410 804u 430 768u

0.4 W

0.5 W

0.66 W

1W

200 2.00m 210 1.91m 219 1.83m 228 1.75m 245 1.63m 253 1.58m 268 1.49m 283 1.41m 297 1.35m 310 1.29m 329 1.22m 346 1.15m 363 1.10m 379 1.05m 395 1.01m 415 964u 434 923u 452 886u 473 845u

224 2.24m 235 2.13m 245 2.04m 255 1.96m 274 1.83m 283 1.77m 300 1.67m 316 1.58m 332 1.51m 346 1.44m 367 1.36m 387 1.29m 406 1.23m 424 1.18m 442 1.13m 464 1.08m 485 1.03m 505 990u 529 945u

257 2.57m 269 2.45m 281 2.35m 293 2.25m 315 2.10m 325 2.03m 345 1.91m 363 1.82m 381 1.73m 398 1.66m 422 1.56m 445 1.48m 467 1.41m 487 1.35m 507 1.30m 533 1.24m 557 1.19m 580 1.14m 608 1.09m

316 3.16m 332 3.02m 346 2.89m 361 2.77m 387 2.58m 400 2.50m 424 2.36m 447 2.24m 469 2.13m 490 2.04m 520 1.92m 548 1.83m 574 1.74m 600 1.67m 624 1.60m 656 1.52m 686 1.46m 714 1.40m 748 1.34m

V A V A V A V A V A V A V A V A V A V A V A V A V i A iV A V A V A V A V A V A

119

Electronics Calculations Data Handbook

120 R

0.33 W

0.4 W

0.5 W

0.66 W

1W

620k

452 730u 474 697u 497 663u 520 634u 548 602u 574 574u 629 524u 704 469u 771 428u 852 387u 944 350u 1.04k 316u 1.13k 291u 1.25k 265u 1.36k 243u 1.50k 220u 1.64k 201u 1.82k 182u

498 803u 522 767u 548 730u 573 698u 603 663u 632 632u 693 577u 775 516u 849 471u 938 426u 1.04k 385u 1.15k 348u 1.25k 320u 1.37k 292u 1.50k 267u 1.65k 243u 1.81k 221u 2.00k 200u

557 898u 583 857u 612 816u 640 781u 675 741u 707 707u 775 645u 866 577u 949 527u 1.05k 477u 1.16k 430u 1.28k 389u 1.40k 358u 1.53k 326u 1.67k 299u 1.84k 271u 2.02k 247u 2.24k 224u

640 1.03m 670 985u 704 938u 736 897u 775 852u 812 812u 890 742u 995 663u 1.09k 606u 1.20k 548u 1.33k 494u 1.48k 447u 1.60k 411u 1.76k 375u 1.92k 343u 2.12k 312u 2.33k 284u 2.57k 257u

787 1.27m 825 1.21m 866 1.15m 906 1.10m 954 1.05m 1.00k 1.00m 1.10k 913u 1.22k 816u 1.34k 745u 1.48k 674u 1.64k 609u 1.82k 550u 1.97k 506u 2.17k 461u 2.37k 423u 2.61k 383u 2.86k 349u 3.16k 316u

680k 750k 820k 910k 1M 1M2 1M5 1M8 2M2 2M7 3M3 3M9 4M7 5M6 6M8 8M2 10M

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.3 Maximum power for resistors between 2 and 5 W R

2W

2.5W

3W

4W

5W

0R01

141m 14.1 200m 10.0 245m 8.16 257m 7.78 307m 6.52 316m 6.32 335m 5.98 369m 5.42 374m 5.35 447m 4.47 490m 4.08 548m 3.65 600m 3.33 663m 3.02 735m 2.72 812m 2.46 883m 2.26 970m 2.06

158m 15.8 224m 11.2 274m 9.13 287m 8.70 343m 7.29 354m 7.07 374m 6.68 412m 6.06 418m 5.98 500m 5.00 548m 4.56 612m 4.08 671m 3.73 742m 3.37 822m 3.04 908m 2.75 987m 2.53 1.08 2.31

173m 17.3 245m 12.2 300m 10.0 315m 9.53 375m 7.99 387m 7.75 410m 7.32 452m 6.64 458m 6.55 548m 5.48 600m 5.00 671m 4.47 735m 4.08 812m 3.69 900m 3.33 995m 3.02 1.08 2.77 1.19 2.53

200m 20.0 283m 14.1 346m 11.5 363m 11.0 434m 9.23 447m 8.94 473m 8.45 522m 7.67 529m 7.56 632m 6.32 693m 5.77 775m 5.16 849m 4.71 938m 4.26 1.04 3.85 1.15 3.48 1.25 3.20 1.37 2.92

224m 22.4 316m 15.8 387m 12.9 406m 12.3 485m 10.3 500m 10.0 529m 9.45 583m 8.57 592m 8.45 707m 7.07 775m 6.45 866m 5.77 949m 5.27 1.05 4.77 1.16 4.30 1.28 3.89 1.40 3.58 1.53 3.26

0R02 0R03 0R033 0R047 0R05 0R056 0R068 0R07 0R10 0R12 0R15 0R18 0R22 0R27 0R33 0R39 0R47

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Electronics Calculations Data Handbook

122 R

0R56 0R68 0R82 1R 1R2 1R5 1R8 2R2 2R7 3R3 3R9 4R7 5R6 6R8 8R2 10R 12R 15R 18R

2W

2.5W

3W

4W

5W

1.06 1.89 1.17 1.71 1.28 1.56 1.41 1.41 1.55 1.29 1.73 1.15 1.90 1.05 2.10 953m 2.32 861m 2.57 778m 2.79 716m 3.07 652m 3.35 598m 3.69 542m 4.05 494m 4.47 447m

1.18 2.11 1.30 1.92 1.43 1.75 1.58 1.58 1.73 1.44 1.94 1.29 2.12 1.18 2.35 1.07 2.60 962m 2.87 870m 3.12 801m 3.43 729m 3.74 668m 4.12 606m 4.53 552m 5.00 500m

1.30 2.31 1.43 2.10 1.57 1.91 1.73 1.73 1.90 1.58 2.12 1.41 2.32 1.29 2.57 1.17 2.85 1.05 3.15 953m 3.42 877m 3.75 799m 4.10 732m 4.52 664m 4.96 605m 5.48 548m

1.50 2.67 1.65 2.43 1.81 2.21 2.00 2.00 2.19 1.83 2.45 1.63 2.68 1.49 2.97 1.35 3.29 1.22 3.63 1.10 3.95 1.01 4.34 923m 4.73 845m 5.22 767m 5.73 698m 6.32 632m

1.67 2.99 1.84 2.71 2.02 2.47 2.24 2.24 2.45 2.04 2.74 1.83 3.00 1.67 3.32 1.51 3.67 1.36 4.06 1.23 4.42 1.13 4.85 1.03 5.29 945m 5.83 857m 6.40 781m 7.07 707m

4.90 408m 5.48 365m 6.00

5.48 456m 6.12 408m 6.71

6.00 500m 6.71 447m 7.35

6.93 577m 7.75 516m 8.49

7.75 645m 8.66 577m 9.49

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V

Table 7.3 Maximum power for resistors between 2 and 5 W R

22R 27R 33R 39R 47R 56R 68R 82R 100R 120R 150R 180R 220R 270R 330R 390R 470R 560R

2W

2.5W

3W

4W

5W

333m 6.63 302m 7.35 272m 8.12 246m 8.83 226m 9.70 206m 10.6 189m 11.7 171m 12.8 156m 14.1 141m 15.5 129m 17.3 l15m 19.0 105m 21.0 95.3m 23.2 86.1m 25.7 77.8m 27.9 71.6m 30.7 65.2m 33.5 59.8m

373m 7.42 337m 8.22 304m 9.08 275m 9.87 253m 10.8 231m 11.8 211m 13.0 192m 14.3 175m 15.8 158m 17.3 144m 19.4 129m 21.2 l18m 23.5 107m 26.0 96.2m 28.7 87.0m 31.2 80.1m 34.3 72.9m 37.4 66.8m

408m 8.12 369m 9.00 333m 9.95 302m 10.8 277m 11.9 253m 13.0 231m 14.3 210m 15.7 191m 17.3 173m 19.0 158m 21.2 141m 23.2 129m 25.7 l17m 28.5 105m 31.5 95.3m 34.2 87.7m 37.5 79.9m 41.0 73.2m

471m 9.38 426m 10.4 385m 11.5 348m 12.5 320m 13.7 292m 15.0 267m 16.5 243m 18.1 221m 20.0 200m 21.9 183m 24.5 163m 26.8 149m 29.7 135m 32.9 122m 36.3 ll0m 39.5 101m 43.4 92.3m 47.3 84.5m

527m 10.5 477m 11.6 430m 12.8 389m 14.0 358m 15.3 326m 16.7 299m 18.4 271m 20.2 247m 22.4 224m 24.5 204m 27.4 183m 30.0 167m 33.2 151m 36.7 136m 40.6 123m 44.2 l13m 48.5 103m 52.9 94.5m

A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

123

Electronics Calculations Data Handbook

124 R

680R 820R lk lk2 lk5 lk8 2k2 2k7 3k3 3k9 4k7 5k6 6k8 8k2 10k 12k 15k 18k 22k

2W

2.5W

3W

4W

5W

36.9 54.2m 40.5 49.4m 44.7 44.7m 49.0 40.8m 54.8 36.5m 60.0 33.3m 66.3 30.2m 73.5 27.2m 81.2 24.6m 88.3 22.6m 97.0 20.6m 106 18.9m 117 17.1m 128 i 15.6m !141 14.1m 155 12.9m

41.2 60.6m 45.3 55.2m 50.0 50.0m 54.8 45.6m 61.2 40.8m 67.1 37.3m 74.2 33.7m 82.2 30.4m 90.8 27.5m 98.7 25.3m 108 23.1m 118 21.1m 130 19.2m 143 17.5m 158 15.8m 173 14.4m

45.2 66.4m 49.6 60.5m 54.8 54.8m 60.0 50.0m 67.1 44.7m 73.5 40.8m 81.2 36.9m 90.0 33.3m 99.5 30.2m 108 27.7m 119 25.3m 130 23.1m 143 21.0m 157 19.1m 173 17.3m 190 15.8m

52.2 76.7m 57.3 69.8m 63.2 63.2m 69.3 57.7m 77.5 51.6m 84.9 47.1m 93.8 42.6m 104 38.5m 115 34.8m 125 32.0m 137 29.2m 150 26.7m 165 24.3m 181 22.1m 200 20.0m 219 18.3m

173 ll.5m 190 10.5m

194 12.9m 212 ll.8m

212 14.1m 232 12.9m

245 16.3m 268 14.9m

210

235

257

297

58.3 85.7m 64.0 78.1m 70.7 70.7m 77.5 64.5m 86.6 57.7m 94.9 52.7m 105 47.7m 116 43.0m 128 38.9m 140 35.8m 153 32.6m 167 29.9m 184 27.1m 202 24.7m 224 22.4m 245 20.4m 274 18.3m 300 16.7m 332

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V

Table 7.3 Maximum power for resistors between 2 and 5 W R

27k 33k 39k 47k 56k 68k 82k 100k 120k 150k 180k 220k 270k 330k 390k 470k 560k 680k

2W

2.5W

3W

4W

5W

9.53m 232 8.61m 257 7.78m

10.7m 260 9.62m 287 8.70m

ll.7m 285 10.5m 315 9.53m

13.5m 329 12.2m 363 ll.0m

15.1m 367 13.6m 406 12.3m

312 8.01m 343 7.29m 374 6.68m 412 6.06m 453 5.52m 500 5.00m 548 4.56m 612 4.08m 671 3.73m 742 3.37m 822 3.04m 908 2.75m 987 2.53m 1.08k 2.31m 1.18k 2.11m 1.30k 1.92m

342 8.77m 375 7.99m 410 7.32m 452 6.64m 496 6.05m 548 5.48m 600 5.00m 671 4.47m 735 4.08m 812 3.69m 900 3.33m 995 3.02m 1.08k 2.77m 1.19k 2.53m 1.30k 2.31m 1.43k 2.10m

395 10.1m 434 9.23m 473 8.45m 522 7.67m 573 6.98m 632 6.32m 693 5.77m 775 5.16m 849 4.71m 938 4.26m 1.04k 3.85m 1.15k 3.48m 1.25k 3.20m 1.37k 2.92m 1.50k 2.67m 1.65k 2.43m

442 ll.3m 485 10.3m 529 9.45m 583 8.57m 640 7.81m 707 7.07m 775 6.45m 866 5.77m 949 5.27m 1.05k 4.77m 1.16k 4.30m 1.28k 3.89m 1.40k 3.58m 1.53k 3.26m 1.67k 2.99m 1.84k 2.71m

279 7.16m 307 6.52m 335 5.98m 369 5.42m 405 4.94m 447 4.47m 490 4.08m 548 3.65m 600 3.33m :i 663 ! 3.02m 735 2.72m 812 2.46m 883 2.26m 970 2.06m 1.06k 1.89m 1.17k 1.71m

A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

125

Electronics Calculations Data Handbook

126 R

2W

2.5W

3W

4W

5W

820k

1.28k 1.56m 1.41k 1.41m

1.43k 1.75m 1.58k 1.58m

1.57k 1.91m 1.73k 1.73m

1.81k 2.21m 2.00k 2.00m

2.02k 2.47m 2.24k 2.24m

1M

V A V A

Table 7.4

Maximum power for resistors between 6 and 10 W

R

6W

7W

7.5W

9W

10W

0R01

245m 24.5 346m 17.3 424m 14.1 445m 13.5 531m 11.3 548m 11.0 580m 10.4 639m 9.39 648m 9.26 775m 7.75 849m 7.07 949m 6.32 1.04 5.77 1.15 5.22 1.27 4.71 1.41 4.26 1.53 3.92 1.68 3.57

265m 26.5 374m 18.7 458m 15.3 481m 14.6 574m 12.2 592m 11.8 626m 11.2 690m 10.1 700m 10.0 837m 8.37 917m 7.64 1.02 6.83 1.12 6.24 1.24 5.64 1.37 5.09 1.52 4.61 1.65 4.24 1.81 3.86

274m 27.4 387m 19.4 474m 15.8 497m 15.1 594m 12.6 612m 12.2 648m 11.6 714m 10.5 725m 10.4 866m 8.66 949m 7.91 1.06 7.07 1.16 6.45 1.28 5.84 1.42 5.27 1.57 4.77 1.71 4.39 1.88 3.99

300m 30.0 424m 21.2 520m 17.3 545m 16.5 650m 13.8 671m 13.4 710m 12.7 782m 11.5 794m 11.3 949m 9.49 1.04 8.66 1.16 7.75 1.27 7.07 1.41 6.40 1.56 5.77 1.72 5.22 1.87 4.80 2.06 4.38

316m 31.6 447m 22.4 548m 18.3 574m 17.4 686m 14.6 707m 14.1 748m 13.4 825m 12.1 837m 12.0 1.00 10.0 1.10 9.13 1.22 8.16 1.34 7.45 1.48 6.74 1.64 6.09 1.82 5.50 1.97 5.06 2.17 4.61

0R02 0R03 0R033 0R047 0R05 0R056 0R068 0R07 0R10 0R12 0R15 0R18 0R22 0R27 0R33 0R39 0R47

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Electronics Calculations Data Handbook

128 R

6W

7W

7.5 W

9W

10 W

0R56

1.83 3.27 2.02 2.97 2.22 2.71 2.45 2.45 2.68 2.24 3.00 2.00 3.29 1.83 3.63 1.65 4.02 1.49 4.45 1.35 4.84 1.24 5.31 1.13 5.80 1.04 6.39 939m 7.01 855m 7.75 775m 8.49 707m 9.49 632m

1.98 3.54 2.18 3.21 2.40 2.92 2.65 2.65 2.90 2.42 3.24 2.16 3.55 1.97 3.92 1.78 4.35 1.61 4.81 1.46 5.22 1.34 5.74 1.22 6.26 1.12 6.90 1.01 7.58 924m 8.37 837m 9.17 764m 10.2 683m

2.05 3.66 2.26 3.32 2.48 3.02 2.74 2.74 3.00 2.50 3.35 2.24 3.67 2.04 4.06 1.85 4.50 1.67 4.97 1.51 5.41 1.39 5.94 1.26 6.48 1.16 7.14 1.05 7.84 956m 8.66 866m 9.49 791m 10.6 707m

2.24 4.01 2.47 3.64 2.72 3.31 3.00 3.00 3.29 2.74 3.67 2.45 4.02 2.24 4.45 2.02 4.93 1.83 5.45 1.65 5.92 1.52 6.50 1.38 7.10 1.27 7.82 1.15 8.59 1.05 9.49 949m 10.4 866m 11.6 775m

2.37 4.23 2.61 3.83 2.86 3.49 3.16 3.16 3.46 2.89 3.87 2.58 4.24 2.36 4.69 2.13 5.20 1.92 5.74 1.74 6.24 1.60 6.86 1.46 7.48 1.34 8.25 1.21 9.06 1.10 10.0 1.00 11.0 913m 12.2 816m

0R68 0R82 1R 1R2 1R5 1R8 2R2 2R7 3R3 3R9 4R7 5R6 6R8 8R2 10R 12R 15R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.4 Maximum power for resistors between 6 and 10 W R

6W

7W

7.5W

9W

10W

18R

10.4 577m 11.5 522m 12.7 471m 14.1 426m 15.3 392m 16.8 357m 18.3 327m 20.2 297m 22.2 271m 24.5 245m 26.8 224m 30.0 200m 32.9 183m 36.3 165m 40.2 149m 44.5 135m 48.4 124m 53.1 l13m

11.2 624m 12.4 564m 13.7 509m 15.2 461m 16.5 424m 18.1 386m 19.8 354m 21.8 321m 24.0 292m 26.5 265m 29.0 242m 32.4 216m 35.5 197m 39.2 178m 43.5 161m 48.1 146m 52.2 134m 57.4 122m

11.6 645m 12.8 584m 14.2 527m 15.7 477m 17.1 439m 18.8 399m 20.5 366m 22.6 332m 24.8 302m 27.4 274m 30.0 250m 33.5 224m 36.7 204m 40.6 185m 45.0 167m 49.7 151m 54.1 139m 59.4 126m

12.7 707m 14.1 640m 15.6 577m 17.2 522m 18.7 480m 20.6 438m 22.4 401m 24.7 364m 27.2 331m 30.0 300m 32.9 274m 36.7 245m 40.2 224m 44.5 202m 49.3 183m 54.5 165m 59.2 152m 65.0 138m

13.4 745m 14.8 674m 16.4 609m 18.2 550m 19.7 506m 21.7 461m 23.7 423m 26.1 383m 28.6 349m 31.6 316m 34.6 289m 38.7 258m 42.4 236m 46.9 213m 52.0 192m 57.4 174m 62.4 160m 68.6 146m

22R 27R 33R 39R 47R 56R 68R 82R 100R 120R 150R 180R 220R 270R 330R 390R 470R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

V A V A

129

Electronics Calculations Data Handbook

130 R

6W

7W

7.5W

9W

10W

560R

58.0 104m 63.9 93.9m 70.1 85.5m 77.5 77.5m 84.9 70.7m 94.9 63.2m 104 57.7m 115 52.2m 127 47.1m 141 42.6m 153 39.2m 168 35.7m 183 32.7m 202 29.7m

62.6 l12m 69.0 101m 75.8 92.4m 83.7 83.7m 91.7 76.4m 102 68.3m 112 62.4m 124 56.4m 137 50.9m 152 46.1m 165 42.4m 181 38.6m 198 35.4m 218 32.1m

64.8 l16m 71.4 105m 78.4 95.6m 86.6 86.6m 94.9 79.1m 106 70.7m 116 64.5m 128 58.4m 142 52.7m 157 47.7m 171 43.9m 188 39.9m 205 36.6m 226 33.2m

71.0 127m 78.2 l15m 85.9 105m 94.9 94.9m 104 86.6m 116 77.5m 127 70.7m 141 64.0m 156 57.7m 172 52.2m 187 48.0m 206 43.8m 224 40.1m 247 36.4m

74.8 134m 82.5 121m 90.6 ll0m 100 100m 110 91.3m 122 81.6m 134 74.5m 148 67.4m 164 60.9m 182 55.0m 197 50.6m 217 46.1m 237 42.3m 261 38.3m

V A V A V A V A V A V A V A V A V A V A V A V A V A V A

222 27.1m 245 24.5m 268 22.4m 300 20.0m

240 29.2m 265 26.5m 290 24.2m 324 21.6m

248 30.2m 274 27.4m 300 25.0m 335 22.4m

272 33.1m 300 30.0m 329 27.4m 367 24.5m

286 34.9m 316 31.6m 346 28.9m 387 25.8m

V A V A V A V A

680R 820R lk lk2 lk5 lk8 2k2 2k7 3k3 3k9 4k7 5k6 6k8 8k2 10k 12k 15k

Table 7.4 Maximum power for resistors between 6 and 10 W R

6W

7W

7.5W

9W

10W

18k

329 18.3m 363 16.5m 402 14.9m 445 13.5m 484 12.4m 531 ll.3m 580 10.4m 639 9.39m 701 8.55m 775 7.75m

355 19.7m 392 17.8m 435 16.1m 481 14.6m 522 13.4m 574 12.2m 626 ll.2m 690 10.1m 758 9.24m 837 8.37m

367 20.4m 406 18.5m 450 16.7m 497 15.1m 541 13.9m 594 12.6m 648 ll.6m 714 10.5m 784 9.56m 866 8.66m

402 22.4m 445 20.2m 493 18.3m 545 16.5m 592 15.2m 650 13.8m 710 12.7m 782 ll.5m 859 10.5m 949 9.49m

424 23.6m 469 21.3m 520 19.2m 574 17.4m 624 16.0m 686 14.6m 748 13.4m 825 12.1m 906 ll.0m 1.00k 10.0m

22k 27k 33k 39k 47k 56k 68k 82k 100k

V A V A V A V A V A V A V A V A V A V A

131

Table 7.5

Maximum power for resistors between 11 and 25 W

R

11W

12 W

15 W

17 W

25 W

0R01

332m 33.2 469m 23.5 574m 19.1 602m 18.3 719m 15.3 742m 14.8 785m 14.0 865m 12.7 877m 12.5 1.05 10.5 1.15 9.57 1.28 8.56 1.41 7.82

346m 34.6 490m 24.5 600m 20.0 629m 19.1 751m 16.0 775m 15.5 820m 14.6 903m 13.3 917m 13.1 1.10 11.0 1.20 10.0 1.34 8.94 1.47 8.16

387m 38.7 548m 27.4 671m 22.4 704m 21.3 840m 17.9 866m 17.3 917m 16.4 1.01 14.9 1.02 14.6 1.22 12.2 1.34 11.2 1.50 10.0 1.64 9.13

412m 41.2 583m 29.2 714m 23.8 749m 22.7 894m 19.0 922m 18.4 976m 17.4 1.08 15.8 1.09 15.6 1.30 13.0 1.43 11.9 1.60 10.6 1.75 9.72

500m 50.0 707m 35.4 866m 28.9 908m 27.5 1.08 23.1 1.12 22.4 1.18 21.1 1.30 19.2 1.32 18.9 1.58 15.8 1.73 14.4 1.94 12.9 2.12 11.8

V A V A V A V A V A V A V A V A V A V A V A V A V A

1.56 7.07 1.72 6.38 1.91 5.77 2.07 5.31 2.27 4.84

1.62 7.39 1.80 6.67 1.99 6.03 2.16 5.55 2.37 5.05

1.82 8.26 2.01 7.45 2.22 6.74 2.42 6.20 2.66 5.65

1.93 8.79 2.14 7.93 2.37 7.18 2.57 6.60 2.83 6.01

2.35 10.7 2.60 9.62 2.87 8.70 3.12 8.01 3.43 7.29

V A V A V A V A V A

0R02 0R03 0R033 0R047 0R05 0R056 0R068 0R07 0R10 0R12 0R15 0R18 0R22 0R27 0R33 0R39 0R47

Table 7.5 Maximum power for resistors between 11 and 25 W R

ll W

12 W

15 W

17 W

25 W

0R56

2.48 4.43 2.73 4.02 3.00 3.66 3.32 3.32 3.63 3.03 4.06 2.71 4.45 2.47 4.92 2.24 5.45 2.02 6.02 1.83 6.55 1.68 7.19 1.53 7.85 1.40 8.65 1.27 9.50 1.16 10.5 1.05 11.5 957m 12.8 856m

2.59 4.63 2.86 4.20 3.14 3.83 3.46 3.46 3.79 3.16 4.24 2.83 4.65 2.58 5.14 2.34 5.69 2.11 6.29 1.91 6.84 1.75 7.51 1.60 8.20 1.46 9.03 1.33 9.92 1.21 11.0 1.10 12.0 1.00 13.4 894m

2.90 5.18 3.19 4.70 3.51 4.28 3.87 3.87 4.24 3.54 4.74 3.16 5.20 2.89 5.74 2.61 6.36 2.36 7.04 2.13 7.65 1.96 8.40 1.79 9.17 1.64 10.1 1.49 11.1 1.35 12.2 1.22 13.4 1.12 15.0 1.00

3.09 5.51 3.40 5.00 3.73 4.55 4.12 4.12 4.52 3.76 5.05 3.37 5.53 3.07 6.12 2.78 6.77 2.51 7.49 2.27 8.14 2.09 8.94 1.90 9.76 1.74 10.8 1.58 11.8 1.44 13.0 1.30 14.3 1.19 16.0 1.06

3.74 6.68 4.12 6.06 4.53 5.52 5.00 5.00 5.48 4.56 6.12 4.08 6.71 3.73 7.42 3.37 8.22 3.04 9.08 2.75 9.87 2.53 10.8 2.31 11.8 2.11 13.0 1.92 14.3 1.75 15.8 1.58 17.3 1.44 19.4 1.29

0R68 0R82 1R 1R2 1R5 1R8 2R2 2R7 3R3 3R9 4R7 5R6 6R8 8R2 10R 12R 15R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

133

Electronics Calculations Data Handbook

134 R

11W

12 W

15 W

17 W

25 W

18R

14.1 782m 15.6 707m 17.2 638m 19.1 577m 20.7 531m 22.7 484m 24.8 443m 27.3 402m 30.0 366m 33.2 332m 36.3 303m 40.6 271m 44.5 247m 49.2 224m 54.5 202m 60.2 183m 65.5 168m 71.9 153m

14.7 816m 16.2 739m 18.0 667m 19.9 603m 21.6 555m 23.7 505m 25.9 463m 28.6 420m 31.4 383m 34.6 346m 37.9 316m 42.4 283m 46.5 258m 51.4 234m 56.9 211m 62.9 191m 68.4 175m 75.1 160m

16.4 913m 18.2 826m 20.1 745m 22.2 674m 24.2 620m 26.6 565m 29.0 518m 31.9 470m 35.1 428m 38.7 387m 42.4 354m 47.4 316m 52.0 289m 57.4 261m 63.6 236m 70.4 213m 76.5 196m 84.0 179m

17.5 972m 19.3 879m 21.4 793m 23.7 718m 25.7 660m 28.3 601m 30.9 551m 34.0 500m 37.3 455m 41.2 412m 45.2 376m 50.5 337m 55.3 307m 61.2 278m 67.7 251m 74.9 227m 81.4 209m 89.4 190m

21.2 1.18 23.5 1.07 26.0 962m 28.7 870m 31.2 801m 34.3 729m 37.4 668m 41.2 606m 45.3 552m 50.0 500m 54.8 456m 61.2 408m 67.1 373m 74.2 337m 82.2 304m 90.8 275m 98.7 253m 108 231m

22R 27R 33R 39R 47R 56R 68R 82R 100R 120R 150R 180R 220R 270R 330R 390R 470R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.5 Maximum power for resistors between 11 and 25 W R

ll W

12 W

15 W

17 W

25 W

560R

78.5 140m 86.5 127m 95.0 l16m 105 105m 115 95.7m 128 85.6m 141 78.2m 156 70.7m 172 63.8m 191 57.7m 207 53.1m 227 48.4m 248 44.3m 273 40.2m 300 36.6m 332 33.2m 363 30.3m 406 27.1m

82.0 146m 90.3 133m 99.2 121m 110 ll0m 120 100m 134 89.4m 147 81.6m 162 73.9m 180 66.7m 199 60.3m 216 55.5m 237 50.5m 259 46.3m 286 42.0m 314 38.3m 346 34.6m 379 31.6m 424 28.3m

91.7 164m 101 149m 111 135m 122 122m 134 l12m 150 100m 164 91.3m 182 82.6m 201 74.5m 222 67.4m 242 62.0m 266 56.5m 290 51.8m 319 47.0m 351 42.8m 387 38.7m 424 35.4m 474 31.6m

97.6 174m 108 158m 118 144m 130 130m 143 l19m 160 106m 175 97.2m 193 87.9m 214 79.3m 237 71.8m 257 66.0m 283 60.1m 309 55.1m 340 50.0m 373 45.5m 412 41.2m 452 37.6m 505 33.7m

118 211m 130 192m 143 175m 158 158m 173 144m 194 129m 212 l18m 235 107m 260 96.2m 287 87.0m 312 80.1m 343 72.9m 374 66.8m 412 60.6m 453 55.2m 500 50.0m 548 45.6m 612 40.8m

680R 820R lk lk2 lk5 lk8 2k2 2k7 3k3 3k9 4k7 5k6 6k8 8k2 10k 12k 15k

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

135

Electronics Calculations Data Handbook

136 R

18k 22k 27k 33k 39k 47k 56k 68k 82k 100k

11W

12 W

15 W

17 W

25 W

445 24.7m 492 22.4m 545 20.2m 602 18.3m 655 16.8m ! 719 15.3m 785 14.0m 865 12.7m 950 ll.6m 1.05k 10.5m

465 25.8m 514 23.4m 569 21.1m 629 19.1m 684 17.5m 751 16.0m 820 14.6m 903 13.3m 992 12.1m 1.10k ll.0m

520 28.9m 574 26.1m 636 23.6m 704 21.3m 765 19.6m 840 17.9m 917 16.4m 1.01k 14.9m 1.11k 13.5m 1.22k 12.2m

553 30.7m 612 27.8m 677 25.1m 749 22.7m 814 20.9m 894 19.0m 976 17.4m 1.08k 15.8m 1.18k 14.4m 1.30k 13.0m

671 37.3m 742 33.7m 822 30.4m 908 27.5m 987 25.3m 1.08k 23.1m 1.18k 21.1m 1.30k 19.2m 1.43k 17.5m 1.58k 15.8m

V A V A V A V A V A V A V A V A V A V A

Table 7.6

Maximum power for resistors between 50 and 300 W

R

50 W

100 W

200 W

250 W

300 W

0R01

707m 70.7 1.00 50.0 1.22 40.8 1.28 38.9 1.53 32.6 1.58 31.6 1.67 29.9 1.84 27.1 1.87 26.7 2.24 22.4 2.45 20.4 2.74 18.3 3.00 16.7 3.32 15.1 3.67 13.6 4.06 12.3 4.42 11.3 4.85 10.3

1.00 100 1.41 70.7 1.73 57.7 1.82 55.0 2.17 46.1 2.24 44.7 2.37 42.3 2.61 38.3 2.65 37.8 3.16 31.6 3.46 28.9 3.87 25.8 4.24 23.6 4.69 21.3 5.20 19.2 5.74 17.4 6.24 16.0 6.86 14.6

1.41 141 2.00 100 2.45 81.6 2.57 77.8 3.07 65.2 3.16 63.2 3.35 59.8 3.69 54.2 3.74 53.5 4.47 44.7 4.90 40.8 5.48 36.5 6.00 33.3 6.63 30.2 7.35 27.2 8.12 24.6 8.83 22.6 9.70 20.6

1.58 158 2.24 112 2.74 91.3 2.87 87.0 3.43 72.9 3.54 70.7 3.74 66.8 4.12 60.6 4.18 59.8 5.00 50.0 5.48 45.6 6.12 40.8 6.71 37.3 7.42 33.7 8.22 30.4 9.08 27.5 9.87 25.3 10.8 23.1

1.73 173 2.45 122 3.00 100 3.15 95.3 3.75 79.9 3.87 77.5 4.10 73.2 4.52 66.4 4.58 65.5 5.48 54.8 6.00 50.0 6.71 44.7 7.35 40.8 8.12 36.9 9.00 33.3 9.95 30.2 10.8 27.7 11.9 25.3

0R02 0R03 0R033 0R047 0R05 0R056 0R068 0R07 0R10 0R12 0R15 0R18 0R22 0R27 0R33 0R39 0R47

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Electronics Calculations Data Handbook

138 R

50 W

100 W

200 W

250 W

300 W

0R56

5.29 9.45 5.83 8.57 6.40 7.81 7.07 7.07 7.75 6.45 8.66 5.77 9.49 5.27 10.5 4.77 11.6 4.30 12.8 3.89 14.0 3.58 15.3 3.26 16.7 2.99 18.4 2.71 20.2 2.47 22.4 2.24 24.5 2.04 27.4 1.83

7.48 13.4 8.25 12.1 9.06 11.0 10.0 10.0 11.0 9.13 12.2 8.16 13.4 7.45 14.8 6.74 16.4 6.09 18.2 5.50 19.7 5.06 21.7 4.61 23.7 4.23 26.1 3.83 28.6 3.49 31.6 3.16 34.6 2.89 38.7 2.58

10.6 18.9 11.7 17.1 12.8 15.6 14.1 14.1 15.5 12.9 17.3 11.5 19.0 10.5 21.0 9.53 23.2 8.61 25.7 7.78 27.9 7.16 30.7 6.52 33.5 5.98 36.9 5.42 40.5 4.94 44.7 4.47 49.0 4.08 54.8 3.65

11.8 21.l 13.0 19.2 14.3 17.5 15.8 15.8 17.3 14.4 19.4 12.9 21.2 11.8 23.5 10.7 26.0 9.62 28.7 8.70 31.2 8.01 34.3 7.29 37.4 6.68 41.2 6.06 45.3 5.52 50.0 5.00 54.8 4.56 61.2 4.08

13.0 23.1 14.3 21.0 15.7 19.1 17.3 17.3 19.0 15.8 21.2 14.1 23.2 12.9 25.7 11.7 28.5 10.5 31.5 9.53 34.2 8.77 37.5 7.99 41.0 7.32 45.2 6.64 49.6 6.05 54.8 5.48 60.0 5.00 67.1 4.47

0R68 0R82 1R 1R2 1R5 1R8 2R2 2R7 3R3 3R9 4R7 5R6 6R8 8R2 10R 12R 15R

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.6 Maximum power for resistors between 50 and 300 W

18R 22R 27R 33R 39R 47R 56R 68R 82R 100R 120R 150R 180R 220R 270R 330R 390R 470R

50 W

100 W

200 W

250 W

300 W

30.0 1.67 33.2 1.51 36.7 1.36 40.6 1.23 44.2 1.13 48.5 1.03 52.9 945m 58.3 857m 64.0 781m 70.7 707m 77.5 645m 86.6 577m 94.9 527m 105 477m 116 430m 128 389m 140 358m 153 326m

42.4 2.36 46.9 2.13 52.0 1.92 57.4 1.74 62.4 1.60 68.6 1.46 74.8 1.34 82.5 1.21 90.6 1.10 100 1.00 110 913m 122 816m 134 745m 148 674m 164 609m 182 550m 197 506m 217 461m

60.0 3.33 66.3 3.02 73.5 2.72 81.2 2.46 88.3 2.26 97.0 2.06 106 1.89 117 1.71 128 1.56 141 1.41 155 1.29 173 1.15 190 1.05 210 953m 232 861m 257 778m 279 716m 307 652m

67.1 3.73 74.2 3.37 82.2 3.04 90.8 2.75 98.7 2.53 108 2.31 118 2.11 130 1.92 143 1.75 158 1.58 173 1.44 194 1.29 212 1.18 235 1.07 260 962m 287 870m 312 801m 343 729m

73.5 4.08 81.2 3.69 90.0 3.33 99.5 3.02 108 2.77 119 2.53 130 2.31 143 2.10 157 1.91 173 1.73 190 1.58 212 1.41 232 1.29 257 1.17 285 1.05 315 953m 342 877m 375 799m

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

139

Electronics Calculations Data Handbook

140 R

50 W

100 W

200 W

250 W

300 W

560R

167 299m 184 271m 202 247m 224 224m 245 204m 274 183m 300 167m 332 151m 367 136m 406 123m 442 l13m 485 103m 529 94.5m 583 85.7m 640 78.1m 707 70.7m 775 64.5m 866 57.7m

237 423m 261 383m 286 349m 316 316m 346 289m 387 258m 424 236m 469 213m 520 192m 574 174m 624 160m 686 146m 748 134m 825 121m 906 ll0m 1.00k 100m 1.10k 91.3m 1.22k 81.6m

335 598m 369 542m 405 494m 447 447m 490 408m 548 365m 600 333m 663 302m 735 272m 812 246m 883 226m 970 206m 1.06k 189m 1.17k 171m 1.28k 156m 1.41k 141m 1.55k 129m 1.73k l15m

374 668m 412 606m 453 552m 500 500m 548 456m 612 408m 671 373m 742 337m 822 304m 908 275m 987 253m 1.08k 231m 1.18k 211m 1.30k 192m 1.43k 175m 1.58k 158m 1.73k 144m 1.94k 129m

410 732m 452 664m 496 605m 548 548m 600 500m 671 447m 735 408m 812 369m 900 333m 995 302m 1.08k 277m 1.19k 253m 1.30k 231m 1.43k 210m 1.57k 191m 1.73k 173m 1.90k 158m 2.12k 141m

680R 820R lk lk2 lk5 lk8 2k2 2k7 3k3 3k9 4k7 5k6 6k8 8k2 10k 12k 15k

V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A V A

Table 7.6 Maximum power for resistors between 50 and 300 W R

50 W

100 W

200 W

250 W

300 W

18k

949 52.7m 1.05k 47.7m 1.16k 43.0m 1.28k 38.9m 1.40k 35.8m 1.53k 32.6m 1.67k 29.9m 1.84k 27.1m 2.02k 24.7m 2.24k 22.4m

1.34k 74.5m 1.48k 67.4m 1.64k 60.9m 1.82k 55.0m 1.97k 50.6m 2.17k 46.1m 2.37k 42.3m 2.61k 38.3m 2.86k 34.9m 3.16k 31.6m

1.90k 105m 2.10k 95.3m 2.32k 86.1m 2.57k 77.8m 2.79k 71.6m 3.07k 65.2m 3.35k 59.8m 3.69k 54.2m 4.05k 49.4m 4.47k 44.7m

2.12k l18m 2.35k 107m 2.60k 96.2m 2.87k 87.0m 3.12k 80.1m 3.43k 72.9m 3.74k 66.8m 4.12k 60.6m 4.53k 55.2m 5.00k 50.0m

2.32k 129m 2.57k l17m 2.85k 105m 3.15k 95.3m 3.42k 87.7m 3.75k 79.9m 4.10k 73.2m 4.52k 66.4m 4.96k 60.5m 5.48k 54.8m

22k 27k 33k 39k 47k 56k 68k 82k 100k

V A V A V A V A V A V A V A V A V A V A

141

8

Voltage dividers

Introduction Figure 8.1 shows a voltage divider. It is used everywhere in electronics to reduce the level of AC and/or DC voltages. The attenuation, input resistance and output resistance are as follows:

R2

A= ~ R1 + R 2 dB--20

(8.1)

lOglo(A)

(8.2)

RI = R] + R2

(8.3)

R]R2 Ro --- ~ R1 + R 2

(8.4)

All of these parameters are given in Table 8.1 for various combinations of E24 resistor, and sorted in order of increasing attenuation. The Table starts at 1 dB and ends at 60 dB.

• Vl

R2

OUT

I @

'

!

0

Figure 8.1 A voltage divider The equations assume that the circuit is driven by a perfect voltage source, i.e. a circuit with zero output impedance, and drives a circuit of infinite input

Voltage dividers 143 impedance. If the source is the output pin of an op-amp, and the load a noninverting op-amp circuit, this is as true as makes no difference. If source resistance is a tenth of R I, or load impedance ten times R o , then the error is just under a dB; if the ratios are 100:1, then it is less than 0.1 dB.

Using Table 8.1 in cases where source and load impedances can be ignored We can simply look up the desired attenuation in column A or dB as appropriate, and choose a pair. Example 8.1: A voltage divider of 4 dB could be formed by resistors R1, R2 = 3k6, 6k2 and 3k, 5kl respectively, amongst many.

When source and load impedances cannot be ignored Selecting values for a voltage divider with ideal source and load impedances is pretty straightforward, as we saw above, but what happens when source and load begin affecting the nominal attenuation noticeably? Let us consider what happens. We'll call source impedance R s, input and output impedances of the attenuator R I and R o, as before, and load impedance R L. Ideally, we want R I to be much greater than R s, and R L much greater than R o. This implies that (as R o cannot be greater than R I) R L should be much greater than R s. ( O f course, the situation can arise where the loss due to R s and R L is actually greater than the desired attenuation. If we are in doubt, we can check this by calR,. If 1 culating a value for (Rs+RL); " t hi"S g'ves a greater attenuation than that desired, we need a buffer amplifier, rather than an attenuator.) In Table 8.1, the columns R SMAX and R L M I N give suggested values for, as their names suggest, a m a x i m u m value o f R s and a m i n i m u m o f R L. This is calculated so that, with both in place, they cause the circuit to have an attenuation of 1 dB more than the value given in the dB column. This is true so long as R s is still less than or equal to R SMAX, and R L greater than or equal to R LMIN. T h e column R LS (1 dB) is the ratio of them. (If we wish, we can scale both R: and R2 by factors of 10 in the same sense. T h e n R:,Ro,RsMAX and RLMIN will also be scaled. A, dB and RLS(1 dB) will be unaffected.) If we set out to design an attenuator to work in a circuit where R s and R L are significant, we can start out by calculating their ratio, RL I'm going to call this Rs" R LS (real). Two possible situations now arise: 1. I f R LS (real) is greater than or equal to R LS (1 dB) for the desired value ofdB in

144

Electronics Calculations Data Handbook

Table 8.1, the attenuation with R L and R s in place should be within 1 dB of nominal. (Provided that we can find a pair where R s _ R SMAX and R L ~---R LMIN-) 2. If R LS (real) is less than RLS(1 dB) the error will be more than 1 dB. In this situation the problem could be approached by other methods, or the values in the table used as a starting point. Having selected a pair of values, we can check them numerically, if we are concerned about the accuracy. First we calculate the parallel resistance of R L and R2"

RLR2

(8.5)

Rp = RL + R2 Then: a t t e n u a t i o n -- R s + Rp R1 + R p

(8.6)

T h e best way to see how things work is to look at some examples.

Example 8.2: Form a l0 dB attenuator to go between a source of 100 f] and a load of 10k. O u r ratio of load to source is 100. We look down the dB column at values around 10 dB. RLS(1 dB) is given as 63 or so here, so our error is less than 1 dB. Now look through the available pairs, to find one where we will be able to make R s and R L in range. We can see that we will need to divide by 10 to make R SMAX ~ 100 ~ and R LMIN ~ 10k. We might choose: R1 12k

R2 5k6

A 318m

dB 09.95

RI

Ro

1 7 . 6 k 3.82k

RSMAX

RLMIN RLS (1 dB)

1.03k

65.1k

63.1

This would yield R SMAX = 103 f~, R LMIN = 6.51k. We conclude that the error will be around 0.7 dB. (R s is about equal to R SMAX, so say 0.5 dB, R L is about 1.5 times R LMIN, we could guess at 0.2 dB. O r we might calculate the actual attenuation using Eqns(3.5) and (3.6). So we aim up the table to lines where dB - 9.3 or thereabouts. We find (again selecting for R SMAX > 100 9t and RLMIN ~ lOk): R1 13k

R2 6k8

A 343m

dB 09.28

RI

Ro

RSMAX

RLMIN RLS (1 dB)

19.8k

4.46k

1.16k

76.1k

65.6

and decide to try R1 = lk3, R2 - 680 f~, as RSMAX -- 116 f~, RLMIN -- 7.6k then. To check, we work backwards and calculate that R p -- 680 ~ in parallel with 10k, or 634 Q, and we get: attenuation = which is pretty good.

634 100 + 1300 + 634

- 0.312 or 10.1 dB

Voltage dividers 145 Here's another example, where the values of R L and R s make things tougher.

Example 8.3: An attenuator of 3 dB, with a source of 400 f~, and a load of 3k. Here we see that our ratio is a lot lower, a4~0~= 7.5. If we go to the part of the table where dB = 3, we see that the R LS (1 dB) column gives figures of about 67, telling us that we will lose a lot more than 1 dB due to R s and R L. Obviously we need less nominal attenuation; we want the error due to R s and R L and the nominal attenuation of the attenuator chosen to total 3 dB. A possible solution is to use the load resistance itself as R2. T h e load is 3k; looking up the table, we see: R1 lk2

R2 3k

A 714m

dB 02.92

RI 4.20k

Ro 857

R S M A X RLMIN R L s ( l d B ) 235 15.3k 65.4

which is, by good luck, ideal. R1 would ideally be lk2, but we already have a source of 400 f~, so we want the nearest value to 800 f~, which is 820 Ft. If we wanted to check, we would calculate 3ooo+3ooo 4oo+ 82o -- 0.711 -- 2.96 dB, very close.

Example 8.4: R s - lk, RL - 5k and the attenuation desired is 8 dB. Here our ratio is again low, 5. O u r loss will be too great again, so we look for values of R2 near to 5k. We find: R1 R2 h dB RI Ro RSMAX RLMIN RLS (ldB) 7k5 5kl 405m 07.86 12.6k 3.04k 732 52.3k 71.5 suggesting that we need a series resistor between source and load of ( 7 k 5 - lk), or 6k5. T h e nearest preferred value is 6k8, giving an attenuation of 5 --: 0.391 or 8.16 dB, very close. 5+6.8+1 Note that in cases where the load and source resistances form a part of the attenuator itself, we should check that they have a suitable power rating.

Table 8.1 R1

R2

6k8 6k2 lk 10k 2k2 3k3 2k7 lk6 2k lk5 3k lk3 3k9 5k6 4k3 4k7 5kl lk2 6k2 8k2 lk lk6 2k 2k4 3k6 6k8 10k 9kl 7k5 lkl 2k7 lk5 3k 2k2 3k3 lk8

56k 51k 8k2 82k 18k 27k 22k 13k 16k 12k 24k 10k 30k 43k 33k 36k 39k 9kl 47k 62k 7k5 12k 15k 18k 27k 51k 75k 68k 56k 8k2 20k llk 22k 16k 24k 13k

Voltagedividers A

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

892m 892m 891m 891m 891m 891m 891m 890m 889m 889m 889m 885m 885m 885m 885m 885m 884m 883m 883m 883m 882m 882m 882m 882m 882m 882m 882m 882m 882m 882m 881m 880m 880m 879m 879m 878m

01.00 01.00 01.00 01.00 01.00 01.00 01.01 01.01 01.02 01.02 01.02 01.06 01.06 01.06 01.06 01.07 01.07 01.08 01.08 01.08 01.09 01.09 01.09 01.09 01.09 01.09 01.09 01.09 01.09 01.09 01.10 01.11 01.11 01.12 01.12 01.13

62.8k 57.2k 9.20k 92.0k 20.2k 30.3k 24.7k 14.6k 18.0k 13.5k 27.0k ll.3k 33.9k 48.6k 37.3k 40.7k 44.1k 10.3k 53.2k 70.2k 8.50k 13.6k 17.0k 20.4k 30.6k 57.8k 85.0k 77.1k 63.5k 9.30k 22.7k 12.5k 25.0k 18.2k 27.3k 14.8k

6.06k 5.53k 891 8.91k 1.96k 2.94k 2.40k 1.42k 1.78k 1.33k 2.67k 1.15k 3.45k 4.95k 3.80k 4.16k 4.51k 1.06k 5.48k 7.24k 882 1.41k 1.76k 2.12k 3.18k 6.00k 8.82k 8.03k 6.61k 970 2.38k 1.32k 2.64k 1.93k 2.90k 1.58k

3.13k 2.85k 459 4.59k 1.01k 1.51k 1.23k 728 895 672 1.34k 568 1.70k 2.44k 1.87k 2.05k 2.22k 517 2.67k 3.52k 426 682 853 1.02k 1.54k 2.90k 4.26k 3.87k 3.19k 467 1.14k 627 1.25k 923 1.38k 749

122k lllk 17.9k 179k 39.3k 59.0k 48.2k 28.6k 35.7k 26.8k 53.6k 22.9k 68.7k 98.6k 75.7k 82.7k 89.7k 21.1k 109k 144k 17.6k 28.1k 35.2k 42.2k 63.3k 120k 176k 160k 132k 19.3k 47.4k 26.3k 52.6k 38.1k 57.2k 31.2k

38.9 38.9 39.0 39.0 39.1 39.1 39.2 39.3 39.9 39.9 39.9 40.3 40.3 40.3 40.4 40.4 40.5 40.9 40.9 41.0 41.2 41.2 41.2 41.2 41.2 41.2 41.2 41.3 41.4 41.4 41.6 41.9 41.9 41.3 41.3 41.7

Table 8.1 Voltage dividers R1 5kl 4k7 lk3 4k3 5k6 6k2 3k9 6k8 lk6 lk2 8k2 lkl 2k2 9kl lk 7k5 10k 2k4 lk5 lk8 2k7 3k 3k3 3k6 2k 5kl 5k6 4k7 6k8 lk3 6k2 4k3 7k5 lk2 2k4 lk6 8k2

R2 36k 33k 9kl 30k 39k 43k 27k 47k llk 8k2 56k 7k5 15k 62k 6k8 51k 68k 16k 10k 12k 18k 20k 22k 24k 13k 33k 36k 30k 43k 8k2 39k 27k 47k 7k5 15k 10k 51k

876m 875m 875m 875m 874m 874m 874m 874m 873m 872m 872m 872m 872m 872m 872m 872m 872m 870m 870m 870m 870m 870m 870m 870m 867m 866m 865m 865m 863m 863m 863m 863m 862m 862m 862m 862m 861m

147

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

01.15 01.16 01.16 01.16 01.17 01.17 01.17 01.17 01.18 01.19 01.19 01.19 01.19 01.19 01.19 01.19 01.19 01.21 01.21 01.21 01.21 01.21 01.21 01.21 01.24 01.25 01.26 01.26 01.28 01.28 01.28 01.28 01.29 01.29 01.29 01.29 01.30

41.1k 37.7k 10.4k 34.3k 44.6k 49.2k 30.9k 53.8k 12.6k 9.40k 64.2k 8.60k 17.2k 71.1k 7.80k 58.5k 78.0k 18.4k ll.5k 13.8k 20.7k 23.0k 25.3k 27.6k 15.0k 38.1k 41.6k 34.7k 49.8k 9.50k 45.2k 31.3k 54.5k 8.70k 17.4k ll.6k 59.2k

4.47k 4.11k 1.14k 3.76k 4.90k 5.42k 3.41k 5.94k 1.40k 1.05k 7.15k 959 1.92k 7.94k 872 6.54k 8.72k 2.09k 1.30k 1.57k 2.35k 2.61k 2.87k 3.13k 1.73k 4.42k 4.85k 4.06k 5.87k 1.12k 5.35k 3.71k 6.47k 1.03k 2.07k 1.38k 7.06k

2.08k 1.91k 526 1.74k 2.26k 2.49k 1.56k 2.72k 643 480 3.28k 439 878 3.63k 398 2.99k 3.98k 939 587 704 1.06k 1.17k 1.29k 1.41k 764 1.94k 2.14k 1.79k 2.56k 489 2.33k 1.61k 2.81k 448 896 597 3.05k

88.3k 81.3k 22.5k 74.3k 96.7k 107k 67.3k l17k 27.4k 20.5k 140k 18.8k 37.6k 155k 17.1k 128k 171k 40.9k 25.6k 30.7k 46.0k 51.1k 56.2k 61.3k 34.0k 86.6k 94.1k 78.9k l14k 21.8k 104k 72.0k 126k 20.1k 40.2k 26.8k 137k

42.5 42.6 42.7 42.8 42.9 43.0 43.0 43.1 42.6 42.7 42.8 42.8 42.8 42.8 42.9 42.9 42.9 43.5 43.5 43.5 43.5 43.5 43.5 43.5 44.5 44.6 43.9 44.2 44.5 44.6 44.6 44.7 44.8 44.9 44.9 44.9 45.0

148

Electronics Calculations Data Handbook

R1

R2

lk 10k lkl 3k9 9kl lk8 3k6 lk5 3k3 2k 3k 2k7 2k2 5k6 5kl 6k2 lk3 4k7 6k8 7k5 8k2 lk6 lk2 3k9 lkl 9kl lk 10k 4k3 lk8 2k7 3k6 2k lk5 2k2 3k3 2k4

6k2 62k 6k8 24k 56k llk 22k 9kl 20k 12k 18k 16k 13k 33k 30k 36k 7k5 27k 39k 43k 47k 9kl 6k8 22k 6k2 51k 5k6 56k 24k 10k 15k 20k llk 8k2 12k 18k 13k

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

861m 861m 861m 860m 860m 859m 859m 858m 858m 857m 857m 856m 855m 855m 855m 853m 852m 852m 852m 851m 851m 850m 850m 849m 849m 849m 848m 848m 848m 847m 847m 847m 846m 845m 845m 845m 844m

01..30 01.30 01.30 01.31 01.31 01.32 01.32 01.33 01.33 01.34 01.34 01.35 01.36 01.36 01.36 01.38 01.39 01.39 01.40 01.40 01.40 01.41 01.41 01.42 01.42 01.43 01.43 01.43 01.43 01.44 01.44 01.44 01.45 01.46 01.46 01.46 01.47

7.20k 72.0k 7.90k 27.9k 65.1k 12.8k 25.6k 10.6k 23.3k 14.0k 21.0k 18.7k 15.2k 38.6k 35.1k 42.2k 8.80k 31.7k 45.8k 50.5k 55.2k 10.7k 8.00k 25.9k 7.30k 60.1k 6.60k 66.0k 28.3k ll.8k 17.7k 23.6k 13.0k 9.70k 14.2k 21.3k 15.4k

861 8.61k 947 3.35k 7.83k 1.55k 3.09k 1.29k 2.83k 1.71k 2.57k 2.31k 1.88k 4.79k 4.36k 5.29k 1.11k 4.00k 5.79k 6.39k 6.98k 1.36k 1.02k 3.31k 934 7.72k 848 8.48k 3.65k 1.53k 2.29k 3.05k 1.69k 1.27k 1.86k 2.79k 2.03k

371 3.71k 407 1.44k 3.35k 658 1.32k 545 1.20k 720 1.08k 971 790 2.00k 1.82k 2.19k 457 1.64k 2.38k 2.62k 2.86k 555 415 1.34k 379 3.12k 342 3.42k 1.47k 612 918 1.22k 681 508 744 1.12k 807

16.7k 167k 18.4k 65.2k 152k 30.1k 60.2k 25.0k 55.1k 33.3k 50.0k 44.5k 36.2k 92.2k 83.9k 102k 21.3k 77.2k l12k 123k 135k 26.2k 19.7k 63.9k 18.0k 149k 16.4k 164k 70.3k 29.4k 44.1k 58.8k 32.3k 24.2k 35.5k 53.2k 38.7k

45.1 45.1 45.2 45.4 45.4 45.7 45.7 46.0 46.0 46.3 46.3 45.8 45.9 46.0 46.0 46.5 46.7 47.0 47.0 47.0 47.0 47.3 47.4 47.6 47.6 47.8 47.8 47.8 47.9 48.0 48.0 48.O 47.4 47.6 47.7 47.7 47.9

Table 8. 1 Voltage dividers R1 5k6 3k 6k2 5kl 6k8 8k2 lk3 7k5 lk2 9kl 3k9 lk6 4k3 4k7 lk 10k lkl lk8 lk5 2k 2k2 2k4 3k 3k6 6k8 3k3 6k2 5k6 2k7 7k5 lk3 8k2 9kl 5kl lk 10k lk6

R2 30k 16k 33k 27k 36k 43k 6k8 39k 6k2 47k 20k 8k2 22k 24k 5kl 51k 5k6 9kl 7k5 10k llk 12k 15k 18k 33k 16k 30k 27k 13k 36k 6k2 39k 43k 24k 4k7 47k 7k5

843m 842m 842m 841m 841m 840m 840m 839m 838m 838m 837m 837m 837m 836m 836m 836m 836m 835m 833m 833m 833m 833m 833m 833m 829m 829m 829m 828m 828m 828m 827m 826m 825m 825m 825m 825m 824m

149

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

01.49 01.49 01.50 01.50 01.50 01.52 01.52 01.53 01.54 01.54 01.55 01.55 01.55 01.55 01.56 01.56 01.56 01.57 01.58 01.58 01.58 01.58 01.58 01.58 01.63 01.63 01.63 01.64 01.64 01.64 01.65 01.66 01.67 01.67 01.68 01.68 01.68

35.6k 19.0k 39.2k 32.1k 42.8k 51.2k 8.10k 46.5k 7.40k 56.1k 23.9k 9.80k 26.3k 28.7k 6.10k 61.0k 6.70k 10.9k 9.00k 12.0k 13.2k 14.4k 18.0k 21.6k 39.8k 19.3k 36.2k 32.6k 15.7k 43.5k 7.50k 47.2k 52.1k 29.1k 5.70k 57.0k 9.10k

4.72k 2.53k 5.22k 4.29k 5.72k 6.89k 1.09k 6.29k 1.01k 7.62k 3.26k 1.34k 3.60k 3.93k 836 8.36k 919 1.50k 1.25k 1.67k 1.83k 2.00k 2.50k 3.00k 5.64k 2.74k 5.14k 4.64k 2.24k 6.21k 1.07k 6.78k 7.51k 4.21k 825 8.25k 1.32k

1.86k 994 2.05k 1.68k 2.24k 2.68k 424 2.43k 387 2.94k 1.25k 513 1.38k 1.50k 319 3.19k 351 571 475 634 697 760 950 1.14k 2.10k 1.02k 1.91k 1.72k 829 2.30k 396 2.49k 2.75k 1.54k 301 3.01k 481

90.2k 48.3k 99.7k 82.0k 109k 132k 20.9k 120k 19.2k 146k 62.4k 25.6k 68.7k 75.1k 16.0k 160k 17.6k 28.7k 23.7k 31.6k 34.7k 37.9k 47.3k 56.8k 107k 51.8k 97.3k 87.8k 42.3k l18k 20.4k 128k 142k 79.7k 15.6k 156k 25.0k

48.4 48.6 48.6 48.8 48.8 49.1 49.2 49.4 49.6 49.6 49.8 49.9 49.9 50.0 50.0 50.0 50.1 50.2 49.8 49.8 49.8 49.8 49.8 49.8 50.8 50.8 50.9 51.0 51.1 51.2 51.4 51.5 51.7 51.8 51.9 51.9 52.0

150

Electronics Calculations Data Handbook

R1

R2

4k7 lk2 4k3 lkl 3k9 2k4 lk8 2k 3k3 2k2 lk5 2k7 3k6 6k8 7k5 8k2 6k2 3k 5kl lk3 lk 10k 5k6 9kl lkl 4k7 lk6 lk2 4k3 lk8 2k4 3k6 2k2 lk5 3k9 2k 2k7

22k 5k6 20k 5kl 18k Ilk 8k2 9kl 15k 10k 6k8 12k 16k 30k 33k 36k 27k 13k 22k 5k6 4k3 43k 24k 39k 4k7 20k 6k8 5kl 18k 7k5 10k 15k 9kl 6k2 16k 8k2 llk

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

824m 824m 823m 823m 822m 821m 820m 820m 820m 820m 819m 816m 816m 815m 815m 814m 813m 813m 812m 812m 811m 811m 811m 811m 810m 810m 810m 810m 807m 806m 806m 806m 805m 805m 804m 804m 803m

01.68 01.69 01.69 01.70 01.70 01.71 01.72 01.73 01.73 01.73 01.73 01.76 01.76 01.77 01.78 01.78 01.80 01.80 01.81 01.81 01.82 01.82 01.82 01.82 01.83 01.83 01.84 01.84 01.86 01.87 01.87 01.87 01.88 01.88 01.89 01.90 01.91

26.7k 6.80k 24.3k 6.20k 21.9k 13.4k 10.0k ll.lk 18.3k 12.2k 8.30k 14.7k 19.6k 36.8k 40.5k 44.2k 33.2k 16.0k 27.1k 6.90k 5.30k 53.0k 29.6k 48.1k 5.80k 24.7k 8.40k 6.30k 22.3k 9.30k 12.4k 18.6k ll.3k 7.70k 19.9k 10.2k 13.7k

3.87k 988 3.54k 905 3.21k 1.97k 1.48k 1.64k 2.70k 1.80k 1.23k 2.20k 2.94k 5.54k 6.11k 6.68k 5.04k 2.44k 4.14k 1.06k 811 8.11k 4.54k 7.38k 891 3.81k 1.30k 971 3.47k 1.45k 1.94k 2.90k 1.77k 1.21k 3.14k 1.61k 2.17k

1.41k 359 1.28k 328 1.17k 714 533 591 975 650 442 783 1.04k 1.96k 2.16k 2.36k 1.77k 853 1.44k 368 282 2.82k 1.58k 2.56k 309 1.32k 447 335 1.20k 500 667 1.00k 608 414 1.07k 549 737

73.3k 18.7k 67.0k 17.1k 60.2k 37.0k 27.7k 30.8k 50.8k 33.8k 23.1k 41.4k 55.1k 104k ll5k 125k 94.6k 45.7k 77.7k 19.8k 15.2k 152k 85.2k 138k 16.7k 71.5k 24.3k 18.2k 64.5k 27.0k 36.0k 54.0k 32.9k 22.5k 58.3k 29.9k 40.3k

52.0 52.1 52.2 52.3 51.5 51.8 52.0 52.0 52.1 52.1 52.1 52.8 52.8 53.0 53.1 53.2 53.5 53.7 53.8 53.8 53.9 53.9 54.0 54.0 54.1 54.4 54.4 54.4 53.8 54.0 54.0 54.0 54.2 54.2 54.5 54.5 54.7

Table 8. 1 Voltage dividers R1

R2

8k2 7k5 3k 6k8 9kl 3k3 5k6 lk3 5kl lk2 lkl lk 10k lk6 6k2 3k9 4k7 2k4 lk8 2k lk5 2k2 4k3 2k7 3k 8k2 3k3 9kl lk3 3k6 lk 7k5 10k lk2 5k6 6k2 lkl

33k 30k 12k 27k 36k 13k 22k 5kl 20k 4k7 4k3 3k9 39k 6k2 24k 15k 18k 9kl 6k8 7k5 5k6 8k2 16k 10k llk 30k 12k 33k 4k7 13k 3k6 27k 36k 4k3 20k 22k 3k9

801m 800m 800m 799m 798m 798m 797m 797m 797m 797m 796m 796m 796m 795m 795m 794m 793m 791m 791m 789m 789m 788m 788m 787m 786m 785m 784m 784m 783m 783m 783m 783m 783m 782m 781m 780m 780m

151

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

01.93 01.94 01.94 01.95 01..96 01.96 01.97 01.97 01.97 01.98 01.98 01.98 01.98 01.99 02.00 02.01 02.02 02.03 02.04 02.05 02.06 02.06 02.07 02.08 02.09 02.10 02.11 02.12 02.12 02.12 02.13 02.13 02.13 02.14 02.14 02.16 02.16

41.2k 37.5k 15.0k 33.8k 45.1k 16.3k 27.6k 6.40k 25.1k 5.90k 5.40k 4.90k 49.0k 7.80k 30.2k 18.9k 22.7k ll.5k 8.60k 9.50k 7.10k 10.4k 20.3k 12.7k 14.0k 38.2k 15.3k 42.1k 6.00k 16.6k 4.60k 34.5k 46.0k 5.50k 25.6k 28.2k 5.00k

6.57k 6.00k 2.40k 5.43k 7.26k 2.63k 4.46k 1.04k 4.06k 956 876 796 7.96k 1.27k 4.93k 3.10k 3.73k 1.90k 1.42k 1.58k 1.18k 1.73k 3.39k 2.13k 2.36k 6.44k 2.59k 7.13k 1.02k 2.82k 783 5.87k 7.83k 938 4.38k 4.84k 858

2.22k 2.02k 807 1.82k 2.43k 877 1.48k 344 1.35k 317 290 264 2.64k 419 1.62k 1.02k 1.22k 618 467 516 385 565 1.10k 689 760 2.07k 831 2.29k 326 901 250 1.87k 2.50k 299 1.39k 1.53k 271

122k l12k 44.6k 101k 135k 48.9k 83.0k 19.3k 75.6k 17.8k 16.3k 14.8k 148k 23.7k 91.7k 57.6k 69.4k 35.3k 26.2k 29.1k 21.8k 32.0k 62.4k 39.2k 43.4k l19k 47.7k 131k 18.8k 51.9k 14.4k 108k 144k 17.3k 80.6k 89.1k 15.8k

55.1 55.3 55.3 55.6 55.7 55.8 55.9 56.0 56.0 56.0 56.1 56.2 56.2 56.5 56.5 56.7 56.9 57.1 56.2 56.4 56.6 56.6 56.7 56.8 57.1 57.2 57.4 57.5 57.6 57.6 57.7 57.7 57.7 57.9 58.0 58.2 58.2

152

R1 5kl 6k8 lk6 4k3 lk8 2k4 2k2 4k7 2k lk5 2k7 3k9 3k 3k3 3k6 lk3 lk 10k 9kl 8k2 lkl lk2 6k8 6k2 5k6 7k5 4k7 lk6 5kl lk5 2k4 lk8 2k 2k2 3k9 3k6 2k7

Electronics Calculations Data Handbook

R2 18k 24k 5k6 15k 6k2 8k2 7k5 16k 6k8 5kl 9kl 13k 10k llk 12k 4k3 3k3 33k 30k 27k 3k6 3k9 22k 20k 18k 24k 15k 5kl 16k 4k7 7k5 5k6 6k2 6k8 12k llk 8k2

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

779m 779m 778m 777m 775m 774m 773m 773m 773m 773m 771m 769m 769m 769m 769m 768m 767m 767m 767m 767m 766m 765m 764m 763m 763m 762m 761m 761m 758m 758m 758m 757m 756m 756m 755m 753m 752m

02.17 02.17 02.18 02.19 02.21 02.23 02.23 02.24 02.24 02.24 02.26 02.28 02.28 02.28 02.28 02.29 02.30 02.30 02.30 02.30 02.32 02.33 02.34 02.35 02.35 02.36 02.37 02.37 02.40 02.41 02.41 02.42 02.43 02.43 02.44 02.46 02.47

23.1k 30.8k 7.20k 19.3k 8.00k 10.6k 9.70k 20.7k 8.80k 6.60k ll.8k 16.9k 13.0k 14.3k 15.6k 5.60k 4.30k 43.0k 39.1k 35.2k 4.70k 5.10k 28.8k 26.2k 23.6k 31.5k 19.7k 6.70k 21.1k 6.20k 9.90k 7.40k 8.20k 9.00k 15.9k 14.6k 10.9k

3.97k 5.30k 1.24k 3.34k 1.40k 1.86k 1.70k 3.63k 1.55k 1.16k 2.08k 3.00k 2.31k 2.54k 2.77k 998 767 7.67k 6.98k 6.29k 843 918 5.19k 4.73k 4.27k 5.71k 3.58k 1.22k 3.87k 1.14k 1.82k 1.36k 1.51k 1.66k 2.94k 2.71k 2.03k

1.25k 1.67k 390 1.05k 434 575 526 1.12k 477 358 640 926 712 784 855 307 236 2.36k 2.14k 1.93k 258 279 1.58k 1.44k 1.29k 1.73k 1.08k 367 1.16k 339 542 405 449 493 870 799 597

73.2k 97.6k 22.9k 61.6k 25.7k 34.2k 31.4k 67.0k 28.5k 21.4k 38.4k 54.8k 42.1k 46.3k 50.5k 18.2k 14.0k 140k 127k l15k 15.4k 16.7k 94.8k 86.4k 78.0k 104k 65.3k 22.2k 70.6k 20.8k 33.2k 24.9k 27.6k 30.4k 53.8k 49.5k 37.1k

58.4 58.4 58.8 58.9 59.3 59.6 59.6 59.7 59.7 59.7 59.9 59.1 59.1 59.1 59.1 59.4 59.4 59.4 59.5 59.5 59.7 59.9 60.1 60.2 60.3 60.4 60.5 60.5 61.2 61.2 61.3 61.4 61.5 61.6 61.8 62.0 62.2

Table 8. 1 Voltage dividers R1 3k 3k3 4k3 lk lkl lk2 lk3 10k 9kl 5kl 6k8 lk6 7k5 8k2 6k2 lk5 5k6 2k4 lk8 3k9 2k2 2k 4k3 2k7 3k6 lk3 4k7 3k3 lk2 3k lkl 10k lk lk6 8k2 5k6 7k5

R2 9kl 10k 13k 3k 3k3 3k6 3k9 30k 27k 15k 20k 4k7 22k 24k 18k 4k3 16k 6k8 5kl llk 6k2 5k6 12k 7k5 10k 3k6 13k 9kl 3k3 8k2 3k 27k 2k7 4k3 22k 15k 20k

752m 752m 751m 750m 750m 750m 750m 750m 748m 746m 746m 746m 746m 745m 744m 741m 741m 739m 739m 738m 738m 737m 736m 735m 735m 735m 734m 734m 733m 732m 732m 730m 730m 729m 728m 728m 727m

153

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

02.47 02.48 02.48 02.50 02.50 02.50 02.50 02.50 02.52 02.54 02.54 02.54 O2.55 O2.55 02.57 02.60 02.61 02.63 02.63 02.64 02.64 02.65 02.66 02.67 02.67 02.68 02.68 02.69 02.69 02.71 02.71 02.74 02.74 02.75 02.75 02.76 02.77

12.1k 13.3k 17.3k 4.00k 4.40k 4.80k 5.20k 40.0k 36.1k 20.1k 26.8k 6.30k 29.5k 32.2k 24.2k 5.80k 21.6k 9.20k 6.90k 14.9k 8.40k 7.60k 16.3k 10.2k 13.6k 4.90k 17.7k 12.4k 4.50k ll.2k 4.10k 37.0k 3.70k 5.90k 30.2k 20.6k 27.5k

2.26k 2.48k 3.23k 750 825 900 975 7.50k 6.81k 3.81k 5.07k 1.19k 5.59k 6.11k 4.61k 1.11k 4.15k 1.77k 1.33k 2.88k 1.62k 1.47k 3.17k 1.99k 2.65k 955 3.45k 2.42k 880 2.20k 805 7.30k 730 1.17k 5.97k 4.08k 5.45k

662 728 947 219 241 263 285 2.19k 1.98k 1.10k 1.47k 345 1.63k 1.78k 1.34k 321 1.19k 509 382 824 465 420 902 564 752 271 978 685 249 619 227 2.05k 205 326 1.67k 1.14k 1.52k

41.2k 45.3k 59.0k 13.7k 15.1k 16.4k 17.8k 137k 124k 69.5k 92.6k 21.8k 101k ll0k 83.4k 20.1k 75.0k 32.1k 24.1k 52.1k 29.4k 26.6k 57.2k 35.9k 47.9k 17.3k 62.5k 43.8k 15.9k 39.7k 14.6k 132k 13.2k 21.1k 108k 73.8k 98.7k

62.2 62.2 62.3 62.6 62.6 62.6 62.6 62.6 62.9 63.1 63.1 63.1 62.0 62.0 62.3 62.7 62.8 63.0 63.0 63.2 63.2 63.4 63.5 63.6 63.6 63.8 63.8 63.9 64.0 64.2 64.3 64.6 64.6 64.7 64.7 64.8 64.9

154 R1 6k8 9kl lk8 lk5 2k4 6k2 3k9 4k3 4k7 2k 5kl 2k2 lk3 3k6 2k7 lk2 3k 3k3 lkl 8k2 lk6 6k2 9kl lk5 10k lk 7k5 lk8 5kl 6k8 2k 4k7 2k4 3k9 4k3 5k6 2k2

Electronics Calculations Data Handbook R2 18k 24k 4k7 3k9 6k2 16k 10k llk 12k 5kl 13k 5k6 3k3 9kl 6k8 3k 7k5 8k2 2k7 20k 3k9 15k 22k 3k6 24k 2k4 18k 4k3 12k 16k 4k7 llk 5k6 9kl 10k 13k 5kl

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

726m 725m 723m 722m 721m 721m 719m 719m 719m 718m 718m 718m 717m 717m 716m 714m 714m 713m 711m 709m 709m 708m 707m 706m 706m 706m 706m 705m 702m 702m 701m 701m 700m 700m 699m 699m 699m

02.78 02.79 02.82 02.83 02.84 02.84 02.86 02.87 02.87 02.87 02.87 02.88 02.88 02.90 02.90 02.92 02.92 02.94 02.97 02.98 02.99 03.00 03.01 03.03 03.03 03.03 03.03 03.04 03.08 03.08 03.08 03.09 03.10 03.10 03.11 03.11 03.12

24.8k 33.1k 6.50k 5.40k 8.60k 22.2k 13.9k 15.3k 16.7k 7.10k 18.1k 7.80k 4.60k 12.7k 9.50k 4.20k 10.5k ll.5k 3.80k 28.2k 5.50k 21.2k 31.1k 5.10k 34.0k 3.40k 25.5k 6.10k 17.1k 22.8k 6.70k 15.7k 8.00k 13.0k 14.3k 18.6k 7.30k

4.94k 6.60k 1.30k 1.08k 1.73k 4.47k 2.81k 3.09k 3.38k 1.44k 3.66k 1.58k 933 2.58k 1.93k 857 2.14k 2.35k 782 5.82k 1.13k 4.39k 6.44k 1.06k 7.06k 706 5.29k 1.27k 3.58k 4.77k 1.40k 3.29k 1.68k 2.73k 3.01k 3.91k 1.54k

1.37k 1.83k 359 298 475 1.23k 768 846 923 392 1.00k 431 254 702 525 235 586 642 212 1.57k 307 1.18k 1.74k 285 1.90k 190 1.42k 340 954 1.27k 374 876 446 726 798 1.04k 407

89.3k ll9k 23.5k 19.6k 31.3k 80.8k 50.8k 55.9k 61.1k 26.0k 66.3k 28.6k 16.9k 46.7k 34.9k 15.3k 38.4k 42.1k 14.0k 104k 20.3k 78.6k l15k 19.0k 126k 12.6k 94.9k 22.7k 64.1k 85.5k 25.1k 59.0k 30.1k 48.9k 53.9k 70.1k 27.5k

65.1 65.3 65.5 65.7 65.9 65.9 66.1 66.1 66.2 66.2 66.2 66.3 66.3 66.4 66.5 65.4 65.4 65.6 65.9 66.1 66.1 66.3 66.4 66.7 66.7 66.7 66.7 66.8 67.2 67.2 67.2 67.3 67.4 67.4 67.5 67.6 67.6

Table 8. 1 Voltage dividers R1 lk3 2k7 3k6 3k3 3k lk6 lk2 6k8 lk lk5 10k 9kl 8k2 lkl lk8 5kl 2k 5k6 2k2 7k5 4k7 2k4 4k3 3k9 6k2 3k6 lk3 2k7 3k lk6 3k3 lk lk5 lk8 7k5 lkl lk2

R2 3k 6k2 8k2 7k5 6k8 3k6 2k7 15k 2k2 3k3 22k 20k 18k 2k4 3k9 llk 4k3 12k 4k7 16k 10k 5kl 9kl 8k2 13k 7k5 2k7 5k6 6k2 3k3 6k8 2k 3k 3k6 15k 2k2 2k4

698m 697m 695m 694m 694m 692m 692m 688m 688m 688m 688m 687m 687m 686m 684m 683m 683m 682m 681m 681m 680m 680m 679m 678m 677m 676m 675m 675m 674m 673m 673m 667m 667m 667m 667m 667m 667m

155

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

03.13 03.14 03.16 03.17 03.17 03.19 03.19 03.25 03.25 03.25 03.25 03.26 03.26 03.28 03.30 03.31 03.32 03.33 03.34 03.34 03.35 03.35 03.36 03.38 03.39 03.41 03.41 03.42 03.43 03.43 03.44 03.52 03.52 03.52 03.52 03.52 03.52

4.30k 8.90k ll.8k 10.8k 9.80k 5.20k 3.90k 21.8k 3.20k 4.80k 32.0k 29.1k 26.2k 3.50k 5.70k 16.1k 6.30k 17.6k 6.90k 23.5k 14.7k 7.50k 13.4k 12.1k 19.2k ll.lk 4.00k 8.30k 9.20k 4.90k lO.lk 3.00k 4.50k 5.40k 22.5k 3.30k 3.60k

907 1.88k 2.50k 2.29k 2.08k 1.11k 831 4.68k 688 1.03k 6.88k 6.25k 5.63k 754 1.23k 3.48k 1.37k 3.82k 1.50k 5.11k 3.20k 1.63k 2.92k 2.64k 4.20k 2.43k 878 1.82k 2.02k 1.08k 2.22k 667 1.OOk 1.20k 5.00k 733 800

240 497 659 603 547 290 218 1.22k 179 268 1.79k 1.62k 1.46k 195 318 899 352 982 385 1.31k 821 419 748 682 1.08k 626 226 468 519 276 570 169 254 304 1.27k 186 203

16.3k 33.7k 44.8k 41.1k 37.3k 19.8k 14.9k 83.8k 12.3k 18.5k 123k l12k 101k 13.5k 22.1k 62.4k 24.5k 68.4k 26.9k 91.5k 57.3k 29.2k 52.3k 46.9k 74.4k 43.1k 15.6k 32.3k 35.9k 19.1k 39.4k ll.8k 17.7k 21.3k 88.7k 13.0k 14.2k

67.7 67.9 68.1 68.1 68.2 68.4 68.4 68.9 69.0 69.0 69.0 69.0 69.0 69.2 69.4 69.5 69.6 69.7 69.7 69.8 69.8 69.8 69.9 68.7 68.8 68.9 69.0 69.0 69.1 69.2 69.2 70.0 70.0 70.0 70.0 70.0 70.0

156

R1

Electronics Calculations Data Handbook

R2

lOk 20k 9kl 18k 5k6 llk 5kl lOk 2k4 4k7 2k2 4k3 8k2 16k 2k 3k9 4k7 9kl 6k2 12k 3k9 7k5 6k8 13k 4k3 8k2 2k7 5kl 3k6 6k8 3k3 6k2 lk6 3k 3k 5k6 lk3 2k4 lk8 3k3 lk2 2k2 8k2 15k lkl 2k lk lk8 lk5 2k7 2k 3k6 lOk 18k 2k4 4k3 5k6 lOk 5kl 9kl 6k2 llk 2k2 3k9 6k8 12k 9kl 16k 4k7 8k2 4k3 7k5 3k9 6k8

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

667m 664m 663m 662m 662m 662m 661m 661m 659m 659m 658m 657m 656m 654m 654m 653m 652m 651m 649m 647m 647m 647m 645m 643m 643m 643m 643m 642m 641m 641m 640m 639m 638m 637m 636m 636m 636m

03.52 03.55 03.57 03.58 03.58 03.59 03.59 03.60 03.62 03.62 03.64 03.65 03.66 03.69 03.69 03.71 03.71 03.73 03.76 03.78 03.78 03.79 03.81 03.84 03.84 03.84 03.84 03.85 03.86 03.86 03.88 03.89 03.90 03.91 03.94 03.94 03.94

30.Ok 27.1k 16.6k 15.1k 7.10k 6.50k 24.2k 5.90k 13.8k 18.2k ll.4k 19.8k 12.5k 7.80k lO.4k 9.50k 4.60k 8.60k 3.70k 5.10k 3.40k 23.2k 3.10k 2.80k 4.20k 5.60k 28.0k 6.70k 15.6k 14.2k 17.2k 6.10k 18.8k 25.1k 12.9k ll.8k lO.7k

6.67k 6.04k 3.71k 3.38k 1.59k 1.46k 5.42k 1.32k 3.10k 4.09k 2.57k 4.46k 2.82k 1.77k 2.35k 2.15k 1.04k 1.95k 843 1.16k 776 5.30k 710 643 964 1.29k 6.43k 1.54k 3.59k 3.27k 3.97k 1.41k 4.34k 5.80k 2.99k 2.73k 2.48k

1.69k 1.53k 935 851 400 366 1.36k 332 778 1.03k 642 1.12k 704 440 586 535 259 485 209 287 192 1.31k 175 158 237 316 1.58k 378 879 800 969 344 1.06k 1.41k 727 665 603

l18k 107k 65.8k 59.9k 28.2k 25.8k 96.2k 23.5k 55.0k 72.5k 45.5k 79.2k 50.1k 31.3k 41.8k 38.2k 18.5k 34.7k 15.Ok 20.7k 13.8k 94.1k 12.6k ll.4k 17.1k 22.8k l14k 27.3k 63.7k 58.0k 70.4k 25.0k 77.0k 103k 53.0k 48.5k 44.0k

70.0 70.2 70.4 70.4 70.5 70.5 70.5 70.6 70.7 70.7 70.9 71.0 71.1 71.3 71.3 71.4 71.4 71.5 71.8 71.9 71.9 72.0 72.1 72.3 72.3 72.3 72.3 72.4 72.5 72.5 72.6 72.6 72.7 72.8 72.9 72.9 72.9

Table 8. 1 Voltage dividers R1

R2

2k7 7k5 3k6 3k 3k3 lk3 lk6 lk2 lk8 2k 9kl lkl 2k2 2k4 5k6 6k8 6k2 5kl lk 7k5 10k lk5 4k7 2k7 3k9 8k2 4k3 3k 3k6 3k3 lk3 lk lk2 lk8 2k 2k2 2k4

4k7 13k 6k2 5kl 5k6 2k2 2k7 2k 3k 3k3 15k lk8 3k6 3k9 9kl llk 10k 8k2 lk6 12k 16k 2k4 7k5 4k3 6k2 13k 6k8 4k7 5k6 5kl 2k lk5 lk8 2k7 3k 3k3 3k6

635m 634m 633m 630m 629m 629m 628m 625m 625m 623m 622m 621m 621m 619m 619m 618m 617m 617m 615m 615m 615m 615m 615m 614m 614m 613m 613m 610m 609m 607m 606m 600m 600m 600m 600m 600m 600m

157

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

03.94 03.96 03.98 04.02 O4.O2 04.03 04.04 04.08 04.08 04.12 04.12 04.14 04.14 04.17 04.17 04.18 04.19 04.20 04.22 04.22 04.22 04.22 04.23 04.23 04.24 04.25 04.26 04.29 04.31 04.33 04.35 04.44 04.44 04.44 04.44 04.44 04.44

7.40k 20.5k 9.80k 8.10k 8.90k 3.50k 4.30k 3.20k 4.80k 5.30k 24.1k 2.90k 5.80k 6.30k 14.7k 17.8k 16.2k 13.3k 2.60k 19.5k 26.0k 3.90k 12.2k 7.00k 10.1k 21.2k ll.lk 7.70k 9.20k 8.40k 3.30k 2.50k 3.00k 4.50k 5.00k 5.50k 6.00k

1.71k 4.76k 2.28k 1.89k 2.08k 817 1.00k 750 1.13k 1.25k 5.66k 683 1.37k 1.49k 3.47k 4.20k 3.83k 3.14k 615 4.62k 6.15k 923 2.89k 1.66k 2.39k 5.03k 2.63k 1.83k 2.19k 2.00k 788 600 720 1.08k 1.20k 1.32k 1.44k

417 1.16k 552 461 507 199 245 182 273 302 1.37k 165 330 359 837 1.01k 922 757 148 1.11k 1.48k 222 694 398 575 1.21k 632 438 524 478 188 142 171 256 285 313 341

30.4k 84.4k 40.4k 33.2k 36.5k 14.4k 17.6k 13.2k 19.8k 21.9k 99.5k 12.0k 24.0k 26.1k 60.9k 73.8k 67.2k 55.3k 10.8k 81.1k 108k 16.2k 50.8k 29.1k 42.1k 88.4k 46.3k 32.2k 38.5k 35.2k 13.8k 10.5k 12.7k 19.0k 21.1k 23.2k 25.3k

73.0 73.1 73.1 71.9 72.0 72.0 72.1 72.3 72.3 72.5 72.6 72.7 72.7 72.8 72.8 72.9 72.9 73.0 73.1 73.1 73.1 73.1 73.1 73.2 73.2 73.2 73.3 73.4 73.5 73.6 73.7 74.1 74.1 74.1 74.1 74.1 74.1

158 R1 10k lk6 5kl 6k8 6k2 lk5 7k5 5k6 8k2 lkl 4k7 2k7 4k3 3k9 3k 9kl 3k3 3k6 lk3 lk6 2k4 lkl 2k2 2k 8k2 5k6 6k8 lk2 lk5 lk8 2k7 5kl 7k5 6k2 4k7 9kl 3k9

Electronics Calculations Data Handbook R2 15k 2k4 7k5 10k 9kl 2k2 llk 8k2 12k lk6 6k8 3k9 6k2 5k6 4k3 13k 4k7 5kl lk8 2k2 3k3 lk5 3k 2k7 llk 7k5 9kl lk6 2k 2k4 3k6 6k8 10k 8k2 6k2 12k 5kl

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

600m 600m 595m 595m 595m 595m 595m 594m 594m 593m 591m 591m 590m 589m 589m 588m 588m 586m 581m 579m 579m 577m 577m 574m 573m 573m 572m 571m 571m 571m 571m 571m 571m 569m 569m 569m 567m

04.44 04.44 04.51 04.51 04.51 04.52 04.52 04.52 04.52 04.54 04.56 04.57 04.58 04.59 04.60 04.61 04.62 04.64 04.72 04.75 04.75 04.78 04.78 04.81 04.84 04.84 04.85 04.86 04.86 04.86 04.86 04.86 04.86 04.89 04.90 04.90 04.93

25.0k 4.00k 12.6k 16.8k 15.3k 3.70k 18.5k 13.8k 20.2k 2.70k ll.5k 6.60k 10.5k 9.50k 7.30k 22.1k 8.00k 8.70k 3.10k 3.80k 5.70k 2.60k 5.20k 4.70k 19.2k 13.1k 15.9k 2.80k 3.50k 4.20k 6.30k ll.9k 17.5k 14.4k 10.9k 21.1k 9.00k

6.00k 960 3.04k 4.05k 3.69k 892 4.46k 3.33k 4.87k 652 2.78k 1.60k 2.54k 2.30k 1.77k 5.35k 1.94k 2.11k 755 926 1.39k 635 1.27k 1.15k 4.70k 3.21k 3.89k 686 857 1.03k 1.54k 2.91k 4.29k 3.53k 2.67k 5.18k 2.21k

1.42k 228 717 956 871 211 1.05k 785 1.15k 154 654 376 598 541 415 1.26k 455 495 176 216 324 148 296 267 1.09k 746 905 159 199 239 359 677 996 820 621 1.20k 518

105k 16.9k 53.3k 71.1k 64.8k 15.7k 78.4k 58.5k 85.6k ll.5k 48.8k 28.0k 44.6k 40.4k 31.1k 94.1k 34.1k 37.1k 13.3k 16.3k 24.4k ll.2k 22.3k 20.2k 82.5k 56.3k 68.4k 12.0k 15.1k 18.1k 27.1k 51.2k 75.3k 62.0k 47.0k 90.9k 38.4k

74.1 74.1 74.4 74.4 74.4 74.4 74.4 74.4 74.5 74.5 74.6 74.6 74.7 74.7 74.7 74.8 74.8 74.9 75.2 75.3 75.3 75.4 75.4 75.5 75.5 75.6 75.6 75.6 75.6 75.6 75.6 75.6 75.6 75.7 75.7 75.7 74.3

Table 8. 1 Voltage dividers R1

R2

3k6 4k7 3k3 4k3 4k3 5k6 lk3 lk 3k9 3k 10k 13k lk2 lk5 lk6 2k 2k4 3k lk3 lk6 2k2 2k7 2k7 3k3 lk8 2k2 8k2 10k 5kl 6k2 5k6 6k8 7k5 9kl 6k2 7k5 llk 9kl 6k8 8k2 3k9 4k7 lk2 lk lk5 lk8 2k4 2k 3k6 3k 10k 12k 3k6 4k3 4k7 5k6 4k3 5kl lk3 lkl 3k3 3k9 lk3 lk5 lk6 lk8 2k4 2k7 lk8 2k 2k7 3k 8k2 9kl

566m 566m 566m 565m 565m 565m 556m 556m 556m 552m 551m 550m 550m 549m 549m 548m 548m 547m 547m 547m 547m 545m 545m 545m 545m 545m 544m 544m 543m 542m 542m 536m 529m 529m 526m 526m 526m

159

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

04.94 04.95 04.95 04.96 04.96 04.96 05.11 05.11 05.11 05.17 05.18 05.19 05.19 O5.20 05.21 05.22 05.22 05.23 05.24 05.25 05.25 05.26 05.26 05.26 05.26 05.26 05.28 05.29 05.31 05.33 05.33 05.42 05.52 05.52 05.58 05.58 05.58

8.30k 7.60k 9.90k 2.30k 6.90k 23.0k 2.70k 3.60k 5.40k 2.90k 4.90k 6.00k 4.00k 18.2k ll.3k 12.4k 16.6k 13.7k 20.1k 15.0k 8.60k 2.20k 3.30k 4.40k 6.60k 22.0k 7.90k 10.3k 9.40k 2.40k 7.20k 2.80k 3.40k 5.10k 3.80k 5.70k 17.3k

2.04k 1.87k 2.43k 565 1.70k 5.65k 667 889 1.33k 717 1.21k 1.49k 990 4.51k 2.80k 3.07k 4.11k 3.39k 4.98k 3.72k 2.13k 545 818 1.09k 1.64k 5.45k 1.96k 2.56k 2.33k 596 1.79k 696 847 1.27k 947 1.42k 4.31k

477 437 569 132 397 1.32k 155 207 310 167 282 345 230 1.05k 650 713 954 787 1.16k 862 494 126 190 253 379 1.26k 454 592 540 138 414 161 195 293 218 328 994

35.5k 32.5k 42.3k 9.83k 29.5k 98.3k ll.6k 15.5k 23.2k 12.5k 21.1k 25.8k 17.2k 78.4k 48.7k 53.4k 71.5k 59.1k 86.6k 64.7k 37.1k 9.49k 14.2k 19.0k 28.5k 94.9k 34.1k 44.5k 40.6k 10.4k 31.1k 12.1k 14.7k 22.1k 16.5k 24.7k 75.0k

74.3 74.3 74.3 74.3 74.3 74.3 74.7 74.7 74.7 74.9 74.9 74.9 74.9 74.9 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.1 75.1 75.1 75.1 75.1 75.3 75.4 75.4 75.5 75.5 75.5

160 R1 5k6 6k8 3k9 lk 2k 3k 10k 9kl 5kl 6k2 7k5 4k3 lkl 2k2 3k3 4k7 lk2 3k6 lk5 lk lkl lk2 lk3 lk5 lk6 lk8 2k 2k2 2k4 2k7 3k 3k3 3k6 3k9 4k3 4k7 5kl

Electronics Calculations Data Handbook

R2 6k2 7k5 4k3 lkl 2k2 3k3 llk 10k 5k6 6k8 8k2 4k7 lk2 2k4 3k6 5kl lk3 3k9 lk6 lk lkl lk2 lk3 lk5 lk6 lk8 2k 2k2 2k4 2k7 3k 3k3 3k6 3k9 4k3 4k7 5kl

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

525m 524m 524m 524m 524m 524m 524m 524m 523m 523m 522m 522m 522m 522m 522m 520m 520m 520m 516m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m 500m

05.59 05.61 05.61 05.62 05.62 05.62 05.62 05.62 05.62 05.63 05.64 05.64 O5.65 05.65 05.65 05.67 O5.68 05.68 05.74 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02 06.02

ll.8k 14.3k 8.20k 2.10k 4.20k 6.30k 21.0k 19.1k 10.7k 13.0k 15.7k 9.00k 2.30k 4.60k 6.90k 9.80k 2.50k 7.50k 3.10k 2.00k 2.20k 2.40k 2.60k 3.00k 3.20k 3.60k 4.00k 4.40k 4.80k 5.40k 6.00k 6.60k 7.20k 7.80k 8.60k 9.40k 10.2k

2.94k 3.57k 2.05k 524 1.05k 1.57k 5.24k 4.76k 2.67k 3.24k 3.92k 2.25k 574 1.15k 1.72k 2.45k 624 1.87k 774 500 550 600 650 750 800 900 1.00k 1.10k 1.20k 1.35k 1.50k 1.65k 1.80k 1.95k 2.15k 2.35k 2.55k

678 822 471 121 241 362 1.21k 1.10k 615 747 902 517 132 264 397 563 144 431 178 115 126 138 149 172 184 207 230 253 276 310 345 379 414 448 494 540 586

51.2k 62.0k 35.6k 9.11k 18.2k 27.3k 91.1k 82.9k 46.4k 56.4k 68.1k 39.1k 9.98k 20.0k 30.0k 42.6k 10.9k 32.6k 13.5k 8.70k 9.57k 10.4k ll.3k 13.0k 13.9k 15.7k 17.4k 19.1k 20.9k 23.5k 26.1k 28.7k 31.3k 33.9k 37.4k 40.9k 44.4k

75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.5 75.6 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.7

Table 8. 1 Voltage dividers R1 5k6 6k2 6k8 7k5 8k2 9kl 10k lk6 lk3 3k9 5kl lk2 2k4 3k6 4k7 8k2 6k8 5k6 10k lkl 2k2 llk 3k3 4k3 7k5 6k2 9kl 2k 3k lk8 2k7 lk5 lk3 3k9 5kl 5k6 4k3

R2 5k6 6k2 6k8 7k5 8k2 9kl 10k lk5 lk2 3k6 4k7 lkl 2k2 3k3 4k3 7k5 6k2 5kl 9kl lk 2k 10k 3k 3k9 6k8 5k6 8k2 lk8 2k7 lk6 2k4 lk3 lkl 3k3 4k3 4k7 3k6

500m 500m 500m 500m 500m 500m 500m 484m 480m 480m 480m 478m 478m 478m 478m 478m 477m 477m 476m 476m 476m 476m 476m 476m 476m 475m 474m 474m 474m 471m 471m 464m 458m 458m 457m 456m 456m

161

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

06.02 06.O2 06.02 O6.02 O6.02 06.02 06.02 06.31 06.38 06.38 06.38 06.41 06.41 06.41 06.42 06.42 06.43 06.44 06.44 06.44 06.44 06.44 06.44 06.45 06.46 06.47 06.48 06.49 06.49 06.55 06.55 06.66 06.78 06.78 06.79 06.81 06.83

ll.2k 12.4k 13.6k 15.0k 16.4k 18.2k 20.0k 3.10k 2.50k 7.50k 9.80k 2.30k 4.60k 6.90k 9.00k 15.7k 13.0k 10.7k 19.1k 2.10k 4.20k 21.0k 6.30k 8.20k 14.3k ll.8k 17.3k 3.80k 5.70k 3.40k 5.10k 2.80k 2.40k 7.20k 9.40k 10.3k 7.90k

2.80k 3.10k 3.40k 3.75k 4.10k 4.55k 5.00k 774 624 1.87k 2.45k 574 1.15k 1.72k 2.25k 3.92k 3.24k 2.67k 4.76k 524 1.05k 5.24k 1.57k 2.05k 3.57k 2.94k 4.31k 947 1.42k 847 1.27k 696 596 1.79k 2.33k 2.56k 1.96k

644 713 782 862 943 1.05k 1.15k 178 145 436 569 134 267 401 523 912 755 621 1.11k 122 244 1.22k 366 476 830 685 1.00k 221 331 197 296 163 139 418 546 598 459

48.7k 53.9k 59.2k 65.2k 71.3k 79.2k 87.0k 13.5k 10.7k 32.2k 42.1k 9.89k 19.8k 29.7k 38.7k 67.5k 55.9k 46.0k 82.1k 9.02k 18.0k 90.2k 27.1k 35.2k 61.4k 50.7k 74.3k 16.3k 24.5k 14.6k 21.9k 12.0k 10.3k 30.8k 40.2k 44.0k 33.8k

75.7 75.7 75.7 75.7 75.7 75.7 75.7 75.6 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 74.0 73.9 73.9 73.8 73.7 73.7 73.6 73.6 73.6

162

R1 lk2 2k4 12k lk8 3k6 4k7 8k2 llk 7k5 9kl 6k8 6k2 10k 2k2 3k3 2k7 lk6 lk5 2k 3k lk3 13k 3k9 5k6 4k3 4k7 5kl 12k 6k2 8k2 2k4 10k lk6 2k 3k6 6k8 9kl L

Electronics Calculations Data Handbook

R2 lk 2k 10k lk5 3k 3k9 6k8 9kl 6k2 7k5 5k6 5kl 8k2 lk8 2k7 2k2 lk3 lk2 lk6 2k4 lk 10k 3k 4k3 3k3 3k6 3k9 9kl 4k7 6k2 lk8 7k5 lk2 lk5 2k7 5kl 6k8

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

455m 455m 455m 455m 455m 453m 453m 453m 453m 452m 452m 451m 451m 450m 450m 449m 448m 444m 444m 444m 435m 435m 435m 434m 434m 434m 433m 431m 431m 431m 429m 429m 429m 429m 429m 429m 428m

06.85 06.85 06.85 06.85 06.85 06.87 06.87 06.88 06.89 06.90 06.90 06.91 06.93 06.94 06.94 06.96 06.97 07.04 07.04 07.04 07.23 07.23 07.23 07.24 07.25 07.26 07.26 07.30 07.31 07.32 07.36 07.36 07.36 07.36 07.36 07.36 07.38

2.20k 4.40k 22.0k 3.30k 6.60k 8.60k 15.0k 20.1k 13.7k 16.6k 12.4k ll.3k 18.2k 4.00k 6.00k 4.90k 2.90k 2.70k 3.60k 5.40k 2.30k 23.0k 6.90k 9.90k 7.60k 8.30k 9.00k 21.1k 10.9k 14.4k 4.20k 17.5k 2.80k 3.50k 6.30k ll.9k 15.9k

545 1.09k 5.45k 818 1.64k 2.13k 3.72k 4.98k 3.39k 4.11k 3.07k 2.80k 4.51k 990 1.49k 1.21k 717 667 889 1.33k 565 5.65k 1.70k 2.43k 1.87k 2.04k 2.21k 5.18k 2.67k 3.53k 1.03k 4.29k 686 857 1.54k 2.91k 3.89k

128 255 1.28k 192 383 499 871 1.17k 795 964 720 656 1.06k 232 348 284 168 157 209 314 134 1.34k 401 575 441 482 523 1.23k 633 836 244 1.02k 163 203 366 691 923

9.39k 18.8k 93.9k 14.1k 28.2k 36.7k 64.0k 85.8k 58.5k 70.8k 52.9k 48.2k 77.6k 17.1k 25.6k 20.9k 12.4k ll.5k 15.3k 23.0k 9.74k 97.4k 29.2k 41.9k 32.2k 35.1k 38.1k 89.1k 46.0k 60.8k 17.7k 73.8k ll.8k 14.8k 26.6k 50.2k 67.0k

73.6 73.6 73.6 73.6 73.6 73.5 73.5 73.5 73.5 73.5 73.5 73.5 73.4 73.4 73.4 73.4 73.4 73.3 73.3 73.3 72.9 72.9 72.9 72.9 72.9 72.9 72.8 72.8 72.8 72.7 72.7 72.7 72.7 72.7 72.7 72.7 72.6

Table 8. 1 Voltage dividers R1 7k5 llk 2k7 lk5 3k 2k2 3k3 lk8 5kl 4k7 13k 4k3 5k6 6k2 3k9 6k8 lk6 12k 8k2 llk 2k2 9kl 10k 7k5 15k lk5 lk8 2k4 2k7 3k 3k3 3k6 2k 5kl 5k6 4k7 6k8

R2 5k6 8k2 2k lkl 2k2 lk6 2k4 lk3 3k6 3k3 9kl 3k 3k9 4k3 2k7 4k7 lkl 8k2 5k6 7k5 lk5 6k2 6k8 5kl 10k lk lk2 lk6 lk8 2k 2k2 2k4 lk3 3k3 3k6 3k 4k3

163

A

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

427m 427m 426m 423m 423m 421m 421m 419m 414m 413m 412m 411m 411m 410m 409m 409m 407m 406m 406m 405m 405m 405m 405m 405m 400m 400m 400m 400m 400m 400m 400m 400m 394m 393m 391m 390m 387m

07.38 07.39 07.42 07.47 07.47 07.51 07.51 07.55 07.66 07.69 07.71 07.72 07.73 07.75 07.76 07.77 07.80 07.83 07.83 07.84 07.84 07.85 07.86 07.86 07.96 07.96 07.96 07.96 07.96 07.96 07.96 07.96 08.09 08.12 08.15 08.19 O8.24

13.1k 19.2k 4.70k 2.60k 5.20k 3.80k 5.70k 3.10k 8.70k 8.00k 22.1k 7.30k 9.50k 10.5k 6.60k ll.5k 2.70k 20.2k 13.8k 18.5k 3.70k 15.3k 16.8k 12.6k 25.0k 2.50k 3.00k 4.00k 4.50k 5.00k 5.50k 6.00k 3.30k 8.40k 9.20k 7.70k ll.lk

3.21k 4.70k 1.15k 635 1.27k 926 1.39k 755 2.11k 1.94k 5.35k 1.77k 2.30k 2.54k 1.60k 2.78k 652 4.87k 3.33k 4.46k 892 3.69k 4.05k 3.04k 6.00k 600 720 960 1.08k 1.20k 1.32k 1.44k 788 2.00k 2.19k 1.83k 2.63k

761 1.11k 273 151 302 221 331 180 505 464 1.28k 424 552 610 383 668 157 1.17k 801 1.07k 215 888 975 732 1.45k 145 174 232 261 290 319 348 192 488 534 447 644

55.2k 80.9k 19.8k 10.9k 21.9k 16.0k 23.9k 13.0k 36.3k 33.4k 92.2k 30.4k 39.6k 43.7k 27.5k 47.9k ll.2k 83.9k 57.3k 76.8k 15.4k 63.5k 69.7k 52.3k 103k 10.3k 12.4k 16.5k 18.6k 20.7k 22.7k 24.8k 13.6k 34.5k 37.7k 31.5k 45.4k

72.6 72.6 72.5 72.4 72.4 72.3 72.3 72.2 72.0 71.9 71.9 71.8 71.8 71.7 71.7 71.7 71.6 71.5 71.5 71.5 71.5 71.5 71.5 71.5 71.2 71.2 71.2 71.2 71.2 71.2 71.2 71.2 70.8 70.8 70.7 70.6 70.4

164

Electronics Calculations Data Handbook

R1

R2

13k 6k2 4k3 7k5 12k lk6 16k 2k4 8k2 10k llk 3k9 9kl lk8 3k6 15k 3k3 2k 3k 2k7 2k2 5k6 5kl 6k2 13k 4k7 6k8 7k5 8k2 16k 12k 3k9 llk 9kl 10k 4k3 18k

8k2 3k9 2k7 4k7 7k5 lk 10k lk5 5kl 6k2 6k8 2k4 5k6 lkl 2k2 9kl 2k lk2 lk8 lk6 lk3 3k3 3k 3k6 7k5 2k7 3k9 4k3 4k7 9kl 6k8 2k2 6k2 5kl 5k6 2k4 10k

A

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

387m 386m 386m 385m 385m 385m 385m 385m 383m 383m 382m 381m 381m 379m 379m 378m 377m 375m 375m 372m 371m 371m 370m 367m 366m 365m 364m 364m 364m 363m 362m 361m 360m 359m 359m 358m 357m

08.25 08.27 08.27 08.29 08.30 08.30 08.30 08.30 08.33 08.34 08.36 08.38 08.38 08.42 08.42 08.46 08.46 08.52 08.52 08.59 08.60 08.62 08.63 08.70 08.73 08.76 08.77 08.77 08.77 08.81 08.83 08.86 08.86 08.89 08.90 08.92 08.94

21.2k 10.1k 7.00k 12.2k 19.5k 2.60k 26.0k 3.90k 13.3k 16.2k 17.8k 6.30k 14.7k 2.90k 5.80k 24.1k 5.30k 3.20k 4.80k 4.30k 3.50k 8.90k 8.10k 9.80k 20.5k 7.40k 10.7k ll.8k 12.9k 25.1k 18.8k 6.10k 17.2k 14.2k 15.6k 6.70k 28.0k

5.03k 2.39k 1.66k 2.89k 4.62k 615 6.15k 923 3.14k 3.83k 4.20k 1.49k 3.47k 683 1.37k 5.66k 1.25k 750 1.13k 1.00k 817 2.08k 1.89k 2.28k 4.76k 1.71k 2.48k 2.73k 2.99k 5.80k 4.34k 1.41k 3.97k 3.27k 3.59k 1.54k 6.43k

1.23k 586 406 708 1.13k 151 1.51k 226 772 941 1.03k 366 853 168 337 1.40k 308 186 279 250 203 517 470 569 1.19k 430 621 685 749 1.46k 1.09k 354 999 824 906 389 1.63k

86.6k 41.2k 28.6k 49.8k 79.5k 10.6k 106k 15.9k 54.2k 65.9k 72.4k 25.6k 59.7k ll.8k 23.5k 97.6k 21.4k 12.9k 19.4k 17.3k 14.1k 35.8k 32.5k 39.2k 81.9k 29.5k 42.7k 47.1k 51.5k 99.9k 74.8k 24.2k 68.3k 56.3k 61.8k 26.5k lllk

70.4 70.3 70.3 70.3 70.2 70.2 70.2 70.2 70.1 70.1 70.0 70.0 70.0 69.8 69.8 69.7 69.7 69.5 69.5 69.3 69.3 69.2 69.2 68.9 68.8 68.7 68.7 68.7 68.7 68.6 68.5 68.4 68.4 68.3 68.3 68.2 68.1

Table 8. 1 Voltage dividers

Ra

R2

lk8 2k7 3k6 2k 15k 3k3 2k2 2k4 5k6 3k 6k2 6k8 5kl 8k2 13k 7k5 12k 9kl 3k9 16k 4k3 4k7 10k llk 18k 15k 2k 3k 3k6 20k 2k2 2k4 6k8 3k3 6k2 5k6 2k7

lk lk5 2k lkl 8k2 lk8 lk2 lk3 3k lk6 3k3 3k6 2k7 4k3 6k8 3k9 6k2 4k7 2k 8k2 2k2 2k4 5kl 5k6 9kl 7k5 lk lk5 lk8 10k lkl lk2 3k3 lk6 3k 2k7 lk3

357m 357m 357m 355m 353m 353m 353m 351m 349m 348m 347m 346m 346m 344m 343m 342m 341m 341m 339m 339m 338m 338m 338m 337m 336m 333m 333m 333m 333m 333m 333m 333m 327m 327m 326m 325m 325m

165

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

08.94 08.94 08.94 09.00 09.03 09.05 09.05 09.09 09.15 09.17 09.18 09.21 09.21 09.27 09.28 09.32 09.35 09.36 09.40 09.40 09.41 09.42 09.43 09.44 09.48 09.54 09.54 09.54 09.54 09.54 09.54 09.54 09.72 09.72 09.73 09.75 09.76

2.80k 4.20k 5.60k 3.10k 23.2k 5.10k 3.40k 3.70k 8.60k 4.60k 9.50k 10.4k 7.80k 12.5k 19.8k ll.4k 18.2k 13.8k 5.90k 24.2k 6.50k 7.10k 15.1k 16.6k 27.1k 22.5k 3.00k 4.50k 5.40k 30.0k 3.30k 3.60k 10.1k 4.90k 9.20k 8.30k 4.00k

643 964 1.29k 710 5.30k 1.16k 776 843 1.95k 1.04k 2.15k 2.35k 1.77k 2.82k 4.46k 2.57k 4.09k 3.10k 1.32k 5.42k 1.46k 1.59k 3.38k 3.71k 6.04k 5.00k 667 1.00k 1.20k 6.67k 733 800 2.22k 1.08k 2.02k 1.82k 878

163 244 325 182 1.36k 299 199 217 504 270 557 610 457 733 1.16k 669 1.07k 809 346 1.42k 381 416 886 974 1.59k 1.32k 176 264 317 1.76k 194 211 592 287 540 487 235

ll.lk 16.6k 22.1k 12.1k 90.4k 19.9k 13.2k 14.4k 33.3k 17.8k 36.7k 40.1k 30.1k 48.1k 76.1k 43.7k 69.7k 52.8k 22.5k 92.4k 24.8k 27.1k 57.6k 63.3k 103k 85.3k ll.4k 17.1k 20.5k l14k 12.5k 13.6k 37.9k 18.4k 34.5k 31.1k 15.0k

68.1 68.1 68.1 66.6 66.4 66.4 66.4 66.3 66.0 65.9 65.9 65.8 65.8 65.6 65.6 65.4 65.3 65.3 65.1 65.1 65.1 65.1 65.0 65.0 64.8 64.6 64.6 64.6 64.6 64.6 64.6 64.6 64.0 63.9 63.9 63.8 63.8

166

R1 7k5 13k 8k2 9kl 5kl lOk 16k 4k7 12k 4k3 llk 3k9 2k4 18k 20k 22k 2k2 3k3 15k 2k7 3k6 6k8 7k5 8k2 6k2 3k 5kl 13k lOk 9kl 5k6 llk 4k7 12k 16k 4k3 18k

Electronics Calculations Data Handbook

R2 3k6 6k2 3k9 4k3 2k4 4k7 7k5 2k2 5k6 2k 5kl lk8 lkl 8k2 9kl lOk lk lk5 6k8 lk2 lk6 3k 3k3 3k6 2k7 lk3 2k2 5k6 4k3 3k9 2k4 4k7 2k 5kl 6k8 lk8 7k5

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

324m 323m 322m 321m 320m 320m 319m 319m 318m 317m 317m 316m 314m 313m 313m 313m 313m 313m 312m 308m 308m 306m 306m 305m 303m 302m 301m 301m 301m 300m 300m 299m 299m 298m 298m 295m 294m

09.78 09.82 09.83 09.87 09.90 09.90 09.92 09.93 09.95 09.97 09.99 10.01 10.05 10.09 10.10 10.10 10.10 10.10 10.12 10.24 10.24 10.28 10.30 10.31 10.36 10.39 10.42 10.43 10.44 10.46 10.46 10.48 10.50 10.51 10.51 10.60 10.63

ll.lk 19.2k 12.1k 13.4k 7.50k 14.7k 23.5k 6.90k 17.6k 6.30k 16.1k 5.70k 3.50k 26.2k 29.1k 32.0k 3.20k 4.80k 21.8k 3.90k 5.20k 9.80k lO.8k ll.8k 8.90k 4.30k 7.30k 18.6k 14.3k 13.Ok 8.00k 15.7k 6.70k 17.1k 22.8k 6.10k 25.5k

2.43k 4.20k 2.64k 2.92k 1.63k 3.20k 5.11k 1.50k 3.82k 1.37k 3.48k 1.23k 754 5.63k 6.25k 6.88k 688 1.03k 4.68k 831 1.11k 2.08k 2.29k 2.50k 1.88k 907 1.54k 3.91k 3.01k 2.73k 1.68k 3.29k 1.40k 3.58k 4.77k 1.27k 5.29k

651 1.13k 710 786 440 862 1.38k 405 1.03k 369 944 334 205 1.54k 1.71k 1.88k 188 282 1.28k 229 3O5 575 633 692 522 252 428 1.09k 839 762 469 921 393 1.OOk 1.34k 358 1.50k

41.5k 71.6k 45.1k 49.8k 27.8k 54.5k 87.1k 25.6k 65.1k 23.3k 59.4k 21.Ok 12.9k 96.1k 107k l17k ll.7k 17.6k 79.8k 14.2k 18.9k 35.5k 39.1k 42.7k 32.1k 15.5k 26.2k 66.7k 51.3k 46.5k 28.6k 56.1k 23.9k 61.Ok 81.4k 21.6k 90.3k

63.7 63.6 63.5 63.4 63.3 63.2 63.2 63.1 63.1 63.0 62.9 62.8 62.7 62.5 62.5 62.5 62.5 62.5 62.4 61.9 61.9 61.8 61.7 61.6 61.4 61.3 61.2 61.2 61.1 61.0 61.0 61.0 60.9 60.8 60.8 60.5 60.4

Table 8.1 Voltage dividers R1 24k 2k4 3k6 22k 15k 3k9 20k 2k7 8k2 3k 7k5 6k8 9kl 3k3 5k6 13k 5kl 12k llk 10k 16k 6k2 3k9 4k7 24k 18k 20k 15k 22k 4k3 27k 2k7 3k 8k2 3k3 9kl 13k

R2 10k lk lk5 9kl 6k2 lk6 8k2 lkl 3k3 lk2 3k 2k7 3k6 lk3 2k2 5kl 2k 4k7 4k3 3k9 6k2 2k4 lk5 lk8 9kl 6k8 7k5 5k6 8k2 lk6 10k lk lkl 3k lk2 3k3 4k7

294m 294m 294m 293m 292m 291m 291m 289m 287m 286m 286m 284m 283m 283m 282m 282m 282m 281m 281m 281m 279m 279m 278m 277m 275m 274m 273m 272m 272m 271m 270m 270m 268m 268m 267m 266m 266m

167

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

10.63 10.63 10.63 10.67 10.68 10.72 10.73 10.77 10.84 10.88 10.88 10.93 10.95 10.98 10.99 11.00 11.00 11.01 11.02 11.04 11.08 11.09 11.13 11.15 11.22 11.24 11.29 11.31 11.32 11.33 11.36 11.36 11.43 11.44 11.48 11.50 11.52

34.0k 3.40k 5.10k 31.1k 21.2k 5.50k 28.2k 3.80k ll.5k 4.20k 10.5k 9.50k 12.7k 4.60k 7.80k 18.1k 7.10k 16.7k 15.3k 13.9k 22.2k 8.60k 5.40k 6.50k 33.1k 24.8k 27.5k 20.6k 30.2k 5.90k 37.0k 3.70k 4.10k ll.2k 4.50k 12.4k 17.7k

7.06k 706 1.06k 6.44k 4.39k 1.13k 5.82k 782 2.35k 857 2.14k 1.93k 2.58k 933 1.58k 3.66k 1.44k 3.38k 3.09k 2.81k 4.47k 1.73k 1.08k 1.30k 6.60k 4.94k 5.45k 4.08k 5.97k 1.17k 7.30k 730 805 2.20k 880 2.42k 3.45k

1.99k 199 299 1.82k 1.24k 323 1.65k 223 674 246 616 557 745 270 457 1.06k 416 979 897 815 1.30k 504 317 381 1.94k 1.45k 1.61k 1.21k 1.77k 346 2.17k 217 240 657 264 727 1.04k

120k 12.0k 18.1k ll0k 74.8k 19.3k 99.2k 13.3k 40.1k 14.6k 36.5k 33.0k 44.0k 15.9k 26.9k 62.5k 24.5k 57.6k 52.7k 47.8k 76.2k 29.5k 18.5k 22.2k l13k 84.2k 93.0k 69.5k 102k 19.9k 124k 12.4k 13.7k 37.4k 15.0k 41.3k 58.9k

60.4 60.4 60.4 60.2 60.2 60.0 60.0 59.8 59.5 59.3 59.3 59.1 59.0 58.9 58.9 58.8 58.8 58.8 58.7 58.7 58.5 58.5 58.3 58.2 58.0 57.9 57.7 57.5 57.5 57.5 57.3 57.3 57.1 57.0 56.9 56.8 56.7

168

R1 3k6 7k5 10k 12k 5k6 6k2 Ilk 5kl 6k8 16k 4k3 18k 24k 22k 4k7 15k 20k 27k 30k 3k 3k3 3k6 3k9 13k 10k 9kl 8k2 llk 12k 6k8 6k2 5k6 7k5 4k7 16k 5kl 15k

Electronics Calculations Data Handbook

R2 lk3 2k7 3k6 4k3 2k 2k2 3k9 lk8 2k4 5k6 lk5 6k2 8k2 7k5 lk6 5kl 6k8 9kl 10k lk lkl lk2 lk3 4k3 3k3 3k 2k7 3k6 3k9 2k2 2k lk8 2k4 lk5 5kl lk6 4k7

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

265m 265m 265m 264m 263m 262m 262m 261m 261m 259m 259m 256m 255m 254m 254m 254m 254m 252m 250m 250m 250m 250m 250m 249m 248m 248m 248m 247m 245m 244m 244m 243m 242m 242m 242m 239m 239m

11.53 11.54 11.54 11.57 11.60 11.64 11.64 11.67 11.67 11.73 11.75 11.83 11.88 11.90 11.90 11.91 11.91 11.97 12.04 12.04 12.04 12.04 12.04 12.09 12.11 12.11 12.12 12.16 12.21 12.24 12.26 12.28 12.31 12.33 12.33 12.44 12.45

4.90k 10.2k 13.6k 16.3k 7.60k 8.40k 14.9k 6.90k 9.20k 21.6k 5.80k 24.2k 32.2k 29.5k 6.30k 20.1k 26.8k 36.1k 40.0k 4.00k 4.40k 4.80k 5.20k 17.3k 13.3k 12.1k 10.9k 14.6k 15.9k 9.00k 8.20k 7.40k 9.90k 6.20k 21.1k 6.70k 19.7k

955 1.99k 2.65k 3.17k 1.47k 1.62k 2.88k 1.33k 1.77k 4.15k 1.11k 4.61k 6.11k 5.59k 1.19k 3.81k 5.07k 6.81k 7.50k 750 825 900 975 3.23k 2.48k 2.26k 2.03k 2.71k 2.94k 1.66k 1.51k 1.36k 1.82k 1.14k 3.87k 1.22k 3.58k

287 598 798 956 446 493 874 405 540 1.27k 340 1.42k 1.89k 1.73k 369 1.18k 1.57k 2.12k 2.35k 235 258 282 305 1.01k 780 710 639 856 933 528 481 434 581 364 1.24k 393 1.16k

16.3k 33.8k 45.1k 54.0k 25.1k 27.7k 49.1k 22.7k 30.2k 70.7k 19.0k 78.6k 104k 95.4k 20.4k 64.9k 86.5k l16k 128k 12.8k 14.1k 15.3k 16.6k 55.1k 42.3k 38.5k 34.6k 46.2k 50.2k 28.3k 25.8k 23.2k 31.0k 19.4k 65.9k 20.8k 61.0k

56.7 56.6 56.6 56.5 56.4 56.2 56.2 56.1 56.1 55.8 55.7 55.4 55.2 55.1 55.1 55.0 55.0 54.8 54.5 54.5 54.5 54.5 54.5 54.3 54.2 54.2 54.2 54.0 53.8 53.7 53.6 53.5 53.4 53.3 53.3 52.8 52.8

Table 8.1 Voltage dividers R1 24k 18k 20k 22k 3k9 3k6 27k 30k 3k3 33k 4k3 llk 12k 13k 10k 9kl 6k8 5kl 16k 7k5 8k2 6k2 15k 5k6 18k 24k 3k9 22k 20k 4k3 27k 36k 3k6 13k 4k7 33k 12k

R2 7k5 5k6 6k2 6k8 lk2 lkl 8k2 9kl lk 10k lk3 3k3 3k6 3k9 3k 2k7 2k lk5 4k7 2k2 2k4 lk8 4k3 lk6 5kl 6k8 lkl 6k2 5k6 lk2 7k5 10k lk 3k6 lk3 9kl 3k3

238m 237m 237m 236m 235m 234m 233m 233m 233m 233m 232m 231m 231m 231m 231m 229m 227m 227m 227m 227m 226m 225m 223m 222m 221m 221m 220m 220m 219m 218m 217m 217m 217m 217m 217m 216m 216m

169

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

12.46 12.49 12.52 12.54 12.57 12.61 12.65 12.66 12.67 12.67 12.68 12.74 12.74 12.74 12.74 12.81 12.87 12.87 12.88 12.89 12.90 12.96 13.04 13.06 13.12 13.12 13.15 13.16 13.20 13.22 13.26 13.26 13.26 13.28 13.28 13.30 13.32

31.5k 23.6k 26.2k 28.8k 5.10k 4.70k 35.2k 39.1k 4.30k 43.0k 5.60k 14.3k 15.6k 16.9k 13.0k ll.8k 8.80k 6.60k 20.7k 9.70k 10.6k 8.00k 19.3k 7.20k 23.1k 30.8k 5.00k 28.2k 25.6k 5.50k 34.5k 46.0k 4.60k 16.6k 6.00k 42.1k 15.3k

5.71k 4.27k 4.73k 5.19k 918 843 6.29k 6.98k 767 7.67k 998 2.54k 2.77k 3.00k 2.31k 2.08k 1.55k 1.16k 3.63k 1.70k 1.86k 1.40k 3.34k 1.24k 3.97k 5.30k 858 4.84k 4.38k 938 5.87k 7.83k 783 2.82k 1.02k 7.13k 2.59k

1.85k 1.38k 1.54k 1.69k 299 276 2.06k 2.29k 252 2.52k 328 839 915 991 762 692 516 387 1.21k 569 622 469 1.13k 422 1.35k 1.81k 293 1.65k 1.50k 323 2.02k 2.70k 270 974 352 2.47k 897

97.4k 72.8k 80.7k 88.6k 15.6k 14.4k 107k l19k 13.1k 131k 17.0k 43.3k 47.2k 51.2k 39.3k 35.5k 26.4k 19.8k 61.9k 29.0k 31.7k 23.8k 57.0k 21.2k 67.8k 90.3k 14.6k 82.5k 74.6k 16.0k 100k 133k 13.3k 48.1k 17.4k 122k 44.1k

52.7 52.6 52.5 52.4 52.3 52.1 51.9 51.9 51.9 51.9 51.8 51.6 51.6 51.6 51.6 51.3 51.1 51.1 51.0 51.0 50.9 50.7 50.3 50.2 50.0 50.0 49.9 49.9 49.7 49.6 49.5 49.5 49.5 49.4 49.3 49.3 49.2

170

R1 30k llk 10k 16k 8k2 5k6 7k5 6k8 9kl 18k 15k 24k 6k2 39k 3k9 4k3 4k7 20k 5kl 22k 13k 36k 27k 30k 12k 33k llk 8k2 16k 6k2 9kl 15k 7k5 10k 18k 6k8 5kl

Electronics Calculations Data Handbook

R2 8k2 3k 2k7 4k3 2k2 lk5 2k lk8 2k4 4k7 3k9 6k2 lk6 10k lk lkl lk2 5kl lk3 5k6 3k3 9kl 6k8 7k5 3k 8k2 2k7 2k 3k9 lk5 2k2 3k6 lk8 2k4 4k3 lk6 lk2

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

215m 214m 213m 212m 212m 211m 211m 209m 209m 207m 206m 205m 205m 204m 204m 204m 203m 203m 203m 203m 202m 202m 201m 200m 200m 199m 197m 196m 196m 195m 195m 194m 194m 194m 193m 190m 190m

13.36 13.38 13.45 13.48 13.49 13.50 13.53 13.58 13.61 13.68 13.71 13.75 13.76 13.80 13.80 13.82 13.83 13.84 13.84 13.85 13.87 13.90 13.93 13.98 13.98 14.02 14.11 14.15 14.16 14.21 14.21 14.26 14.26 14.26 14.30 14.40 14.40

38.2k 14.0k 12.7k 20.3k 10.4k 7.10k 9.50k 8.60k ll.5k 22.7k 18.9k 30.2k 7.80k 49.0k 4.90k 5.40k 5.90k 25.1k 6.40k 27.6k 16.3k 45.1k 33.8k 37.5k 15.0k 41.2k 13.7k 10.2k 19.9k 7.70k ll.3k 18.6k 9.30k 12.4k 22.3k 8.40k 6.30k

6.44k 2.36k 2.13k 3.39k 1.73k 1.18k 1.58k 1.42k 1.90k 3.73k 3.10k 4.93k 1.27k 7.96k 796 876 956 4.06k 1.04k 4.46k 2.63k 7.26k 5.43k 6.00k 2.40k 6.57k 2.17k 1.61k 3.14k 1.21k 1.77k 2.90k 1.45k 1.94k 3.47k 1.30k 971

2.24k 821 745 1.19k 610 416 557 504 674 1.33k 1.11k 1.77k 457 2.87k 287 317 346 1.47k 375 1.62k 956 2.65k 1.98k 2.20k 880 2.42k 804 598 1.17k 452 663 1.09k 545 727 1.31k 493 369

ll0k 40.2k 36.2k 57.8k 29.6k 20.2k 26.9k 24.3k 32.4k 63.5k 52.8k 84.0k 21.7k 136k 13.6k 14.9k 16.3k 69.3k 17.7k 76.1k 44.9k 124k 92.6k 102k 40.9k l12k 37.0k 27.4k 53.5k 20.6k 30.2k 49.5k 24.8k 33.0k 59.2k 22.1k 16.6k

49.0 48.9 48.7 48.5 48.5 48.4 48.3 48.1 48.0 47.7 47.6 47.4 47.4 47.2 47.2 47.2 47.1 47.1 47.1 47.0 46.9 46.8 46.7 46.5 46.5 46.3 46.0 45.8 45.8 45.6 45.6 45.4 45.4 45.4 45.2 44.8 44.8

Table 8. 1 Voltage dividers R1

R2

20k 4k7 4k7 lkl 24k 5k6 39k 9kl 4k3 lk 43k 10k 5k6 lk3 22k 5kl 13k 3k 27k 6k2 36k 8k2 33k 7k5 30k 6k8 12k 2k7 16k 3k6 6k8 lk5 15k 3k3 10k 2k2 9kl 2k 8k2 lk8 llk 2k4 18k 3k9 lkl 5kl 20k 4k3 5k6 lk2 22k 4k7 7k5 lk6 47k 10k 4k7 lk 24k 5kl 43k 9kl 39k 8k2 6k2 lk3 36k 7k5 13k 2k7 27k 5k6 30k 6k2

171

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

190m 190m 189m 189m 189m 189m 188m 188m 188m 187m 186m 185m 185m 184m 184m 181m 180m 180m 180m 180m 179m 178m 177m 177m 176m 176m 176m 175m 175m 175m 175m 174m 173m 172m 172m 172m 171m

14.41 14.44 14.46 14.46 14.49 14.49 14.50 14.51 14.54 14.57 14.63 14.65 14.67 14.72 14.72 14.86 14.88 14.88 14.89 14.89 14.94 14.99 15.02 15.04 15.07 15.09 15.10 15.12 15.12 15.13 15.16 15.20 15.22 15.27 15.29 15.30 15.33

24.7k 5.80k 29.6k 48.1k 5.30k 53.0k 6.90k 27.1k 16.0k 33.2k 44.2k 40.5k 36.8k 14.7k 19.6k 8.30k 18.3k 12.2k ll.lk 10.0k 13.4k 21.9k 6.20k 24.3k 6.80k 26.7k 9.10k 57.0k 5.70k 29.1k 52.1k 47.2k 7.50k 43.5k 15.7k 32.6k 36.2k

3.81k 891 4.54k 7.38k 811 8.11k 1.06k 4.14k 2.44k 5.04k 6.68k 6.11k 5.54k 2.20k 2.94k 1.23k 2.70k 1.80k 1.64k 1.48k 1.97k 3.21k 905 3.54k 988 3.87k 1.32k 8.25k 825 4.21k 7.51k 6.78k 1.07k 6.21k 2.24k 4.64k 5.14k

1.45k 340 1.74k 2.82k 311 3.11k 405 1.59k 938 1.95k 2.59k 2.38k 2.16k 862 1.15k 487 1.07k 716 651 587 786 1.28k 364 1.43k 399 1.57k 534 3.34k 334 1.71k 3.06k 2.77k 440 2.55k 921 1.91k 2.12k

64.9k 15.2k 77.4k 126k 13.8k 138k 18.0k 70.6k 41.6k 86.0k l14k 104k 94.5k 37.6k 50.1k 21.0k 46.1k 30.7k 28.0k 25.2k 33.6k 54.7k 15.4k 60.3k 16.8k 66.0k 22.5k 141k 14.1k 71.7k 128k l16k 18.3k 106k 38.1k 79.1k 87.6k

44.8 44.7 44.6 44.6 44.5 44.5 44.5 44.4 44.3 44.2 43.9 43.9 43.8 43.6 43.6 43.0 43.0 43.0 42.9 42.9 42.7 42.6 42.4 42.3 42.2 42.2 42.1 42.1 42.1 42.0 41.9 41.7 41.7 41.5 41.4 41.4 41.3

172

R1 16k 33k llk 12k 15k 18k 7k5 lOk 9kl 5k6 51k 5kl 24k 22k 8k2 20k 47k 6k2 39k 6k8 43k 27k 36k 33k 16k 30k 13k 18k 12k 8k2 llk 15k 20k lOk 24k 56k 5k6

Electronics Calculations Data Handbook

R2 3k3 6k8 2k2 2k4 3k 3k6 lk5 2k lk8 lkl lOk lk 4k7 4k3 lk6 3k9 9kl lk2 7k5 lk3 8k2 5kl 6k8 6k2 3k 5k6 2k4 3k3 2k2 lk5 2k 2k7 3k6 lk8 4k3 lOk lk

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

171m 171m 167m 167m 167m 167m 167m 167m 165m 164m 164m 164m 164m 163m 163m 163m 162m 162m 161m 160m 160m 159m 159m 158m 158m 157m 156m 155m 155m 155m 154m 153m 153m 153m 152m 152m 152m

15.34 15.35 15.56 15.56 15.56 15.56 15.56 15.56 15.64 15.69 15.71 15.71 15.72 15.73 15.74 15.75 15.80 15.80 15.85 15.89 15.91 15.98 15.98 16.02 16.03 16.07 16.15 16.20 16.20 16.21 16.26 16.33 16.33 16.33 16.37 16.39 16.39

19.3k 39.8k 13.2k 14.4k 18.Ok 21.6k 9.00k 12.Ok lO.9k 6.70k 61.Ok 6.10k 28.7k 26.3k 9.80k 23.9k 56.1k 7.40k 46.5k 8.10k 51.2k 32.1k 42.8k 39.2k 19.Ok 35.6k 15.4k 21.3k 14.2k 9.70k 13.Ok 17.7k 23.6k ll.8k 28.3k 66.0k 6.60k

2.74k 5.64k 1.83k 2.00k 2.50k 3.00k 1.25k 1.67k 1.50k 919 8.36k 836 3.93k 3.60k 1.34k 3.26k 7.62k 1.Olk 6.29k 1.09k 6.89k 4.29k 5.72k 5.22k 2.53k 4.72k 2.03k 2.79k 1.86k 1.27k 1.69k 2.29k 3.05k 1.53k 3.65k 8.48k 848

1.13k 2.33k 774 845 1.06k 1.27k 528 704 639 393 3.58k 358 1.68k 1.54k 575 1.40k 3.29k 434 2.73k 475 3.00k 1.88k 2.51k 2.30k 1.11k 2.09k 903 1.26k 841 575 770 1.05k 1.40k 699 1.68k 3.91k 391

46.6k 96.1k 31.3k 34.1k 42.6k 51.2k 21.3k 28.4k 25.6k 15.7k 143k 14.3k 67.0k 61.3k 22.8k 55.6k 130k 17.1k 107k 18.6k l17k 73.1k 97.5k 89.0k 43.1k 80.5k 34.5k 47.1k 31.4k 21.4k 28.6k 38.6k 51.5k 25.7k 61.5k 143k 14.3k

41.2 41.2 40.4 40.4 40.4 40.4 40.4 40.4 40.1 39.9 39.8 39.8 39.8 39.8 39.7 39.7 39.5 39.5 39.3 39.2 39.1 38.8 38.8 38.7 38.7 38.5 38.2 37.3 37.3 37.2 37.1 36.8 36.8 36.8 36.7 36.6 36.6

Table 8. 1 Voltage dividers R1 51k 6k2 22k 6k8 9kl 47k 43k 39k 27k 7k5 36k 30k 33k 13k 16k 12k 18k 20k 9kl llk 22k 24k 56k 6k8 62k 6k2 51k 15k 7k5 10k 47k 27k 39k 8k2 43k 30k 36k

R2 9kl lkl 3k9 lk2 lk6 8k2 7k5 6k8 4k7 lk3 6k2 5kl 5k6 2k2 2k7 2k 3k 3k3 lk5 lk8 3k6 3k9 9kl lkl 10k lk 8k2 2k4 lk2 lk6 7k5 4k3 6k2 lk3 6k8 4k7 5k6

151m 151m 151m 150m 150m 149m 149m 148m 148m 148m 147m 145m 145m 145m 144m 143m 143m 142m 142m 141m 141m 140m 140m 139m 139rn 139m 139m 138m 138m 138m 138m 137m 137m 137m 137m 135m 135m

173

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

16.40 16.44 16.44 16.48 16.51 16.56 16.56 16.57 16.58 16.61 16.66 16.75 16.77 16.79 1.6.81 16.90 16.90 16.98 16.98 17.04 17.04 17.09 17.09 17.12 17.15 17.15 17.17 17.21 17.21 17.21 17.23 17.24 17.25 17.28 17.29 17.36 17.42

60.1k 7.30k 25.9k 8.00k 10.7k 55.2k 50.5k 45.8k 31.7k 8.80k 42.2k 35.1k 38.6k 15.2k 18.7k 14.0k 21.0k 23.3k 10.6k 12.8k 25.6k 27.9k 65.1k 7.90k 72.0k 7.20k 59.2k 17.4k 8.70k ll.6k 54.5k 31.3k 45.2k 9.50k 49.8k 34.7k 41.6k

7.72k 934 3.31k 1.02k 1.36k 6.98k 6.39k 5.79k 4.00k 1.11k 5.29k 4.36k 4.79k 1.88k 2.31k 1.71k 2.57k 2.83k 1.29k 1.55k 3.09k 3.35k 7.83k 947 8.61k 861 7.06k 2.07k 1.03k 1.38k 6.47k 3.71k 5.35k 1.12k 5.87k 4.06k 4.85k

3.56k 433 1.53k 474 634 3.27k 2.99k 2.71k 1.88k 521 2.50k 2.08k 2.29k 901 1.11k 830 1.24k 1.38k 628 758 1.52k 1.65k 3.86k 468 4.27k 427 3.51k 1.03k 516 687 3.23k 1.85k 2.68k 563 2.95k 2.06k 2.46k

130k 15.8k 55.9k 17.2k 23.0k l18k 108k 97.7k 67.6k 18.7k 89.3k 73.6k 80.8k 31.8k 39.0k 28.9k 43.4k 47.8k 21.7k 26.1k 52.2k 56.6k 132k 16.0k 145k 14.5k l19k 34.9k 17.5k 23.3k 109k 62.6k 90.3k 18.9k 99.1k 68.6k 81.8k

36.6 36.5 36.4 36.3 36.2 36.0 36.0 36.0 36.0 35.9 35.7 35.4 35.3 35.3 35.2 34.9 34.9 34.6 34.6 34.4 34.4 34.2 34.2 34.1 34.1 34.1 34.0 33.9 33.9 33.9 33.8 33.8 33.7 33.6 33.6 33.4 33.2

174 R1 33k 13k 12k 16k 18k 20k 22k 24k lOk 51k 68k 6k8 62k 15k 7k5 56k 8k2 llk 47k 27k 43k 39k 30k 9kl 33k 36k 13k 16k 24k llk 22k 20k 8k2 56k 68k 15k 7k5

Electronics Calculations Data Handbook R2 5kl 2k lk8 2k4 2k7 3k 3k3 3k6 lk5 7k5 lOk lk 9kl 2k2 lkl 8k2 lk2 lk6 6k8 3k9 6k2 5k6 4k3 lk3 4k7 5kl lk8 2k2 3k3 lk5 3k 2k7 lkl 7k5 9kl 2k lk

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

134m 133m 130m 130m 130m 130m 130m 130m 130m 128m 128m 128m 128m 128m 128m 128m 128m 127m 126m 126m 126m 126m 125m 125m 125m 124m 122m 121m 121m 120m 120m l19m l18m l18m l18m l18m l18m

17.47 17.50 17.69 17.69 17.69 17.69 17.69 17.69 17.69 17.84 17.84 17.84 17.86 17.86 17.86 17.87 17.88 17.93 17.97 17.98 17.99 18.02 18.04 18.06 18.08 18.13 18.30 18.35 18.35 18.42 18.42 18.49 18.54 18.55 18.56 18.59 18.59

38.1k 15.Ok 13.8k 18.4k 20.7k 23.0k 25.3k 27.6k ll.5k 58.5k 78.0k 7.80k 71.1k 17.2k 8.60k 64.2k 9.40k 12.6k 53.8k 30.9k 49.2k 44.6k 34.3k lO.4k 37.7k 41.1k 14.8k 18.2k 27.3k 12.5k 25.0k 22.7k 9.30k 63.5k 77.1k 17.Ok 8.50k

4.42k 1.73k 1.57k 2.09k 2.35k 2.61k 2.87k 3.13k 1.30k 6.54k 8.72k i 872 7.94k 1.92k 959 7.15k 1.05k 1.40k 5.94k 3.41k 5.42k 4.90k 3.76k 1.14k 4.11k 4.47k 1.58k 1.93k 2.90k 1.32k 2.64k 2.38k 970 6.61k 8.03k 1.76k 882

2.26k 889 818 1.09k 1.23k 1.36k 1.50k 1.64k 681 3.47k 4.62k 462 4.21k 1.02k 510 3.80k 557 747 3.19k 1.83k 2.92k 2.64k 2.03k 616 2.23k 2.44k 877 1.08k 1.62k 741 1.48k 1.35k 551 3.76k 4.57k 1.Olk 504

74.5k 29.3k 26.4k 35.2k 39.6k 44.0k 48.4k 52.8k 22.0k llOk 147k 14.7k 134k 32.4k 16.2k 121k 17.7k 23.6k 100k 57.5k 91.4k 82.6k 63.5k 19.2k 69.4k 75.4k 26.7k 32.6k 49.0k 22.3k 44.6k 40.1k 16.4k l12k 135k 29.8k 14.9k

33.0 32.9 32.3 32.3 32.3 32.3 32.3 32.3 32.3 31.8 31.8 31.8 31.8 31.8 31.8 31.7 31.7 31.6 31.4 31.4 31.4 31.3 31.2 31.2 31.1 31.0 30.4 30.3 30.3 30.1 30.1 29.8 29.7 29.7 29.6 29.6 29.6

Table 8. 1 Voltage dividers

R1 12k 18k 27k 51k 75k 62k 47k 9kl 39k 36k 33k 43k 30k lOk 12k 16k 24k 13k 22k 18k 27k 82k 8k2 51k 56k 75k 62k 9kl 68k 39k 15k 20k 30k lOk 36k 47k 43k

R2 lk6 2k4 3k6 6k8 lOk 8k2 6k2 lk2 5kl 4k7 4k3 5k6 3k9 lk3 lk5 2k 3k lk6 2k7 2k2 3k3 lOk lk 6k2 6k8 9kl 7k5 lkl 8k2 4k7 lk8 2k4 3k6 lk2 4k3 5k6 5kl

175

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

l18m l18m l18m l18m l18m l17m l17m l17m l16m l15m l15m l15m l15m l15m lllm lllm lllm llOm 109m 109m 109m 109m 109m 108m 108m 108m 108m 108m 108m 108m 107m 107m 107m 107m 107m 106m 106m

18.59 18.59 18.59 18.59 18.59 18.65 18.67 18.67 18.74 18.75 18.76 18.77 18.78 18.78 19.08 19.08 19.08 19.20 19.23 19.26 19.26 19.28 19.28 19.30 19.31 19.32 19.34 19.34 19.36 19.37 19.40 19.40 19.40 19.40 19.44 19.46 19.49

13.6k 20.4k 30.6k 57.8k 85.0k 70.2k 53.2k lO.3k 44.1k 40.7k 37.3k 48.6k 33.9k ll.3k 13.5k 18.Ok 27.0k 14.6k 24.7k 20.2k 30.3k 92.0k 9.20k 57.2k 62.8k 84.1k 69.5k lO.2k 76.2k 43.7k 16.8k 22.4k 33.6k ll.2k 40.3k 52.6k 48.1k

1.41k 2.12k 3.18k 6.00k 8.82k 7.24k 5.48k 1.06k 4.51k 4.16k 3.80k 4.95k 3.45k 1.15k 1.33k 1.78k 2.67k 1.42k 2.40k 1.96k 2.94k 8.91k 891 5.53k 6.06k 8.12k 6.69k 981 7.32k 4.19k 1.61k 2.14k 3.21k 1.07k 3.84k 5.00k 4.56k

806 1.21k 1.81k 3.42k 5.04k 4.16k 3.15k 610 2.61k 2.41k 2.21k 2.88k 2.01k 670 800 1.07k 1.60k 865 1.46k 1.20k 1.80k 5.45k 545 3.39k 3.72k 4.98k 4.12k 604 4.52k 2.59k 995 1.33k 1.99k 664 2.39k 3.12k 2.85k

23.8k 35.7k 53.6k lOlk 149k 122k 92.4k 17.9k 76.1k 70.2k 64.2k 83.6k 58.2k 19.4k 22.5k 30.Ok 45.0k 24.0k 40.6k 33.1k 49.6k 150k 15.Ok 93.3k 102k 137k l13k 16.6k 123k 70.8k 27.1k 36.2k 54.2k 18.1k 64.8k 84.4k 76.9k

29.6 29.6 29.6 29.6 29.6 29.4 29.3 29.3 29.1 29.1 29.0 29.0 29.0 29.0 28.1 28.1 28.1 27.8 27.7 27.6 27.6 27.6 27.6 27.5 27.5 27.5 27.4 27.4 27.4 27.3 27.2 27.2 27.2 27.2 27.1 27.1 27.0

176

R1 llk 33k 13k 16k 24k 18k 27k 82k 56k 68k 39k 20k 30k 10k 9kl 91k 51k 62k 75k 43k llk 22k 33k 47k 12k 36k 15k llk 12k 13k 15k 16k 18k 20k 22k 24k 27k

Electronics Calculations Data Handbook

R2 lk3 3k9 lk5 lk8 2k7 2k 3k 9kl 6k2 7k5 4k3 2k2 3k3 lkl lk 10k 5k6 6k8 8k2 4k7 lk2 2k4 3k6 5kl lk3 3k9 lk6 lkl lk2 lk3 lk5 lk6 lk8 2k 2k2 2k4 2k7

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

106m 106m 103m 101m 101m 100m 100m 99.9m 99.7m 99.3m 99.3m 99.1m 99.1m 99.1m 99.0m 99.0m 98.9m 98.8m 98.6m 98.5m 98.4m 98.4m 98.4m 97.9m 97.7m 97.7m 96.4m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m

19.52 19.52 19.71 19.90 19.90 20.00 20.00 20.01 20.03 20.06 20.06 20.08 20.08 20.08 20.09 20.09 20.09 20.10 20.13 20.13 20.14 20.14 20.14 20.19 20.20 20.20 20.32 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83

12.3k 36.9k 14.5k 17.8k 26.7k 20.0k 30.0k 91.1k 62.2k 75.5k 43.3k 22.2k 33.3k ll.lk 10.1k 10.1k 56.6k 68.8k 83.2k 47.7k 12.2k 24.4k 36.6k 52.1k 13.3k 39.9k 16.6k 12.1k 13.2k 14.3k 16.5k 17.6k 19.8k 22.0k 24.2k 26.4k 29.7k

1.16k 3.49k 1.34k 1.62k 2.43k 1.80k 2.70k 8.19k 5.58k 6.75k 3.87k 1.98k 2.97k 991 901 9.01k 5.05k 6.13k 7.39k 4.24k 1.08k 2.16k 3.25k 4.60k 1.17k 3.52k 1.45k 1.00k 1.09k 1.18k 1.36k 1.45k 1.64k 1.82k 2.00k 2.18k 2.45k

729 2.19k 859 1.05k 1.58k 1.19k 1.78k 5.40k 3.69k 4.47k 2.57k 1.32k 1.97k 658 598 5.98k 3.35k 4.08k 4.93k 2.83k 723 1.45k 2.17k 3.09k 788 2.36k 984 717 782 847 978 1.04k 1.17k 1.30k 1.43k 1.56k 1.76k

19.6k 58.9k 22.7k 27.3k 41.0k 30.4k 45.6k 138k 94.2k l14k 65.4k 33.4k 50.2k 16.7k 15.2k 152k 85.2k 103k 125k 71.5k 18.3k 36.5k 54.8k 77.6k 19.8k 59.4k 24.4k 16.9k 18.4k 19.9k 23.0k 24.5k 27.6k 30.7k 33.8k 36.8k 41.4k

26.9 26.9 26.4 25.9 25.9 25.6 25.6 25.6 25.6 25.5 25.5 25.4 25.4 25.4 25.4 25.4 25.4 25.4 25.3 25.3 25.3 25.3 25.3 25.2 25.1 25.1 24.8 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5

Table 8. 1 Voltage dividers

~1 30k 33k 36k 39k 43k 47k 51k 56k 62k 68k 75k 82k 91k 100k 10k 16k 13k 39k 51k 12k 24k 36k 47k 82k 68k 56k 100k llk 22k 33k 43k 75k 62k 91k 20k 30k 18k

~2 3k 3k3 3k6 3k9 4k3 4k7 5kl 5k6 6k2 6k8 7k5 8k2 9kl 10k lk lk5 lk2 3k6 4k7 lkl 2k2 3k3 4k3 7k5 6k2 5kl 9kl lk 2k 3k 3k9 6k8 5k6 8k2 lk8 2k7 lk6

90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 90.9m 85.7m 84.5m 84.5m 84.4m 84.0m 84.0m 84.0m 83.8m 83.8m 83.6m 83.5m 83.4m 83.3m 83.3m 83.3m 83.2m 83.1m 82.8m 82.7m 82.6m 82.6m 81.6m

177

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 20.83 21.34 21.46 21.46 21.48 21.52 21.52 21.52 21.53 21.54 21.56 21.57 21.58 21.58 21.58 21.58 21.60 21.60 21.64 21.65 21.66 21.66 21.76

33.0k 36.3k 39.6k 42.9k 47.3k 51.7k 56.1k 61.6k 68.2k 74.8k 82.5k 90.2k 100.0k ll0.0k ll.0k 17.5k 14.2k 42.6k 55.7k 13.1k 26.2k 39.3k 51.3k 89.5k 74.2k 61.1k 109.0k 12.0k 24.0k 36.0k 46.9k 81.8k 67.6k 99.2k 21.8k 32.7k 19.6k

2.73k 3.00k 3.27k 3.55k 3.91k 4.27k 4.64k 5.09k 5.64k 6.18k 6.82k 7.45k 8.27k 9.09k 909 1.37k 1.10k 3.30k 4.30k 1.01k 2.02k 3.02k 3.94k 6.87k 5.68k 4.67k 8.34k 917 1.83k 2.75k 3.58k 6.23k 5.14k 7.52k 1.65k 2.48k 1.47k

1.96k 2.15k 2.35k 2.54k 2.80k 3.06k 3.32k 3.65k 4.04k 4.43k 4.89k 5.34k 5.93k 6.52k 652 1.04k 841 2.52k 3.30k 776 1.55k 2.33k 3.04k 5.30k 4.40k 3.62k 6.46k 711 1.42k 2.13k 2.78k 4.85k 4.01k 5.88k 1.29k 1.94k 1.16k

46.0k 50.6k 55.2k 59.8k 66.0k 72.1k 78.2k 85.9k 95.1k 104k l15k 126k 140k 153k 15.3k 23.1k 18.5k 55.6k 72.6k 17.0k 34.0k 51.0k 66.5k l16k 95.9k 78.9k 141k 15.5k 30.9k 46.4k 60.3k 105k 86.7k 127k , 27.9k 41.8k 24.8k

23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 23.5 22.3 22.0 22.0 22.0 21.9 21.9 21.9 21.9 21.9 21.8 21.8 21.8 21.8 21.8 21.8 21.7 21..7 21.6 21.6 21.6 21.6 21.4

178 R1 27k 15k 13k 39k 51k 56k 43k 12k 18k 24k 36k 47k 82k llk 75k 91k 68k 62k 100k 22k 33k 27k 16k 15k 20k 30k 13k 39k 56k 43k 47k 51k 12k 62k 82k 16k 20k

Electronics Calculations Data Handbook R2 2k4 lk3 lkl 3k3 4k3 4k7 3k6 lk lk5 2k 3k 3k9 6k8 910R 6k2 7k5 5k6 5kl 8k2 lk8 2k7 2k2 lk3 lk2 lk6 2k4 lk 3k 4k3 3k3 3k6 3k9 910R 4k7 6k2 lk2 lk5

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

81.6m 79.8m 78.0m 78.0m 77.8m 77.4m 77.3m 76.9m 76.9m 76.9m 76.9m 76.6m 76.6m 76.4m 76.4m 76.1m 76.1m 76.0m 75.8m 75.6m 75.6m 75.3m 75.1m 74.1m 74.1m 74.1m 71.4m 71.4m 71.3m 71.3m 71.1m 71.0m 70.5m 70.5m 70.3m 69.8m 69.8m

21.76 21.96 22.16 22.16 22.19 22.22 22.24 22.28 22.28 22.28 22.28 22.31 22.32 22.34 22.34 22.37 22.37 22.38 22.41 22.43 22.43 22.46 22.48 22.61 22.61 22.61 22.92 22.92 22.94 22.94 22.96 22.97 23.04 23.04 23.06 23.13 23.13

29.4k 16.3k 14.1k 42.3k 55.3k 60.7k 46.6k 13.0k 19.5k 26.0k 39.0k 50.9k 88.8k ll.9k 81.2k 98.5k 73.6k 67.1k 108.0k 23.8k 35.7k 29.2k 17.3k 16.2k 21.6k 32.4k 14.0k 42.0k 60.3k 46.3k 50.6k 54.9k 12.9k 66.7k 88.2k 17.2k 21.5k

2.20k 1.20k 1.01k 3.04k 3.97k 4.34k 3.32k 923 1.38k 1.85k 2.77k 3.60k 6.28k 840 5.73k 6.93k 5.17k 4.71k 7.58k 1.66k 2.50k 2.03k 1.20k 1.11k 1.48k 2.22k 929 2.79k 3.99k 3.06k 3.34k 3.62k 846 4.37k 5.76k 1.12k 1.40k

1.74k 966 835 2.51k 3.28k 3.60k 2.76k 770 1.16k 1.54k 2.31k 3.02k 5.26k 706 4.81k 5.84k 4.36k 3.98k 6.41k 1.41k 2.12k 1.73k 1.03k 960 1.28k 1.92k 830 2.49k 3.57k 2.74k 3.00k 3.25k 765 3.95k 5.23k 1.02k 1.27k

37.2k 20.2k 17.1k 51.3k 66.9k 73.2k 56.1k 15.6k 23.4k 31.2k 46.7k 60.8k 106k 14.2k 96.6k l17k 87.3k 79.5k 128k 28.1k 42.1k 34.3k 20.3k 18.8k 25.0k 37.5k 15.7k 47.0k 67.4k 51.7k 56.4k 61.1k 14.3k 73.7k 97.3k 18.8k 23.5k

21.4 20.9 20.5 20.5 20.4 20.3 20.3 20.2 20.2 20.2 20.2 20.2 20.1 20.1 20.1 20.0 20.0 20.0 19.9 19.9 19.9 19.8 19.8 19.5 19.5 19.5 18.9 18.9 18.9 18.9 18.8 18.8 18.7 18.7 18.6 18.5 18.5

Table 8. 1 Voltage dividers

R1 24k 36k 68k 100k 91k 75k llk 27k 15k 30k 22k 33k 18k 51k 47k 13k 43k 56k 62k 39k 68k 16k 12k 82k llk 22k 91k 75k 100k 15k 18k 24k 27k 30k 33k 36k 20k

R2 lk8 2k7 5kl 7k5 6k8 5k6 820R 2k lkl 2k2 lk6 2k4 lk3 3k6 3k3 910R 3k 3k9 4k3 2k7 4k7 lkl 820R 5k6 750R lk5 6k2 5kl 6k8 lk lk2 lk6 lk8 2k 2k2 2k4 lk3

69.8m 69.8m 69.8m 69.8m 69.5m 69.5m 69.4m 69.0m 68.3m 68.3m 67.8m 67.8m 67.4m 65.9m 65.6m 65.4m 65.2m 65.1m 64.9m 64.7m 64.6m 64.3m 64.0m 63.9m 63.8m 63.8m 63.8m 63.7m 63.7m 62.5m 62.5m 62.5m 62.5m 62.5m 62.5m 62.5m 61.0m

179

dB

R1

Ro

RSMAX RLMIN RLs(ldB)

23.13 23.13 23.13 23.13 23.16 23.16 23.18 23.23 23.31 23.31 23.38 23.38 23.43 23.62 23.66 23.69 23.71 23.73 23.76 23.78 23.79 23.83 23.88 23.89 23.90 23.90 23.91 23.92 23.92 24.08 24.08 24.08 24.08 24.08 24.08 24.08 24.29

25.8k 38.7k 73.1k 108.0k 97.8k 80.6k ll.8k 29.0k 16.1k 32.2k 23.6k 35.4k 19.3k 54.6k 50.3k 13.9k 46.0k 59.9k 66.3k 41.7k 72.7k 17.1k 12.8k 87.6k ll.8k 23.5k 97.2k 80.1k 107.0k 16.0k 19.2k 25.6k 28.8k 32.0k 35.2k 38.4k 21.3k

1.67k 2.51k 4.74k 6.98k 6.33k 5.21k 763 1.86k 1.02k 2.05k 1.49k 2.24k 1.21k 3.36k 3.08k 850 2.80k 3.65k 4.02k 2.53k 4.40k 1.03k 768 5.24k 702 1.40k 5.80k 4.78k 6.37k 938 1.13k 1.50k 1.69k 1.88k 2.06k 2.25k 1.22k

1.53k 2.29k 4.33k 6.37k 5.80k 4.78k 700 1.72k 954 1.91k 1.40k 2.10k 1.14k 3.24k 2.98k 824 2.73k 3.55k 3.93k 2.47k 4.31k 1.Olk 760 5.19k 696 1.39k 5.76k 4.75k 6.33k 948 1.14k 1.52k 1.71k 1.90k 2.09k 2.28k 1.26k

28.3k 42.4k 80.1k l18k 107k 87.9k 12.9k 31.4k 17.3k 34.6k 25.2k 37.8k 20.5k 56.7k 52.0k 14.4k 47.3k 61.5k 67.9k 42.6k 74.2k 17.4k 13.Ok 88.5k ll.8k 23.7kl 98.0k 80.6k 107k 15.8k 19.Ok 25.3k 28.5k 31.6k 34.8k 38.0k 20.6k

18.5 18.5 18.5 18.5 18.4 18.4 18.4 18.3 18.1 18.1 18.0 18.0 17.9 17.5 17.5 17.4 17.4 17.3 17.3 17.2 17.2 17.1 17.1 17.0 17.0 17.0 17.0 17.0 17.0 16.7 16.7 16.7 16.7 16.7 16.7 16.7 16.3

180

R1 51k 56k 47k 68k 13k 62k 43k 75k 16k 12k 24k 82k 100k llk 39k 91k 18k 36k 15k 33k 20k 30k 27k 22k 56k 51k 62k 13k 47k 68k 75k 82k 16k 12k 39k llk 91k

Electronics Calculations Data Handbook

R2 3k3 3k6 3k 4k3 820R 3k9 2k7 4k7 lk 750R lk5 5kl 6k2 680R 2k4 5k6 lkl 2k2 910R 2k lk2 lk8 lk6 lk3 3k3 3k 3k6 750R 2k7 3k9 4k3 4k7 910R 680R 2k2 620R 5kl

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

60.8m 60.4m 60.0m 59.5m 59.3m 59.2m 59.1m 59.0m 58.8m 58.8m 58.8m 58.6m 58.4m 58.2m 58.0m 58.0m 57.6m 57.6m 57.2m 57.1m 56.6m 56.6m 55.9m 55.8m 55.6m 55.6m 54.9m 54.5m 54.3m 54.2m 54.2m 54.2m 53.8m 53.6m 53.4m 53.4m 53.1rn

24.33 24.38 24.44 24.51 24.53 24.56 24.57 24.59 24.61 24.61 24.61 24.65 24.67 24.70 24.74 24.74 24.79 24.79 24.85 24.86 24.94 24.94 25.04 25.07 25.09 25.11 25.21 25.26 25.30 25.31 25.32 25.32 25.38 25.41 25.45 25.46 25.50

54.3k 59.6k 50.0k 72.3k 13.8k 65.9k 45.7k 79.7k 17.0k 12.8k 25.5k 87.1k 106.0k ll.7k 41.4k 96.6k 19.1k 38.2k 15.9k 35.0k 21.2k 31.8k 28.6k 23.3k 59.3k 54.0k 65.6k 13.8k 49.7k 71.9k 79.3k 86.7k 16.9k 12.7k 41.2k ll.6k 96.1k

3.10k 3.38k 2.82k 4.04k 771 3.67k 2.54k 4.42k 941 706 1.41k 4.80k 5.84k 640 2.26k 5.28k 1.04k 2.07k 858 1.89k 1.13k 1.70k 1.51k 1.23k 3.12k 2.83k 3.40k 709 2.55k 3.69k 4.07k 4.45k 861 644 2.08k 587 4.83k

3.22k 3.53k 2.96k 4.28k 819 3.90k 2.71k 4.72k 1.01k 755 1.51k 5.16k 6.29k 692 2.45k 5.72k 1.13k 2.26k 943 2.07k 1.26k 1.88k 1.69k 1.38k 3.51k 3.20k 3.89k 815 2.94k 4.26k 4.70k 5.14k 1.00k 751 2.44k 689 5.69k

52.3k 57.1k 47.6k 68.3k 13.0k 61.9k 42.9k 74.6k 15.9k ll.9k 23.8k 81.0k 98.5k 10.8k 38.2k 89.0k 17.5k 35.0k 14.5k 31.8k 19.1k 28.7k 25.5k 20.7k 52.6k 47.8k 57.4k 12.0k 43.1k 62.2k 68.6k 75.0k 14.5k 10.9k 35.1k 9.91k 81.5k

16.3 16.2 16.1 15.9 15.9 15.9 15.8 15.8 15.8 15.8 15.8 15.7 15.7 15.6 15.6 15.6 15.5 15.5 15.4 15.3 15.2 15.2 15.0 15.0 15.0 14.9 14.8 14.7 14.6 14.6 14.6 14.6 14.5 14.5 14.4 14.4 14.3

Table 8.1 Voltage dividers R1 100k 43k 18k 27k 36k 20k 15k 22k 33k 24k 56k 30k 62k 51k 68k 82k 13k 75k 12k 91k 39k 16k 43k 47k 100k llk 18k 15k 20k 22k 24k 30k 36k 68k 33k 62k 56k

R2 5k6 2k4 lk lk5 2k lkl 820R lk2 lk8 lk3 3k lk6 3k3 2k7 3k6 4k3 680R 3k9 620R 4k7 2k 820R 2k2 2k4 5kl 560R 910R 750R lk lkl lk2 lk5 lk8 3k3 lk6 3k 2k7

53.0m 52.9m 52.6m 52.6m 52.6m 52.1m 51.8m 51.7m 51.7m 51.4m 50.8m 50.6m 50.5m 50.3m 50.3m 49.8m 49.7m 49.4m 49.1m 49.1m 48.8m 48.8m 48.7m 48.6m 48.5m 48.4m 48.1m 47.6m 47.6m 47.6m 47.6m 47.6m 47.6m 46.3m 46.2m 46.2m 46.0m

181

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

25.51 25.54 25.58 25.58 25.58 25.66 25.71 25.73 25.73 25.78 25.87 25.91 25.93 25.97 25.97 26.05 26.07 26.12 26.17 26.18 26.24 26.24 26.25 26.27 26.28 26.30 26.35 26.44 26.44 26.44 26.44 26.44 26.44 26.69 26.70 26.72 26.75

106.0k 45.4k 19.0k 28.5k 38.0k 21.1k 15.8k 23.2k 34.8k 25.3k 59.0k 31.6k 65.3k 53.7k 71.6k 86.3k 13.7k 78.9k 12.6k 95.7k 41.0k 16.8k 45.2k 49.4k 105.0k ll.6k 18.9k 15.8k 21.0k 23.1k 25.2k 31.5k 37.8k 71.3k 34.6k 65.0k 58.7k

5.30k 2.27k 947 1.42k 1.89k 1.04k 777 1.14k 1.71k 1.23k 2.85k 1.52k 3.13k 2.56k 3.42k 4.09k 646 3.71k 590 4.47k 1.90k 780 2.09k 2.28k 4.85k 533 866 714 952 1.05k 1.14k 1.43k 1.71k 3.15k 1.53k 2.86k 2.58k

6.26k 2.69k 1.13k 1.69k 2.25k 1.25k 937 1.37k 2.06k 1.50k 3.50k 1.87k 3.87k 3.18k 4.24k 5.11k 811 4.68k 748 5.67k 2.43k 997 2.68k 2.93k 6.23k 685 1.12k 933 1.24k 1.37k 1.49k 1.87k 2.24k 4.22k 2.05k 3.85k 3.48k

89.5k 38.4k 16.0k 24.0k 32.0k 17.6k 13.1k 19.2k 28.8k 20.8k 48.1k 25.6k 52.9k 43.3k 57.7k 69.0k 10.9k 62.6k 9.95k 75.4k 32.1k 13.2k 35.3k 38.5k 81.9k 8.99k 14.6k 12.1k 16.1k 17.7k 19.3k 24.1k 28.9k 53.1k 25.8k 48.3k 43.5k

14.3 14.3 14.2 14.2 14.2 14.1 14.0 14.0 14.0 13.9 13.7 13.7 13.7 13.6 13.6 13.5 13.5 13.4 13.3 13.3 13.2 13.2 13.2 13.2 13.2 13.1 13.0 12.9 12.9 12.9 12.9 12.9 12.9 12.6 12.6 12.5 12.5

182 R1 27k 75k 13k 82k 91k 51k 100k 16k 47k 12k 43k llk 39k 24k 18k 20k 22k 33k 15k 36k 27k 68k 75k 82k 62k 30k 51k 13k 100k 56k 91k llk 47k 12k 16k 43k 18k

Electronics Calculations Data Handbook R2 lk3 3k6 620R 3k9 4k3 2k4 4k7 750R 2k2 560R 2k 510R lk8 lkl 820R 910R lk lk5 680R lk6 lk2 3k 3k3 3k6 2k7 lk3 2k2 560R 4k3 2k4 3k9 470R 2k 510R 680R lk8 750R

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

45.9m 45.8m 45.5m 45.4m 45.1m 44.9m 44.9m 44.8m 44.7m 44.6m 44.4m 44.3m 44.1m 43.8m 43.6m 43.5m 43.5m 43.5m 43.4m 42.6m 42.6m 42.3m 42.1m 42.1m 41.7m 41.5m 41.4m 41.3m 41.2m 41.1m 41.1m 41.0m 40.8m 40.8m 40.8m 40.2m 40.0m

26.76 26.78 26.84 26.86 26.91 26.95 26.96 26.98 26.99 27.02 27.04 27.07 27.11 27.17 27.22 27.23 27.23 27.23 27.26 27.42 27.42 27.48 27.50 27.52 27.59 27.63 27.67 27.68 27.70 27.72 27.72 27.75 27.78 27.79 27.79 27.92 27.96

28.3k 78.6k 13.6k 85.9k 95.3k 53.4k 105.0k 16.8k 49.2k 12.6k 45.0k ll.5k 40.8k 25.1k 18.8k 20.9k 23.0k 34.5k 15.7k 37.6k 28.2k 71.0k 78.3k 85.6k 64.7k 31.3k 53.2k 13.6k 104.0k 58.4k 94.9k ll.5k 49.0k 12.5k 16.7k 44.8k 18.8k

1.24k 3.44k 592 3.72k 4.11k 2.29k 4.49k 716 2.10k 535 1.91k 487 1.72k 1.05k 784 870 957 1.43k 651 1.53k 1.15k 2.87k 3.16k 3.45k 2.59k 1.25k 2.11k 537 4.12k 2.30k 3.74k 451 1.92k 489 652 1.73k 720

1.68k 4.66k 807 5.09k 5.65k 3.16k 6.20k 992 2.92k 744 2.67k 682 2.42k 1.49k 1.12k 1.24k 1.36k 2.04k 929 2.23k 1.67k 4.21k 4.64k 5.07k 3.83k 1.85k 3.15k 803 6.18k 3.46k 5.62k 680 2.90k 741 988 2.65k 1.11k

20.9k 58.0k 9.99k 62.8k 69.3k 38.7k 75.8k 12.1k 35.5k 9.03k 32.3k 8.23k 29.0k 17.8k 13.2k 14.7k 16.1k 24.2k ll.0k 25.9k 19.4k 48.5k 53.3k 58.2k 43.7k 21.0k 35.6k 9.06k 69.6k 38.8k 63.1k 7.61k 32.4k 8.26k ll.0k 29.2k 12.2k

12.5 12.4 12.4 12.3 12.3 12.2 12.2 12.2 12.2 12.1 12.1 12.1 12.0 11.9 11.9 11.9 11.8 11.8 11.8 11.6 11.6 11.5 11.5 11.5 11.4 11.3 11.3 11.3 11.3 11.2 11.2 11.2 11.2 11.1 11.1 11.0 10.9

Table 8. 1 Voltage dividers R1 24k 36k 22k 15k 39k 20k 27k 82k 30k 75k 68k 91k 33k 56k 13k 51k 12k llk 100k 16k 62k 39k 47k 24k 18k 20k 15k 22k 43k 27k 30k 82k 33k 91k 13k 36k 75k

R2 lk lk5 910R 620R lk6 820R lkl 3k3 lk2 3k 2k7 3k6 lk3 2k2 510R 2k 470R 430R 3k9 620R 2k4 lk5 lk8 910R 680R 750R 560R 820R lk6 lk lkl 3k lk2 3k3 470R lk3 2k7

40.0m 40.0m 39.7m 39.7m 39.4m 39.4m 39.1m 38.7m 38.5m 38.5m 38.2m 38.1m 37.9m 37.8m 37.7m 37.7m 37.7m 37.6m 37.5m 37.3m 37.3m 37.0m 36.9m 36.5m 36.4m 36.1m 36.0m 35.9m 35.9m 35.7m 35.4m 35.3m 35.1m 35.0m 34.9m 34.9m 34.7m

183

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

27.96 27.96 28.02 28.03 28.09 28.09 28.15 28.25 28.30 28.30 28.36 28.39 28.43 28.45 28.46 28.46 28.48 28.49 28.51 28.56 28.57 28.63 28.66 28.75 28.78 28.84 28.88 28.89 28.90 28.94 29.03 29.05 29.10 29.12 29.15 29.16 29.18

25.0k 37.5k 22.9k 15.6k 40.6k 20.8k 28.1k 85.3k 31.2k 78.0k 70.7k 94.6k 34.3k 58.2k 13.5k 53.0k 12.5k ll.4k 104.0k 16.6k 64.4k 40.5k 48.8k 24.9k 18.7k 20.8k 15.6k 22.8k 44.6k 28.0k 31.1k 85.0k 34.2k 94.3k 13.5k 37.3k 77.7k

960 1.44k 874 595 1.54k 788 1.06k 3.17k 1.15k 2.88k 2.60k 3.46k 1.25k 2.12k 491 1.92k 452 414 3.75k 597 2.31k 1.44k 1.73k 877 655 723 540 791 1.54k 964 1.06k 2.89k 1.16k 3.18k 454 1.25k 2.61k

1.48k 2.22k 1.36k 926 2.41k 1.23k 1.67k 5.05k 1.85k 4.62k 4.19k 5.61k 2.03k 3.45k 801 3.14k 739 677 6.16k 985 3.82k 2.40k 2.89k 1.48k 1.11k 1.23k 922 1.35k 2.64k 1.66k 1.84k 5.04k 2.03k 5.59k 798 2.21k 4.60k

16.2k 24.3k 14.7k 10.0k 25.9k 13.3k 17.8k 53.5k 19.5k 48.7k 43.8k 58.4k 21.1k 35.7k 8.28k 32.5k 7.63k 6.98k 63.3k 10.1k 39.0k 24.4k 29.3k 14.8k ll.lk 12.2k 9.11k 13.3k 26.0k 16.3k 17.9k 48.8k 19.5k 53.7k 7.66k 21.2k 44.0k

10.9 10.9 10.9 10.9 10.8 10.8 10.7 10.6 10.5 10.5 10.5 10.4 10.4 10.4 10.3 10.3 10.3 10.3 10.3 10.2 10.2 10.2 10.1 10.0 9.99 9.92 9.88 9.87 9.85 9.81 9.72 9.70 9.64 9.62 9.59 9.58 9.55

184 R1 100k 12k 56k 62k llk 51k 68k 16k 43k 18k 24k 22k 47k 15k 20k 27k 30k 33k 36k 39k 13k 100k 91k 82k llk 12k 68k 62k 56k 75k 47k 16k 51k 15k 24k 18k 20k

Electronics Calculations Data Handbook R2 3k6 430R 2k 2k2 390R lk8 2k4 560R lk5 620R 820R 750R lk6 510R 680R 910R lk lkl lk2 lk3 430R 3k3 3k 2k7 360R 390R 2k2 2k lk8 2k4 lk5 510R lk6 470R 750R 560R 620R

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

34.7m 34.6m 34.5m 34.3m 34.2m 34.1m 34.1m 33.8m 33.7m 33.3m 33.0m 33.0m 32.9m 32.9m 32.9m 32.6m 32.3m 32.3m 32.3m 32.3m 32.0m 31.9m 31.9m 31.9m 31.7m 31.5m 31.3m 31.3m 31.1m 31.0m 30.9m 30.9m 30.4m 30.4m 30.3m 30.2m 30.1m

29.18 29.22 29.25 29.30 29.31 29.35 29.35 29.42 29.45 29.55 29.62 29.64 29.65 29.66 29.66 29.73 29.83 29.83 29.83 29.83 29.89 29.91 29.92 29.93 29.98 30.04 30.08 30.10 30.13 30.17 30.19 30.20 30.34 30.35 30.37 30.41 30.44

104.0k 12.4k 58.0k 64.2k ll.4k 52.8k 70.4k 16.6k 44.5k 18.6k 24.8k 22.8k 48.6k 15.5k 20.7k 27.9k 31.0k 34.1k 37.2k 40.3k 13.4k 103.0k 94.0k 84.7k ll.4k 12.4k 70.2k 64.0k 57.8k 77.4k 48.5k 16.5k 52.6k 15.5k 24.8k 18.6k 20.6k

3.47k 415 1.93k 2.12k 377 1.74k 2.32k 541 1.45k 599 793 725 1.55k 493 658 880 968 1.06k 1.16k 1.26k 416 3.19k 2.90k 2.61k 349 378 2.13k 1.94k 1.74k 2.33k 1.45k 494 1.55k 456 727 543 601

6.14k 737 3.44k 3.80k 675 3.13k 4.17k 981 2.64k 1.10k 1.47k 1.35k 2.88k 919 1.23k 1.65k 1.84k 2.02k 2.20k 2.39k 796 6.12k 5.57k 5.02k 673 734 4.16k 3.79k 3.42k 4.59k 2.87k 978 3.12k 917 1.47k 1.10k 1.22k

58.6k 7.01k 32.6k 35.9k 6.36k 29.3k 39.1k 9.13k 24.5k 10.1k 13.4k 12.2k 26.1k 8.32k ll.lk 14.9k 16.3k 18.0k 19.6k 21.2k 7.02k 53.9k 49.0k 44.1k 5.88k 6.37k 36.0k 32.7k 29.4k 39.2k 24.5k 8.34k 26.2k 7.69k 12.3k 9.17k 10.1k

9.55 9.51 9.4.8 9.43 9.42 9.38 9.38 9.31 9.28 9.17 9.10 9.08 9.07 9.06 9.06 8.98 8.89 8.89 8.89 8.89 8.83 8.81 8.80 8.79 8.74 8.68 8.65 8.62 8.59 8.56 8.54 8.53 8.40 8.39 8.37 8.33 8.31

Table 8. 1 Voltage dividers R1 22k 39k 36k 27k 30k 33k 43k Ilk 12k 13k 100k 91k 51k 68k 16k 75k 82k 62k 15k 56k 18k 24k 39k 22k 20k 43k 27k 36k 13k 47k 33k 12k 30k llk 100k 16k 82k

R2 680R lk2 lkl 820R 910R lk lk3 330R 360R 390R 3k 2k7 lk5 2k 470R 2k2 2k4 lk8 430R lk6 510R 680R lkl 620R 560R lk2 750R lk 360R lk3 910R 330R 820R 300R 2k7 430R 2k2

30.0m 29.9m 29.6m 29.5m 29.4m 29.4m 29.3m 29.1m 29.1m 29.1m 29.1m 28.8m 28.6m 28.6m 28.5m 28.5m 28.4m 28.2m 27.9m 27.8m 27.6m 27.6m 27.4m 27.4m 27.2m 27.1m 27.0m 27.0m 26.9m 26.9m 26.8m 26.8m 26.6m 26.5m 26.3m 26.2m 26.1m

185

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

30.46 30.50 30.56 30.61 3O.62 30.63 30.65 30.71 30.71 30.71 30.71 30.81 30.88 30.88 30.89 30.90 30.92 30.99 31.10 31.13 31.20 31.20 31.24 31.24 31.30 31.32 31.36 31.36 31.39 31.40 31.43 31.45 31.50 31.52 31.60 31.64 31.66

22.7k 40.2k 37.1k 27.8k 30.9k 34.0k 44.3k ll.3k 12.4k 13.4k 103.0k 93.7k 52.5k 70.0k 16.5k 77.2k 84.4k 63.8k 15.4k 57.6k 18.5k 24.7k 40.1k 22.6k 20.6k 44.2k 27.8k 37.0k 13.4k 48.3k 33.9k 12.3k 30.8k ll.3k 103.0k 16.4k 84.2k

660 1.16k 1.07k 796 883 971 1.26k 320 35O 379 2.91k 2.62k 1.46k 1.94k 457 2.14k 2.33k 1.75k 418 1.56k 496 661 1.07k 603 545 1.17k 730 973 350 1.27k 886 321 798 292 2.63k 419 2.14k

1.34k 2.38k 2.20k 1.65k 1.83k 2.01k 2.62k 671 732 793 6.10k 5.55k 3.11k 4.15k 976 4.57k 5.00k 3.78k 914 3.41k 1.10k 1.46k 2.38k 1.34k 1.22k 2.62k 1.64k 2.19k 792 2.86k 2.01k 731 1.83k 670 6.09k 974 4.99k

ll.lk 19.6k 18.0k 13.4k 14.9k 16.4k 21.3k 5.41k 5.90k 6.39k 49.2k 44.3k 24.6k 32.8k 7.71k 36.1k 39.4k 29.5k 7.05k 26.3k 8.37k ll.2k 18.1k 10.2k 9.19k 19.7k 12.3k 16.4k 5.91k 21.3k 14.9k 5.42k 13.5k 4.93k 44.4k 7.07k 36.2k

8.28 8.25 8.19 8.15 8.14 8.13 8.11 8.05 8.05 8.05 8.05 7.97 7.91 7.91 7.90 7.89 7.87 7.81 7.72 7.69 7.63 7.63 7.60 7.59 7.55 7.52 7.49 7.49 7.47 7.46 7.44 7.42 7.38 7.36 7.29 7.26 7.25

186 Rt 56k 75k 68k 91k 18k 15k 24k 62k 39k 43k 47k 20k 51k 22k 13k 36k 27k 12k 30k 33k llk 82k 16k 62k 91k 15k 75k 100k 18k 51k 68k 20k 47k 39k 24k 43k 56k

Electronics Calculations Data Handbook R2 lk5 2k lk8 2k4 470R 390R 620R lk6 lk lkl lk2 510R lk3 560R 330R 910R 680R 300R 750R 820R 270R 2k 390R lk5 2k2 360R lk8 2k4 430R lk2 lk6 470R lkl 910R 560R lk lk3

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

26.1m 26.0m 25.8m 25.7m 25.4m 25.3m 25.2m 25.2m 25.0m 24.9m 24.9m 24.9m 24.9m 24.8m 24.8m 24.7m 24.6m 24.4m 24.4m 24.2m 24.0m 23.8m 23.8m 23.6m 23.6m 23.4m 23.4m 23.4m 23.3m 23.0m 23.0m 23.0m 22.9m 22.8m 22.8m 22.7m 22.7m

3i.67 31.71 31.77 31.80 31.89 31.92 31.98 31.99 32.04 32.06 32.08 32.09 32.09 32.10 32.13 32.16 32.19 32.26 32.26 32.31 32.41 32.46 32.47 32.53 32.54 32.60 32.60 32.60 32.64 32.77 32.77 32.78 32.82 32.84 32.84 32.87 32.88

57.5k 77.0k 69.8k 93.4k 18.5k 15.4k 24.6k 63.6k 40.0k 44.1k 48.2k 20.5k 52.3k 22.6k 13.3k 36.9k 27.7k 12.3k 30.8k 33.8k ll.3k 84.0k 16.4k 63.5k 93.2k 15.4k 76.8k 102.0k 18.4k 52.2k 69.6k 20.5k 48.1k 39.9k 24.6k 44.0k 57.3k

1.46k 1.95k 1.75k 2.34k 458 380 604 1.56k 975 1.07k 1.17k 497 1.27k 546 322 888 663 293 732 800 264 1.95k 381 1.46k 2.15k 352 1.76k 2.34k 420 1.17k 1.56k 459 1.07k 889 547 977 1.27k

3.41k 4.56k 4.14k 5.53k 1.09k 912 1.46k 3.77k 2.37k 2.61k 2.86k 1.22k 3.10k 1.34k 790 2.19k 1.64k 729 1.82k 2.00k 668 4.98k 971 3.76k 5.52k 910 4.55k 6.07k 1.09k 3.09k 4.12k 1.21k 2.85k 2.36k 1.46k 2.61k 3.40k

24.7k 32.9k 29.6k 39.5k 7.73k 6.42k 10.2k 26.3k 16.5k 18.1k 19.7k 8.39k 21.4k 9.22k 5.43k 15.0k ll.2k 4.94k 12.3k 13.5k 4.45k 32.9k 6.43k 24.7k 36.3k 5.93k 29.7k 39.6k 7.09k 19.8k 26.4k 7.75k 18.1k 15.0k 9.24k 16.5k 21.4k

7.24 7.21 7.16 7.13 7.06 7.03 6.99 6.98 6.94 6.93 6.91 6.91 6.90 6.89 6.88 6.85 6.83 6.78 6.78 6.74 6.66 6.62 6.62 6.57 6.56 6.52 6.52 6.52 6.49 6.40 6.40 6.39 6.36 6.35 6.35 6.33 6.32

Table 8. 1 Voltage dividers R1 22k 13k 27k 36k 33k 30k 12k 16k 68k 15k 100k 91k 82k llk 18k 51k 20k 56k 22k 75k 47k 24k 43k 39k 62k 36k 13k 27k 30k 16k 33k llk 12k 15k 18k 75k 100k

R2 510R 300R 620R 820R 750R 680R 270R 360R lk5 330R 2k2 2k lk8 240R 390R lkl 430R lk2 470R lk6 lk 510R 910R 820R lk3 750R 270R 560R 620R 330R 680R 220R 240R 300R 360R lk5 2k

dB 22.7m 32.90 22.6m 32.93 22.4m 32.98 22.3m 33.05 22.2m 33.06 22.2m 33.09 22.0m 33.15 22.0m 33.15 21.6m 33.32 21.5m 33.34 21.5m 33.34 21.5m 33.35 21.5m 33.36 21.4m 33.41 21.2m 33.47 21.1m 33.51 21.0m 33.54 21.0m 33.56 20.9m 33.59 20.9m 33.60 20.8m 33.62 20.8m 33.64 20.7m 33.67 20.6m 33.73 20.5m 33.75 20.4m 33.80 20.3m 33.83 20.3m 33.84 20.2m 33.87 20.2m 33.89 20.2m 33.90 19.6m 34.15 19.6m 34.15 19.6m 34.15 19.6m 34.15 19.6m 34.15 19.6m 34.15

187

RI

Ro

RSMAX RLMIN RLS (1 dB)

22.5k 13.3k 27.6k 36.8k 33.8k 30.7k 12.3k 16.4k 69.5k 15.3k 102.0k 93.0k 83.8k ll.2k 18.4k 52.1k 20.4k 57.2k 22.5k 76.6k 48.0k 24.5k 43.9k 39.8k 63.3k 36.8k 13.3k 27.6k 30.6k 16.3k 33.7k ll.2k 12.2k 15.3k 18.4k 76.5k 102.0k

498 293 606 802 733 665 264 352 1.47k 323 2.15k 1.96k 1.76k 235 382 1.08k 421 1.17k 460 1.57k 979 499 891 803 1.27k 735 265 549 607 323 666 216 235 294 353 1.47k 1.96k

1.33k 788 1.64k 2.18k 2.00k 1.82k 727 969 4.12k 908 6.06k 5.51k 4.97k 666 1.09k 3.09k 1.21k 3.39k 1.33k 4.54k 2.84k 1.45k 2.60k 2.36k 3.75k 2.18k 786 1.63k 1.81k 968 2.00k 665 725 907 1.09k 4.53k 6.04k

8.41k 4.95k 10.2k 13.5k 12.4k ll.2k 4.46k 5.94k 24.8k 5.45k 36.3k 33.0k 29.7k 3.96k 6.44k 18.2k 7.10k 19.8k 7.77k 26.4k 16.5k 8.43k 15.0k 13.6k 21.5k 12.4k 4.46k 9.26k 10.3k 5.46k ll.2k 3.64k 3.97k 4.96k 5.96k 24.8k 33.1k

6.31 6.28 6.25 6.20 6.19 6.17 6.13 6.13 6.01 6.00 6.00 5.99 5.99 5.95 5.91 5.89 5.87 5.85 5.83 5.82 5.81 5.80 5.78 5.74 5.73 5.69 5.68 5.67 5.65 5.64 5.63 5.48 5.48 5.48 5.48 5.48 5.48

188

Electronics Calculations Data Handbook

R1

R2

91k 56k 51k 24k 22k 82k 20k 47k 62k 39k 68k 43k 27k 36k 33k 16k 30k 13k 12k 18k 82k llk 20k 100k 15k 24k 56k 51k 62k 22k 68k 91k 47k 43k 39k 27k 75k

lk8 lkl lk 470R 430R lk6 390R 910R lk2 750R lk3 820R 510R 680R 620R 300R 560R 240R 220R 330R lk5 200R 360R lk8 270R 430R lk 910R lkl 390R lk2 lk6 820R 750R 680R 470R lk3

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

19.4m 19.3m 19.2m 19.2m 19.2m 19.1m 19.1m 19.0m 19.0m 18.9m 18.8m 18.7m 18.5m 18.5m 18.4m 18.4m 18.3m 18.1m 18.0m 18.0m 18.0m 17.9m 17.7m 17.7m 17.7m 17.6m 17.5m 17.5m 17.4m 17.4m 17.3m 17.3m 17.1m 17.1m 17.1m 17.1m 17.0m

34.25 34.30 34.32 34.33 34.35 34.36 34.37 34.43 34.43 34.49 34.54 34.56 34.64 34.64 34.68 34.70 34.74 34.83 34.89 34.89 34.91 34.96 35.05 35.05 35.05 35.09 35.12 35.12 35.17 35.18 35.22 35.25 35.32 35.32 35.32 35.34 35.37

92.8k 57.1k 52.0k 24.5k 22.4k 83.6k 20.4k 47.9k 63.2k 39.8k 69.3k 43.8k 27.5k 36.7k 33.6k 16.3k 30.6k 13.2k 12.2k 18.3k 83.5k ll.2k 20.4k 102.0k 15.3k 24.4k 57.0k 51.9k 63.1k 22.4k 69.2k 92.6k 47.8k 43.8k 39.7k 27.5k 76.3k

1.77k 1.08k 981 461 422 1.57k 383 893 1.18k 736 1.28k 805 501 667 609 294 550 236 216 324 1.47k 196 354 1.77k 265 422 982 894 1.08k 383 1.18k 1.57k 806 737 668 462 1.28k

5.50k 3.38k 3.08k 1.45k 1.33k 4.95k 1.21k 2.84k 3.74k 2.36k 4.11k 2.60k 1.63k 2.17k 1.99k 966 1.81k 785 724 1.09k 4.95k 664 1.21k 6.03k 905 1.45k 3.38k 3.08k 3.74k 1.33k 4.10k 5.49k 2.83k 2.59k 2.35k 1.63k 4.52k

29.8k 18.2k 16.6k 7.78k 7.12k 26.5k 6.46k 15.1k 19.9k 12.4k 21.5k 13.6k 8.45k ll.3k 10.3k 4.97k 9.28k 3.98k 3.65k 5.47k 24.9k 3.32k 5.97k 29.8k 4.48k 7.13k 16.6k 15.1k 18.2k 6.47k 19.9k 26.5k 13.6k 12.4k ll.3k 7.80k 21.6k

5.42 5.38 5.37 5.37 5.36 5.35 5.34 5.31 5.31 5.27 5.24 5.23 5.18 5.18 5.16 5.15 5.12 5.07 5.04 5.04 5.02 5.00 4.95 4.95 4.95 4.92 4.91 4.91 4.88 4.87 4.85 4.84 4.80 4.80 4.80 4.79 4.77

Table 8. 1 Voltage dividers

R1 36k 30k 33k 13k 16k 12k 18k 20k 91k Ilk 22k 24k 56k 68k 62k 51k 15k 75k 100k 47k 27k 39k 82k 43k 30k 36k 33k 13k 12k 16k 18k 20k 22k 24k 100k 51k 68k

R2 620R 510R 560R 220R 270R 200R 300R 330R lk5 180R 360R 390R 910R lkl lk 820R 240R lk2 lk6 750R 430R 620R lk3 680R 470R 560R 510R 200R 180R 240R 270R 300R 330R 360R lk5 750R lk

16.9m 16.7m 16.7m 16.6m 16.6m 16.4m 16.4m 16.2m 16.2m 16.1m 16.1m 16.0m 16.0m 15.9m 15.9m 15.8m 15.7m 15.7m 15.7m 15.7m 15.7m 15.6m 15.6m 15.6m 15.4m 15.3m 15.2m 15.2m 14.8m 14.8m 14.8m 14.8m 14.8m 14.8m 14.8m 14.5m 14.5m

189

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

35.43 35.54 35.55 35.58 35.60 35.71 35.71 35.79 35.80 35.86 35.86 35.92 35.92 35.96 35.99 36.01 36.06 36.06 36.06 36.08 36.10 36.11 36.13 36.16 36.24 36.30 36.35 36.39 36.61 36.61 36.61 36.61 36.61 36.61 36.61 36.78 36.78

36.6k 30.5k 33.6k 13.2k 16.3k 12.2k 18.3k 20.3k 92.5k ll.2k 22.4k 24.4k 56.9k 69.1k 63.0k 51.8k 15.2k 76.2k 102.0k 47.8k 27.4k 39.6k 83.3k 43.7k 30.5k 36.6k 33.5k 13.2k 12.2k 16.2k 18.3k 20.3k 22.3k 24.4k 102.0k 51.8k 69.0k

610 501 551 216 266 197 295 325 1.48k 177 354 384 895 1.08k 984 807 236 1.18k 1.57k 738 423 610 1.28k 669 463 551 502 197 177 236 266 296 325 355 1.48k 739 986

2.17k 1.81k 1.99k 783 964 723 1.08k 1.20k 5.48k 662 1.32k 1.45k 3.37k 4.09k 3.73k 3.07k 903 4.52k 6.02k 2.83k 1.63k 2.35k 4.94k 2.59k 1.81k 2.17k 1.99k 782 722 962 1.08k 1.20k 1.32k 1.44k 6.01k 3.07k 4.09k

10.3k 8.46k 9.29k 3.65k 4.48k 3.32k 4.98k 5.48k 24.9k 2.99k 5.98k 6.48k 15.1k 18.3k 16.6k 13.6k 3.99k 19.9k 26.6k 12.5k 7.14k 10.3k 21.6k ll.3k 7.81k 9.31k 8.48k 3.32k 2.99k 3.99k 4.49k 4.99k 5.49k 5.99k 24.9k 12.5k 16.6k

4.74 4.68 4.67 4.66 4.65 4.59 4.59 4.55 4.54 4.51 4.51 4.48 4.48 4.46 4.45 4.44 4.41 4.41 4.41 4.40 4.39 4.39 4.38 4.36 4.33 4.30 4.27 4.25 4.15 4.15 4.15 4.15 4.15 4.15 4.15 4.07 4.07

190

Electronics Calculations Data Handbook

R1

R2

62k 15k 75k 56k 82k llk 47k 27k 43k 39k 30k 91k 33k 36k 13k 16k 24k llk 22k 20k 82k 56k 68k 12k 15k 18k 27k 51k 75k 62k 47k 91k 39k 36k 33k 43k 30k

910R 220R lkl 820R lk2 160R 680R 390R 620R 560R 430R lk3 470R 510R 180R 220R 330R 150R 300R 270R lkl 750R 910R 160R 200R 240R 360R 680R lk 820R 620R lk2 510R 470R 430R 560R 390R

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

14.5m 14.5m 14.5m 14.4m 14.4m 14.3m 14.3m 14.2m 14.2m 14.2m 14.1m 14.1m 14.0m 14.0m 13.7m 13.6m 13.6m 13.5m 13.5m 13.3m 13.2m 13.2m 13.2m 13.2m 13.2m 13.2m 13.2m 13.2m 13.2m 13.1m 13.0m 13.0m 12.9m 12.9m 12.9m 12.9m 12.8m

36.79 36.80 36.80 36.81 36.82 36.87 36.92 36.93 36.95 36.98 37.00 37.03 37.05 37.10 37.29 37.35 37.35 37.42 37.42 37.51 37.56 37.58 37.58 37.62 37.62 37.62 37.62 37.62 37.62 37.69 37.71 37.71 37.78 37.80 37.81 37.82 37.83

62.9k 15.2k 76.1k 56.8k 83.2k ll.2k 47.7k 27.4k 43.6k 39.6k 30.4k 92.3k 33.5k 36.5k 13.2k 16.2k 24.3k ll.2k 22.3k 20.3k 83.1k 56.8k 68.9k 12.2k 15.2k 18.2k 27.4k 51.7k 76.0k 62.8k 47.6k 92.2k 39.5k 36.5k 33.4k 43.6k 30.4k

897 217 1.08k 808 1.18k 158 670 384 611 552 424 1.28k 463 503 178 217 326 148 296 266 1.09k 740 898 158 197 237 355 671 987 809 612 1.18k 503 464 424 553 385

3.73k 902 4.51k 3.37k 4.93k 661 2.83k 1.62k 2.58k 2.34k 1.80k 5.47k 1.98k 2.16k 781 961 1.44k 661 1.32k 1.20k 4.92k 3.36k 4.08k 721 901 1.08k 1.62k 3.06k 4.50k 3.72k 2.82k 5.46k 2.34k 2.16k 1.98k 2.58k 1.80k

15.1k 3.66k 18.3k 13.6k 20.Ok 2.66k ll.3k 6.49k lO.3k 9.32k 7.15k 21.6k 7.82k 8.49k 3.00k 3.66k 5.49k 2.50k 4.99k 4.50k 18.3k 12.5k 15.2k 2.66k 3.33k 4.00k 6.00k ll.3k 16.7k 13.7k lO.3k 20.Ok 8.50k 7.83k 7.16k 9.33k 6.50k

4.06 4.06 4.06 4.05 4.05 4.02 4.00 4.00 3.99 3.97 3.97 3.96 3.94 3.92 3.84 3.81 3.81 3.78 3.78 3.74 3.72 3.71 3.71 3.70 3.70 3.70 3.70 3.70 3.70 3.67 3.66 3.66 3.63 3.62 3.62 3.61 3.61

Table 8. 1 Voltage dividers R1 100k 12k 16k 24k 13k 22k 18k 27k 82k 51k 56k 75k 62k 91k 68k 39k 15k 20k 30k 100k 36k 47k 43k llk 33k 13k 16k 24k 18k 27k 82k 56k 68k 39k 20k 30k 100k

R2 lk3 150R 200R 300R 160R 270R 220R 330R lk 620R 680R 910R 750R lkl 820R 470R 180R 240R 360R lk2 430R 560R 510R 130R 390R 150R 180R 270R 200R 300R 910R 620R 750R 430R 220R 330R lkl

12.8m 12.3m 12.3m 12.3m 12.2m 12.1m 12.1m 12.1m 12.0m 12.0m 12.0m 12.0m 12.0m ll.9m ll.9m ll.9m ll.9m ll.9m ll.9m ll.9m ll.8m ll.8m ll.7m ll.7m ll.7m ll.4m ll.lm ll.lm ll.0m ll.0m ll.0m ll.0m 10.9m 10.9m 10.9m 10.9m 10.9m

191

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

37.83 38.17 38.17 38.17 38.30 38.33 38.36 38.36 38.38 38.41 38.42 38.43 38.45 38.46 38.48 38.48 38.52 38.52 38.52 38.52 38.56 38.58 38.62 38.65 38.65 38.86 39.07 39.07 39.18 39.18 39.19 39.21 39.24 39.25 39.27 39.27 39.27

101.0k 12.2k 16.2k 24.3k 13.2k 22.3k 18.2k 27.3k 83.0k 51.6k 56.7k 75.9k 62.8k 92.1k 68.8k 39.5k 15.2k 20.2k 30.4k 101.0k 36.4k 47.6k 43.5k ll.lk 33.4k 13.2k 16.2k 24.3k 18.2k 27.3k 82.9k 56.6k 68.8k 39.4k 20.2k 30.3k 101.0k

1.28k 148 198 296 158 267 217 326 988 613 672 899 741 1.09k 810 464 178 237 356 1.19k 425 553 504 128 385 148 178 267 198 297 900 613 742 425 218 326 1.09k

6.00k 720 960 1.44k 780 1.32k 1.08k 1.62k 4.92k 3.06k 3.36k 4.50k 3.72k 5.46k 4.08k 2.34k 899 1.20k 1.80k 6.00k 2.16k 2.82k 2.58k 659 1.98k 779 959 1.44k 1.08k 1.62k 4.91k 3.35k 4.07k 2.34k 1.20k 1.80k 5.99k

21.7k 2.50k 3.33k 5.00k 2.67k 4.50k 3.67k 5.50k 16.7k 10.3k ll.3k 15.2k 12.5k 18.3k 13.7k 7.84k 3.00k 4.00k 6.00k 20.0k 7.17k 9.34k 8.51k 2.17k 6.50k 2.50k 3.00k 4.51k 3.34k 5.01k 15.2k 10.3k 12.5k 7.18k 3.67k 5.51k 18.4k

3.61 3.47 3.47 3.47 3.42 3.41 3.40 3.40 3.39 3.38 3.38 3.37 3.36 3.36 3.35 3.35 3.34 3.34 3.34 3.34 3.32 3.31 3.30 3.29 3.29 3.21 3.13 3.13 3.10 3.10 3.09 3.08 3.07 3.07 3.07 3.07 3.07

192

Electronics Calculations Data Handbook

R1

R2

91k 51k 62k 75k 43k llk 22k 33k 47k 36k 12k 15k llk 12k 13k 15k 16k 18k 20k 22k 24k 27k 30k 33k 36k 39k 43k 47k 51k 56k 62k 68k 75k 82k 91k 100k 16k

lk 560R 680R 820R 470R 120R 240R 360R 510R 390R 130R 160R ll0R 120R 130R 150R 160R 180R 200R 220R 240R 270R 300R 330R 360R 390R 430R 470R 510R 560R 620R 680R 750R 820R 910R lk 150R

A 10.9m 10.9m 10.8m 10.8m 10.8m 10.8m 10.8m 10.8m 10.7m 10.7m 10.7m 10.6m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.90m 9.29m

dB 39.28 39.28 39.29 39.32 39.32 39.34 39.34 39.34 39.38 39.40 39.40 39.53 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.09 40.64

RI

Ro

RSMAX RLMIN RLS (1 dB)

92.0k 51.6k 62.7k 75.8k 43.5k ll.lk 22.2k 33.4k 47.5k 36.4k 12.1k 15.2k ll.lk 12.1k 13.1k 15.2k 16.2k 18.2k 20.2k 22.2k 24.2k 27.3k 30.3k 33.3k 36.4k 39.4k 43.4k 47.5k 51.5k 56.6k 62.6k 68.7k 75.8k 82.8k 91.9k 101.0k 16.2k

989 554 673 811 465 119 237 356 505 386 129 158 109 119 129 149 158 178 198 218 238 267 297 327 356 386 426 465 5O5 554 614 673 743 812 901 990 149

5.45k 3.06k 3.71k 4.49k 2.58k 659 1.32k 1.98k 2.82k 2.16k 719 898 658 718 778 898 958 1.08k 1.20k 1.32k 1.44k 1.62k 1.80k 1.97k 2.15k 2.33k 2.57k 2.81k 3.05k 3.35k 3.71k 4.07k 4.49k 4.91k 5.45k 5.98k 957

16.7k 9.35k ll.4k 13.7k 7.85k 2.00k 4.01k 6.01k 8.51k 6.51k 2.17k 2.67k 1.84k 2.01k 2.17k 2.51k 2.67k 3.01k 3.34k 3.68k 4.01k 4.51k 5.01k 5.51k 6.02k 6.52k 7.19k 7.85k 8.52k 9.36k 10.4k ll.4k 12.5k 13.7k 15.2k 16.7k 2.51k

3.06 3.06 3.06 3.05 3.05 3.04 3.04 3.04 3.02 3.02 3.02 2.97 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.79 2.62

Table 8. 1 Voltage dividers R1 13k 39k 51k 12k 24k 36k 47k 82k 68k 56k 100k Ilk 22k 33k 43k 75k 62k 91k 20k 30k 18k 27k 15k 13k 39k 51k 56k 43k 12k 18k 24k 36k 47k 82k 75k 91k 68k

R2 120R 360R 470R ll0R 220R 330R 430R 750R 620R 510R 910R 100R 200R 300R 390R 680R 560R 820R 180R 270R 160R 240R 130R ll0R 330R 430R 470R 360R 100R 150R 200R 300R 390R 680R 620R 750R 560R

9.15m 9.15m 9.13m 9.08m 9.08m 9.08m 9.07m 9.06m 9.04m 9.02m 9.02m 9.01m 9.01m 9.01m 8.99m 8.99m 8.95m 8.93m 8.92m 8.92m 8.81m 8.81m 8.59m 8.39m 8.39m 8.36m 8.32m 8.30m 8.26m 8.26m 8.26m 8.26m 8.23m 8.22m 8.20m 8.17m 8.17m

193

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

40.78 40.78 40.79 40.84 40.84 40.84 40.85 4O.85 40.88 40.89 40.90 40.91 40.91 40.91 40.93 40.93 40.96 40.98 40.99 40.99 41.10 41.10 41.32 41.52 41.52 41.55 41.59 41.62 41.66 41.66 41.66 41.66 41.69 41.70 41.72 41.75 41.76

13.1k 39.4k 51.5k 12.1k 24.2k 36.3k 47.4k 82.8k 68.6k 56.5k 101.0k ll.lk 22.2k 33.3k 43.4k 75.7k 62.6k 91.8k 20.2k 30.3k 18.2k 27.2k 15.1k 13.1k 39.3k 51.4k 56.5k 43.4k 12.1k 18.2k 24.2k 36.3k 47.4k 82.7k 75.6k 91.8k 68.6k

119 357 466 109 218 327 426 743 614 505 902 99.1 198 297 386 674 555 813 178 268 159 238 129 109 327 426 466 357 99.2 149 198 298 387 674 615 744 555

777 2.33k 3.05k 718 1.44k 2.15k 2.81k 4.90k 4.07k 3.35k 5.98k 658 1.32k 1.97k 2.57k 4.48k 3.71k 5.44k 1.20k 1.79k 1.08k 1.61k 897 777 2.33k 3.05k 3.35k 2.57k 717 1.08k 1.43k 2.15k 2.81k 4.90k 4.48k 5.44k 4.06k

2.01k 6.02k 7.86k 1.84k 3.68k 5.52k 7.19k 12.5k 10.4k 8.53k 15.2k 1.67k 3.34k 5.02k 6.52k ll.4k 9.37k 13.7k 3.01k 4.52k 2.68k 4.01k 2.18k 1.84k 5.52k 7.20k 7.87k 6.03k 1.67k 2.51k 3.35k 5.02k 6.53k ll.4k 10.4k 12.6k 9.37k

2.58 2.58 2.58 2.56 2.56 2.56 2.56 2.56 2.55 2.55 2.55 2.54 2.54 2.54 2.54 2.54 2.53 2.52 2.52 2.52 2.49 2.49 2.43 2.37 2.37 2.36 2.35 2.35 2.33 2.33 2.33 2.33 2.32 2.32 2.32 2.31 2.31

194

R1 62k 100k 22k 33k 27k 16k 15k 20k 30k 13k 39k 56k 43k 47k 51k 62k 82k 16k 20k 24k 36k 68k 100k 91k 75k 27k 15k 30k 22k 33k 18k 51k 47k 43k 56k 62k 39k

Electronics Calculations Data Handbook

R2 510R 820R 180R 270R 220R 130R 120R 160R 240R 100R 300R 430R 330R 360R 390R 470R 620R 120R 150R 180R 270R 510R 750R 680R 560R 200R ll0R 220R 160R 240R 130R 360R 330R 300R 390R 430R 270R

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

8.16m 8.13m 8.12m 8.12m 8.08m 8.06m 7.94m 7.94m 7.94m 7.63m 7.63m 7.62m 7.62m 7.60m 7.59m 7.52m 7.50m 7.44m 7.44m 7.44m 7.44m 7.44m 7.44m 7.42m 7.41m 7.35m 7.28m 7.28m 7.22m 7.22m 7.17m 7.01m 6.97m 6.93m 6.92m 6.89m 6.88m

41.77 41.79 41.81 41.81 41.85 41.87 42.01 42.01 42.01 42.35 42.35 42.36 42.37 42.38 42.40 42.47 42.49 42.56 42.56 42.56 42.56 42.56 42.56 42.60 42.60 42.67 42.76 42.76 42.83 42.83 42.89 43.09 43.13 43.19 43.20 43.24 43.25

62.5k 101.0k 22.2k 33.3k 27.2k 16.1k 15.1k 20.2k 30.2k 13.1k 39.3k 56.4k 43.3k 47.4k 51.4k 62.5k 82.6k 16.1k 20.2k 24.2k 36.3k 68.5k 101.0k 91.7k 75.6k 27.2k 15.1k 30.2k 22.2k 33.2k 18.1k 51.4k 47.3k 43.3k 56.4k 62.4k 39.3k

506 813 179 268 218 129 119 159 238 99.2 298 427 327 357 387 466 615 119 149 179 268 506 744 675 556 199 109 218 159 238 129 357 328 298 387 427 268

3.70k 5.97k 1.31k 1.97k 1.61k 956 896 1.19k 1.79k 776 2.33k 3.34k 2.57k 2.81k 3.05k 3.70k 4.90k 955 1.19k 1.43k 2.15k 4.06k 5.97k 5.43k 4.48k 1.61k 895 1.79k 1.31k 1.97k 1.07k 3.04k 2.80k 2.57k 3.34k 3.70k 2.33k

8.54k 13.7k 3.01k 4.52k 3.68k 2.18k 2.01k 2.68k 4.02k 1.67k 5.02k 7.20k 5.53k 6.03k 6.53k 7.87k 10.4k 2.01k 2.51k 3.02k 4.52k 8.54k 12.6k ll.4k 9.38k 3.35k 1.84k 3.69k 2.68k 4.02k 2.18k 6.03k 5.53k 5.03k 6.54k 7.21k 4.53k

2.30 2.30 2.29 2.29 2.28 2.28 2.24 2.24 2.24 2.16 2.16 2.15 2.15 2.15 2.15 2.13 2.12 2.10 2.10 2.10 2.10 2.10 2.10 2.10 2.10 2.08 2.06 2.06 2.04 2.04 2.03 1.98 1.97 1.96 1.96 1.95 1.94

Table 8. 1 Voltage dividers R1 68k 16k 82k 22k 91k 75k 100k 15k 18k 24k 27k 30k 33k 36k 20k 51k 56k 47k 68k 62k 43k 75k 16k 24k 82k 100k 39k 91k 18k 36k 33k 20k 30k 27k 22k 56k 51k

R2 470R ll0R 560R 150R 620R 510R 680R 100R 120R 160R 180R 200R 220R 240R 130R 330R 360R 300R 430R 390R 270R 470R 100R 150R 510R 620R 240R 560R ll0R 220R 200R 120R 180R 160R 130R 330R 300R

6.86m 6.83m 6.78m 6.77m 6.77m 6.75m 6.75m 6.62m 6.62m 6.62m 6.62m 6.62m 6.62m 6.62m 6.46m 6.43m 6.39m 6.34m 6.28m 6.25m 6.24m 6.23m 6.21m 6.21m 6.18m 6.16m 6.12m 6.12m 6.07m 6.07m 6.02m 5.96m 5.96m 5.89m 5.87m 5.86m 5.85m

195

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

43.27 43.31 43.37 43.39 43.39 43.41 43.41 43.58 43.58 43.58 43.58 43.58 43.58 43.58 43.80 43.84 43.89 43.95 44.04 44.08 44.10 44.11 44.14 44.14 44.18 44.21 44.27 44.27 44.33 44.33 44.40 44.49 44.49 44.60 44.62 44.64 44.66

68.5k 16.1k 82.6k 22.2k 91.6k 75.5k 101.0k 15.1k 18.1k 24.2k 27.2k 30.2k 33.2k 36.2k 20.1k 51.3k 56.4k 47.3k 68.4k 62.4k 43.3k 75.5k 16.1k 24.2k 82.5k 101.0k 39.2k 91.6k 18.1k 36.2k 33.2k 20.1k 30.2k 27.2k 22.1k 56.3k 51.3k

467 109 556 149 616 507 675 99.3 ll9 159 179 199 219 238 129 328 358 298 427 388 268 467 99.4 149 507 616 239 557 109 219 199 119 179 159 129 328 298

4.06k 955 4.89k 1.31k 5.43k 4.47k 5.97k 895 1.07k 1.43k 1.61k 1.79k 1.97k 2.15k 1.19k 3.04k 3.34k 2.80k 4.05k 3.70k 2.56k 4.47k 954 1.43k 4.89k 5.96k 2.33k 5.43k 1.07k 2.15k 1.97k 1.19k 1.79k 1.61k 1.31k 3.34k 3.04k

7.88k 1.84k 9.39k 2.51k 10.4k 8.55k ll.4k 1.68k 2.01k 2.68k 3.02k 3.35k 3.69k 4.02k 2.18k 5.53k 6.04k 5.03k 7.21k 6.54k 4.53k 7.88k 1.68k 2.52k 8.55k 10.4k 4.03k 9.39k 1.85k 3.69k 3.35k 2.01k 3.02k 2.68k 2.18k 5.54k 5.03k

1.94 1.93 1.92 1.92 1.91 1.91 1.91 1.87 1.87 1.87 1.87 1.87 1.87 1.87 1.83 1.82 1.81 1.80 1.78 1.77 1.77 1.76 1.76 1.76 1.75 1.74 1.73 1.73 1.72 1.72 1.71 1.69 1.69 1.67 1.66 1.66 1.66

196

R1 62k 47k 68k 75k 82k 39k 91k 100k 43k 18k 27k 36k 20k 22k 33k 24k 56k 30k 62k 51k 68k 82k 75k 91k 39k 43k 47k 100k 20k 22k 24k 30k 36k 68k 33k 62k 56k

Electronics Calculations Data Handbook

R2 360R 270R 390R 430R 470R 220R 510R 560R 240R 100R 150R 200R ll0R 120R 180R 130R 300R 160R 330R 270R 360R 430R 390R 470R 200R 220R 240R 510R 100R ll0R 120R 150R 180R 330R 160R 300R 270R

A

dB

RI

Ro

RSMAX RLMIN RLS (1 dB)

5.77m 5.71m 5.70m 5.70m 5.70m 5.61m 5.57m 5.57m 5.55m 5.52m 5.52m 5.52m 5.47m 5.42m 5.42m 5.39m 5.33m 5.31m 5.29m 5.27m 5.27m 5.22m 5.17m 5.14m 5.10m 5.09m 5.08m 5.07m 4.98m 4.98m 4.98m 4.98m 4.98m 4.83m 4.83m 4.82m 4.80m

44.77 44.86 44.88 44.88 44.88 45.02 45.08 45.08 45.11 45.15 45.15 45.15 45.24 45.31 45.31 45.37 45.47 45.51 45.52 45.57 45.57 45.65 45.72 45.78 45.85 45.87 45.88 45.89 46.06 46.06 46.06 46.06 46.06 46.32 46.33 46.35 46.38

62.4k 47.3k 68.4k 75.4k 82.5k 39.2k 91.5k 101.0k 43.2k 18.1k 27.2k 36.2k 20.1k 22.1k 33.2k 24.1k 56.3k 30.2k 62.3k 51.3k 68.4k 82.4k 75.4k 91.5k 39.2k 43.2k 47.2k 101.0k 20.1k 22.1k 24.1k 30.2k 36.2k 68.3k 33.2k 62.3k 56.3k

358 268 388 428 467 219 507 557 239 99.4 149 199 109 119 179 129 298 159 328 269 358 428 388 468 199 219 239 507 99.5 109 119 149 179 328 159 299 269

3.70k 2.80k 4.05k 4.47k 4.89k 2.32k 5.42k 5.96k 2.56k 1.07k 1.61k 2.14k 1.19k 1.31k 1.97k 1.43k 3.34k 1.79k 3.69k 3.04k 4.05k 4.88k 4.47k 5.42k 2.32k 2.56k 2.80k 5.96k 1.19k 1.31k 1.43k 1.79k 2.14k 4.05k 1.96k 3.69k 3.33k

6.04k 4.53k 6.54k 7.22k 7.89k 3.69k 8.56k 9.40k 4.03k 1.68k 2.52k 3.36k 1.85k 2.01k 3.02k 2.18k 5.04k 2.69k 5.54k 4.53k 6.04k 7.22k 6.55k 7.89k 3.36k 3.69k 4.03k 8.56k 1.68k 1.85k 2.02k 2.52k 3.02k 5.54k 2.69k 5.04k 4.53k

1.63 1.62 1.61 1.61 1.61 1.59 1.58 1.58 1.57 1.56 1.56 1.56 1.55 1.54 1.54 1.53 1.51 1.50 1.50 1.49 1.49 1.48 1.47 1.46 1.45 1.44 1.44 1.44 1.41 1.41 1.41 1.41 1.41 1.37 1.37 1.36 1.36

Table 8. 1 Voltage dividers

R1 27k 75k 82k 91k 51k 100k 47k 43k 39k 24k 22k 33k 27k 36k 68k 75k 82k 62k 30k 51k 100k 56k 91k 47k 43k 24k 36k 39k 27k 82k 30k 75k 68k 91k 33k 56k 51k

R2 130R 360R 390R 430R 240R 470R 220R 200R 180R ll0R 100R 150R 120R 160R 300R 330R 360R 270R 130R 220R 430R 240R 390R 200R 180R 100R 150R 160R ll0R 330R 120R 300R 270R 360R 130R 220R 200R

4.79m 4.78m 4.73m 4.70m 4.68m 4.68m 4.66m 4.63m 4.59m 4.56m 4.52m 4.52m 4.42m 4.42m 4.39m 4.38m 4.37m 4.34m 4.31m 4.30m 4.28m 4.27m 4.27m 4.24m 4.17m 4.15m 4.15m 4.09m 4.06m 4.01m 3.98m 3.98m 3.95m 3.94m 3.92m 3.91m 3.91m

197

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

46.39 46.42 46.50 46.55 46.59 46.60 46.63 46.69 46.76 46.82 46.89 46.89 47.08 47.08 47.15 47.17 47.19 47.26 47.30 47.34 47.37 47.40 47.40 47.46 47.60 47.64 47.64 47.77 47.83 47.94 47.99 47.99 48.06 48.09 48.13 48.15 48.16

27.1k 75.4k 82.4k 91.4k 51.2k 100.0k 47.2k 43.2k 39.2k 24.1k 22.1k 33.2k 27.1k 36.2k 68.3k 75.3k 82.4k 62.3k 30.1k 51.2k 100.0k 56.2k 91.4k 47.2k 43.2k 24.1k 36.2k 39.2k 27.1k 82.3k 30.1k 75.3k 68.3k 91.4k 33.1k 56.2k 51.2k

129 358 388 428 239 468 219 199 179 109 99.5 149 119 159 299 329 358 269 129 219 428 239 388 199 179 99.6 149 159 110 329 120 299 269 359 129 219 199

1.61k 4.47k 4.88k 5.42k 3.04k 5.95k 2.80k 2.56k 2.32k 1.43k 1.31k 1.96k 1.61k 2.14k 4.05k 4.46k 4.88k 3.69k 1.79k 3.03k 5.95k 3.33k 5.42k 2.80k 2.56k 1.43k 2.14k 2.32k 1.61k 4.88k 1.78k 4.46k 4.05k 5.41k 1.96k 3.33k 3.03k

2.18k 6.05k 6.55k 7.22k 4.03k 7.89k 3.70k 3.36k 3.02k 1.85k 1.68k 2.52k 2.02k 2.69k 5.04k 5.54k 6.05k 4.54k 2.18k 3.70k 7.23k 4.03k 6.55k 3.36k 3.03k 1.68k 2.52k 2.69k 1.85k 5.55k 2.02k 5.04k 4.54k 6.05k 2.19k 3.70k 3.36k

1.36 1.35 1.34 1.33 1.33 1.33 1.32 1.31 1.30 1.29 1.28 1.28 1.25 1.25 1.25 1.24 1.24 1.23 1.22 1.22 1.21 1.21 1.21 1.20 1.18 1.18 1.18 1.16 1.15 1.14 1.13 1.13 1.12 1.12 1.11 1.11 1.11

198

R1 100k 62k 39k 47k 43k 27k 30k 82k 33k 91k 36k 75k 100k 56k 62k 51k 68k 43k 47k 30k 33k 36k 39k 100k 91k 82k 68k 62k 56k 75k 47k 51k 39k 36k 33k 43k 100k

Electronics Calculations Data Handbook

R2 390R 240R 150R 180R 160R 100R ll0R 300R 120R 330R 130R 270R 360R 200R 220R 180R 240R 150R 160R 100R ll0R 120R 130R 330R 300R 270R 220R 200R 180R 240R 150R 160R 120R ll0R 100R 130R 300R

A 3.88m 3.86m 3.83m 3.82m 3.71m 3.69m 3.65m 3.65m 3.62m 3.61m 3.60m 3.59m 3.59m 3.56m 3.54m 3.52m 3.52m 3.48m 3.39m 3.32m 3.32m 3.32m 3.32m 3.29m 3.29m 3.28m 3.22m 3.22m 3.20m 3.19m 3.18m 3.13m 3.07m 3.05m 3.02m 3.01m 2.99m

dB 48.21 48.28 48.33 48.37 48.62 48.66 48.75 48.77 48.82 48.84 48.88 48.91 48.91 48.97 49.03 49.08 49.08 49.18 49.39 49.57 49.57 49.57 49.57 49.66 49.67 49.68 49.83 49.86 49.89 49.92 49.95 50.10 50.26 50.32 50.40 50.42 50.48

RI

Ro

RSMAX RLMIN RLS (1 dB)

100.0k 62.2k 39.2k 47.2k 43.2k 27.1k 30.1k 82.3k 33.1k 91.3k 36.1k 75.3k 100.0k 56.2k 62.2k 51.2k 68.2k 43.2k 47.2k 30.1k 33.1k 36.1k 39.1k 100.0k 91.3k 82.3k 68.2k 62.2k 56.2k 75.2k 47.2k 51.2k 39.1k 36.1k 33.1k 43.1k 100.0k

388 239 149 179 159 99.6 110 299 120 329 130 269 359 199 219 179 239 149 159 99.7 110 120 130 329 299 269 219 199 179 239 150 159 120 110 99.7 130 299

5.95k 3.69k 2.32k 2.80k 2.56k 1.61k 1.78k 4.88k 1.96k 5.41k 2.14k 4.46k 5.95k 3.33k 3.69k 3.03k 4.04k 2.56k 2.79k 1.78k 1.96k 2.14k 2.32k 5.94k 5.41k 4.87k 4.04k 3.69k 3.33k 4.46k 2.79k 3.03k 2.32k 2.14k 1.96k 2.56k 5.94k

6.56k 4.03k 2.52k 3.03k 2.69k 1.68k 1.85k 5.04k 2.02k 5.55k 2.19k 4.54k 6.05k 3.36k 3.70k 3.03k 4.04k 2.52k 2.69k 1.68k 1.85k 2.02k 2.19k 5.55k 5.05k 4.54k 3.70k 3.36k 3.03k 4.04k 2.52k 2.69k 2.02k 1.85k 1.68k 2.19k 5.05k

1.10 1.09 1.09 1.08 1.05 1.05 1.04 1.03 1.03 1.03 1.02 1.02 1.02 1.01 1.00 998m 998m 987m 963m 943m 943m 943m 943m 934m 933m 932m 916m 913m 910m 906m 903m 888m 871m 865m 858m 856m 849m

Table 8. 1 Voltage dividers R1 91k 51k 68k 75k 82k 62k 56k 39k 43k 36k 47k 100k 82k 56k 75k 68k 91k 62k 39k 43k 47k 51k 82k 62k 91k 75k 100k 51k 68k 47k 43k 56k 68k 100k 91k 82k 51k

R2 270R 150R 200R 220R 240R 180R 160R ll0R 120R 100R 130R 270R 220R 150R 200R 180R 240R 160R 100R ll0R 120R 130R 200R 150R 220R 180R 240R 120R 160R ll0R 100R 130R 150R 220R 200R 180R ll0R

199

A

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

2.96m 2.93m 2.93m 2.92m 2.92m 2.89m 2.85m 2.81m 2.78m 2.77m 2.76m 2.69m 2.68m 2.67m 2.66m 2.64m 2.63m 2.57m 2.56m 2.55m 2.55m 2.54m 2.43m 2.41m 2.41m 2.39m 2.39m 2.35m 2.35m 2.33m 2.32m 2.32m 2.20m 2.20m 2.19m 2.19m 2.15m

5O.58 50.66 50.66 50.68 50.70 50.77 50.91 51.02 51.11 51.15 51.19 51.40 51.45 51.47 51.50 51.57 51.60 51.79 51.84 51.86 51.88 51.89 52.28 52.35 52.35 52.42 52.42 52.59 52.59 52.63 52.69 52.71 53.15 53.17 53.18 53.19 53.34

91.3k 51.2k 68.2k 75.2k 82.2k 62.2k 56.2k 39.1k 43.1k 36.1k 47.1k 100.0k 82.2k 56.2k 75.2k 68.2k 91.2k 62.2k 39.1k 43.1k 47.1k 51.1k 82.2k 62.2k 91.2k 75.2k 100.0k 51.1k 68.2k 47.1k 43.1k 56.1k 68.2k 100.0k 91.2k 82.2k 51.1k

269 150 199 219 239 179 160 110 120 99.7 130 269 219 150 199 180 239 160 99.7 110 120 130 200 150 219 180 239 120 160 110 99.8 130 150 220 200 180 110

5.41k 3.03k 4.04k 4.46k 4.87k 3.68k 3.33k 2.32k 2.56k 2.14k 2.79k 5.94k 4.87k 3.33k 4.46k 4.04k 5.41k 3.68k 2.32k 2.55k 2.79k 3.03k 4.87k 3.68k 5.41k 4.45k 5.94k 3.03k 4.04k 2.79k 2.55k 3.33k 4.04k 5.94k 5.40k 4.87k 3.03k

4.54k 2.52k 3.37k 3.70k 4.04k 3.03k 2.69k 1.85k 2.02k 1.68k 2.19k 4.54k 3.70k 2.52k 3.37k 3.03k 4.04k 2.69k 1.68k 1.85k 2.02k 2.19k 3.37k 2.53k 3.70k 3.03k 4.04k 2.02k 2.69k 1.85k 1.68k 2.19k 2.53k 3.70k 3.37k 3.03k 1.85k

840m 833m 833m 831m 829m 822m 809m 799m 790m 787m 783m 765m 760m 759m 755m 750m 747m 731m 727m 725m 723m 722m 691m 686m 685m 680m 680m 667m 667m 663m 659m 658m 626m 624m 623m 622m 612m

200 R1 56k 75k 47k 62k 75k 100k 91k 56k 51k 82k 62k 68k 82k 100k 56k 62k 68k 91k 75k 91k 68k 62k 75k 100k 82k 100k 68k 75k 82k 91k 82k 75k 91k 100k 82k 91k 100k

Electronics Calculations Data Handbook R2 120R 160R 100R 130R 150R 200R 180R ll0R 100R 160R 120R 130R 150R 180R 100R ll0R 120R 160R 130R 150R ll0R 100R 120R 160R 130R 150R 100R ll0R 120R 130R ll0R 100R 120R 130R 100R ll0R 120R

A

dB

RI

Ro

RSMAX RLMIN RLs(ldB)

2.14m 2.13m 2.12m 2.09m 2.00m 2.00m 1.97m 1.96m 1.96m 1.95m 1.93m 1.91m 1.83m 1.80m 1.78m 1.77m 1.76m 1.76m 1.73m 1.65m 1.62m 1.61m 1.60m 1.60m 1.58m 1.50m 1.47m 1.46m 1.46m 1.43m 1.34m 1.33m 1.32m 1.30m 1.22m 1.21m 1.20m

53.40 53.44 53.46 53.59 54.00 54.00 54.09 54.15 54.17 54.21 54.28 54.39 54.77 54.91 54.98 55.04 55.08 55.11 55.24 55.67 55.84 55.86 55.93 55.93 56.01 56.49 56.66 56.69 56.71 56.91 57.46 57.51 57.61 57.73 58.29 58.36 58.43

56.1k 75.2k 47.1k 62.1k 75.2k 100.0k 91.2k 56.1k 51.1k 82.2k 62.1k 68.1k 82.2k 100.0k 56.1k 62.1k 68.1k 91.2k 75.1k 91.2k 68.1k 62.1k 75.1k 100.0k 82.1k 100.0k 68.1k 75.1k 82.1k 91.1k 82.1k 75.1k 91.1k 100.0k 82.1k 91.1k 100.0k

120 160 99.8 130 150 200 180 110 99.8 160 120 130 150 180 99.8 110 120 160 130 150 110 99.8 120 160 130 150 99.9 110 120 130 110 99.9 120 130 99.9 110 120

3.33k 4.45k 2.79k 3.68k 4.45k 5.94k 5.40k 3.32k 3.03k 4.87k 3.68k 4.04k 4.87k 5.94k 3.32k 3.68k 4.04k 5.40k 4.45k 5.40k 4.04k 3.68k 4.45k 5.93k 4.87k 5.93k 4.04k 4.45k 4.87k 5.40k 4.87k 4.45k 5.40k 5.93k 4.86k 5.40k 5.93k

2.02k 2.69k 1.68k 2.19k 2.53k 3.37k 3.03k 1.85k 1.68k 2.69k 2.02k 2.19k 2.53k 3.03k 1.68k 1.85k 2.02k 2.70k 2.19k 2.53k 1.85k 1.68k 2.02k 2.70k 2.19k 2.53k 1.69k 1.85k 2.02k 2.19k 1.85k 1.69k 2.02k 2.19k 1.69k 1.85k 2.02k

608m 605m 603m 595m 567m 567m 561m 557m 556m 554m 549m 542m 519m 511m 507m 504m 501m 499m 492m 468m 459m 458m 454m 454m 450m 426m 418m 417m 416m 406m 381m 379m 375m 369m 346m 343m 341m

Table 8.1 Voltage dividers R1

R2

100k ll0R 91k 100R 100k 100R

A

dB

1.10m 59.18 1.10m 59.19 999u 60.01

201

RI

Ro

RSMAX RLMIN RLS (1 dB)

100.0k 91.1k 100.0k

ll0 99.9 99.9

5.93k 5.40k 5.93k

1.85k 1.69k 1.69k

313m 312m 284m

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Pa rt Three Reactive Circuits

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9

First-order CR and LR circuits

Introduction There are two first-order CR and two first-order LR circuits which we will consider here. One circuit of each type forms an integrator, or a low-pass filter, and one a differentiator, or a high-pass filter. All four circuits can be considered to be variations on the voltage dividers which we looked at in Chapter 8. In each case, either the input resistor or the output resistor is replaced with either a capacitor or an inductor. Where we call them integrators and differentiators we will look at their output waveforms when their input is a pulse. This is called the time response. Then we will consider their action as filters; that is, we will look at the amplitude and phase of their outputs when the input is a sine wave of varying frequency. This is the frequency response. The two approaches are in fact different ways of looking at the same thing, which is their transfer function- in other words their output for any given input. Both methods can be both understood and quantified without much mathematics, and one, other or both is usually very helpful when we need to use them in a circuit, or understand their use.

Time response A quick explanation of CR and LR circuit waveforms The four circuits, with their associated waveforms, are shown in Figure 9.1. We assume that the resistance of the source is negligible, and the load on the circuit is high enough to be ignored. Both CR circuits have the same current waveform, and so do both LR circuits. (As discussed in Chapter 5, the current in a series circuit is the same through each of its components, and putting them in a different order makes no difference to that current.) Also, the sum of the capacitor's and the resistor's, or the inductor's and the resistor's, voltages always equals the input voltage (by Kirchhoff's voltage law).

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First-order CR and LR circuits

207

A capacitor will always resist a sudden change in the voltage across its terminals. Hence, when the leading edge of the pulse arrives, its voltage remains, initially, at zero. All of the available voltage is, at that moment, across the resistor. Therefore the current at that moment is I = v. The current charges the capacitor, causing its voltage to increase from zero. As this happens the voltage across the resistor decreases. The current (proportional always to the voltage across the resistor) falls accordingly. This in turn slows down the charge rate of the capacitor. Hence the rate of change of the voltage across the capacitor decreases as thatT,voltage approaches the input voltage. The current in the circuit falls from I -- v towards zero, and the voltage across the r e sistor falls from V towards zero. Eventually, the capacitor is fully charged, and the voltage across it is equal to the input voltage. Things will stay like this until the input changes again. When it falls to zero the voltage across the cap cannot change instantly; it must now discharge, back through the resistor, and into the source (the only possible p a t h remember that the source has a low, and the load a high, resistance). Hence a current o f - V now flows for an instant (the minus sign indicating that the direction R has reversed). This current decreases towards zero again as the voltage which created it, that across the plates of the capacitor, falls. Eventually, there is no charge left in the capacitor, no voltage across its terminals and no current in the circuit. The circuit is once again at rest, as it was in the beginning. Because an inductor resists a sudden change in current, an LR circuit's current is at zero when the leading edge of the pulse arrives. So then is the voltage across the resistor at that moment. For the sum of the resistor's and the inductor's voltage to equal the input voltage, as it must, the inductor sets up a back EMF across its terminals, opposing the input voltage. The back EMF decays with time, and current begins to flow in the circuit, creating a voltage across the resistor. EvenV The voltually there is no back EMF, and the current arrives at a final value ofT. K tage across the inductor is now zero, and the voltage across the resistor is V. When the trailing edge of the pulse arrives at the input (i.e. the input voltage falls towards zero again) the current in the circuit also will try to fall to zero. Again the inductor will resist change. To do this it will set up another back EMF, opposing the voltage across the resistor nob: This back EMF will also decay with time, allowing the current in the circuit and the voltage across the resistor to fall towards zero. The only difference between the two CR (or the two LR) circuits is which device, resistor or capacitor (inductor), is on the output side. The voltages across the components, and the currents through them, are identical. IL

Time constants It can be seen that, essentially, only two waveform shapes exist for both output voltage and for current in all four circuits. These two waveforms are shown in more detail in Figure 9.2. All of the curves are exponential in shape. How long they take to change from initial to final values is determined by the circuit time constant T (not to be

208

Electronics Calculations Data Handbook

confused with the T used for period of an AC waveform), which is in turn a function of component values in the circuit. A=Vor

V R

-A

-A

0 A=Vor

VR

-- -

-A -A = - V o r - V R

Figure 9.2 Detail of Figure 9.1 T h e formulae for T are: for a C R circuit:

T-

CR

(9.1)

and for an L R circuit: L T = ~

J

(9.2)

T is tabulated for various values of C and R in Table 9.1, and for L and R inTable 9.2. These tables also give values of frequency constants which we will look at later under 'Frequency response'. T h e tables are sorted in order of T, increasing for C R and decreasing for LR. T is given in #s. Should we want to obtain a value of T which is outside the range of the table we should do it by scaling one or both components by factors of 10 appropriately. As always, some examples: Example 9.1: Find values for a C R circuit with T - 56 ns. From Table 9.1: f(Hz) 2842 2842

T(#s) 56.00 56.00

R lk 5k6

C 56n 10n

We want T - 56 ns, so we need to make R and C between them 1000 times smaller.We could for example make R - 100 f~ and C - 560p, or R = 56 f~ and C = lrr

First-order CR and LR circuits

209

Example 9.2: Find values for an L R circuit with T -- 4 #s. From Table 9.2: f(Hz) T(#s) 4063 39.17

R lk2

L 47m

To make T 10 times smaller we could either make R 10 times larger or L 10 times smaller. So R - 12k and L - 47m or R - lk2 and L - 4.7m would both work.

Values of voltage and current as a function of t and T Once we have determined a value of T, we can find the value of Vt or It, that is output voltage for any m o m e n t in time, t, after the rising or falling edge of the input waveform. T h e formulae are as follows. For a curve going from zero to a final value:

VtorIt-(Vor

V)(1 -eT)

(9.3)

and for a curve going back down to zero:

Vt or It - ( - ) ( V

or V ) e ~

(9.4)

Table 9.3 gives values of Eqns (9.3) and (9.4) for various values of-~.

Example 9.3: Find out to what the voltage out from a 2k2,1 # F differentiator will be after 6 ms, when the input is a rising edge of 6 V: First we calculate T, from Eqn(9.1).

T = CR

= 2k2 x 10u = 22 ms

Now we evaluate-~. If t - 6 ms, -~ = 26- 2 _- 0.27. Refi~rring to Figures 9.1 and 9.2, we see that the waveform is a rising edge, governed by the 1 - e:~ function. So we use Table 9.1 to find a value for that function where -~ = 0.27. We find: _t T 0.3

1 - e~ 0.7408

e9 0.2592

which is the nearest to 0.27. T h e final value of the voltage will be 6 V. S 9 its value after 6 ms will be 0.741 x 6 - 4.45 V.

210

Electronics Calculations Data Handbook

Example 9.4: Design a circuit whose output voltage will be -7 V 220 ms after the falling edge of a + 10 V pulse input. Give a C R and an L R alternative. By referring to Figure 9.,1, we see that the circuit must be a differentiator, as that circuit has an output voltage which goes from - V to 0 after the falling edge of the input. T h e equation for that curve is -Ve:~, where V - 10 V in this case. So we can write: -t

-7 = -10e7,

-t

or e-r -- 0.7

and we can use Table 9.1 in reverse to find: _t

1 - e~

e~

1.2

0.3012

0.6988

T

Now we know that t - 220 ms, and that -~ - 1.2, so we know that T - 22o _ 183.3 ms. Now we can useTable 9.3 to find suitable C and R values, 1.2 and Table 9.4 to find L and R. From Table 9.3: f(Hz) 8682

T(#s) 18.33

R 4k7

C 3n9

T is in #s, so we need to scale up by 183.3 m = 10 000.We could do this by multia8.33~ plying both C and R by 100. So we get _~ -- 470 k, C - 390 n. From Table 9.4: f(Hz) 8681

T(#s) 18.33

R lk8

L 33m

Here we need to scale by m a k i n g R smaller and L larger. We could say theoretical values of R - 18 f~ and L - 3.3 H. A 3.3 H inductor would be huge (though not unknown!), which illustrates why C R circuits tend to be more c o m m o n than L R ones.

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212

Electronics Calculations Data Handbook

Frequency response Now we look at the behaviour of the same circuits when their input is a continuous sine wave. We are interested in what happens as the frequency of the input is varied.

H o w first-order filters work As we saw in Chapter 4, capacitive reactance falls with increasing frequency:

1

Xc = 2rrfC

(9.5)

Inductive reactance increases with frequency:

X L - - 27rfL

(9.6)

Each obeys O h m s Law, in that Vc = IXc, or XL = I X L - that is the voltage across a capacitor or an inductor is the current through it multiplied by its reactance, like a resistor. However, whereas voltage and current are in phase with a resistor, they are 90 ~ out of phase with inductors and capacitors. T h e four basic filter circuits are shown in Figure 9.3. We can view them all as being similar to the voltage divider which we looked at in Chapter 6, except that one component in each has a'resistance' which varies with frequency. Hence the overall attenuation of each varies with frequency too. Where the component on the input side of the circuit has higher impedance at higher frequencies, the circuit is a low-pass filter. These are the two circuits on the left hand side of Figure 9.3, a C R with the capacitor across the output or an L R with the inductor on the input. Conversely, a high-pass filter is formed by a C R with the capacitor on the input side or by an L R with the inductor across the output.

Frequency constants The frequency at which the reactance of the capacitor or inductor is the equal to the resistor is known as the 'turnover frequency' OCt).T h e attenuation at this frequency is not 6 dB, as it would be if both components were resistive. Because of the fact that the voltage across the reactive component is 90 ~ out of phase with the voltage across the resistor the attenuation is only 3 dB. The turnover frequency can be calculated from the component values (or component values selected to give a desiredft). The governing formulae are: For a C R circuit: R = 2~tC which becomes

First-order CR and LR circuits

1 ft = 27rRC

213

(9.7)

For an L R circuit: R = 2~AL or

R

ft = 27rL

(9.8)

Values forft are given in Table 9.1 for C R circuits and in Table 9.2 for L R circuits. As before, component values can be scaled to get frequencies which are outside the range of the table.

Example 9.5: Give component values for a C R filter with ft = 12 kHz. From Table 9.1: f(Hz) 1205

T(#s)

R

C

132.00

lkl

120n

We need to multiply the frequency by 10, so we could divide either C or R by 10 to achieve this. So both R = 110 ~, C = 120n and R = lkl, (7 = 12n would do it.

Example 9.6: Give component values for an L R filter with ft = 500kHz. From Table 9.2: f(Hz) 5079

T(#s) 31.33

R lk5

L 47m

We need ft 100 times larger, so we can make L smaller and/or R larger. We could choose, for instance, R = 15k, L = 4.7m.

Determining the level and phase at any frequency The level of the output voltage, relative to the input, is determined by the ratio of the signal frequency andft: For a LPF: VOUT =

1

(9.9)

214

Electronics Calculations Data Handbook

We can see that whenfis much less than f,, the value of Vv-~Nis very close to 1, and hence the signal is not much attenuated by the circuit. When ~ is much greater than 1, the value o f ~ approximates to: VOUT _ 1 _f_t

(9.10)

V~N -~ - f

From this simplified expression, it can be seen that a doubling in frequency will lead to a halving in output signal, or multiplying the input frequency by 10 will reduce its output level to one-tenth. Hence it is customary to say that the filter slope, above the turnover frequency, i s - 6 db/octave, or-20 dB/decade. The equation for the attenuation of a HPF is:

VOU_______!T =

1

(9.1 1)

and a similar argument applies; this time the slope is-6 dB/octave or-20 dB/decade below the turnover frequency. These filters affect the relative phase (~b), as well as the level, of the signal. The LPF causes the output signal to be between 0 and 90 ~ lagging the input signal, the HPF 0 ~ to 90 ~ leading. In both cases the phase angle is 45 o at ft. These functions are again determined by the ratio o f f andft: For a HPF: ~b(leading) = arctan ( - ~ )

(9.12)

(s)

(9.13)

For a LPF: 4) (lagging) = arctan

Hence it is possible to predict both attenuation and phase shift through a filter for any given frequency, provided thatft is known. Table 9.4 gives both at intervals of a third of an octave, for six octaves either side offt. The first column of Table 9.4 gives the frequency in terms of the number of octaves away from ft. (The minus sign means higher in frequency for an HPF, lower for an LPF.) The second gives the ratio of frequencies, which we call F OCt/]"for an HPF, f/ft for an LPF). The third column is the attenuation as the ratio VOUT/VIN, the fourth is attenuation in dBs. The fifth column is the phase shift in degrees.

First-order CR and LR circuits

215

Example 9.6: W h a t is the approximate attenuation and phase shift at a frequency of 5 kHz for a LPFconsisting of a 3n3 capacitor and a 15k resistor? 1 ft = 27r x 15k x 3n3 = 3215 Hz F = f = 5000 = 1.56 ft 3215 From Table 9.4: Octaves 0 2/3

F 01.59

Att 0.533

dB 05.47

r~ 57.8

Nearest value in the table is 1.59 (2/3 octave) where attenuation is 5.5 dB, phase shift is 58 ~.

Example 9.7: A circuit is needed to low-pass filter a signal such that the level at 100 kHz is 15 dB down on the signal below ft. W h a t would ft be (using the table to get the nearest approximation)? W h a t will the attenuation be at 50 kHz? From Table 9.4: Octaves 21/3

F 05.04

Att 0.195

dB 14.22

r~ 78.8

This tells us that for a 14 dB attenuation at 100 kHz, F - Z - 5, so ft -- 100gkHz or 20 kHz. At 50 kHz F = 50 or 2.5, and we get: Octaves 0 2/3

F 01.59

Att 0.533

and the attenuation is 5.5 dB.

dB 05.47

r~ 57.8

Table 9.1 Time and frequency constants for first-order CR circuits f(Hz)

T(#s)

R

C

f(Hz)

T(#s)

R

C

1020 1026 1026 1046 1053 1053 1061 1061 1064 1064 1078 1078 1105 1122 1129 1134 1156 1166 1167 1170 1179 1184 1206 1213 1224 1237 1237 1254 1254 1292 1292 1294 1294 1300 1300 1326

156.00 155.10 155.10 152.10 151.20 151.20 150.00 150.00 149.60 149.60 147.60 147.60 144.00 141.90 141.00 140.40 137.70 136.50 136.40 136.00 135.00 134.40 132.00 131.20 130.00 128.70 128.70 126.90 126.90 123.20 123.20 123.00 123.00 122.40 122.40 120.00

lk3 3k3 4k7 3k9 2k7 5k6 lk lk5 2k2 6k8 lk8 8k2 lk2 4k3 3k 3k6 5kl 9kl 6k2 2k 7k5 2k4 lkl lk6 lk3 3k3 3k9 2k7 4k7

120n 47n 33n 39n 56n 27n 150n 100n 68n 22n 82n 18n 120n 33n 47n 39n 27n 15n 22n 68n 18n 56n 120n 82n 100n 39n 33n 47n 27n 56n

1326 1340 1360 1371 1411 1415 1418 1421 1426 1447 1457 1461 1463 1493 1511 1511 1539 1539 1560 1560 1579 1579 1592 1608 1617 1617 1637 1682 1693 1700 1711 1734 1749 1764 1768 1776

120.00 118.80 117.00 116.10 112.80 112.50 112.20 112.00 111.60 110.00 109.20 108.90 108.80 106.60 105.30 105.30 103.40 103.40 102.00 102.00 100.80 100.80 100.00 99.00 98.40 98.40 97.20 94.60 94.00 93.60 93.00 91.80 91.00 90.20 90.00 89.60

lk2 3k6 3k 4k3 2k4 7k5 5kl 2k 6k2 lkl 9kl 3k3 lk6 lk3 3k9 2k7 2k2 4k7 6k8 lk5 lk8 5k6 lk 3k 8k2 lk2 3k6 4k3

100n 33n 39n 27n 47n 15n

2k2 5k6 lk5 8k2 6k8 lk8 lk

22n 82n 15n 18n 68n 120n

2k 2k4 6k2 5kl 9kl lkl 7k5 lk6

22n 56n 18n 100n 12n 33n 68n 82n 27n 39n 47n 22n 15n 68n 56n 18n 100n 33n 12n 82n 27n 22n 47n 39n 15n 18n 10n 82n 12n 56n

Table 9. 1 Time and frequency constants for first-order CR circuits

217

f(Hz)

T(#s)

R

C

f(Hz)'

T(#s)

R

C

1786 1786 1800 1855 1855 1881 1881 1895 1895 1941 1941 1950 1950 1965 2010 2010 2040 2056 2080 211.6 2122 2128 2133 2139 2183 2186 2192 2192 2258 2258 2267 2267 2341 2341 2367 2368 2368

89.10 89.10 88.40 85.80 85.80 84.60 84.60 84.00 84.00 82.00 82.00 81.60 81.60 81.00 79.20 79.20 78.00 77.40 76.50 75.20 75.00 74.80 74.62 74.40 72.90 72.80 72.60 72.60 70.50 70.50 70.20 70.20 68.00 68.00 67.24 67.20 67.20

2k7 3k3 lk3 2k2 3k9 lk8 4k7 lk5 5k6 lk 8k2 6k8 lk2 3k 2k4 3k6 2k 4k3 5kl lk6 7k5 lkl 9kl 6k2 2k7 lk3 2k2 3k3 lk5 4k 7 lk8 3k9 lk 6k8 8k2 lk2 5k6

33n 27n 68n 39n 22n 47n 18n 56n 15n 82n 10n 12n 68n 27n 33n 22n 39n 18n 15n 47n lOn 68n 8n2 12n 27n 56n 33n 22n 47n 15n 39n 18n 68n 10n 8n2 56n 12n

2411 2411 2456 2456 2468 2551 2567 2572 2584 2588 2601 2605 2679 2679 2679 2679 2721 2721 2822 2822 2842 2842 2854 2854 2947 2947 2947 3014 3014 3078 3084 3121 3121 3123 3131 3139 3215

66.00 66.00 64.80 64.80 64.50 62.40 62.00 61.88 61.60 61.50 61.20 61.10 59.40 59.40 59.40 59.40 58.50 58.50 56.40 56.40 56.00 56.00 55.76 55.76 54.00 54.00 54.00 52.80 52.80 51.70 51.60 51.00 51.00 50.96 50.84 50.70 49.50

2k 3k 2k4 3k6 4k3 lk6 6k2 9kl lkl 7k5 5kl lk3 2k2 3k3 lk8 2k7 3k9 lk5 4k7 lk2 lk 5k6 6k8 8k2 2k 3k6 3k lk6 2k4 lkl 4k3 7k5 5kl 9kl 6k2 lk3 lk5

33n 22n 27n 18n 15n 39n lOn 6n8 56n 8n2 12n 47n 27n 18n 33n 22n 15n 39n 12n 47n 56n lOn 8n2 6n8 27n 15n 18n 33n 22n 47n 12n 6n8 lOn 5n6 8n2 39n 33n

218

Electronics Calculations Data Handbook

f(Hz)

T(#s)

R

C

f(Hz)

T(#s)

3215 3275 3275 3288 3386 3386 3401 3401 3442 3466 3466 3537 3617 3684 3684 3684 3701 3710 3710 3721 3775 3789 3806 3930 3930 4019 4019 4019 4019 4081 4081 4130 4130 4179 4179 4384 4421

49.50 48.60 48.60 48.40 47.00 47.00 46.80 46.80 46.24 45.92 45.92 45.00 44.00 43.20 43.20 43.20 43.00 42.90 42.90 42.77 42.16 42.00 41.82 40.50 40.50 39.60 39.60 39.60 39.60 39.00 39.00 38.54 38.54 38.08 38.08 36.30 36.00

3k3 lk8 2k7 2k2 lk 4k7 lk2 3k9 6k8 8k2 5k6 3k 2k lk6 2k4 3k6 4k3 lkl lk3 9kl 6k2 7k5 5kl lk5 2k7 3k3 lk2 lk8 2k2 lk 3k9 4k7 8k2 6k8 5k6 lkl 2k4

15n 27n 18n 22n 47n lOn 39n 12n 6n8 5n6 8n2 15n 22n 27n 18n 12n lOn 39n 33n 4n7 6n8 5n6 8n2 27n 15n 12n 33n 22n 18n 39n lOn 8n2 4n7 5n6 6n8 33n 15n

4421 4421 4421 4485 4514 4515 4521 4534 4584 4589 4823 4823 4823 4823 4912 4912 4912 4977 4977 4980 4980 5075 5300 5305 5305 5359 5391 5441 5443 5462 5526 5526 5565 5573 5882 5882 5895

36.00 36.00 36.00 35.49 35.26 35.25 35.20 35.10 34.72 34.68 33.00 33.00 33.00 33.00 32.40 32.40 32.40 31.98 31.98 31.96 31.96 31.36 30.03 30.00 30.00 29.70 29.52 29.25 29.24 29.14 28.8O 28.80 28.60 28.56 27.06 27.06 27.00

3k 2k 3k6 9kl 4k3 7k5 lk6 lk3 6k2 5kl lk 2k2 lk5 3k3 lk2 2k7 lk8 3k9 8k2 4k7 6k8 5k6 9kl 2k 3k lkl 3k6 7k5 4k3 6k2 2k4 lk6 lk3 5kl 3k3 8k2 lk

12n 18n lOn 3n9 8n2 4n7 22n 27n 5n6 6n8 33n 15n 22n lOn 27n 12n 18n 8n2 3n9 6n8 4n7 5n6 3n3 15n lOn 27n 8n2 3n9 6n8 4n7 12n 18n 22n 5n6 8n2 3n3 27n

Table 9.1 Time and frequency constants for first-order CR circuits f(Hz)

T(#s)

5895 5895 5895 6001 6001 6029 6029 6047 6047 6431 6470 6478 6501 6577 6582 6609 6631 6631 6631 6640 6801 7074 7092 7092 7189 7189 7205 7234 7234 7287 7287 7368 7368 7779

27.00 27.00 27.00 i 26.52 26.52 26.40 26.40 26.32 26.32 24.75 24.60 24.57 24.48 24.20 24.18 24.08 24.00 24.00 24.00 23.97 23.40 22.50 22.44 22.44 22.14 22.14 22.09 22.00 22.00 21.84 21.84 21.60 21.60 20.46

R

C

f(Hz)

T(#s)

lk8 lk5 2k7 3k9 6k8 2k2 lk2 4k7 5k6 7k5 3k 9kl 3k6 lkl 6k2 4k3 lk6 2k 2k4 5kl lk3 lk5 3k3 6k8 2k7 8k2 4k 7 lk 2k2 3k9 5k6 lk2 lk8 6k2

15n 18n 10n 6n8 3n9 12n 22n 5n6 4n7 3n3 8n2 2n7 6n8 22n 3n9 5n6 15n 12n 10n 4n7 18n 15n 6n8 3n3 8n2 2n7 4n 7 22n lOn 5n6 3n9 18n 12n 3n3

7802 7860 7875 7895 7950 7958 8002 8038 8087 8162 8289 8612 8612 8669 8669 8683 8683 8822 8822 8842 8842 8842 8842 9406 9457 9474 9490 9507 9646 9646 9705 9716 9752 9947

120.40 20.25 20.21 i 20.16 20.02 20.00 19.89 19.80 19.68 19.50 19.20 i 18.48 18.48 i 18.36 18.36 18.33 18.33 18.04 18.04 18.00 18.00 18.00 18.00 16.92 16.83 16.80 16.77 16.74 16.50 16.50 16.40 16.38 16.32 16.00 i

i

i

219

R

C

3k 7k5 4k3 3k6 9kl 2k 5kl lkl 2k4 lk3 lk6 3k3 5k6 2k7 6k8 3k9 4k7 2k2 8k2 lk2 lk5 lk lk8 3k6 5kl 3k 4k3 6k2 7k5 lkl 2k 9kl 2k4 lk6

6n8 2n7 4n7 5n6 2n2 lOn 3n9 18n 8n2 15n 12n 5n6 3n3 6n8 2n7 4n7 3n9 8n2 2n2 15n 12n 18n lOn 4n7 3n3 5n6 3n9 2n7 2n2 15n 8n2 ln8 6n8 lOn

Table 9.2

Time and frequency constants for first-order LR circuits

f(Hz)

T(#s)

R

L

f(Hz)

1592 1751 1910 2069 2341 2387 2546 2575 2809 2865 3043 3183 3386 3501 3511 3725 3745 3820 4064 4213 4297 4402 4681 4775 4823 5079 5149 5252 5305

100.00 90.91 83.33 76.92 68.00 66.67 62.50 61.82 56.67 55.56 52.31 50.00 47.00 45.45 45.33 42.73 42.50 41.67 39.17 37.78 37.04 36.15 34.00 33.33 33.00 31.33 30.91 30.30 30.00

lk lkl lk2 lk3 lk lk5 lk6 lkl lk2 lk8 lk3 2k lk 2k2 lk5 lkl lk6 2k4 lk2 lk8 2k7 lk3 2k 3k lk lk5 2k2 3k3 lkl

100m 100m 100m 100m 68m 100m 100m 68m 68m 100m 68m 100m 47m 100m 68m 47m 68m 100m 47m 68m 100m 47m 68m 100m 33m 47m 68m 100m 33m

5418 5617 5730 5787 6095 6207 6270 6319 6773 6844 7022 7234 7234 7450 7480 7717 7724 7958 8117 8127 8426 8681 8681 8913 9128 9143 9405 9646 9868

T(#s) 29.37 28.33 27.78 27.50 26.11 25.64 25.38 25.19 23.50 23.26 22.67 22.00 22.00 21.36 21.28 20.62 20.61 20.00 19.61 19.58 18.89 18.33 18.33 17.86 17.44 17.41 16.92 16.50 16.13

R

L

lk6 2k4 3k6 lk2 lk8 3k9 lk3 2k7 2k 4k3 3k lk lk5 2k2 4k7 lk6 3k3 lkl 5kl 2k4 3k6 lk2 lk8 5k6 3k9 2k7 lk3 2k 6k2

47m 68m 100m 33m 47m 100m 33m 68m 47m 100m 68m 22m 33m 47m 100m 33m 68m 22m 100m 47m 68m 22m 33m 100m 68m 47m 22m 33m 100m

Table 9.3

Step response of first-order CR and LR circuits -t

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.O 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

-t

e7

1 - e7

0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066 0.3679 0.3329 0.3012 0.2725 0.2466 0.2231 0.2019 0.1827 0.1653 0.1496 0.1353 0.1225 0.1108 0.1003 0.0907 0.0821

0.O952 0.1813 0.2592 0.3297 0.3935 0.4512 0.5034 0.5507 0.5934 0.6321 0.6671 0.6988 0.7275 0.7534 0.7769 0.7981 0.8173 0.8347 0.8504 0.8647 0.8775 0.8892 0.8997 0.9093 0.9179

2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0

-_t eT

1 - e~

0.0743 0.0672 0.0608 0.0550 0.0498 0.0450 0.0408 0.0369 0.0334 0.0302 O.0273 O.0247 0.0224 0.0202 0.0183 0.0166 0.0150 0.0136 0.0123 0.0111 0.0101 0.0091 0.0082 0.0074 0.0067

0.9257 0.9328 0.9392 0.9450 0.9502 0.9550 0.9592 0.9631 0.9666 0.9698 0.9727 0.9753 0.9776 0.9798 0.9817 0.9834 0.9850 0.9864 0.9877 0.9889 0.9899 0.9909 0.9918 0.9926 0.9933

Table 9.4 Frequencyand phase response of first-order CR and LR circuits Octaves

F

Att

dB

~(~

-6 -61/3 -6 2/3 -5 -51/3

00.02 00.02 00.O2 00.03 00.04 OO.O5 00.06 00.08 00.10 00.12 00.16 00.20 00.25 00.31 00.40 00.50 00.63 00.79 01.00 01.26 01.59 02.OO 02.52 03.17 04.00 05.04 06.35 O8.00 10.08 12.70 16.00 20.16 25.40 32.00 40.32 50.80 64.00

1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.997 0.995 0.992 0.988 0.981 0.970 0.954 0.929 0.894 0.846 0.783 0.707 0.622 0.533 0.447 0.369 0.300 0.243 0.195 0.156 0.124 0.099 0.079 0.062 0.050 0.039 0.031 0.025 0.020 0.016

00.00 00.00 00.00 00.00 00.01 00.01 00.02 00.03 00.04 00.07 00.11 00.17 00.26 00.41 00.64 00.97 01.45 02.12 03.01 04.13 05.47 06.99 08.66 10.45 12.30 14.22 16.16 18.13 20.11 22.10 24.10 26.10 28.10 30.11 32.11 34.12 36.12

00.9 01.1 01.4 01.8 02.3 02.8 03.6 04.5 05.7 07.1 09.0 11.2 14.0 17.5 21.6 26.6 32.2 38.4 45.0 51.6 57.8 63.4 68.4 72.5 76.0 78.8 81.0 82.9 84.3 85.5 86.4 87.2 87.7 88.2 88.6 88.9 89.1

-52/3 -4 -41/3 - 4 2/3 -3 -31/3

-32/3 -2

-21/3 -22/3 -1 -1 1/3 -12/3 0

o 1/3 02/3 1

11/3 12/3 2 21/3 22/3 a 31/3 32/3 4 41/3 4 2/3 5

5 ~/3 52/3 6

10

LC tuned circuits

Introduction When inductors and capacitors are combined the circuit is called a tuned circuit. Where the circuits in Chapter 9 were termed first-order, we call these secondorder, because there are two frequency-dependent elements rather than one. The capacitor and inductor can be combined in either series or parallel, giving rise to two types which we shall consider separately. These circuits both display an effect known as resonance, by which we mean that their impedance is at a minimum or a m a x i m u m at one specific frequency.

Series tuned circuit A series tuned circuit is an inductor and a capacitor in series. A resistive component is also assumed to exist which may be considered to consist solely of the circuit's residual resistances (the inductor's internal resistance being, usually, the only significant one) or perhaps of residual resistances plus a physical resistor. The circuit is shown in Figure 10.1.

v,N

\ 7 /t

C L

II 1I

_

i

|l

,, |,L

\

vo /" Figure 10.1 Series tuned circuit

What the circuit does The reactance of the capacitor decreases with frequency, while the reactance of the inductor increases. As we know, we cannot just add the impedance of each

224

Electronics Calculations Data Handbook

component at some frequency together because the phase angles of the voltages will be different. But we can deduce what is happening. We will take the current in the circuit as being our phase reference, as it is common to all components. The voltage across the capacitor lags it by 90 ~ the voltage across the inductor leads it by 90 ~ and the voltage across the resistor is in phase with it. The input voltage, which we would divide by input current to find the impedance, will be the phasor sum of these. (If you're a beginner, and this is losing you, look back at 'Calculations on AC quantities' in Chapter 4.) IfXc decreases with increasing frequency, and XL increases, then they must be equal at some point. At this frequency the capacitor's and the inductor's voltage are equal, but opposing each other in phase. (Their magnitudes can be calculated by using IXL and IXc respectively, and I is the same for each.) This means that they cancel each o t h e r - their phasor sum is zero. So the input voltage is equal to the voltage across the resistor- the resistor has the m a x i m u m amount of voltage across it that it can have. This causes the current in the circuit to be at a maximum, and hence impedance is at a minimum, and in phase (resistive). We call this frequency the resonant frequency of the circuit (fo). Below resonance Xc is greater than XL, and the impedance is overall capacitive. This means that the current leads the input voltage by some small angle when the impedances are almost equal, and by nearly 90 ~ when the frequency is very low. Above resonance XL is more significant and the impedance is inductive. Then input voltage leads current by between 0 and 90 ~

Calculating resonant frequency We can deduce the frequency where the two impedances are equal:

1 = 27rfoL 27rfoC After a little algebra this becomes:

fo

=

1

24Z--d

(10.1)

The impedance at resonance, which we term Zo is simply: Zo = R

(10.2)

Q factor Although Vc and VL cancel at resonance, they are still definitely there. In fact they can be larger than the input voltage. This is because the current can be large, given by ~N--5if R is small. The voltage across, say, the capacitor, will be IXc, or v~R____~N Xc. We call the ratio of this magnified voltages to the input voltage the Q, or

LC tuned circuits

225

quality factor, of the circuit. Q can be calculated:

Vc -

giN

---~ Xc

(because the impedance at resonance is simply R). So: Vc Xc 1 Q = VI--N~= - R - = 27rfo-------C-R

(10.3)

or giN VL = IXL -- ~ XL SO

Q_

VL

XL

27rfoL

~I-r-NN= R =

R

(10.4)

The result should be the same whichever equation we use to calculate Q. From these equations it can be seen that Q can be decreased quite easily by simply adding more resistance in series with the circuit. Conversely the maximum obtainable Q is set by the leftover resistance in the circuit when we have no physical resistor present. The inductor will normally possess far more resistance than the capacitor, so it is common to talk about the Q of an inductor at some specified frequency- this is the highest Q obtainable with that inductor in a tuned circuit with that fo.

Q as an i n d i c a t i o n o f b a n d w i d t h

The fact that the impedance of a series tuned circuit drops to a minimum at resonance makes it very useful for applications where we need some mechanism for picking a certain group of frequencies out of a wideband signal- for instance radio tuners, or audio filters. In these situations we need to know how selective the circuit actually is. The Q t~ctor, conveniently, tells us t h i s - the circuit's bandwidth, or B W. The bandwidth is the difference, in Hz, between the frequencies above and below resonance where the current is 3 dB less than at resonance, tbr the same level of input voltage - i.e. where the impedance drops by 3 dB. The formula we need is this: Bid/" = f o

O

(10.5)

For circuits of high selectivity (low B W), the requirement is that Q be high, and hence R low. This will influence the selection of components used in the design, particularly that an inductor with low internal resistance be found relative to its impedance at f o . Often we design the circuit with Q higher than needed, and then add a suitable series resistor, to reduce the bandwidth to the desired value. This is called a'damping' resistor. Table 10.1 lists the resonant frequencies from 500 Hz to 50 MHz obtainable

226

Electronics Calculations Data Handbook

with E6 inductors and El2 capacitors. A column is also provided, X, showing the value of Xc or XL at resonance. This can be used to find the highest possible Q, provided that the resistance of the inductor is known.

Example 10.1: (a) W h a t values of C and L can we use to give a series resonant circuit with fo = 8 kHz? FromTable 10.1: fo 8k 8k 8k 8k

C 12n 18n 120n 180n

L 33m 22m 3m3 2m2

X 1.66k 1.11k 166 111

This gives us a choice of four pairs. (b) By consulting suppliers catalogues, we source a 3.3 m H inductor with R = 6.6 f~, and a 2.2 m H inductor with resistance, RL, of 4.1 Ft, W h a t is the best possible Q with each of these? W h a t will the bandwidth be? 166 With 3.3 mH, X is given as 166 Ft, so Q will be ~ = 25.2 at best. The bandwidth will be 2-g-y.2 8ooo= 318 Hz 111 = 27.1 at best. The bandWith 2.2 mH, X is given as lll f~, so Q will be Z]width will be 2-~T.1 8000= 295 Hz (c) Now calculate values for a series resistor to reduce Q to around 3 for each. For 3.3 mH: If X - 166 fl, and Q - 3, then R = xQ _ 16__fi6= 55.3 fL As the inductor already has 6.6f~ of resistance, we should add a resistor of 55.3 - 6.6 = 48.7 Ft. (with typical inductor tolerances of 10%, 47 f~ would be fine). x _- -5111 -_ 37 f~. Resistor should be 3 7 - 4.1 - 32.9 f~ - say a For 2.2 m t t : R ~ standard value of 33 f~. _

Parallel tuned circuits A parallel tuned circuit consists of a capacitor and an inductor in parallel. The circuit can be understood by using a similar approach to the one which we took for the series tuned circuit. However, the practical circuit is slightly complicated by the fact that the inductive branch possesses more resistance than the

LC tuned circuits

227

capacitive branch, which makes it somewhat asymmetrical. In many cases this effect can be ignored, but not all, so we need to be able to predict whether it will be significant or not. But to make the analysis one step at a time, it makes sense to start by considering an ideal version of the circuit, where the effect does not come into play at all.

Example 10.2: If the 2.2 m H inductor of Example 10.1 has a 10% tolerance, how much might fo and Q vary in practice, assuming that both inductance and resistance increase together? If the inductance and resistance increase by 10%, we would have L ( m a x ) 2 . 2 m H x 1.1 = 2 . 4 2 m H , and RL(max) = 4.1 x 1.1 = 4.51fl. This would give, using Eqn (6.1): fo =

1 27rx/'2.42m • 180n

= 7.63 kHz

and a corresponding Q __ 27rx 337"63k+ 4.51x 2.42m ---- 3.1 Decreasing by 10% gives L(min) = 2.2m x 0.9 = 1.98 m H and RL(min) 4.1 x 0.9 = 3.69 f~ fo =

1 27rV'1.98m x 180n

= 8.43 kHz

with Q=

27r x 8.43k x 1.98m 33 + 3.69

= 2.9

The ideal parallel tuned circuit This consists of an ideal inductor and capacitor in p a r a l l e l - each has no resistance. In this circuit we take the voltage across the circuit, VIN, as our phase reference, as it is c o m m o n to both components, and look at the current that each branch draws from the source at different frequencies. These currents will always be in a n t i p h a s e - the capacitor's current, Ic, leading Vii by 90 ~ the inductor's, IL, lagging. T h e input current,/IN, will be their phasor sum. As they are in antiphase, their phasor sum is simply the difference between them. We can once again say that Xc will fall with increasing frequency, and XL will rise. And once again, Xc will equal XL at some frequency, that given by Eqn (10.1). At this frequency, a g a i n f o , the current in each branch will be equal, and hence the input current will be zero. The impedance is VX-~N , and is infinite. The circuit looks like an open circuit to the source at resonance, and its resonant frequency is calculated identically to that of the series tuned circuit.

228

Electronics Calculations Data Handbook

Below resonance, the capacitor will have the greater impedance of the two devices, and the impedance will appear inductive with current lagging voltage by 90 ~. Above, the inductor possesses more impedance and the impedance is capacitive, with VIN in lagging/IN. At resonance, the input current is zero, while Ic and IL are ~c and ~ respectively. The Q factor, ~ or ~ in would therefore be infinite.

The practical parallel tuned circuit The practical circuit differs from the ideal mostly in that the inductor possesses resistance. Such a circuit is shown in Figure 10.2, with RL representing the internal resistance of the inductor.

IIN C,

IIlI

-

/\

,~/

tc

vL

______

~m

C

Rt

o

vR~

,,

Figure 10.2 Practical parallel tuned circuit The addition of the resistive element in series with the inductor causes IL to be less than 90 ~ lagging VIN. In turn, this causes /IN, at the frequency at which Xc = XL, to be leading VIN by some angle, rather than in phase, as it was with the ideal circuit--the circuit is overall capacitive, rather than resistive. To compensate, and bring/IN back in phase with//'IN, making the circuit truly resonant, the frequency of VIN must be lowered. This has the effect of making Ic smaller and IL larger. It can be seen that the effect becomes more pronounced the greater the inductor's resistance is, compared to its reactance.

L C tuned circuits

229

To what degree all this affects Eqn (10.1) depends on the Q of the inductor at the resonant frequency, as defined in Eqn (10.4).

Resonant frequency error The resonant frequency as found from Eqn (10.1) must be multiplied by the term: k =

1

CR2 L =

1

1 Q2

(10.6)

to find the true resonant frequency. In practice, the Q has to be pretty low to cause much deviation; a Q of 4 gives k = 0.97, a Q of 2 gives k = 0.87. Eqn (10.1) is often used as it stands.

Dynamic impedance The practical circuit no longer looks like an open circuit to the source at resonance. Its impedance is purely resistive however, and is often called the dynamic impedance. It is given by: Zo=

L CRL

(10.7)

From this we can see that dynamic impedance is inversely proportional to the resistance of the inductor.

Q factor With the practical parallel tuned circuit the Q is, as with the series resonant circuit, the same as the Q of the inductor at the resonant frequency. We might ask ourselves what happens when we wish to deliberately reduce the circuit's Q.; for if we placed our damping resistor in series with the inductoi, it would also affect our resonant frequency. The solution is that the damping resistor is placed across the whole tuned circuit, as shown in Figure 10.3, where it has the desired effect without affecting fo. The value of the damping resistor can be calculated as follows:

Oo

RD = Zo Q I - QD

(10.8)

where RD is the damping resistor value, QD is the desired Q ( Q damped), Z o - L as previously, and Q1 is the Q of the inductor at resonance, or the Q of the circuit with no damping resistor. QD must obviously be less than QI.

230

Electronics Calculations Data Handbook

) ~) L

Figure 10.3 Practical parallel tuned circuit with damping resistor

Maximum capacitor value We can see that as R becomes larger, k Eqn (10.6) goes from 1 towards zero, and the resonant frequency falls, also towards zero. When:

CR2L L

L

= 1 orC--R2 L

(10.9)

then k = 0, and the circuit ceases to resonate. This tells us that for any practical inductor, there is a maximum value of capacitor which can be placed across it for it to remain resonant. This value is easily calculated from Eqn (10.9). Example 10.3: design a parallel tuned circuit with fo = 120 kHz +/-2 kHz, Q = 20 and the highest feasible dynamic impedance, with the restriction that C is greater than 100 pE What is the dynamic impedance, with and without the damping resistor? (Assume that the resistance of the inductor is 5 f~.) From Table 10.1, we choose C = 120pF, L = 15 mH, giving a nominal frequency of 119 kHz. We can calculate the Q of the inductor by taking X from the t a b l e - ll.2k- and dividing by 5 f~. This gives Q = 2240. Now we calculate Zo, using Eqn (10.7): Zo =

15m = 25 Mfl 120p x 5

and so 2O = 225 k f~ 2 2 4 0 - 20 As Zo is so much larger than RD, we can take the dynamic impedance with RD fitted to be equal to RD, 225 k 9t. RD -- 25M x

Table 10.1 Frequency constants for L C circuits fo

C

L

X

fo

C

L

X

503 556 610 610 673 674 734 734 740 806 811 816 876 876 890 890 968 969 977 981 1.06k 1.06k 1.07k 1.07k 1.07k 1.17k 1.17k 1.18k 1.18k 1.19k 1.28k 1.28k 1.30k 1.30k 1.30k 1.30k

lu 820n 680n lu 560n 820n 470n lu 680n 390n 820n 560n 330n lu 680n 470n 820n 270n 390n 560n 330n 680n 470n 220n lu 560n 270n 390n 820n 180n 470n 330n 150n lu 220n 680n

lOOm lOOm lOOm 68m 100m 68m 100m 47m 68m lOOm 47m 68m lOOm 33m 47m 68m 33m 100m 68m 47m 68m 33m 47m 100m 22m 33m 68m 47m 22m lOOm 33m 47m lOOm 15m 68m 22m

316 349 383 261 423 288 461 217 316 506 239 348 550 182 263 380 201 609 418 290 454 220 316 674 148 243 502 347 164 745 265 377 816 122 556 180

1.40k 1.41k 1.43k 1.44k 1.44k 1.45k 1.53k 1.57k 1.57k 1.58k 1.58k 1.59k 1.59k 1.69k 1.72k 1.73k 1.74k 1.76k 1.76k 1.76k 1.87k 1.87k 1.90k 1.90k 1.93k 1.93k 1.93k 1.93k 2.07k 2.07k 2.08k 2.12k 2.13k 2.13k 2.13k 2.13k

390n 270n 560n 820n 180n 120n 330n 220n 470n 680n 150n 100n lu 270n 390n 180n 560n 820n 82n 120n 220n 330n 150n 470n 68n lOOn 680n lu 180n 270n 390n 120n 56n 560n 82n 820n

33m 47m 22m 15m 68m 100m 33m 47m

291 417 198 135 615 913 316 462 216 149 673 1.OOk 100 35O 238 511 164 110 1.10k 753 387 258 560 179 1.21k 825 121 82.5 428 285 196 626 1.34k 134 911 91.1

22m 15m 68m 100m lOm 33m 22m 47m 15m lOm lOOm 68m 33m 22m 47m 15m lOOm 68m lOm 6m8 33m 22m 15m 47m lOOm lOm 68m 6m8

232

Electronics Calculations Data Handbook

fo

C

L

X

fo

C

L

X

2.26k 2.26k 2.29k 2.32k 2.32k 2.32k 2.32k 2.34k 2.34k 2.50k 2.53k 2.53k 2.55k 2.55k 2.56k 2.56k 2.58k 2.58k 2.77k 2.77k 2.77k 2.77k 2.77k 2.77k 2.82k 2.82k 2.82k 2.82k 3.06k 3.06k 3.06k 3.06k 3.06k 3.09k 3.09k 3.10k 3.10k

150n 330n 220n 47n lOOn 470n lu 68n 680n 270n 120n 180n 39n 390n 82n 820n 56n 560n 33n 100n 150n 220n 330n lu 680n 47n 68n 470n 82n 820n 27n 180n 270n 390n 39n 120n 56n

33m 15m 22m 100m 47m lOm 4m7 68m 6m8 15m 33m 22m 100m lOm 47m 4m7 68m 6m8 100m 33m 22m 15m lOm 3m3 4m7 68m 47m 6m8 33m 3m3 100m 15m lOm 6m8 68m 22m 47m

469 213 316 1.46k 686 146 68.6 1.OOk 100 236 524 350 1.60k 160 757 75.7 1.10k 110 1.74k 574 383 261 174 57.4 83.1 1.20k 831 120 634 63.4 1.92k 289 192 132 1.32k 428 916

3.10k 3.36k 3.36k 3.36k 3.36k 3.36k 3.39k 3.39k 3.39k 3.39k 3.39k 3.39k 3.70k 3.70k 3.71k 3.71k 3.72k 3.72k 3.75k 3.75k 3.75k 3.75k 3.75k 4.04k 4.04k 4.04k 4.04k 4.11k 4.11k 4.11k 4.11k 4.11k 4.11k 4.11k 4.11k 4.44k 4.44k

560n 150n 33n 68n 330n 680n 47n 470n 22n lOOn 220n lu 56n 560n 27n 270n 39n 390n 82n 820n 18n 120n 180n 33n 47n 330n 470n 15n lOOn 150n lu 22n 68n 220n 680n 390n 39n

4m7 15m 68m 33m 6m8 3m3 47m 4m7 lOOm 22m lOm 2m2 33m 3m3 68m 6m8 47m 4m7 22m 2m2 lOOm 15m lOm 47m 33m 4m7 3m3 100m 15m lOm lm5 68m 22m 6m8 2m2 3m3 33m

91.6 316 1.44k 697 144 69.7 1.OOk 100 2.13k 469 213 46.9 768 76.8 1.59k 159 1.10k 110 518 51.8 2.36k 354 236 1.19k 838 119 83.8 2.58k 387 258 38.7 1.76k 569 176 56.9 92.0 920

Table 10. 1 Frequency constants for LC circuits fo

C

L

4.47k 4.47k 4.53k 4.53k 4.54k 4.54k 4.55k 4.55k 4.59k 4.59k 4.82k 4.82k 4.95k 4.95k 4.95k 4.95k 4.98k 4.98k 4.98k 4.98k 5.03k 5.03k 5.03k 5.33k 5.33k 5.43k 5.43k 5.47k 5.47k 5.49k 5.49k 5.56k 5.56k 5.56k 5.57k 5.57k 5.91k

27n 270n 56n 560n 820n 82n 18n 180n 12n 120n 33n 330n 22n 47n 220n 470n 680n 15n 68n 150n lOn lOOn lu 27n 270n 39n 390n 180n 18n 56n 560n 8n2 82n 820n 12n 120n 22n

47m 4m7 22m 2m2 lm5 15m 68m 6m8 lOOm lOm 33m 3m3 47m 22m 4m7 2m2 lm5 68m 15m 6m8 100m lOm lm 33m 3m3 22m 2m2 4m7 47m 15m lm5 100m lOm lm 68m 6m8 33m

X 1.32k ~ 132 627 62.7 42.8 428 1.94k 194 2.89k 289 1.OOk 100 1.46k 684 146 68.4 47.0 2.13k 470 213 3.16k 316 31.6 1.11k 111 751 75.1 162 1.62k 518 51.8 3.49k 349 34.9 2.38k 238 1.22k

fo 5.91k 5.91k 5.91k 5.99k 5.99k 5.99k 5.99k 6.10k 6.10k 6.10k 6.10k 6.10k 6.10k 6.53k 6.53k 6.53k 6.53k 6.58k 6.58k 6.70k 6.70k 6.73k 6.73k 6.73k 6.74k 6.74k 6.74k 7.15k 7.15k 7.15k 7.15k 7.23k ii 7.23k 7.34k 7.34k 7.34k 7.34k

233

C

L

X

33n 220n 330n 15n 47n 150n 470n 6n8 lOOn 680n lOn 68n lu 18n 180n 27n 270n 390n 39n 12n 120n 5n6 56n 560n 8n2 82n 820n 15n 33n 150n 330n 22n 220n 4n7 lOn 47n lOOn

22m 3m3 2m2 47m 15m 4m7 lm5 lOOm 6m8 lm 68m lOm 680u 33m 3m3 22m 2m2 lm5 15m 47m 4m7 lOOm lOm lm 68m 6m8 680u 33m 15m 3m3 lm5 22m 2m2 100m 47m lOm 4m7

816 122 81.6 1.77k 565 177 56.5 3.83k 261 38.3 2.61k 383 26.1 1.35k 135 903 90.3 62.0 620 1.98k 198 4.23k 423 42.3 2.88k 288 28.8 1.48k 674 148 67.4 1.OOk 100 4.61k 2.17k 461 217

234

Electronics Calculations Data Handbook

fo

c

L

X

fo

C

L

X

7.34k 7.34k 7.40k 7.40k 7.40k 7.91k 7.91k 8.00k 8.00k 8.00k 8.00k 8.06k 8.06k 8.06k 8.11k 8.11k 8.11k 8.16k 8.16k 8.16k 8.76k 8.76k 8.76k 8.76k 8.76k 8.76k 8.76k 8.76k 8.76k 8.76k 8.90k 8.90k 8.90k 8.90k 8.90k 8.90k 9.68k

470n lu 6n8 68n 680n 27n 270n 12n 18n 120n 180n 3n9 39n 390n 8n2 82n 820n 5n6 56n 560n 3n3 lOn 15n 22n 33n lOOn 150n 220n 330n lu 6n8 68n 680n 4n7 47n 470n 8n2

lm 470u 68m 6m8 680u 15m lm5 33m 22m 3m3 2m2 100m lOm lm 47m 4m7 470u 68m 6m8 680u 100m 33m 22m 15m lOm 3m3 2m2 lm5 lm 330u 47m 4m7 470u 68m 6m8 680u 33m

46.1 21.7 3.16k 316 31.6 745 74.5 1.66k 1.11k 166 111 5.06k 506 50.6 2.39k 239 23.9 3.48k 348 34.8 5.50k 1.82k 1.21k 826 550 182 121 82.6: 55.0 18.2 2.63k 263 26.3 3.80k 380 38.0 2.01k

9.68k 9.68k 9.69k 9.69k 9.69k 9.69k 9.69k 9.77k 9.77k 9.77k 9.80k 9.80k 9.81k 9.81k 9.81k lO.6k lO.6k lO.6k 10.6k lO.6k 10.6k 10.6k lO.6k lO.7k 10.7k lO.7k 10.7k lO.7k lO.7k lO.7k lO.7k lO.7k ll.7k ll.7k ll.7k ll.7k ll.7k

82n 820n 2n7 18n 180n 27n 270n 3n9 39n 390n 12n 120n 5n6 56n 560n 15n 150n 3n3 6n8 33n 68n 330n 680n 4n7 47n 470n 2n2 1On

3m3 330u lOOm 15m lm5 10m lm 68m 6m8 680u 22m 2m2 47m 4m7 470u 15m lm5 68m 33m 6m8 3m3 680u 330u 47m 4m7 470u lOOm 22m 10m 2m2 lm

201 20.1 6.09k 913 91.3 609 60.9 4.18k 418 41.8 1.35k 135 2.90k 290 29.0 1.OOk 100 4.54k 2.20k 454 220 45.4 22.0 3.16k 316 31.6 6.74k 1.48k 674 148 67.4 14.8 2.43k 243 24.3 5.02k 502

22n lOOn 220n lu 5n6 56n 560n 2n7 27n

220u 33m 3m3 330u 68m 6m8

Table 10. 1 Frequency constants for L C circuits

235

fo

C

L

X

fo

C

L

X

ll.7k ll.8k ll.8k ll.8k ll.8k ll.8k ll.8k ll.9k ll.9k ll.9k ll.9k ll.9k 12.8k 12.8k 12.8k 12.8k 12.8k 12.8k 13.Ok 13.Ok 13.0k 13.Ok 13.0k 13.0k 13.0k 13.Ok 13.Ok 13.Ok 13.Ok 13.0k 14.Ok 14.0k 14.Ok 14.1k 14.1k 14.1k 14.3k

270n 3n9 39n 390n 8n2 82n 820n ln8 12n 18n 120n 18On 3n3 4n7 33n 47n 330n 470n ln5 lOn 15n lOOn 150n lu 2n2 6n8 22n 220n 680n 68n 3n9 390n 39n 2n7 27n 270n 5n6

680u 47m 4m7 470u 22m 2m2 220u lOOm 15m lOm lm5 lm 47m 33m 4m7 3m3 470u 330u lOOm 15m lOm lm5 lm 150u 68m 22m 6m8 680u 220u 2m2 33m 330u 3m3 47m 4m7 470u 22m

50.2 3.47k 347 34.7 1.64k 164 16.4 7.45k 1.12k 745 112 74.5 3.77k 2.65k 377 265 37.7 26.5 8.16k 1.22k 816 122 81.6 12.2 5.56k 1.80k 556 55.6 18.0 180 2.91k 29.1 291 4.17k 417 41.7 1.98k

14.3k 14.3k 14.4k 14.4k 14.4k 14.4k 14.4k 14.4k 14.5k 14.5k 14.5k 15.3k 15.3k 15.3k 15.7k 15.7k 15.7k 15.7k 15.7k 15.7k 15.8k 15.8k 15.8k 15.8k 15.8k 15.8k 15.9k 15.9k 15.9k 15.9k 16.9k 16.9k 16.9k 17.2k 17.2k 17.2k 17.3k

56n 560n 8n2 82n 820n ln8 18n 180n 12n ln2 120n 3n3 33n 330n 2n2 4n7 22n 47n 220n 470n ln5 6n8 15n 68n 150n 680n In lOn lOOn lu 2n7 27n 270n 3n9 39n 390n ln8

2m2 220u 15m lm5 150u 68m 6m8 680u lOm lOOm lm 33m 3m3 330u 47m 22m 4m7 2m2 470u 220u 68m 15m 6m8 lm5 680u 150u lOOm 10m lm lOOu 33m 3m3 330u 22m 2m2 220u 47m

198 19.8 1.35k 135 13.5 6.15k 615 61.5 913 9.13k 91.3 3.16k 316 31.6 4.62k 2.16k 462 216 46.2 21.6 6.73k 1.49k 673 149 67.3 14.9 10.0k 1.00k 100 10.0 3.50k 350 35.0 2.38k 238 23.8 5.11k

236

Electronics Calculations Data Handbook

fo

C

L

X

fo

C

L

17.3k 17.3k 17.4k 17.4k 17.4k 17.6k 17.6k 17.6k 17.6k 17.6k 17.6k 17.6k 18.7k 18.7k 18.7k 18.7k 18.7k 18.7k 19.Ok 19.0k 19.Ok 19.Ok 19.Ok 19.Ok 19.3k 19.3k 19.3k 19.3k 19.3k 19.3k 19.3k 19.3k 20.7k 20.7k 20.7k 20.7k 20.7k

18n 18On 5n6 56n 560n 820p 8n2 82n 820n ln2 12n 120n 2n2 3n3 22n 33n 220n 330n ln5 4n7 15n 47n 150n 470n 680p In 6n8 lOn lOOn 680n lu 68n ln8 2n7 18n 27n 180n

4m7 470u 15m lm5 150u lOOm 10m lm 100u 68m 6m8 680u 33m 22m 3m3 2m2 330u 220u 47m 15m 4m7 lm5 470u 150u 100m 68m lOm 6m8 680u lOOu 68u lm 33m 22m 3m3 2m2 330u

511 51.1 1.64k 164 16.4 ll.Ok 1.10k 110 11.0 7.53k 753 75.3 3.87k 2.58k 387 258 38.7 25.8 5.60k 1.79k 560 179 56.0 17.9 12.1k 8.25k 1.21k 825 82.5 12.1 8.25 121 4.28k 2.85k 428 285 42.8

20.7k 20.8k 20.8k 20.8k 21.2k 21.2k 21.2k 21.3k 21.3k 21.3k 21.3k 21.3k 21.3k 21.3k 21.3k 22.6k 22.6k 22.6k 22.6k 22.6k 22.6k 22.9k 22.9k 22.9k 23.2k 23.2k 23.2k 23.2k 23.2k 23.2k 23.2k 23.2k 23.4k 23.4k 23.4k 23.4k 25.0k

270n 3n9 39n 390n ln2 12n 12On 560p 5n6 56n 560n 8n2 820n 820p 82n ln5 3n3 15n 33n 150n 330n 2n2 22n 220n 470p In 4n7 1On 47n lOOn 470n lu 6n8 680n 680p 68n 2n7

220u 15m lm5 150u 47m 4m7 470u lOOm 10m lm 100u 6m8 68u 68m 680u 33m 15m 3m3 lm5 330u 150u 22m 2m2 220u lOOm 47m 10m 4m7 lm 470u lOOu 47u 6m8 68u 68m 680u 15m

li X 28.5 1.96k 196 19.6 6.26k 626 62.6 13.4k 1.34k 134 13.4 911 9.11 9.11k 91.1 4.69k .2.13k 469 213 46.9 21.3 3.16k 316 31.6 14.6k 6.86k 1.46k 686 146 68.6 14.6 6.86 1.00k 10.0 10.0k 100 2.36k

Table 10.1 Frequency constants for L C circuits fo

l

C

25.0k 27n 25.0k 270n 25.3k ln2 25.3k ln8 25.3k 12n 25.3k 18n 25.3k 120n 25.3k 180n 25.5k 3n9 25.5k 390n 25.5k 390p 25.5k 39n 25.6k 820p 25.6k 8n2 25.6k 82n 25.6k 820n 25.8k 560p 25.8k 5n6 25.8k 56n 25.8k 560n 27.7k 330p 27.7k In 27.7k ln5 27.7k 2n2 27.7k 3n3 27.7k lOn 27.7k 15n 27.7k i 22n 27.7k 33n 27.7k lOOn 27.7k 150n 27.7k 220n 27.7k 330n 27.7k lu 28.2k 470p 28.2k 680p 28.2k 4n7

237

L

X

fo

C

L

X

lm5 150u 33m 22m 3m3 2m2 330u 220u lOm lOOu lOOm lm 47m 4m7 470u 47u 68m 6m8 680u 68u lOOm 33m 22m 15m lOm 3m3 2m2 lm5 lm 330u 220u 150u lOOu 33u 68m 47m 6m8

236 23.6 5.24k 3.50k 524 350 52.4 35.0 1.60k 16.0 16.Ok 160 7.57k 757 75.7 7.57 ll.Ok 1.10k 110 11.0 17.4k 5.74k 3.83k 2.61k 1.74k 574 383 261 174 57.4 38.3 26.1 17.4 5.74 12.Ok 8.31k 1.20k

28.2k 28.2k 28.2k 28.2k 28.2k 30.6k 30.6k 30.6k 30.6k 30.6k 30.6k 30.6k 30.6k 30.6k 30.6k 30.6k 30.9k 30.9k 30.9k 30.9k 31.Ok 31.Ok 31.Ok 31.Ok 31.Ok 31.Ok 31.Ok 33.6k 33.6k 33.6k 33.6k 33.6k 33.6k 33.6k 33.6k 33.6k 33.6k

6n8 47n 68n 470n 680n 820p 8n2 82n 820n 270p ln8 2n7 18n 27n 180n 270n 390p 3n9 39n 390n ln2 12n 120n 560p 5n6 56n 560n ln5 15n 150n 330p 680p 3n3 6n8 33n 330n 680n

4m7 680u 470u 68u 47u 33m 3m3 330u 33u 100m 15m lOm lm5 lm 150u lOOu 68m 6m8 680u 68u 22m 2m2 220u 47m 4m7 470u 47u 15m lm5 i 150u i 68m 33m 6m8 3m3 680u 68u 33u

831 120 83.1 12.0 8.31 6.34k 634 63.4 6.34 19.2k 2.89k 1.92k 289 192 28.9 19.2 13.2k 1.32k 132 13.2 4.28k 428 42.8 9.16k 916 91.6 9.16 3.16k 316 31.6 14.4k 6.97k 1.44k 697 144 14.4 6.97

238

Electronics Calculations Data Handbook

fo

C

L

33.6k 33.9k 33.9k 33.9k 33.9k 33.9k 33.9k 33.9k 33.9k 33.9k 33.9k 33.9k 33.9k 37.0k 37.0k 37.0k 37.0k 37.1k 37.1k 37.1k 37.1k 37.2k 37.2k 37.2k 37.2k 37.5k 37.5k 37.5k 37.5k 37.5k 37.5k 37.5k 37.5k 37.5k 37.5k 37.5k i 40.4k

68n 470p 4n7 47n 470n 220p In 2n2 lOn 22n lOOn 220n lu 5n6 560p 56n 560n 2n7 270n 270p 27n 3n9 390n 390p 39n 820p 8n2 82n 820n 180p ln2 ln8 12n 18n 120n 180n 470p

330u 47m 4m7 470u 47u lOOm 22m lOm 2m2 lm 220u 100u 22u 3m3 33m 330u 33u 6m8 68u 68m 680u 4m7 47u 47m 470u 22m 2m2 220u 22u lOOm 15m lOm lm5 lm 150u lOOu 33m

i

X

fo

69.7 lO.Ok 1.OOk 100 10.0 21.3k 4.69k 2.13k 469 213 46.9 21.3 4.69 768 7.68k 76.8 7.68 1.59k 15.9 15.9k 159 1.1Ok 11.0 ll.Ok 110 5.18k 518 51.8 5.18 23.6k 3.54k 2.36k 354 236 35.4 23.6 8.38k

40.4k 40.4k 40.4k 40.4k 40.4k 40.4k 40.4k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 41.1k 44.4k 44.4k 44.4k 44.4k 44.7k 44.7k 44.7k 44.7k 45.3k 45.3k 45.3k 45.3k 45.4k 45.4k

X 3n3 330p 4n7 33n 47n 330n 470n 150p In ln5 lOn 15n lOOn 150n lu 220p 680p 2n2 6n8 22n 68n 220n 680n 390p 3n9 39n 390n 270p 2n7 27n 270n 560p 5n6 56n 560n 820p 8n2

4m7 47m 3m3 470u 330u 47u 33u lOOm 15m 10m lm5 lm 150u 100u 15u 68m 22m 6m8 2m2 680u 220u 68u 22u 33m 3m3 330u 33u 47m 4m7 470u 47u 22m 2m2 220u 22u 15m lm5

1.19k ll.9k 838 119 83.8 ll.9 8.38 25.8k 3.87k 2.58k 387 258 38.7 25.8 3.87 17.6k 5.69k 1.76k 569 176 56.9 17.6 5.69 9.20k 920 92.0 9.20 13.2k 1.32k 132 13.2 6.27k 627 62.7 6.27 4.28k 428

Table 10. 1 Frequency constants for L C circuits

239

fo

C

L

X

fo

C

L

X

45.4k 45.4k 45.5k 45.5k 45.5k 45.5k 45.9k 45.9k 45.9k 45.9k 48.2k 48.2k 48.2k 48.2k 49.5k 49.5k 49.5k 49.5k 49.5k 49.5k 49.5k 49.5k 49.8k 49.8k 49.8k 49.8k 49.8k 49.8k 49.8k 49.8k 50.3k 50.3k 50.3k 50.3k 50.3k 53.3k 53.3k

82n 820n ln8 180n 180p 18n 120p ln2 12n 120n 330p 3n3 33n 330n 2n2 220n 220p 470p 22n 47n 470n 4n7 680p ln5 6n8 680n 150p 15n 68n 150n 100n lOOp In lOn lu 270p 2n7

150u 15u 6m8 68u 68m 680u lOOm lOm lm lOOu 33m 3m3 330u 33u 4m7 47u 47m 22m 470u 220u 22u 2m2 15m 6m8 lm5 15u 68m 680u 150u 68u lOOu lOOm lOm lm lOu 33m 3m3

42.8 4.28 1.94k 19.4 19.4k 194 28.9k 2.89k 289 28.9 lO.Ok 1.OOk 100 10.0 1.46k 14.6 14.6k 6.84k 146 68.4 6.84 684 4.70k 2.13k 470 4.70 21.3k 213 47.0 21.3 31.6 31.6k 3.16k 316 3.16 ll.lk 1.11k

53.3k 53.3k 54.3k 54.3k 54.3k 54.3k 54.7k 54.7k 54.7k 54.7k 54.9k 54.9k 54.9k 54.9k 55.6k 55.6k 55.6k 55.6k 55.6k 55.7k 55.7k 55.7k 55.7k 59.1k 59.1k 59.1k 59.1k 59.1k 59.1k 59.1k 59.1k 59.9k 59.9k 59.9k 59.9k 59.9k 59.9k

27n 270n 390n 390p 3n9 39n 180p ln8 18n 180n 560p 5n6 56n 560n 82p 820p 8n2 82n 820n 120p ln2 12n 120n 220p 2n2 3n3 330p 22n 33n 220n 330n 150p 470p ln5 4n7 15n 47n

330u 33u 22u 22m 2m2 220u 47m 4m7 470u 47u 15m lm5 150u 15u lOOm lOm lm lOOu lOu 68m 6m8 680u 68u 33m 3m3 2m2 22m 330u 220u 33u 22u 47m 15m 4m 7 lm5 470u 150u

111 11.1 7.51 7.51k 751 75.1 16.2k 1.62k 162 16.2 5.18k 518 51.8 5.18 34.9k 3.49k 349 34.9 3.49 23.8k 2.38k 238 23.8 12.2k 1.22k 816 8.16k 122 81.6 12.2 8.16 17.7k 5.65k 1.77k 565 177 56.5

240

Electronics Calculations Data Handbook

fo

C

L

X

fo

C

L

X

59.9k 59.9k 61.Ok 61.Ok 61.Ok 61.Ok 61.Ok 61.Ok 61.Ok 61.0k 61.Ok 61.0k 65.3k 65.3k 65.3k 65.3k 65.3k 65.3k 65.3k 65.3k 65.8k 65.8k 65.8k 65.8k 67.0k 67.0k 67.0k 67.0k 67.3k 67.3k 67.3k 67.3k 67.3k 67.4k 67.4k 67.4k 67.4k

470n 150n lOOp 680p In 6n8 68n lOOn 680n lu 68p 1On 180p 270p ln8 2n7 18n 27n 180n 270n 3n9 390p 39n 390n ln2 12n 120p 120n 56p 560p 5n6 56n 560n 820n 82p 820p 8n2

15u 47u 68m 10m 6m8 lm 100u 68u lOu 6u8 100m 680u 33m 22m 3m3 2m2 330u 220u 33u 22u lm5 15m 150u 15u 4m7 470u 47m 47u 100m lOm lm 100u lOu 6u8 68m 6m8 680u

5.65 17.7 26.1k 3.83k 2.61k 383 38.3 26.1 3.83 2.61 38.3k 261 13.5k 9.03k 1.35k 903 135 90.3 13.5 9.03 620 6.20k 62.0 6.20 1.98k 198 19.8k 19.8 42.3k 4.23k 423 42.3 4.23 2.88 28.8k 2.88k 288

67.4k 71.5k 71.5k 71.5k 71.5k 71.5k 71.5k 71.5k 71.5k 72.3k 72.3k 72.3k 72.3k 73.4k 73.4k 73.4k 73.4k 73.4k 73.4k 73.4k 73.4k 73.4k 73.4k 74.0k 74.0k 74.0k 74.0k 74.0k 79.1k 79.1k 79.1k 79.1k 80.Ok 80.Ok 80.Ok 80.Ok 80.Ok

82n 150p 330p ln5 3n3 15n 33n 330n 150n 220p 2n2 22n 220n 100p 470p In 1On 47n 100n 470n lu 47p 4n7 6n8 680n 68p 680p 68n 2n7 270p 27n 270n 120p 180p ln2 ln8 12n

68u 33m 15m 3m3 lm5 330u 150u 15u 33u 22m 2m2 220u 22u 47m 10m 4m7 470u 100u 47u 10u 4u7 lOOm lm 680u 6u8 68m 6m8 68u lm5 15m 150u 15u 33m 22m 3m3 2m2 330u

28.8 14.8k 6.74k 1.48k 674 148 67.4 6.74 14.8 lO.Ok 1.OOk 100 10.0 21.7k 4.61k 2.17k 217 46.1 21.7 4.61 2.17 46.1k 461 316 3.16 31.6k 3.16k 31.6 745 7.45k 74.5 7.45 16.6k ll.lk 1.66k 1.11k 166

Table 10. 1 Frequency constants for LC circuits

241

fo

C

L

X

fo

C

L

X

80.0k 80.0k 80.0k 80.6k 80.6k 80.6k 80.6k 80.6k 81.1k 81.1k 81.1k 81.1k 81.1k 81.6k 81.6k 81.6k 81.6k 81.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 87.6k 89.0k

18n 120n 180n 39p 390p 3n9 39n 390n 820p 8n2 820n 82p 82n 5n6 56n 56p 560p 560n 2n2 100p 150p 220p In ln5 15n 22n 220n 330n 330p 3n3 33n 150n lu 33p lOn lOOn 680p

220u 33u 22u lOOm lOm lm lOOu lOu 4m7 470u 4u7 47m 47u 680u 68u 68m 6m8 6u8 lm5 33m 22m 15m 3m3 2m2 220u 150u 15u lOu lOm lm lOOu 22u 3u3 lOOm 330u 33u 4m7

Ill 16.6 ll.1 50.6k 5.06k 506 50.6 5.06 2.39k 239 2.39 23.9k 23.9 348 34.8 34.8k 3.48k 3.48 826 18.2k 12.1k 8.26k 1.82k 1.21k 121 82.6 8.26 5.50 5.50k 550 55.0 12.1 1.82 55.0k 182 18.2 2.63k

89.0k 89.0k 89.0k 89.0k 89.0k 89.0k 89.0k 89.0k 89.0k 96.8k 96.8k 96.8k 96.8k 96.8k 96.9k 96.9k 96.9k 96.9k 96.9k 96.9k 96.9k 96.9k 96.9k 97.7k 97.7k 97.7k 97.7k 97.7k 98.0k 98.0k 98.0k 98.0k 98.1k 98.1k 98.1k 98.1k 98.1k

6n8 47n 470n 680n 47p 68p 470p 4n7 68n 82p 820p 8n2 820n 82n ln8 180p 270p 18n 180n 27p 2n7 27n 270n 3n9 39n 390n 39p 390p 120p ln2 12n 120n 56p 560p 5n6 56n 560n

470u 68u 6u8 4u7 68m 47m 6m8 680u 47u 33m 3m3 330u 3u3 33u lm5 15m lOm 150u 15u lOOm lm lOOu 10u 680u 68u 6u8 68m 6m8 22m 2m2 220u 22u 47m 4m7 470u 47u 4u7

263 38.0 3.80 2.63 38.0k 26.3k 3.80k 380 26.3 20.1k 2.01k 201 2.01 20.1 913 9.13k 6.09k 91.3 9.13 60.9k 609 60.9 6.09 418 41.8 4.18 41.8k 4.18k 13.5k 1.35k 135 13.5 29.0k 2.90k 290 29.0 2.90

242

Electronics Calculations Data Handbook

fo

C

L

X

fo

C

L

X

106k 106k 106k 106k 106k 106k 106k 106k 106k 106k 106k 106k 106k 106k 107k 107k 107k 107k 107k 107k 107k 107k 107k 107k 107k 107k 107k 107k 107k l17k l17k l17k l17k l17k l17k l17k l17k

ln5 150p 15n 150n 33p 68p 330p 680p 3n3 6n8 33n 330n 680n 68n 4n7 47p 470p 47n 470n 22p 100p 220p In 2n2 lOn 22n 100n 220n lu 56p 560p 5n6 56n 560n 27n 27p 270p

lm5 15m 150u 15u 68m 33m 6m8 3m3 680u 330u 68u 6u8 3u3 33u 470u 47m 4m7 47u 4u7 100m 22m lOm 2m2 lm 220u lOOu 22u lOu 2u2 33m 3m3 330u 33u 3u3 68u 68m 6m8

1.OOk lO.Ok 100 10.0 45.4k 22.0k 4.54k 2.20k 454 220 45.4 4.54 2.20 22.0 316 31.6k 3.16k 31.6 3.16 67.4k 14.8k 6.74k 1.48k 674 148 67.4 14.8 6.74 1.48 24.3k 2.43k 243 24.3 2.43 50.2 50.2k 5.02k

l17k l17k l18k l18k l18k l18k l18k l18k l18k l18k l18k l18k l19k l19k l19k l19k ll9k l19k l19k l19k l19k 128k 128k 128k 128k 128k 128k 128k 128k 128k 128k 130k 130k 130k 130k 130k 130k

2n7 270n 39p 390p 3n9 39n 390n 82p 820p 8n2 82n 820n ln2 18p 120p 180p ln8 12n 18n 120n 180n 33p 47p 330p 470p 3n3 330n 470n 4n7 33n 47n 100p 15p 150p In ln5 lOn

680u 6u8 47m 4m7 470u 47u 4u7 22m 2m2 220u 22u 2u2 lm5 100m 15m lOm lm 150u lOOu 15u lOu 47m 33m 4m7 3m3 470u 4u7 3u3 330u 47u 33u 15m lOOm lOm lm5 lm 150u

5O2 5.02 34.7k 3.47k 347 34.7 3.47 16.4k 1.64k 164 16.4 1.64 1.12k 74.5k ll.2k 7.45k 745 112 74.5 11.2 7.45 37.7k 26.5k 3.77k 2.65k 377 3.77 2.65 265 37.7 26.5 12.2k 81.6k 8.16k 1.22k 816 122

Table 10. 1 Frequency constants for LC circuits

243

fo

C

L

X

fo

C

L

X

130k 130k 130k 130k 130k 130k 130k 130k 130k 130k 130k 130k 130k 130k 140k 140k 140k 140k 140k 141k 141k 141k 141k 141k 143k 143k 143k 143k 143k 144k 144k 144k 144k 144k 144k 144k 144k

15n lOOn 150n lu 2n2 6n8 22n 220n 680n 22p 68p 220p 680p 68n 39p 390p 3n9 390n 39n 27p 270p 2n7 27n 270n 5n6 56n 56p 560p 560n 82p 820p 8n2 82n 820n 18p 180p ln8

lOOu 15u lOu lu5 680u 220u 68u 6u8 2u2 68m 22m 6m8 2m2 22u 33m 3m3 330u 3u3 33u 47m 4m7 470u 47u 4u7 220u 22u 22m 2m2 2u2 15m lm5 150u 15u lu5 68m 6m8 680u

81.6 12.2 8.16 1.22 556 180 55.6 5.56 1.80 55.6k 18.Ok 5.56k 1.80k 18.0 29.1k 2.91k 291 2.91 29.1 41.7k 4.17k 417 41.7 4.17 198 19.8 19.8k 1.98k 1.98 13.5k 1.35k 135 13.5 1.35 61.5k 6.15k 615

144k 144k 145k 145k 145k 145k 145k 153k 153k 153k 153k 153k 157k 157k 157k 157k 157k 157k 157k 157k 157k 157k 158k 158k 158k 158k 158k 158k 158k 158k 158k 158k 159k 159k 159k 159k 159k

18n 180n 12p 120p ln2 12n 120n 33p 330p 3n3 33n 330n 22p 47p 220p 470p 2n2 4n7 22n 47n 220n 470n 15p 68p 150p 680p ln5 6n8 15n 150n 680n 68n lOp 100p In lOn 100n

68u 6u8 100m lOm lm lOOu lOu 33m 3m3 330u 33u 3u3 47m 22m 4m7 2m2 470u 220u 47u 22u 4u7 2u2 68m 15m 6m8 lm5 680u 150u 68u 6u8 lu5 15u 100m lOm lm lOOu lOu

61.5 6.15 91.3k 9.13k 913 91.3 9.13 31.6k 3.16k 316 31.6 3.16 46.2k 21.6k 4.62k 2.16k 462 216 46.2 21.6 4.62 2.16 67.3k 14.9k 6.73k 1.49k 673 149 67.3 6.73 1.49 14.9 100k lO.Ok 1.OOk 100 10.0

244

Electronics Calculations Data Handbook

fo

c

L

X

fo

159k 169k 169k 169k 169k 169k 172k 172k 172k 172k 172k 173k 173k 173k 173k 173k 174k 174k 174k 174k 174k 176k 176k 176k 176k 176k 176k 176k 176k 176k 176k 187k 187k 187k 187k 187k 187k

lu 27p 270p 2n7 270n 27n 3n9 390n 39p 390p 39n 18p 180p ln8 180n 18n 5n6 56p 560p 56n 560n 8n2 82p 820p 82n 820n 120p ln2 12n 120n 12p 22p 220p 330p 2n2 3n3 220n

lu 33m 3m3 330u 3u3 33u 220u 2u2 22m 2m2 22u 47m 4m7 470u 4u7 47u 150u 15m lm5 15u lu5 100u 10m lm 10u lu 6m8 680u 68u 6u8 68m 33m 3m3 2m2 330u 220u 3u3

1.00 35.0k 3.50k 350 3.50 35.0 238 2.38 23.8k 2.38k 23.8 51.1k 5.11k 511 5.11 51.1 164 16.4k 1.64k 16.4 1.64 110 ll.Ok 1.10k 11.0 1.10 7.53k 753 75.3 7.53 75.3k 38.7k 3.87k 2.58k 387 258 3.87

187k 187k 187k 187k 190k 190k 190k 190k 190k 190k 190k 190k 190k 190k 193k 193k 193k 193k 193k 193k 193k 193k 193k 193k 207k 207k 207k 207k 207k 207k 207k 207k 207k 207k 208k 208k 208k

X 330n 33p 22n 33n 15p 47p 150p 470p ln5 4n7 15n 47n 150n 470n lOp 100p 6n8 lOn 100n 680n 68p 680p In 68n 18p 27p 180p ln8 2n7 27n 180n 270p 18n 270n 390n 39p 390p

2u2 22m 33u 22u 47m 15m 4m 7 lm5 470u 150u 47u 15u 4u7 lu5 68m 6m8 lOOu 68u 6u8 lu 10m lm 680u 10u 33m 22m 3m3 330u 220u 22u 3u3 2m2 33u 2u2 lu5 15m lm5

2.58 25.8k 38.7 25.8 56.0k 17.9k 5.60k 1.79k 560 179 56.0 17.9 5.60 1.79 82.5k 8.25k 121 82.5 8.25 1.21 12.1k 1.21k 825 12.1 42.8k 28.5k 4.28k 428 285 28.5 4.28 2.85k 42.8 2.85 1.96 19.6k 1.96k

Table 10. 1 Frequency constants for LC circuits fo

C

L

X

fo

208k 208k 212k 212k 212k 212k 212k 213k 213k 213k 213k 213k 213k 213k 213k 213k 226k 226k 226k 226k 226k 226k 226k 226k 226k 226k 229k 229k 229k 229k 229k 232k 232k 232k 232k 232k 232k

3n9 39n 12p 120p ln2 12n 120n 56p 5n6 56n 560p 560n 8n2 82p 820p 82n 15p 33p 150p 330p ln5 3n3 33n 150n 330n 15n 22p 220p 2n2 22n 220n 10p 100p 4n7 100n 47p 470p

150u 15u 47m 4m 7 470u 47u 4u 7 lOm lOOu lOu lm lu 68u 6m8 680u 6u8 33m 15m 3m3 lm5 330u 150u 15u 3u3 lu5 33u 22m 2m2 220u 22u 2u2 47m 4m7 lOOu 4u7 lOm lm

196 19.6 62.6k 6.26k 626 62.6 6.26 13.4k 134 13.4 1.34k 1.34 91.1 9.11k 911 9.11 46.9k 21.3k 4.69k 2.13k 469 213 21.3 4.69 2.13 46.9 31.6k 3.16k 316 31.6 3.16 68.6k 6.86k 146 6.86 14.6k 1.46k

232k 232k 232k 232k 234k 234k 234k 234k 250k 250k 250k 250k 250k 253k 253k 253k 253k 253k 253k 253k 253k 253k 253k 255k 255k 255k 255k 255k 256k 256k 256k 256k 258k 258k 258k 258k 277k

i

245

C

L

X

In lOn 47n 470n 6n8 68p 680p 68n 27p 270p 2n7 27n 270n 12p 18p 120p 180p ln2 ln8 12n 18n 120n 180n 39p 390p 3n9 39n 390n 82p 820p 8n2 82n 5n6 56n 56p 560p 10p

470u 47u lOu lu 68u 6m8 680u 6u8 15m lm5 150u 15u lu5 33m 22m 3m3 2m2 330u 220u 33u 22u 3u3 2u2 lOm lm lOOu lOu lu 4m7 470u 47u 4u7 68u 6u8 6m8 680u 33m

686 68.6 14.6 1.46 100 lO.Ok 1.OOk 10.0 23.6k 2.36k 236 23.6 2.36 52.4k 35.0k 5.24k 3.50k 524 350 52.4 35.0 5.24 3.50 16.Ok 1.60k 160 16.0 1.60 7.57k 757 75.7 7.57 110 11.0 ll.Ok 1.10k 57.4k

246

Electronics Calculations Data Handbook

fo

C

L

X

fo

C

L

X

277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 277k 282k 282k 282k 282k 282k 282k 282k 282k 306k 306k 306k 306k 306k 306k 306k 306k 306k 306k

22p 150p 220p ln5 2n2 3n3 100n 220n 15p 33p 100p 330p In lOn 15n 22n 33n 150n 330n 47p 68p 470p 680p 4n7 6n8 47n 68n 82p 820p 8n2 82n 18p 180p ln8 180n 27p 270p

15m 2m2 lm5 220u 150u 100u 3u3 lu5 22m lOm 3m3 lm 330u 33u 22u 15u lOu 2u2 lu 6m8 4m7 680u 470u 68u 47u 6u8 4u7 3m3 330u 33u 3u3 15m lm5 150u lu5 lOm lm

26.1k 3.83k 2.61k 383 261 174 5.74 2.61 38.3k 17.4k 5.74k 1.74k 574 57.4 38.3 26.1 17.4 3.83 1.74 12.Ok 8.31k 1.20k 831 120 83.1 12.0 8.31 6.34k 634 63.4 6.34 28.9k 2.89k 289 2.89 19.2k 1.92k

306k 306k 306k 306k 309k 309k 309k 309k 310k 310k 310k 310k 310k 310k 310k 310k 310k 336k 336k 336k 336k 336k 336k 336k 336k 336k 336k 336k 336k 336k 339k 339k 339k 339k 339k 339k 339k

2n7 18n 27n 270n 3n9 39n 39p 390p 12p 120p ln2 12n 120n 56p 560p 5n6 56n 15p 150p ln5 15n 150n 3n3 33p 68p 330p 680p 6n8 33n 68n 47p 470p 4n7 47n lOp 22p lOOp

lOOu 15u 10u lu 68u 6u8 6m8 680u 22m 2m2 220u 22u 2u2 4m7 470u 47u 4u7 15m lm5 150u 15u lu5 68u 6m8 3m3 680u 330u 33u 6u8 3u3 4m7 470u 47u 4u7 22m lOm 2m2

192 28.9 19.2 1.92 132 13.2 13.2k 1.32k 42.8k 4.28k 428 42.8 4.28 9.16k 916 91.6 9.16 31.6k 3.16k 316 31.6 3.16 144 14.4k 6.97k 1.44k 697 69.7 14.4 6.97 lO.Ok 1.OOk 100 10.0 46.9k 21.3k 4.69k

Table 10. 1 Frequency constants for L C circuits fo

C

L

X

fo

339k 339k 339k 339k 339k 339k 339k 370k 370k 370k 370k 371k 371k 371k 371k 372k 372k 372k 372k 375k 375k 375k 375k 375k 375k 375k 375k 375k 375k 375k 375k 375k 375k 404k 404k 404k 404k

2n2 lOOn 220n 220p In lOn 22n 56p 5n6 56n 560p 27p 270p 2n7 27n 39p 390p 3n9 39n 82p 820p 8n2 82n 12p 18p 120p ln2 ln8 12n 18n 120n 180n 180p 33p 47p 330p 3n3

lOOu 2u2 lu lm 220u 22u lOu 3m3 33u 3u3 330u 6m8 680u 68u 6u8 4m7 470u 47u 4u7 2m2 220u 22u 2u2 15m lOm lm5 150u lOOu 15u lOu lu5 lu lm 4m 7 3m3 470u 47u

213 4.69 2.13 2.13k 469 46.9 21.3 7.68k 76.8 7.68 768 15.9k 1.59k 159 15.9 ll.Ok 1.10k 110 11.0 5.18k 518 51.8 5.18 35.4k 23.6k 3.54k 354 236 35.4 23.6 3.54 2.36 2.36k ll.9k 8.38k 1.19k 119

404k 404k 404k 404k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 411k 444k 444k 444k 444k 447k 447k 447k 447k 453k 453k 453k 453k 454k 454k 454k

i

247

C

L

X

33n 47n 470p 4n7 10p 15p 100p 150p In ln5 lOn 15n 100n 150n 2n2 22p 68p 680p 6n8 22n 220p 68n 39p 390p 39n 3n9 27p 270p 2n7 27n 5n6 56n 56p 560p 82p 820p 8n2

4u7 3u3 330u 33u 15m lOm lm5 lm 150u lOOu 15u lOu lu5 lu 68u 6m8 2m2 220u 22u 6u8 680u 2u2 3m3 330u 3u3 33u 4m7 470u 47u 4u7 22u 2u2 2m2 220u lm5 150u 15u

11.9 8.38 838 83.8 38.7k 25.8k 3.87k 2.58k 387 258 38.7 25.8 3.87 2.58 176 17.6k 5.69k 569 56.9 17.6 1.76k 5.69 9.20k 920 9.20 92.0 13.2k 1.32k 132 13.2 62.7 6.27 6.27k 627 4.28k 428 42.8

248

Electronics Calculations Data Handbook

fo

C

L

X

fo

454k 455k 455k 455k 455k 459k 459k 459k 459k 459k 482k 482k 482k 482k 495k 495k 495k 495k 495k 495k 495k 495k 498k 498k 498k 498k 498k 498k 498k 498k 503k 503k 503k 503k 503k 533k 533k

82n 18p 180p ln8 18n ln2 12n 12p 120n 120p 33p 330p 3n3 33n 22p 220p 2n2 47p 470p 4n7 22n 47n ln5 15p 68p 150p 680p 6n8 15n 68n lOp lOOp In lOn lOOn 27p 27n

lu5 6m8 680u 68u 6u8 100u lOu lOm lu lm 3m3 330u 33u 3u3 4m7 470u 47u 2m2 220u 22u 4u7 2u2 68u 6m8 lm5 680u 150u 15u 6u8 lu5 lOm lm 100u lOu lu 3m3 3u3

4.28 19.4k 1.94k 194 19.4 289 28.9 28.9k 2.89 2.89k lO.Ok 1.0Ok 100 10.0 14.6k 1.46k 146 6.84k 684 68.4 14.6 6.84 213 21.3k 4.70k 2.13k 470 47.0 21.3 4.70 31.6k 3.16k 316 31.6 3.16 ll.lk 11.1

533k 533k 543k 543k 543k 543k 547k 547k 547k 547k 549k 549k 549k 549k 556k 556k 556k 556k 557k 557k 557k 557k 591k 591k 591k 591k 591k 591k 591k 591k 599k 599k 599k 599k 599k 599k 599k

X 270p 2n7 39p 390p 3n9 39n 18p 180p ln8 18n 56p 560p 5n6 56n 82p 820p 8n2 82n 120p ln2 12n 12p 3n3 22p 33p 220p 330p 2n2 22n 33n 15p 47p 150p 470p ln5 4n7 15n

330u 33u 2m2 220u 22u 2u2 4m7 470u 47u 4u7 lm5 150u 15u lu5 lm lOOu lOu lu 680u 68u 6u8 6m8 22u 3m3 2m2 330u 220u 33u 3u3 2u2 4m7 lm5 470u 150u 47u 15u 4u7

1.11k 111 7.51k 751 75.1 7.51 16.2k 1.62k 162 16.2 5.18k 518 51.8 5.18 3.49k 349 34.9 3.49 2.38k 238 23.8 23.8k 81.6 12.2k 8.16k 1.22k 816 122 12.2 8.16 17.7k 5.65k 1.77k 565 177 56.5 17.7

Table 10. 1 Frequency constants for L C circuits

249

fo

c

L

X

fo

C

L

X

599k 610k 610k 610k 610k 610k 610k 610k 610k 653k 653k 653k 653k 653k 653k 653k 653k 658k 658k 658k 658k 670k 670k 670k 670k 673k 673k 673k 673k 674k 674k 674k 715k 715k 715k 715k 715k

47n 680p In 6n8 1On lOp 68p 100p 68n 18p 27p 180p 270p ln8 2n7 18n 27n 39p 390p 3n9 39n 12p 120p ln2 12n 56p 560p 5n6 56n 820p 8n2 82p 33p 150p 330p 3n3 15n

lu5 100u 68u lOu 6u8 6m8 lm 680u lu 3m3 2m2 330u 220u 33u 22u 3u3 2u2 lm5 150u 15u lu5 4m 7 470u 47u 4u7 lm lOOu lOu lu 68u 6u8 680u lm5 330u 150u 15u 3u3

5.65 383 261 38.3 26.1 26.1k 3.83k 2.61k 3.83 13.5k 9.03k 1.35k 903 135 90.3 13.5 9.03 6.20k 620 62.0 6.20 19.8k 1.98k 198 19.8 4.23k 423 42.3 4.23 288 28.8 2.88k 6.74k 1.48k 674 67.4 14.8

715k 715k 715k 723k 723k 723k 723k 734k 734k 734k 734k 734k 734k 734k 734k 740k 740k 740k 791k 791k 791k 791k 800k 800k 800k 800k 800k 800k 800k 800k 806k 806k 806k 806k 811k 811k 811k

33n 15p ln5 22p 220p 2n2 22n lOp 47p lOOp 470p In 4n7 lOn 47n 680p 6n8 68p 27p 270p 2n7 27n 12p 18p 180p ln8 12n 18n 120p ln2 3n9 39p 390p 39n 82p 820p 8n2

lu5 3m3 33u 2m2 220u 22u 2u2 4m7 lm 470u 100u 47u lOu 4u7 lu 68u 6u8 680u lm5 150u 15u lu5 3m3 2m2 220u 22u 3u3 2u2 330u 33u lOu lm 100u lu 470u 47u 4u7

6.74 14.8k 148 lO.Ok 1.OOk 100 10.0 21.7k 4.61k 2.17k 461 217 46.1 21.7 4.61 316 31.6 3.16k 7.45k 745 74.5 7.45 16.6k ll.lk 1.11k 111 16.6 11.1 1.66k 166 50.6 5.06k 506 5.06 2.39k 239 23.9

250

Electronics Calculations Data Handbook

fo

C

L

X

fo

816k 816k 816k 876k 876k 876k 876k 876k 876k 876k 876k 876k 876k 876k 876k 876k 876k 876k 876k 890k 890k 890k 890k 890k 890k 968k 968k 968k 969k 969k 969k 969k 969k 969k 969k 969k 977k

560p 5n6 56p lOp 15p 22p 33p 100p 150p 220p 330p In ln5 2n2 3n3 lOn 15n 22n 33n 47p 68p 470p 680p 4n7 6n8 82p 820p 8n2 18p 180p 270p ln8 2n7 18n 27p 27n 3n9

68u 6u8 680u 3m3 2m2 lm5 lm 330u 220u 150u 100u 33u 22u 15u 10u 3u3 2u2 lu5 lu 680u 470u 68u 47u 6u8 4u7 330u 33u 3u3 lm5 150u 100u 15u 10u lu5 lm lu 6u8

348 34.8 3.48k 18.2k 12.1k 8.26k 5.50k 1.82k 1.21k 826 550 182 121 82.6 55.0 18.2 12.1 8.26 5.50 3.80k 2.63k 380 263 38.0 26.3 2.01k 201 20.1 9.13k 913 609 91.3 60.9 9.13 6.09k 6.09 41.8

977k 977k 980k 980k 980k 980k 981k 981k 981k 1.06M 1.06M 1.06M 1.06M 1.06M 1.06M 1.06M 1.06M 1.06M 1.06M 1.07M 1.07M 1.07M 1.07M 1.07M 1.07M 1.07M 1.07M 1.07M 1.07M 1.07M 1.17M 1.17M 1.17M 1.17M 1.17M 1.17M 1.18M

X 39p 390p 12p 120p ln2 12n 56p 5n6 560p 15p 150p ln5 15n 33p 68p 330p 680p 3n3 6n8 47p 4n7 470p 220p 2n2 10p 22p 100p In lOn 22n 5n6 56p 560p 270p 2n7 27p 39p

680u 68u 2m2 220u 22u 2u2 470u 4u7 47u lm5 150u 15u lu5 680u 330u 68u 33u 6u8 3u3 470u 4u7 47u 100u 10u 2m2 lm 220u 22u 2u2 lu 3u3 330u 33u 68u 6u8 680u 470u

4.18k 418 13.5k 1.35k 135 13.5 2.90k 29.0 290 10.0k 1.00k 100 10.0 4.54k 2.20k 454 220 45.4 22.0 3.16k 31.6 316 674 67.4 14.8k 6.74k 1.48k 148 14.8 6.74 24.3 2.43k 243 5O2 50.2 5.02k 3.47k

Table 10. 1 Frequency constants for LC circuits

251

fo

C

L

X

fo

C

L

X

1.18M 1.18M 1.18M 1.18M 1.18M 1.19M 1.19M 1.19M 1.19M 1.19M 1.19M 1.19M 1.19M 1.28M 1.28M 1.28M 1.28M 1.28M 1.28M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.30M 1.40M 1.40M 1.40M 1.41M

390p 3n9 82p 820p 8n2 12p 18p 120p 180p ln2 ln8 12n 18n 3n3 33p 47p 330p 470p 4n7 10p lOOp 150p In ln5 lOn 15n 15p 2n2 22p 68p 220p 680p 6n8 39p 3n9 390p 2n7

47u 4u7 220u 22u 2u2 lm5 lm 150u lOOu 15u lOu lu5 lu 4u7 470u 330u 47u 33u 3u3 lm5 150u lOOu 15u lOu lu5 lu lm 6u8 680u 220u 68u 22u 2u2 330u 3u3 33u 4u7

347 34.7 1.64k 164 16.4 ll.2k 7.45k 1.12k 745 112 74.5 11.2 7.45 37.7 3.77k 2.65k 377 265 26.5 12.2k 1.22k 816 122 81.6 12.2 8.16 8.16k 55.6 5.56k 1.80k 556 180 18.0 2.91k 29.1 291 41.7

1.41M 1.41M 1.43M 1.43M 1.43M 1.44M 1.44M 1.44M 1.44M 1.44M 1.44M 1.45M 1.45M 1.45M 1.45M 1.53M 1.53M 1.53M 1.57M 1.57M 1.57M 1.57M 1.57M 1.57M 1.58M 1.58M 1.58M 1.58M 1.58M 1.58M 1.59M 1.59M 1.59M 1.59M 1.69M 1.69M 1.69M

27p 270p 56p 560p 5n6 820p 8n2 82p 18p 180p ln8 120p ln2 12p 12n 3n3 33p 330p 2n2 22p 47p 220p 470p 4n7 ln5 6n8 15p 68p 150p 680p 10p 100p In lOn 27p 270p 2n7

470u 47u 220u 22u 2u2 15u lu5 150u 680u 68u 6u8 lOOu lOu lm lu 3u3 330u 33u 4u7 470u 220u 47u 22u 2u2 6u8 lu5 680u 150u 68u 15u lm lOOu lOu lu 330u 33u 3u3

4.17k 417 1.98k 198 19.8 135 13.5 1.35k 6.15k 615 61.5 913 91.3 9.13k 9.13 31.6 3.16k 316 46.2 4.62k 2.16k 462 216 21.6 67.3 14.9 6.73k 1.49k 673 149 10.Ok 1.OOk 100 10.0 3.50k 350 35.0

252

Electronics Calculations Data Handbook

fo 1.72M 1.72M 1.72M 1.73M 1.73M 1.73M 1.74M 1.74M 1.74M 1.76M 1.76M 1.76M 1.76M 1.76M 1.76M 1.87M 1.87M 1.87M 1.87M 1.87M 1.87M 1.90M 1.90M 1.90M 1.90M 1.90M 1.90M 1.93M 1.93M 1.93M 1.93M 1.93M 1.93M 2.07M 2.07M 2.07M 2.07M

C 3n9 39p 390p 18p ln8 180p 56p 560p 5n6 82p 820p 8n2 12p 120p ln2 330p 2n2 3n3 22p 33p 220p 15p 150p 470p ln5 4n7 47p lOp lOOp 680p In 6n8 68p ln8 2n7 18p 27p

L

X

fo

C

L

X

2u2 220u 22u 470u 4u7 47u 150u 15u lu5 lOOu lOu lu 680u 68u 6u8 22u 3u3 2u2 330u 220u 33u 470u 47u 15u 4u7 lu5 150u 680u 68u lOu 6u8 lu lOOu 3u3 2u2 330u 220u

23.8 2.38k 238 5.11k 51.1 511 1.64k 164 16.4 1.10k 110 11.0 7.53k 753 75.3 258 38.7 25.8 3.87k 2.58k 387 5.60k 560 179 56.0 17.9 1.79k 8.25k 825 121 82.5 12.1 1.21k 42.8 28.5 4.28k 2.85k

2.07M 2.07M 2.08M 2.08M 2.08M 2.12M 2.12M 2.12M 2.13M 2.13M 2.13M 2.13M 2.13M 2.26M 2.26M 2.26M 2.26M 2.26M 2.26M 2.29M 2.29M 2.29M 2.32M 2.32M 2.32M 2.32M 2.32M 2.32M 2.34M 2.34M 2.50M 2.50M 2.50M 2.53M 2.53M 2.53M 2.53M

270p 180p 3n9 39p 390p 12p 120p ln2 56p 560p 5n6 82p 820p 33p 330p ln5 3n3 15p 150p 220p 2n2 22p lOp 47p lOOp 470p In 4n7 68p 680p 27p 270p 2n7 12p 18p 180p ln2

22u 33u lu5 150u 15u 470u 47u 4u7 lOOu lOu lu 68u 6u8 150u 15u 3u3 lu5 330u 33u 22u 2u2 220u 470u lOOu 47u lOu 4u7 lu 68u 6u8 150u 15u lu5 330u 220u 22u 3u3

285 428 19.6 1.96k 196 6.26k 626 62.6 1.34k 134 13.4 911 91.1 2.13k 213 46.9 21.3 4.69k 469 316 31.6 3.16k 6.86k 1.46k 686 146 68.6 14.6 1.OOk 100 2.36k 236 23.6 5.24k 3.50k 35O 52.4

Table 10. 1 Frequency constants for LC circuits fo 2.53M 2.53M 2.55M 2.55M 2.55M 2.56M 2.56M 2.58M 2.58M 2.77M 2.77M 2.77M 2.77M 2.77M 2.77M 2.77M 2.77M 2.77M 2.77M 2.77M 2.77M 2.82M 2.82M 2.82M 2.82M 3.06M 3.06M 3.06M 3.06M 3.06M 3.06M 3.06M 3.06M 3.09M 3.09M 3.10M 3.10M

ln8 120p 39p 390p 3n9 82p 820p 56p 560p 2n2 22p 150p 220p ln5 3n3 lOp 15p 33p 100p 330p In 47p 68p 470p 680p 820p 82p 18p 27p 180p 270p ln8 2n7 39p 390p 12p ln2

2u2 33u lOOu lOu lu 47u 4u7 68u 6u8 lu5 150u 22u 15u 2u2 lu 330u 220u lOOu 33u lOu 3u3 68u 47u 6u8 4u7 3u3 33u 150u lOOu 15u lOu lu5 lu 68u 6u8 220u 2u2

253

X

fo

C

L

X

35.0 524 1.60k 160 16.0 757 75.7 1.10k 110 26.1 2.61k 383 261 38.3 17.4 5.74k 3.83k 1.74k 574 174 57.4 1.20k 831 120 83.1 63.4 634 2.89k 1.92k 289 192 28.9 19.2 1.32k 132 4.28k 42.8

3.10M 3.10M 3.10M 3.36M 3.36M 3.36M 3.36M 3.36M 3.36M 3.36M 3.39M 3.39M 3.39M 3.39M 3.39M 3.39M 3.39M 3.39M 3.70M 3.70M 3.71M 3.71M 3.72M 3.72M 3.75M 3.75M 3.75M 3.75M 3.75M 3.75M 3.75M 3.75M 4.04M 4.04M 4.04M 4.04M 4.11M

120p 56p 560p 150p ln5 15p 33p 330p 680p 68p 47p 470p lOp 22p lOOp 220p In 2n2 56p 560p 27p 270p 39p 390p 820p 82p ln2 12p 18p 120p 180p ln8 33p 330p 470p 47p lOp

22u 47u 4u7 15u lu5 150u 68u 6u8 3u3 33u 47u 4u7 220u lOOu 22u lOu 2u2 lu 33u 3u3 68u 6u8 47u 4u7 2u2 22u lu5 150u lOOu 15u lOu lu 47u 4u7 3u3 33u 150u

428 916 91.6 316 31.6 3.16k 1.44k 144 69.7 697 1.OOk 100 4.69k 2.13k 469 213 46.9 21.3 768 76.8 1.59k 159 1.10k 110 51.8 518 35.4 3.54k 2.36k 354 236 23.6 1.19k 119 83.8 838 3.87k

254

Electronics Calculations Data Handbook

fo

C

L

X

fo

C

L

X

4.11M 4.11M 4.11M 4.11M 4.11M 4.11M 4.11M 4.11M 4.11M 4.44M 4.44M 4.47M 4.47M 4.53M 4.53M 4.54M 4.54M 4.55M 4.55M 4.59M 4.59M 4.59M 4.82M 4.82M 4.95M 4.95M 4.95M 4.95M 4.98M 4.98M 4.98M 4.98M 5.03M 5.03M 5.03M 5.33M 5.33M

15p lOOp 150p In ln5 22p 68p 220p 680p 39p 390p 27p 270p 56p 560p 82p 820p 18p 180p 12p 120p ln2 33p 330p 22p 47p 220p 470p 15p 68p 150p 680p 10p lOOp In 270p 27p

lOOu 15u lOu lu5 lu 68u 22u 6u8 2u2 33u 3u3 47u 4u7 22u 2u2 15u lu5 68u 6u8 lOOu lOu lu 33u 3u3 47u 22u 4u7 2u2 68u 15u 6u8 lu5 lOOu lOu lu 3u3 33u

2.58k 387 258 38.7 25.8 1.76k 569 176 56.9 920 92.0 1.32k 132 627 62.7 428 42.8 1.94k 194 2.89k 289 28.9 1.OOk 100 1.46k 684 146 68.4 2.13k 470 213 47.0 3.16k 316 31.6 111 1.11k

5.43M 5.43M 5.47M 5.47M 5.49M 5.49M 5.56M 5.56M 5.57M 5.57M 5.91M 5.91M 5.91M 5.91M 5.99M 5.99M 5.99M 5.99M 6.10M 6.10M 6.10M 6.10M 6.53M 6.53M 6.53M 6.53M 6.58M 6.58M 6.70M 6.70M 6.73M 6.73M 6.74M 7.15M 7.15M 7.15M 7.15M

39p 390p 18p 180p 56p 560p 82p 820p 12p 120p 22p 33p 220p 330p 15p 47p 150p 470p lOp 100p 68p 680p 27p 180p 270p 18p 39p 390p 120p 12p 56p 560p 82p 150p 330p 33p 15p

22u 2u2 47u 4u7 15u lu5 lOu lu 68u 6u8 33u 22u 3u3 2u2 47u 15u 4u7 lu5 68u 6u8 lOu lu 22u 3u3 2u2 33u 15u lu5 4u7 47u lOu lu 6u8 3u3 lu5 15u 33u

751 75.1 1.62k 162 518 51.8 349 34.9 2.38k 238 1.22k 816 122 81.6 1.77k 565 177 56.5 2.61k 261 383 38.3 903 135 90.3 1.35k 620 62.0 198 1.98k 423 42.3 288 148 67.4 674 1.48k

Table 10.1 Frequency constants for LC circuits

255

fo

C

L

X

fo

C

L

X

7.23M 7.23M 7.34M 7.34M 7.34M 7.34M 7.40M 7.91M 7.91M 8.00M 8.00M 8.00M 8.00M 8.06M 8.06M 8.11M 8.16M 8.76M 8.76M 8.76M 8.76M 8.76M 8.76M 8.76M 8.76M 8.90M 8.90M 9.68M 9.69M 9.69M 9.69M 9.69M 9.77M 9.80M 9.80M 9.81M lO.6M

22p 220p lOp 47p lOOp 470p 68p 27p 270p 18p 120p 180p 12p 39p 390p 82p 56p 22p 100p 150p 220p lOp 15p 33p 330p 47p 68p 82p 18p 180p 27p 270p 39p 12p 120p 56p 150p

22u 2u2 47u lOu 4u7 lu 6u8 15u lu5 22u 3u3 2u2 33u lOu lu 4u7 6u8 15u 3u3 2u2 lu5 33u 22u lOu lu 6u8 4u7 3u3 15u lu5 lOu lu 6u8 22u 2u2 4u7 lu5

1.OOk 100 2.17k 461 217 46.1 316 745 74.5 1.11k 166 111 1.66k 506 50.6 239 348 826 182 121 82.6 1.82k 1.21k 550 55.0 380 263 201 913 91.3 609 60.9 418 1.35k 135 290 100

10.6M lO.6M 10.6M lO.7M lO.7M 10.7M 10.7M lO.7M ll.7M ll.7M ll.8M ll.8M ll.9M ll.9M ll.9M ll.9M 12.8M 12.8M 13.0M 13.0M 13.0M 13.0M 13.0M 13.0M 14.0M 14.1M 14.3M 14.4M 14.4M 14.5M 14.5M 15.3M 15.7M 15.7M 15.8M 15.8M 15.9M

15p 33p 68p 47p 10p 22p lOOp 220p 56p 27p 39p 82p 12p 18p 120p 180p 33p 47p 10p 15p 100p 150p 22p 68p 39p 27p 56p 82p 18p 12p 120p 33p 22p 47p 15p 68p lOp

15u 6u8 3u3 4u7 22u lOu 2u2 lu 3u3 6u8 4u7 2u2 15u lOu lu5 lu 4u7 3u3 15u lOu lu5 lu 6u8 2u2 3u3 4u7 2u2 lu5 6u8 lOu lu 3u3 4u7 2u2 6u8 lu5 lOu

1.OOk 454 220 316 1.48k 674 148 67.4 243 502 347 164 1.12k 745 112 74.5 377 265 1.22k 816 122 81.6 556 180 291 417 198 135 615 913 91.3 316 462 216 673 149 1.OOk

256

Electronics Calculations Data Handbook

fo

C

L

X

fo

C

15.9M 16.9M 17.2M 17.3M 17.4M 17.6M 17.6M 18.7M 18.7M 19.0M 19.0M 19.3M 19.3M 20.7M 20.7M 20.8M 21.2M 21.3M 22.6M 22.6M 22.9M 23.2M

lOOp 27p 39p 18p 56p 82p 12p 22p 33p 15p 47p 10p 68p 18p 27p 39p 12p 56p 15p 33p 22p 10p

lu 3u3 2u2 4u7 lu5 lu 6u8 3u3 2u2 4u7 lu5 6u8 lu 3u3 2u2 lu5 4u7 lu 3u3 lu5 2u2 4u7

100 350 238 511 164 110 753 387 258 560 179 825 121 428 285 196 626 134 469 213 316 686

23.2M 25.0M 25.3M 25.3M 25.5M 27.7M 27.7M 27.7M 27.7M 30.6M 30.6M 31.OM 33.6M 33.9M 33.9M 37.5M 37.5M 41.1M 41.1M 45.9M 50.3M

47p 27p 12p 18p 39p lOp 15p 22p 33p 18p 27p 12p 15p lOp 22p 12p 18p 10p 15p 12p 10p

! X lu

lu5 3u3 2u2 lu 3u3 2u2 lu5 lu lu5 lu 2u2 lu5 2u2 lu lu5 lu lu5 lu lu lu

146 236 524 350 160 574 383 261 174 289 192 428 316 469 213 354 236 387 258 289 316

Part Four 0 perational Amplifier Circuits

This Page Intentionally Left Blank

11 Amplifier gains Introduction Operational amplifiers, or op-amps, are perhaps the most common building blocks found in analogue circuits. They can be used to create amplification stages very easily, and many other types of circuit besides. There are very many 'opamp cookbooks' around that give lots of these circuits, so we won't add to them here. The main purpose of this chapter is to present you with a pair of tables to enable easy selection of resistor values for any desired gain. We'll take a moment, however, to state the two rules that govern an op-amp's behaviour for the purpose of achieving a first-off analysis of their circuits: 1. The input terminals ofop-amps draw no current. 2. The output of the op-amp does whatever it can to keep the voltage between the input terminals at zero. These two statements are something of a generalization, but they are fine if you want to work out what an op-amp circuit is doing. There are two common ways to use op-amps as amplifier stages. We look at them next.

Inverting op-amp Figure 11.1shows a basic inverting op-amp circuit. This circuit can be used to give either attenuation or gain with two resistors. The output is in antiphase with the input. The gain is given by:

R2

Av = R--~

(11.1)

Values of R1 and R2 can be found fromTable 11.1, where gain is given both as a ratio and in dBs. R1 and R2 may, of course, be scaled by factors of 10 without affecting the gain. The Table only shows values above unity gain (0 dB). If you need to select a pair of resistors to give attenuation, then the Table can still be used, but the positions of R1 and R2 should be switched. The dB column then reads attenuation directly, or the Av column the reciprocal of gain expressed as a ratio.

260

Electronics Calculations Data Handbook R=

Vl

UT

Figure 11.1 Inverting op-amp The input resistance of the circuit is equal to the value of the input resistor, R1. The output resistance is, for practical purposes, negligible. (Limitations on its ability to drive a load will be dependent on maximum values of output current, voltage swing and slew rate, for which the manufacturer's data on the chip used should be consulted.) It is sometimes desirable to limit the frequency response of the circuit. The standard method is to add suitable value capacitors, as in Figure 11.2. C1, in series with the input resistor, limits low frequency response, while C2, in parallel with R2, limits high frequency response. Each gives a 6 dB/octave slope, as for the first order LPF and HPF described in Chapter 9. The equations for the lower-3 dB point,ft_, and the upper-3 dB point,ft+, are also similar: 1

1

f t - = 27rR1C1 and ft+ = 2~rR2C2

(11.2a)

Example 11.1: give suitable values for an inverting op-amp circuit with a gain of 15 dB, and an input resistance of between 20k and 30k. Determine suitable values for (71 and C2 to make the upper and lower-3 dB points as near as possible to 100 Hz and 15 kHz respectively, using standard El2 capacitors. Table 11.1gives many combinations, close to 15 dB, but to meet the requirement for input resistance R1 should be between 20k and 30k. We take the pair 2k7/15k, and multiply by 10, so that R1 - 27k and R2 - 150k. To find values for C1 and C2, we transpose Eqn (ll.2a): C = and get: 1.

1

2~ftR

(11.2b)

59 nF (ideal) - nearest is 56 nF, substitute back into Eqn (11.2) to get ft- = 105 Hz 2. C2 - 71 pF (ideal) - nearest is 68 pF, giving ft+ - 15.6 kHz C1 -

c~

Ampfifier gains

261

c, R

o--,......-

V?

I----

----I"Voo,

Figure 11.2 Inverting op-amp with restricted bandwidth

Non-inverting op-amp Figure 11.3 shows a non-inverting op-amp circuit, in its most basic configuration. This circuit has a gain as follows: Av =

Rl + R 2 Rl

(11.3)

This means that the circuit can only provide gain of greater than 1. Its input impedance is very large, and is not usually taken into account. As with the inverting op-amp, its output impedance is very low, with the same restrictions on output drive applying (Figure 11.4). Where it is desired to restrict the bandwidth of the stage, capacitors CI and C2 are added. The calculations are identical to those for the inverting stage. Note that with C1 in this position the input signal must have some defined DC level. If the input is connected using a DC block capacitor then Cl must be omitted so that the op-amp has a DC reference. If it is desired to limit the low frequency response of the stage it is sometimes better to connect the input via a suitable high-pass filter, as described in Chapter 9.

262

Electronics Calculations Data Handbook

i

--L

VIN

O

i

VOUT

|i

Figure 11.3 Non-inverting op-amp

1_

/\

V,N R1

/\

II

Voo~

c,

Figure 11.4 Non-inverting op-amp with restricted bandwidth The main advantage of this stage (other than its being non-inverting) is that of its input impedance. It makes an ideal buffer stage, after circuits which are sensitive to load impedance (such as the reactive circuits described in Part Two). Where it is desired to use this circuit without gain, purely as a buffer stage, it is customary to omit R1 and make R2 short circuit-i.e, to link the output terminal to the inverting input terminal, as in Figure 11.5.This is a'voltage follower'. The output is identical to the input, but comes from a very low source impedance.

Amplifier gains

263

c

I Figure 11.5 A voltage follower Values for R1 and R 2 for the non-inverting amplifier can be selected using Table 8.1, in the 'Voltage dividers' chapter. The dB column gives values of gain directly, and the A column values of the reciprocal of gain as a ratio. R1 from the table should be fitted as position R2 from Figure 11.3 and R2 as R1. As usual, Rl and R2 can be scaled by factors of 10 if desired.

Table 11.1 Inverting op-amp gains Av 1.07 1.08 1.08 1.09 1.09 1.09 1.09 1.09 1.09 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.11 1.11 1.11 1.11 1.13 1.13 1.15 1.18 1.18 1.19 1.19 1.19 1.20 1.20 1.20 1.20 1.21 1.21 1.21

dB

R1

R2

00.56 00.70 00.70 00.71 00.76 00.76 00.76 00.77 00.78 00.80 00.81 00.82 00.83 00.83 00.83 00.85 00.85 00.88 00.90 00.92 00.92 01.02 01.02 01.24 01.45 01.45 01.48 01.52 01.54 01.58 01.58 01.58 01.58 01.62 01.63 01.65

lk5 lk2 3k6 4k7 lkl 2k2 3k3 4k3 7k5 6k2 5kl 9kl lk 2k 3k 3k9 6k8 5k6 8k2 lk8 2k7 lk6 2k4 lk3 lkl 3k3 4k3 4k7 3k6 lk 2k lk5 3k 3k9 6k8 9kl

lk6 lk3 3k9 5kl lk2 2k4 3k6 4k7 8k2 6k8 5k6 10k lkl 2k2 3k3 4k3 7k5 6k2 9kl 2k 3k lk8 2k7 lk5 lk3 3k9 5kl 5k6 4k3 lk2 2k4 lk8 3k6 4k7 8k2 Ilk

Av 1.21 1.21 1.21 1.22 1.22 1.22 1.22 1.23 1.23 1.25 1.25 1.25 1.30 1.30 1.30 1.30 1.31 1.31 1.32 1.32 1.32 1.33 1.33 1.33 1.33 1.33 1.33 1.34 1.34 1.34 1.35 1.36 1.36 1.38 1.38 1.38

dB

R1

R2

01.65 01.68 01.69 01.70 01.72 01.74 01.74 01.78 01.80 01.94 01.94 01.94 02.28 02.28 02.29 02.30 02.32 02.33 02.40 02.41 02.43 O2.50 02.50 02.5O 02.50 02.50 02.50 02.53 02.54 02.55 02.61 02.69 02.69 02.77 02.77 02.83

6k2 7k5 5k6 5kl 8k2 lk8 2k7 2k2 lk3 lk2 lk6 2k4 lk 3k 4k3 3k3 3k6 3k9 9kl 4k7 6k2 lk8 7k5 lk2 lk5 2k7 5kl 6k8 5k6 8k2 2k lkl 2k2 lk6 2k4 lk3

7k5 9kl 6k8 6k2 10k 2k2 3k3 2k7 lk6 lk5 2k 3k lk3 3k9 5k6 4k3 4k7 5kl 12k 6k2 8k2 2k4 10k lk6 2k 3k6 6k8 9kl 7k5 llk 2k7 lk5 3k 2k2 3k3 lk8

Table 11.1 Inverting op-amp gains 265 Av 1.42 1.42 1.43 1.43 1.44 1.44 1.44 1.45 1.45 1.46 1.46 1.47 1.47 1.47 1.47 1.47 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.54 1.55 1.56 1.57 1.58 1.59 1.59 1.59 1.60 1.60 1.60 1.60 1.61 1.61

dB

R1

R2

03.03 03.07 03.10 03.13 03.14 03.18 03.19 03.21 03.25 03.31 03.31 03.33 03.33 03.33 03.35 03.35 03.52 03.52 03.52 03.52 03.52 03.52 03.52 03.74 03.78 03.84 03.90 03.98 04.0O 04.03 04.04 04.06 04.08 04.08 04.08 04.12 04.15

3k6 3k3 9kl 3k 3k9 4k3 2k7 4k7 lkl 8k2 5k6 lk5 7k5 6k2 5kl 6k8 lk lk2 lk6 lk8 2k 2k2 2k4 lk3 3k3 3k6 3k 4k3 8k2 3k9 2k7 4k7 lk lk5 7k5 5kl 6k2

5kl 4k7 13k 4k3 5k6 6k2 3k9 6k8 lk6 12k 8k2 2k2 llk 9kl 7k5 10k lk5 lk8 2k4 2k7 3k 3k3 3k6 2k 5kl 5k6 4k7 6k8 13k 6k2 4k3 7k5 lk6 2k4 12k 8k2 10k

Av 1.62 1.63 1.63 1.64 1.64 1.65 1.65 1.67 1.67 1.69 1.69 1.70 1.70 1.72 1.73 1.74 1.74 1.74 1.74 1.76 1.76 1.77 1.77 1.78 1.79 1.79 1.80 1.80 1.80 1.82 1.83 1.83 1.83 1.85 1.87 1.88 1.88

dB

R1

R2

04.18 O4.22 04.22 04.28 04.28 04.34 04.35 04.44 04.44 04.54 04.57 04.59 04.61 04.72 04.78 04.81 04.83 04.83 04.83 04.90 04.93 04.97 04.98 05.03 05.04 05.07 05.11 05.11 05.11 05.19 05.25 05.26 05.26 05.33 05.42 05.46 05.48

6k8 2k4 5k6 lkl 2k2 9kl 2k lk2 lk8 lk6 lk3 3k3 3k 3k6 7k5 2k7 3k9 4k3 4k7 9kl 6k8 2k2 6k2 5kl 5k6 2k4 lk lk5 2k lkl 8k2 lk2 lk8 lk3 3k lk6 3k3

llk 3k9 9kl lk8 3k6 15k 3k3 2k 3k 2k7 2k2 5k6 5kl 6k2 13k 4k7 6k8 7k5 8k2 16k 12k 3k9 llk 9kl 10k 4k3 lk8 2k7 3k6 2k 15k 2k2 3k3 2k4 5k6 3k 6k2

Electronics Calculations Data Handbook

266 Av

1.89 1.89 1.91 1.91 1.92 1.94 1.94 1.95 1.95 1.95 1.96 1.96 1.96 1.98 2.00 2.00 2.00 2.00 2.00 2.00 2.06 2.06 2.07 2.07 2.08 2.08 2.10 2.10 2.12 2.13 2.13 2.13 2.14 2.14 2.15 2.16 2.17

dB

R1

R2

05.52 05.52 05.61 05.63 05.68 05.74 05.74 05.80 05.81 05.82 05.84 05.85 05.86 05.92 06.02 06.02 06.02 06.02 06.02 06.02 06.28 06.29 06.31 06.34 06.35 06.38 06.43 06.45 06.51 06.55 06.56 06.58 06.59 06.62 06.65 06.68 06.72

2k7 3k6 4k3 6k8 3k9 6k2 4k7 2k 8k2 2k2 2k4 5kl 5k6 9kl lk lkl lk2 lk5 lk8 7k5 3k3 lk6 3k 2k7 lk3 3k6 6k2 3k9 4k3 2k4 4k7 7k5 2k2 5k6 2k 5kl lk8

5kl 6k8 8k2 13k 7k5 12k 9kl 3k9 16k 4k3 4k7 10k llk 18k 2k 2k2 2k4 3k 3k6 15k 6k8 3k3 6k2 5k6 2k7 7k5 13k 8k2 9kl 5kl 10k 16k 4k7 12k 4k3 llk 3k9

Av 2.18 2.20 2.20 2.20 2.20 2.21 2.25 2.25 2.27 2.27 2.28 2.30 2.31 2.32 2.32 2.33 2.33 2.33 2.34 2.35 2.35 2.35 2.39 2.40 2.40 2.40 2.42 2.42 2.44 2.44 2.45 2.48 2.50 2.50 2.52 2.53 2.54

dB

R1

R2

06.78 06.83 06.84 06.85 06.85 06.87 07.04 07.04 07.11 07.13 07.15 07.22 07.26 07.30 07.32 07.33 07.36 07.36 07.39 07.42 07.43 07.43 07.56 07.60 07.60 07.60 07.67 07.67 07.74 07.74 07.80 07.91 07.96 07.96 08.02 08.05 08.09

lkl 8k2 9kl lk lk5 6k8 lk2 lk6 3k 3k3 3k6 2k7 lk3 2k2 5k6 4k3 2k4 3k9 4k7 2k 5kl 6k8 lk8 lk 7k5 lk5 9kl 6k2 lk6 8k2 lkl 3k3 lk2 3k 2k7 3k6 lk3

2k4 18k 20k 2k2 3k3 15k 2k7 3k6 6k8 7k5 8k2 6k2 3k 5kl 13k 10k 5k6 9kl llk 4k7 12k 16k 4k3 2k4 18k 3k6 22k 15k 3k9 20k 2k7 8k2 3k 7k5 6k8 9kl 3k3

Table 11.1 Inverting op-amp gains 267 Av 2.55 2.55 2.55 2.55 2.56 2.56 2.58 2.58 2.6O 2.61 2.64 2.65 2.67 2.68 2.68 2.69 2.70 2.73 2.73 2.75 2.76 2.77 2.77 2.78 2.78 2.79 2.80 2.82 2.82 2.83 2.83 2.86 2.87 2.90 2.93 2.93 2.94

dB

R1

R2

08.12 08.13 08.13 08.14 08.16 08.18 08.23 08.24 08.30 08.34 08.42 08.46 08.52 08.56 08.57 08.59 08.63 08.71 08.73 08.79 08.81 08.84 08.85 08.87 08.87 08.91 08.94 09.00 09.01 09.05 09.05 09.12 09.15 09.26 09.33 09.35 09.36

2k2 5kl 2k 4k7 4k3 3k9 6k2 2k4 lk5 lk8 9kl 6k8 7k5 5k6 8k2 lk6 lk lkl 3k lk2 3k3 4k7 lk3 2k7 3k6 4k3 2k 2k2 3k9 lk8 2k4 5k6 lk5 6k2 8k2 7k5 lk6

5k6 13k 5kl 12k Ilk 10k 16k 6k2 3k9 4k7 24k 18k 20k 15k 22k 4k3 2k7 3k 8k2 3k3 9kl 13k 3k6 7k5 10k 12k 5k6 6k2 llk 5kl 6k8 16k 4k3 18k 24k 22k 4k7

Av 2.94 2.94 2.97 3.00 3.00 3.00 3.00 3.02 3.03 3.03 3.04 3.06 3.08 3.09 3.10 3.11 3.13 3.13 3.14 3.19 3.19 3.20 3.21 3.23 3.24 3.25 3.27 3.29 3.30 3.30 3.31 3.33 3.33 3.33 3.33 3.37 3.40

dB

R1

R2

09.37 09.37 09.45 09.54 09.54 09.54 09.54 09.61 09.63 09.64 09.65 09.70 09.76 09.80 09.83 09.86 09.90 09.92 09.93 10.07 10.08 10.10 10.14 10.17 10.20 10.24 10.30 10.35 10.36 10.37 10.39 10.46 10.46 10.46 10.46 10.55 10.63

5kl 6k8 9kl lk lkl lk2 lk3 4k3 3k3 3k 2k7 3k6 3k9 2k2 2k lk8 2k4 lk5 5kl lk6 4k7 7k5 5k6 6k2 6k8 lk2 lkl 8k2 9kl lk lk3 3k 3k3 3k6 3k9 2k7 lk5

15k 20k 27k 3k 3k3 3k6 3k9 13k 10k 9kl 8k2 llk 12k 6k8 6k2 5k6 7k5 4k7 16k 5kl 15k 24k 18k 20k 22k 3k9 3k6 27k 30k 3k3 4k3 10k llk 12k 13k 9kl 5kl

Electronics Calculations Data Handbook

268 Av

3.40 3.40 3.41 3.42 3.44 3.49 3.50 3.53 3.53 3.55 3.55 3.57 3.58 3.60 3.60 3.61 3.62 3.63 3.64 3.66 3.67 3.70 3.72 3.73 3.73 3.75 3.78 3.79 3.83 3.85 3.87 3.88 3.90 3.91 3.92 3.92 3.92

dB 10.63 10.64 10.65 10.67 10.74 10.85 10.88 10.95 10.95 10.99 11.00 11.06 11.09 11.13 11.13 11.15 11.16 11.19 11.21 11.27 11.29 11.37 11.41 11.43 11.44 11.48 11.54 11.58 11.66 11.70 11.76 11.77 11.82 11.84 11.86 11.87 11.87

R1

R2

2k 4k7 2k2 2k4 lk8 4k3 lk6 5kl 6k8 lkl 6k2 5k6 lk2 lk 7k5 3k6 lk3 9kl 3k3 8k2 3k 2k7 4k3 2k2 lk5 2k lk8 2k4 4k7 3k9 6k2 lk6 lk lkl lk2 5kl lk3

6k8 16k 7k5 8k2 6k2 15k 5k6 18k 24k 3k9 22k 20k 4k3 3k6 27k 13k 4k7 33k 12k 30k llk 10k 16k 8k2 5k6 7k5 6k8 9kl 18k 15k 24k 6k2 3k9 4k3 4k7 20k 5kl

Av 3.93 3.94 3.96 3.97 4.00 4.00 4.02 4.07 4.10 4.10 4.13 4.14 4.17 4.17 4.17 4.19 4.25 4.25 4.26 4.27 4.29 4.29 4.30 4.31 4.31 4.33 4.35 4.39 4.40 4.41 4.44 4.44 4.53 4.55 4.55 4.55 4.56

dB 11.88 11.91 11.95 11.98 12.04 12.04 12.09 12.20 12.26 12.26 12.33 12.33 12.40 12.40 12.40 12.44 12.57 12.57 12.58 12.61 12.64 12.64 12.67 12.68 12.70 12.74 12.78 12.85 12.87 12.89 12.96 12.96 13.13 13.15 13.15 13.16 13.17

R1

R2

5k6 3k3 9kl 6k8 3k 7k5 8k2 2k7 2k 3k9 lk5 2k2 lk8 2k4 3k6 4k3 lk2 lk6 4k7 lkl 5k6 9kl lk lk3 5kl 3k 6k2 8k2 7k5 6k8 2k7 3k6 lk5 2k2 3k3 2k lk8

22k 13k 36k 27k 12k 30k 33k llk 8k2 16k 6k2 9kl 7k5 10k 15k 18k 5kl 6k8 20k 4k7 24k 39k 4k3 5k6 22k 13k 27k 36k 33k 30k 12k 16k 6k8 10k 15k 9kl 8k2

Table 11.1 Inverting op-amp gains Av 4.58 4.62 4.64 4.65 4.67 4.68 4.69 4.70 4.71 4.73 4.76 4.77 4.80 4.81 4.82 4.84 4.85 4.85 5.00 5.00 5.00 5.00 5.00 5.00 5.06 5.09 5.10 5.11 5.12 5.13 5.13 5.16 5.17 5.2O 5.23 5.24 5.29

dB 13.22 13.28 13.32 13.35 13.38 13.41 13.42 13.44 13.45 13.49 13.55 13.57 13.62 13.65 13.66 13.69 13.71 13.72 13.98 13.98 13.98 13.98 13.98 13.98 14.08 14.14 14.15 14.16 14.18 14.19 14.20 14.26 14.26 14.32 14.37 14.39 14.48

R1

R2

2k4 3k9 lkl 4k3 lk2 4k7 lk6 lk 5kl 9kl 8k2 lk3 7k5 2k7 5k6 6k2 3k3 6k8 lk5 2k 2k2 2k4 3k 3k6 lk8 lkl lk 4k7 4k3 lk6 3k9 9kl lk2 7k5 lk3 8k2 5kl

Ilk 18k 5kl 20k 5k6 22k 7k5 4k7 24k 43k 39k 6k2 36k 13k 27k 30k 16k 33k 7k5 10k llk 12k 15k 18k 9kl 5k6 5kl 24k 22k 8k2 20k 47k 6k2 39k 6k8 43k 27k

Av 5.29 5.32 5.33 5.36 5.42 5.45 5.45 5.47 5.50 5.56 5.56 5.56 5.58 5.60 5.60 5.64 5.64 5.67 5.69 5.73 5.73 5.74 5.74 5.77 5.81 5.88 5.89 5.91 5.93 6.00 6.00 6.06 6.07 6.11 6.11 6.15 6.15

dB 14.48 14.52 14.54 14.58 14.67 14.74 14.74 14.75 14.81 14.89 14.89 14.89 14.93 14.96 14.97 15.02 15.03 15.07 15.10 15.17 15.17 15.17 15.19 15.22 15.28 15.39 15.41 15.43 15.46 15.56 15.56 15.65 15.66 15.72 1.5.72 15.78 15.78

269

R1

R2

6k8 6k2 3k 5k6 2k4 3k3 2k2 lk5 2k lk8 2k7 3k6 4k3 lk 9kl lkl 3k9 lk2 lk6 8k2 7k5 6k8 4k7 lk3 6k2 5kl 5k6 2k2 2k7 2k 3k 3k3 lk5 lk8 3k6 3k9 9kl

36k 33k 16k 30k 13k 18k 12k 8k2 llk 10k 15k 20k 24k 5k6 51k 6k2 22k 6k8 9kl 47k 43k 39k 27k 7k5 36k 30k 33k 13k 16k 12k 18k 20k 9kl llk 22k 24k 56k

Electronics Calculations Data Handbook

270 Av

6.18 6.20 6.22 6.25 6.25 6.25 6.27 6.28 6.29 6.31 6.32 6.38 6.43 6.47 6.50 6.67 6.67 6.67 6.67 6.67 6.67 6.67 6.80 6.80 6.81 6.82 6.82 6.83 6.83 6.88 6.91 6.92 6.94 6.96 6.98 7.00 7.02

dB 15.82 15.85 15.88 15.92 15.92 15.92 15.94 15.96 15.97 16.00 16.02 16.10 16.16 16.22 16.26 16.48 16.48 16.48 16.48 16.48 16.48 16.48 16.65 16.65 16.67 16.67 16.67 16.69 16.69 16.75 16.79 16.81 16.82 16.86 16.87 16.90 16.93

R1

R2

lkl lk 8k2 lk2 lk6 2k4 7k5 4k3 6k2 lk3 6k8 4k7 5k6 5kl 2k lk5 lk8 2k4 2k7 3k 3k3 3k6 lk 7k5 9kl lkl 2k2 8k2 lk2 lk6 6k8 3k9 6k2 5k6 4k3 lk3 4k7

6k8 6k2 51k 7k5 10k 15k 47k 27k 39k 8k2 43k 30k 36k 33k 13k 10k 12k 16k 18k 20k 22k 24k 6k8 51k 62k 7k5 15k 56k 8k2 llk 47k 27k 43k 39k 30k 9kl 33k

Av 7.06 7.22 7.27 7.27 7.33 7.33 7.41 7.45 7.47 7.47 7.50 7.50 7.50 7.50 7.50 7.50 7.56 7.58 7.58 7.65 7.66 7.67 7.68 7.69 7.69 8.00 8.00 8.00 8.13 8.15 8.18 8.18 8.20 8.23 8.24 8.24 8.27

dB 16.97 17.17 17.23 17.23 17.31 17.31 17.39 17.45 17.46 17.47 17.50 17.50 17.50 17.50 17.50 17.50 17.57 17.59 17.60 17.67 17.68 17.70 17.71 17.72 17.72 18.06 18.06 18.06 18.20 18.22 18.26 18.26 18.28 18.30 18.31 18.32 18.35

R1

R2

5kl lk8 3k3 2k2 lk5 3k 2k7 lkl 7k5 9kl lk lk6 2k 2k4 3k6 6k8 8k2 6k2 lk2 5kl 4k7 4k3 5k6 lk3 3k9 lk5 2k 3k lk6 2k7 2k2 3k3 lk 6k2 6k8 9kl 7k5

36k 13k 24k 16k Ilk 22k 20k 8k2 56k 68k 7k5 12k 15k 18k 27k 51k 62k 47k 9kl 39k 36k 33k 43k 10k 30k 12k 16k 24k 13k 22k 18k 27k 8k2 51k 56k 75k 62k

Table 11.1 Inverting op-amp gains 271 Av 8.27 8.29 8.30 8.33 8.33 8.33 8.33 8.37 8.39 8.43 8.46 8.46 8.67 8.89 8.89 9.00 9.00 9.01 9.03 9.07 9.07 9.09 9.09 9.09 9.10 9.11 9.12 9.15 9.15 9.17 9.17 9.17 9.22 9.23 9.23 9.38 10.0

dB 18.35 18.37 18.38 18.42 18.42 18.42 18.42 18.46 18.48 18.52 18.55 18.55 18.76 18.98 18.98 19.08 19.08 19.10 19.12 19.15 19.15 19.17 19.17 19.17 19.18 19.19 19.20 19.22 19.23 19.24 19.24 19.24 19.29 19.30 19.30 19.44 20.00

R1

R2

lkl 8k2 4k7 lk2 lk8 2k4 3k6 4k3 5k6 5kl lk3 3k9 lk5 lk8 2k7 2k 3k 9kl 6k2 7k5 4k3 lkl 2k2 3k3 lk 5k6 6k8 8k2 4k7 3k6 lk2 2k4 5kl lk3 3k9 lk6 lk

9kl 68k 39k 10k 15k 20k 30k 36k 47k 43k llk 33k 13k 16k 24k 18k 27k 82k 56k 68k 39k 10k 20k 30k 9kl 51k 62k 75k 43k 33k llk 22k 47k 12k 36k 15k 10k

Av 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.7 10.8 10.8 10.9 10.9 10.9 10.9 10.9 10.9 11.0 11.0 11.0 11.0 11.0

dB

R1

R2

20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 2O.O0 20.0O 20.00 20.00 20.00 20.00 20.00 20.00 2O.O0 20.O0 20.00 20.00 20.00 20.56 20.70 20.70 20.71 20.76 20.76 20.76 20.77 20.78 20.80 20.81 20.82 20.82 20.83

lkl lk2 lk3 lk5 lk6 lk8 2k 2k2 2k4 2k7 3k 3k3 3k6 3k9 4k3 4k7 5kl 5k6 6k2 6k8 7k5 8k2 9kl lk5 lk2 3k6 4k7 3k3 lkl 2k2 4k3 7k5 6k2 5kl 9kl 910R lk

llk 12k 13k 15k 16k 18k 20k 22k 24k 27k 30k 33k 36k 39k 43k 47k 51k 56k 62k 68k 75k 82k 91k 16k 13k 39k 51k 36k 12k 24k 47k 82k 68k 56k 100k 10k llk

272

Electronics Calculations Data Handbook

Av 11.0 11.0 11.0 11.0 11.1 11.1 11.1 11.1 11.3 11.3 11.5 11.8 11.8 11.9 11.9 11.9 12.0 12.0 12.0 12.0 12.1 12.1 12.1 12.1 12.1 12.1 12.2 12.2 12.2 12.2 12.2 12.3 12.3 12.5 12.5 12.5 13.0

dB

R1

R2

20.83 20.83 20.85 20.85 20.88 20.90 20.92 20.92 21.02 21.02 21.24 21.45 21.45 21.48 21.52 21.54 21.58 21.58 21.58 21.58 21.62 21.63 21.65 21.65 21.68 21.69 21.70 21.72 21.72 21.74 21.74 21.78 21.80 21.94 21.94 21.94 22.28

2k 3k 3k9 6k8 5k6 8k2 lk8 2k7 lk6 2k4 lk3 lkl 3k3 4k3 4k7 3k6 lk lk5 2k 3k 3k9 6k8 910R 6k2 7k5 5k6 5kl 8k2 820R lk8 2k7 2k2 lk3 lk2 lk6 2k4 lk

22k 33k 43k 75k 62k 91k 20k 30k 18k 27k 15k 13k 39k 51k 56k 43k 12k 18k 24k 36k 47k 82k llk 75k 91k 68k 62k 100k 10k 22k 33k 27k 16k 15k 20k 30k 13k

Av 13.0 13.0 13.0 13.1 13.1 13.2 13.2 13.2 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.4 13.4 13.4 13.5 13.6 13.6 13.8 13.8 13.8 14.2 14.2 14.3 14.3 14.4 14.4 14.4 14.5 14.5 14.6 14.6 14.7 14.7

dB

R1

R2

22.28 22.29 22.30 22.32 22.33 22.40 22.41 22.43 22.50 22.50 22.50 22.50 22.50 22.50 22.50 22.53 22.54 22.55 22.61 22.69 22.69 22.77 22.77 22.83 23.03 23.07 23.10 23.13 23.14 23.18 23.19 23.21 23.25 23.31 23.31 23.33 23.33

3k 4k3 3k3 3k6 3k9 910R 4k7 6k2 lk2 lk5 lk8 2k7 5kl 7k5 750R 6k8 5k6 820R 2k lkl 2k2 lk6 2k4 lk3 3k6 3k3 910R 3k 3k9 4k3 2k7 4k7 lkl 820R 5k6 lk5 750R

39k 56k 43k 47k 51k 12k 62k 82k 16k 20k 24k 36k 68k 100k 10k 91k 75k llk 27k 15k 30k 22k 33k 18k 51k 47k 13k 43k 56k 62k 39k 68k 16k 12k 82k 22k llk

Table 11.1 Inverting op-amp gains 273 Av 14.7 14.7 14.7 14.7 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.4 15.5 15.6 15.7 15.8 15.9 15.9 15.9 16.0 16.0 16.0 16.0 16.1 16.1 16.1 16.2 16.3 16.3 16.4 16.4 16.5 16.5 16.7 16.7 16.9 16.9

dB

R1

R2

23.33 23.35 23.35 23.35 23.52 23.52 23.52 23.52 23.52 23.52 23.52 23.74 23.78 23.84 23.90 23.98 24.00 24.03 24.04 24.06 24.08 24.08 24.08 24.12 24.15 24.15 24.18 24.22 24.22 24.28 24.28 24.34 24.35 24.44 24.44 24.54 24.57

6k2 5kl 6k8 680R lk lk2 lk6 lk8 2k 2k2 2k4 lk3 3k3 3k6 3k 4k3 820R 3k9 2k7 4k7 lk lk5 750R 5kl 6k2 620R 680R 2k4 5k6 lkl 2k2 910R 2k lk2 lk8 lk6 lk3

91k 75k 100k 10k 15k 18k 24k 27k 30k 33k 36k 20k 51k 56k 47k 68k 13k 62k 43k 75k 16k 24k 12k 82k 100k 10k llk 39k 91k 18k 36k 15k 33k 20k 30k 27k 22k

Av 17.0 17.0 17.2 17.3 17.4 17.4 17.4 17.4 17.6 17.6 17.7 17.7 17.8 17.9 17.9 17.9 18.0 18.0 18.0 18.2 18.3 18.3 18.3 18.5 18.7 18.8 18.8 18.9 18.9 19.1 19.1 19.2 19.4 19.4 19.5 19.5 19.5

dB

R1

R2

24.59 24.61 24.72 24.78 24.81 24.83 24.83 24.83 24.90 24.93 24.97 24.98 25.03 25.04 25.04 25.07 25.11 25.11 25.11 25.19 25.25 25.26 25.26 25.33 25.42 25.46 25.48 25.52 25.52 25.61 25.63 25.68 25.74 25.74 25.80 25.81 25.82

3k3 3k 3k6 750R 2k7 3k9 4k3 4k7 910R 680R 2k2 620R 5kl 5k6 560R 2k4 lk lk5 2k lkl 820R lk8 lk2 lk3 3k lk6 3k3 3k6 2k7 4k3 680R 3k9 620R 4k7 2k 820R 2k2

56k 51k 62k 13k 47k 68k 75k 82k 16k 12k 39k llk 91k 100k 10k 43k 18k 27k 36k 20k 15k 33k 22k 24k 56k 30k 62k 68k 51k 82k 13k 75k 12k 91k 39k 16k 43k

274

Electronics Calculations Data Handbook

Av 19.6 19.6 19.6 19.6 19.8 20.0 20.0 2O.0 20.0 20.0 20.0 20.6 20.6 20.7 20.7 20.8 20.8 21.0 21.0 21.2 21.3 21.3 21.3 21.3 21.4 21.4 21.5 21.6 21.7 21.8 22.0 22.0 22.0 22.0 22.1 22.5 22.5

dB

R1

R2

25.84 25.85 25.85 25.86 25.92 26.02 26.02 26.O2 26.02 26.02 26.02 26.28 26.29 26.31 26.34 26.35 26.38 26.43 26.45 26.51 26.55 26.56 26.56 26.58 26.59 26.62 26.65 26.68 26.72 26.78 26.83 26.84 26.85 26.85 26.87 27.04 27.04

2k4 510R 5kl 560R 910R lk lkl lk2 lk5 lk8 750R 3k3 lk6 3k 2k7 lk3 3k6 620R 3k9 4k3 2k4 470R 4k7 750R 2k2 560R 2k 510R lk8 lkl 820R 910R lk lk5 680R lk2 lk6

47k 10k 100k llk 18k 20k 22k 24k 30k 36k 15k 68k 33k 62k 56k 27k 75k 13k 82k 91k 51k 10k 100k 16k 47k 12k 43k llk 39k 24k 18k 20k 22k 33k 15k 27k 36k

Av 22.7 22.7 22.8 23.0 23.1 23.2 23.2 23.3 23.3 23.3 23.3 23.4 23.5 23.5 23.5 23.9 24.0 24.0 24.0 24.2 24.2 24.4 24.4 24.5 24.8 25.0 25.0 25.2 25.3 25.4 25.5 25.5 25.5 25.5 25.6 25.6 25.6

dB

R1

R2

27.11 27.13 27.15 27.22 27.26 27.30 27.32 27.33 27.33 27.36 27.36 27.39 27.42 27.43 27.43 27.56 27.60 27.60 27.60 27.67 27.67 27.74 27.74 27.80 27.91 27.96 27.96 28.02 28.O5 28.09 28.12 28.13 28.13 28.14 28.16 28.18 28.18

3k 3k3 3k6 2k7 lk3 2k2 560R 430R 4k3 3k9 2k4 470R 2k 510R 680R lk8 lk lk5 750R 910R 620R lk6 820R lkl 3k3 lk2 3k 2k7 3k6 lk3 2k2 510R 2k 470R 430R 3k9 390R

68k 75k 82k 62k 30k 51k 13k 10k 100k 91k 56k llk 47k 12k 16k 43k 24k 36k 18k 22k 15k 39k 20k 27k 82k 30k 75k 68k 91k 33k 56k 13k 51k 12k llk 100k 10k

Table 11.1 Inverting op-amp gains 275 Av 25.8 25.8 26.0 26.1 26.4 26.5 26.7 26.8 26.8 26.9 27.0 27.3 27.3 27.5 27.6 27.7 27.7 27.8 27.8 27.8 27.9 28.0 28.2 28.2 28.3 28.3 28.6 28.7 29.0 29.3 29.3 29.4 29.4 29.4 29.7 30.0 30.0

dB

R1

R2

28.23 28.24 28.30 28.34 28.42 28.46 28.52 28.56 28.57 28.59 28.63 28.71 28.73 28.79 28.81 28.84 28.85 28.87 28.87 28.87 28.91 28.94 29.00 29.01 29.05 29.05 29.12 29.15 29.26 29.33 29.35 29.36 29.37 29.37 29.45 29.54 29.54

620R 2k4 lk5 lk8 910R 680R 750R 560R 820R lk6 lk lkl 3k lk2 3k3 470R lk3 2k7 3k6 360R 430R 2k 2k2 390R lk8 2k4 560R lk5 620R 820R 750R lk6 510R 680R 910R lk lkl

16k 62k 39k 47k 24k 18k 20k 15k 22k 43k 27k 30k 82k 33k 91k 13k 36k 75k 100k 10k 12k 56k 62k llk 51k 68k 16k 43k 18k 24k 22k 47k 15k 20k 27k 30k 33k

Av 30.0 30.0 30.2 30.3 30.3 30.3 30.4 30.6 30.8 30.9 31.0 31.1 31.3 31.3 31.4 31.9 31.9 32.0 32.1 32.3 32.4 32.5 32.7 32.9 33.0 33.0 33.1 33.3 33.3 33.3 33.3 33.3 33.7 34.0 34.0 34.0 34.1

dB

R1

R2

29.54 29.54 29.61 29.63 29.63 29.64 29.65 29.70 29.76 29.80 29.83 29.86 29.90 29.92 29.93 30.07 30.08 30.10 30.14 30.17 30.20 30.24 30.30 30.35 30.36 30.37 30.39 30.46 30.46 30.46 30.46 30.46 30.55 30.63 30.63 30.64 30.65

lk2 lk3 430R 3k3 330R 3k 2k7 360R 390R 2k2 2k lk8 2k4 lk5 510R lk6 470R 750R 560R 620R 680R lk2 lkl 820R 910R lk lk3 3k 300R 330R 360R 390R 2k7 lk5 2k 470R 2k2

36k 39k 13k 100k 10k 91k 82k llk 12k 68k 62k 56k 75k 47k 16k 51k 15k 24k 18k 20k 22k 39k 36k 27k 30k 33k 43k 100k 10k llk 12k 13k 91k 51k 68k 16k 75k

276

Electronics Calculations Data Handbook

Av 34.2 34.4 34.9 35.0 35.3 35.3 35.5 35.5 35.7 35.8 36.0 36.0 36.1 36.2 36.3 36.4 36.6 36.7 37.0 37.0 37.2 37.3 37.3 37.5 37.8 37.9 38.3 38.5 38.7 38.8 39.0 39.1 39.2 39.2 39.2 39.3 39.4

dB

R1

R2

30.67 30.74 30.85 30.88 30.95 30.95 30.99 31.00 31.06 31.09 31.13 31.13 31.15 31.16 31.19 31.21 31.27 31.29 31.37 31.37 31.41 31.43 31.44 31.48 31.54 31.58 31.66 31.70 31.76 31.77 31.82 31.84 31.86 31.87 31.87 31.88 31.91

2k4 lk8 430R lk6 510R 680R lkl 620R 560R lk2 lk 750R 360R lk3 910R 330R 820R 300R 2k7 270R 430R 2k2 lk5 2k lk8 2k4 470R 390R 620R lk6 lk lkl lk2 510R lk3 560R 330R

82k 62k 15k 56k 18k 24k 39k 22k 20k 43k 36k 27k 13k 47k 33k 12k 30k llk 100k 10k 16k 82k 56k 75k 68k 91k 18k 15k 24k 62k 39k 43k 47k 20k 51k 22k 13k

Av 39.6 39.7 40.0 40.0 40.2 40.7 41.0 41.0 41.3 41.4 41.7 41.7 41.7 41.7 41.9 42.5 42.5 42.6 42.7 42.9 42.9 43.0 43.1 43.1 43.3 43.5 43.9 44.0 44.1 44.4 44.4 45.3 45.5 45.5 45.5 45.5 45.6

dB

R1

R2

31.95 31.98 32.04 32.04 32.09 32.20 32.26 32.26 32.33 32.33 32.40 32.40 32.40 32.40 32.44 32.57 32.57 32.58 32.61 32.64 32.64 32.67 32.68 32.70 32.74 32.78 32.85 32.87 32.89 32.96 32.96 33.13 33.15 33.15 33.15 33.16 33.17

910R 680R 300R 750R 820R 270R 2k 390R lk5 2k2 lk8 240R 2k4 360R 430R lk2 lk6 470R lkl 910R 560R lk lk3 510R 300R 620R 820R 750R 680R 270R 360R lk5 220R 2k2 330R 2k lk8

36k 27k 12k 30k 33k llk 82k 16k 62k 91k 75k 10k 100k 15k 18k 51k 68k 20k 47k 39k 24k 43k 56k 22k 13k 27k 36k 33k 30k 12k 16k 68k 10k 100k 15k 91k 82k

Table 11.1 Inverting op-amp gains 277 Av 45.8 46.2 46.4 46.5 46.7 46.8 46.9 47.0 47.1 47.3 47.6 47.7 48.0 48.1 48.2 48.4 48.5 48.5 50.0 50.0 50.0 50.0 50.0 50.0 50.0 50.6 50.9 51.0 51.1 51.2 51.3 51.3 51.6 51.7 52.0 52.3 52.4

dB

R1

R2

33.22 33.28 33.32 33.35 33.38 33.41 33.42 33.44 33.45 33.49 33.55 33.57 33.62 33.65 33.66 33.69 33.71 33.72 33.98 33.98 33.98 33.98 33.98 33.98 33.98 34.08 34.14 34.15 34.16 34.18 34.19 34.20 34.26 34.26 34.32 34.37 34.39

240R 390R lkl 430R lk2 470R lk6 lk 510R 910R 820R lk3 750R 270R 560R 620R 330R 680R lk5 2k 200R 220R 240R 300R 360R lk8 lkl lk 470R 430R lk6 390R 910R lk2 750R lk3 820R

llk 18k 51k 20k 56k 22k 75k 47k 24k 43k 39k 62k 36k 13k 27k 30k 16k 33k 75k 100k 10k llk 12k 15k 18k 91k 56k 51k 24k 22k 82k 20k 47k 62k 39k 68k 43k

Av 52.9 52.9 53.2 53.3 53.6 54.2 54.5 54.5 54.7 55.0 55.6 55.6 55.6 55.6 55.8 56.0 56.0 56.4 56.4 56.7 56.9 57.3 57.3 57.4 57.4 57.7 58.1 58.8 58.9 59.1 59.3 60.0 60.0 60.6 60.7 61.1 61.1

dB

R1

R2

34.48 34.48 34.52 34.54 34.58 34.67 34.74 34.74 34.75 34.81 34.89 34.89 34.89 34.89 34.93 34.96 34.97 35.02 35.03 35.07 35.10 35.17 35.17 35.17 35.19 35.22 35.28 35.39 35.41 35.43 35.46 35.56 35.56 35.65 35.66 35.72 35.72

510R 680R 620R 300R 560R 240R 220R 330R lk5 200R lk8 180R 360R 270R 430R lk 910R lkl 390R lk2 lk6 820R 750R 680R 470R lk3 620R 510R 560R 220R 270R 200R 300R 330R lk5 180R 360R

27k 36k 33k 16k 30k 13k 12k 18k 82k llk 100k 10k 20k 15k 24k 56k 51k 62k 22k ,68k 91k 47k 43k 39k 27k 75k 36k 30k 33k 13k 16k 12k 18k 20k 91k llk 22k

278

Electronics Calculations Data Handbook

Av 61.5 61.5 61.8 62.0 62.2 62.5 62.5 62.5 62.5 62.7 62.8 62.9 63.1 63.2 63.8 64.3 64.7 65.0 66.7 66.7 66.7 66.7 66.7 66.7 66.7 66.7 68.0 68.0 68.1 68.2 68.2 68.3 68.3 68.8 69.1 69.2 69.4

dB

R1

R2

35.78 35.78 35.82 35.85 35.88 35.92 35.92 35.92 35.92 35.94 35.96 35.97 36.00 36.02 36.10 36.16 36.22 36.26 36.48 36.48 36.48 36.48 36.48 36.48 36.48 36.48 36.65 36.65 36.67 36.67 36.67 36.69 36.69 36.75 36.79 36.81 36.82

390R 910R lkl lk 820R lk2 lk6 160R 240R 750R 430R 620R lk3 680R 470R 560R 510R 200R lk5 150R 180R 240R 270R 300R 330R 360R lk 750R 910R lkl 220R 820R lk2 160R 680R 390R 620R

24k 56k 68k 62k 51k 75k 100k 10k 15k 47k 27k 39k 82k 43k 30k 36k 33k 13k 100k 10k 12k 16k 18k 20k 22k 24k 68k 51k 62k 75k 15k 56k 82k llk 47k 27k 43k

Av 69.6 69.8 70.0 70.2 70.6 72.2 72.7 72.7 73.3 73.3 74.1 74.5 74.7 74.7 75.0 75.0 75.0 75.0 75.0 75.0 75.6 75.8 75.8 76.5 76.6 76.7 76.8 76.9 76.9 76.9 80.0 80.0 80.0 81.3 81.5 81.8 81.8

dB

R1

R2

36.86 36.87 36.90 36.93 36.97 37.17 37.23 37.23 37.31 37.31 37.39 37.45 37.46 37.47 37.50 37.50 37.50 37.50 37.50 37.50 37.57 37.59 37.60 37.67 37.68 37.70 37.71 37.72 37.72 37.72 38.06 38.06 38.06 38.20 38.22 38.26 38.26

560R 430R lk3 470R 510R 180R 220R 330R 150R 300R 270R lkl 750R 910R lk 160R 200R 240R 360R 680R 820R 620R lk2 510R 470R 430R 560R lk3 130R 390R 150R 200R 300R 160R 270R 220R 330R

39k 30k 91k 33k 36k 13k 16k 24k llk 22k 20k 82k 56k 68k 75k 12k 15k 18k 27k 51k 62k 47k 91k 39k 36k 33k 43k 100k 10k 30k 12k 16k 24k 13k 22k 18k 27k

Table 11.1 Inverting op-amp gains 279 Av

dB

R1

R2

Av

dB

R1

R2

82.0 82.3 82.4 82.4 82.7 82.7 82.9 83.0 83.3 83.3 83.3 83.3 83.3 83.7 83.9 84.3 84.6 84.6 86.7 88.9 88.9 90.0 90.0 90.1 90.3 90.7 90.7 90.9 90.9 90.9 90.9 91.0 91.1 91.2 91.5 91.5 91.7

38.28 38.30 38.31 38.32 38.35 38.35 38.37 38.38 38.42 38.42 38.42 38.42 38.42 38.46 38.48 38.52 38.55 38.55 38.76 38.98 38.98 39.08 39.08 39.10 39.12 39.15 39.15 39.17 39.17 39.17 39.17 39.18 39.19 39.20 39.22 39.23 39.24

lk 620R 680R 910R 750R lkl 820R 470R 120R 240R lk2 180R 360R 430R 560R 510R 390R 130R 150R 180R 270R 200R 300R 910R 620R 750R 430R ll0R 220R lkl 330R lk 560R 680R 820R 470R 120R

82k 51k 56k 75k 62k 91k 68k 39k 10k 20k 100k 15k 30k 36k 47k 43k 33k llk 13k 16k 24k 18k 27k 82k 56k 68k 39k 10k 20k 100k 30k 91k 51k 62k 75k 43k llk

91.7 91.7 92.2 92.3 92.3 93.8 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 107 108 108 109 109 109

39.24 39.24 39.29 39.30 39.30 39.44 40.00 40.00 40.O0 40.00 40.00 40.00 40.00 4O.00 40.00 40.00 40.00 40.0O 4O.O0 40.00 40.O0 40.OO 40.O0 40.00 40.00 40.00 40.O0 40.O0 40.OO 40.00 40.00 40.56 40.70 40.70 40.71 40.76 40.76

240R 360R 510R 390R 130R 160R lk 100R ll0R 120R 130R 150R 160R 180R 200R 220R 240R 270R 300R 330R 360R 390R 430R 470R 510R 560R 620R 680R 750R 820R 910R 150R 120R 360R 470R ll0R 220R

22k 33k 47k 36k 12k 15k 100k 10k llk 12k 13k 15k 16k 18k 20k 22k 24k 27k 30k 33k 36k 39k 43k 47k 51k 56k 62k 68k 75k 82k 91k 16k 13k 39k 51k 12k 24k

280

Electronics Calculations Data Handbook

Av

dB

R1

R2

Av

dB

R1

R2

109 109 109 110 110 110 110 110 110 110 110 111 111 111 111 113 113 115 118 118 119 119 119 120 120 120 120 121 121 121 121 121 122 122 122 122 123

40.76 40.77 40.78 40.80 40.81 40.82 40.83 40.83 40.83 40.85 40.85 40.88 40.90 40.92 40.92 41.02 41.02 41.24 41.45 41.45 41.48 41.52 41.54 41.58 41.58 41.58 41.58 41.62 41.63 41.65 41.68 41.69 41.70 41.72 41.74 41.74 41.78

330R 430R 750R 620R 510R 910R 100R 200R 300R 390R 680R 560R 820R 180R 270R 160R 240R 130R ll0R 330R 430R 470R 360R 100R 150R 200R 300R 390R 680R 620R 750R 560R 510R 820R 180R 270R 220R

36k 47k 82k 68k 56k 100k llk 22k 33k 43k 75k 62k 91k 20k 30k 18k 27k 15k 13k 39k 51k 56k 43k 12k 18k 24k 36k 47k 82k 75k 91k 68k 62k 100k 22k 33k 27k

123 125 125 125 130 130 130 130 131 131 132 132 133 133 133 133 133 133 134 134 135 136 136 138 138 138 142 142 143 144 144 144 145 145 146 147 147

41.80 41.94 41.94 41.94 42.28 42.28 42.29 42.30 42.32 42.33 42.41 42.43 42.50 42.50 42.50 42.50 42.50 42.50 42.53 42.54 42.61 42.69 42.69 42.77 42.77 42.83 43.03 43.07 43.13 43.14 43.18 43.19 43.21 43.25 43.31 43.33 43.33

130R 120R 160R 240R 100R 300R 430R 330R 360R 390R 470R 620R 120R 150R 180R 270R 510R 750R 680R 560R 200R ll0R 220R 160R 240R 130R 360R 330R 300R 390R 430R 270R 470R ll0R 560R 150R 620R

16k 15k 20k 30k 13k 39k 56k 43k 47k 51k 62k 82k 16k 20k 24k 36k 68k 100k 91k 75k 27k 15k 30k 22k 33k 18k 51k 47k 43k 56k 62k 39k 68k 16k 82k 22k 91k

Table 11.1 Inverting op-amp gains 281 Av

dB

R1

R2

147 147 150 150 150 150 150 150 150 154 155 156 157 158 159 159 160 160 160 161 161 163 163 164 164 165 167 167 169 169 170 170 172 174 174 174 174

43.35 43.35 43.52 43.52 43.52 43.52 43.52 43.52 43.52 43.74 43.78 43.84 43.90 43.98 44.03 44.04 44.06 44.08 44.08 44.12 44.15 44.22 44.22 44.28 44.28 44.35 44.44 44.44 44.54 44.57 44.59 44.61 44.72 44.81 44.83 44.83 44.83

510R 680R 100R 120R 160R 180R 200R 220R 240R 130R 330R 360R 300R 430R 390R 270R 470R 100R 150R 510R 620R 240R 560R ll0R 220R 200R 120R 180R 160R 130R 330R 300R 360R 270R 390R 430R 470R

75k 100k 15k 18k 24k 27k 30k 33k 36k 20k 51k 56k 47k 68k 62k 43k 75k 16k 24k 82k 100k 39k 91k 18k 36k 33k 20k 30k 27k 22k 56k 51k 62k 47k 68k 75k 82k

Av 177 178 179 179 180 180 180 182 183 183 185 187 188 188 189 189 191 192 194 195 195 196 196 200 200 200 200 200 206 206 207 207 208 208 210 212 213

dB

R1

R2

44.97 45.03 45.04 45.07 45.11 45.11 45.11 45.19 45.26 45.26 45.33 45.42 45.46 45.48 45.52 45.52 45.61 45.68 45.74 45.80 45.82 45.84 45.85 46.02 46.02 46.02 46.02 46.02 46.28 46.29 46.31 46.34 46.35 46.38 46.45 46.51 46.55

220R 510R 560R 240R 100R 150R 200R ll0R 120R 180R 130R 300R 160R 330R 270R 360R 430R 390R 470R 200R 220R 240R 510R 100R ll0R 120R 150R 180R 330R 160R 300R 270R 130R 360R 390R 430R 240R

39k 91k 100k 43k 18k 27k 36k 20k 22k 33k 24k 56k 30k 62k 51k 68k 82k 75k 91k 39k 43k 47k 100k 20k 22k 24k 30k 36k 68k 33k 62k 56k 27k 75k 82k 91k 51k

282 Av 213 214 215 217 218 220 220 225 225 227 227 228 230 231 232 233 233 233 235 239 240 240 244 245 248 250 250 252 253 254 255 255 256 258 260 261 269

Electronics Calculations Data Handbook dB

R1

R2

46.56 46.59 46.65 46.72 46.78 46.85 46.85 47.04 47.04 47.11 47.13 47.15 47.22 47.26 47.30 47.33 47.36 47.36 47.42 47.56 47.60 47.60 47.74 47.80 47.91 47.96 47.96 48.02 48.05 48.09 48.12 48.13 48.18 48.24 48.30 48.34 48.59

470R 220R 200R 180R ll0R 100R 150R 120R 160R 300R 330R 360R 270R 130R 220R 430R 240R 390R 200R 180R 100R 150R 160R ll0R 330R 120R 300R 270R 360R 130R 220R 200R 390R 240R 150R 180R 160R

100k 47k 43k 39k 24k 22k 33k 27k 36k 68k 75k 82k 62k 30k 51k 100k 56k 91k 47k 43k 24k 36k 39k 27k 82k 30k 75k 68k 91k 33k 56k 51k 100k 62k 39k 47k 43k

Av 270 273 273 275 276 277 278 278 280 282 283 283 287 294 3OO 3OO 3OO 3OO 303 303 304 309 310 311 313 313 319 325 327 330 331 333 337 340 340 341 342

dB

R1

R2

48.63 48.71 48.73 48.79 48.81 48.85 48.87 48.87 48.94 49.00 49.05 49.05 49.15 49.36 49.54 49.54 49.54 49.54 49.63 49.64 49.65 49.80 49.83 49.86 49.90 49.92 50.07 50.24 50.30 50.37 50.39 50.46 50.55 50.63 50.63 50.65 50.67

100R ll0R 300R 120R 330R 130R 270R 360R 200R 220R 240R 180R 150R 160R 100R ll0R 120R 130R 330R 300R 270R 220R 200R 180R 240R 150R 160R 120R ll0R 100R 130R 300R 270R 150R 200R 220R 240R

27k 30k 82k 33k 91k 36k 75k 100k 56k 62k 68k 51k 43k 47k 30k 33k 36k 39k 100k 91k 82k 68k 62k 56k 75k 47k 51k 39k 36k 33k 43k 100k 91k 51k 68k 75k 82k

Table 11.1 Inverting op-amp gains 283 Av 344 350 355 358 360 362 370 373 373 375 378 379 388 390 391 392 392 410 413 414 417 417 425 425 427 430 431 453 455 455 456 464 467 469 470 477

dB

R1

R2

50.74 50.88 50.99 51.09 51.13 51.16 51.37 51.43 51.44 51.48 51.54 51.58 51.77 51.82 51.84 51.86 51.87 52.26 52.33 52.33 52.40 52.40 52.57 52.57 52.61 52.67 52.68 53.13 53.15 53.16 53.17 53.32 53.38 53.42 53.44 53.57

180R 160R ll0R 120R 100R 130R 270R 220R 150R 200R 180R 240R 160R 100R ll0R 120R 130R 200R 150R 220R 180R 240R 120R 160R ll0R 100R 130R 150R 220R 200R 180R ll0R 120R 160R 100R 130R

62k 56k 39k 43k 36k 47k 100k 82k 56k 75k 68k 91k 62k 39k 43k 47k 51k 82k 62k 91k 75k 100k 51k 68k 47k 43k 56k 68k 100k 91k 82k 51k 56k 75k 47k 62k

Av 500 500 506 509 510 513 517 523 547 556 560 564 567 569 577 607 618 620 625 625 631 667 680 682 683 700 745 750 758 769 820 827 833 909 910 1.00k

dB

R1

R2

53.98 53.98 54.08 54.14 54.15 54.19 54.26 54.37 54.75 54.89 54.96 55.02 55.07 55.10 55.22 55.66 55.82 55.85 55.92 55.92 56.00 56.48 56.65 56.67 56.69 56.90 57.45 57.50 57.60 57.72 58.28 58.35 58.42 59.17 59.18 60.00

150R 200R 180R ll0R 100R 160R 120R 130R 150R 180R 100R ll0R 120R 160R 130R 150R ll0R 100R 120R 160R 130R 150R 100R ll0R 120R 130R ll0R 100R 120R 130R 100R ll0R 120R ll0R 100R 100R

75k 100k 91k 56k 51k 82k 62k 68k 82k 100k 56k 62k 68k 91k 75k 91k 68k 62k 75k 100k 82k 100k 68k 75k 82k 91k 82k 75k 91k 100k 82k 91k 100k 100k 91k 100k

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Appendix 1 Units, symbols and suffixes I have used standard units, symbols and suffixes throughout this work. Here they are: Units Ft or R: ohms (resistance) F: farads (capacitance) H: henries (inductance) s: seconds (time) Hz: hertz (frequency) ~ (phase angle) V: volts (electrical potential) A: amperes (electrical current) W: watts (power) J: joules (energy or work) Symbols R: resistance G': capacitance L: inductance V: voltage I: current Xc: capacitive reactance )25" inductive reactance Z: impedance f: frequency r phase angle fo: resonant frequency Zo: dynamic (resonant) impedance

286

Electronics Calculations Data Handbook

Electronics engineers tend to deal in a very wide range of numbers, from millionmillionths of farads to millions of ohms. Hence it is usual to use a range of letter suffixes to indicate the order of magnitude of a number. These are the standard suffixes used in this book: p: x 10 -12 n: x l 0 -9 /z: x l O -6 m: x l 0 -3 k: x 10 a M: x 10 6 So, for instance, ~

= l m A ; 1M x 1 n F - lms; and so on.

Appendix 2 Colour codes The following colour codes are used on resistors, and sometimes on capacitors and inductors, to indicate value: Number bands Black 0 Brown 1 Red 2 Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Grey 8 White 9 Tolerance bands Brown 1% Red 2% Gold 5 % Silver 10% Figure A2 shows the significance of the bands for a resistor. For example; a four band resistor with colours yellow-violet-red-red (the last one thick) is 47 x 102 = 4k7, 2%. A five band with brown-grey-black-brownbrown (again the last thick) is 180 x 10 = lk8,1%.

288

Electronics Calculations Data Handbook 4 band

digit 1

digit 2

multiplier

tolerance

5 band

digit 1

digit 2

digit 3

multiplier

Figure A2 Resistor colour codes

tolerance

Appendix 3 The decibel The decibel, or dB, is a logarithmic unit for expressing ratios, much beloved of engineers. Its popularity is due to the fact that it enables a wide range of numbers to be expressed conveniently. Where we are talking about a ratio of two voltages then:

(Aa.1)

dB = 201o91o ~

which means that A is twice B' is often expressed as A is 6dB greater than B', and A is ten times B' becomes A is 20dB up on B'. Gain or attenuation of circuit blocks are very well expressed like this (a negative gain is an attenuation, or a ratio of less than one). The ratio is 'output/input'. dB's are also used to express signal levels a lot. Here some reference level should be stated to make the situation clear. The most c o m m o n are: d B V = 20 lOgl0(Vrms)- reference to 1Vrms

0,ogl0(V; ;)ro orenoo o

000,

though you may very well come across others. Where there is doubt it is often wise to try to find out what reference was used, as it can be a source of confusion. The beauty of this system is that the level of a signal at various point in a chain can be found just by adding the dB values together. See Figure A. 3. It is apparent that the calculation in dB's is trivial compared to that using VRMS and gain/attenuation as ratios.

290

Electronics Calculations Data Handbook

dB's are also used sometimes to express relative power. The equation then used is: P1) d B - lOloglo ~-~

(A3.2)

This is because power varies proportionally to the square of voltage, as implied by Eqs 2.4d and 2.4e. -60 dBu

0 dBu

-60 dB i

0.775 V x

\ /

-15 dBu

45 dB

/

-15 dBu

0 dB

\

0 dBu

15 dB

--->

i

1 1000

= 0.775 mV x 177.8 = 138 mV x 1 = 138 mV x 5.62 = 0.775 VRMs

Figure A3 Illustration of signal level calculations using dB's

A ppendix 4 Complex number analysis The standard way to analyse a circuit containing AC quantities at a fixed frequency is to use complex numbers. A complex number has two parts, real and imaginary. The imaginary part is some function of the quantity j (i to pure mathematicians, but that would be confused with current by us), where j represents V / ( - i ) . This is clearly a'nonsense number', or at least unquantifiable, yet it has some useful properties: j2 = - 1

(A4.1a)

j3 = _ j

(A4.1b)

j4= 1

(A4.1c)

We use multiplication by j to signify advancing its phase by 90 ~ Complex numbers owe their usefulness to the fact that they can be seen as representations of phasors. For example:

V=a+jb is a voltage which can be represented in the j-plane as in Figure A. 4. This number could also be represented as 'magnitude and phase' (as in Chapter 4) by using some trigonometry: M--- v/a 2 + b2 r

arctan(b)

Then we are able to write the phasor in polar form:

V=M
(A4.2) (A4.3)

292

Electronics Calculations Data Handbook

Should we wish to convert a quantity from polar to complex form we need a little more trigonometry: a = Mcosr

(A4.4)

b = Msinr

(A4.5)

Mathematical operations with complex numbers We treat complex numbers like any other algebraic quantity, keeping the j part separate as we would with x or y, but also applying Eqs A4.1 as necessary. So: Addition: (a + jb) + (c + jd) = (a + b) + j(c + d)

(A4.6)

Subtraction" (a + jb) - (c + jd) = (a - c) + j(b - d)

(A4.7)

Multiplication" (a + jb)(c + jd) - (ac - bd) + j(bc + ad)

(A4.8)

Division: a useful tool for separating fractions is multiplication by the 'complex conjugate', which makes the denominator wholly real: as: (c + j d ) ( c - jd) = c 2 + j c d - j c d - j2d 2 = c 2 + d 2 then: a + jb (a + j b ) ( c - jd) = c + jd c2 + d2

(A4.9)

However, multiplication and division are sometimes more easily performed by converting to polar form and then: Multiplication in polar form: M1 < r

< r

= M I M 2 < (r

+ r

(A4.10)

Division in polar form:

M1
M1 < (r - r M2

= --

(A4.11)

Representation of capacitors and inductors Complex numbers come into their own when we use them to represent reactive components in equations. The impedance of a capacitor becomes: X c - ~- J 27rfC

(A4.12)

Appendix

293

and an inductor: (A4.13)

X L -- j 2 ~ f L

and all of the analysis techniques of Chapter 5 can be used, following the algebraic rules given above. j (+90 ~

b

_71V=a+jb

~ m m ~ m ~ l

- real (180~

""

-j (270 ~ o r - 9 0

|

" a

~

Figure A4 The j-plane

P h a s e reference (0 ~ + real

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Further reading Should the reader wish to gain greater understanding of any of the topics which this book touches on, I have found the following to be excellent: Schuler, C. A. and Fowler, R.J. (1993) Electric Circuit Analysis, McGraw-Hill, London. A clear and thorough explanation of circuit analysis techniques which also contains good chapters on electromagnetism and electrostatics. Marston, R. (1993) ElectronicCircuits PocketBook, Vols One and Two, ButterworthHeinemann, Oxford. A comprehensive and informed circuit sourcebook that also analyses the ideas used in sufficient depth to make them really useful. Contains many useful circuits. Horowitz, E and Hill, W. (1989) The Art of Electronics, Cambridge University Press, Cambridge. Deservedly considered to be the classic all-round electronics text. Clear, concise and entertaining too. Phillips, G. (1993) Newnes ElectronicsToolkit, Butterworth-Heinemann, Oxford. A great deal of useful information in a small space; an ideal source of reference for the workshop or lab.

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Index AC, defined, 26 alternating current, definition of, 26 ampere, definition of, 7 antiphase, 30 atoms, fanciful behaviour of, 5,14 insecurity about, 5 bad smells, 23 bandwidth, see series and parallel'tuned circuit cable, capacitance of, 16 current rating of, 11 long, 11,16 resistance of, 11 calculations, checking, 40, 41, 46 involving phase, 30 labelling circuits for, 42 capacitance, definition of, 15 explanation of, 15 capacitors, 15 as DC block, 22 as ramp generators, 22 effect on phase, 32 in series and parallel, 17 non-standard values, 57 polarized, 16 power in, 37 reactance of, 31 similarity with inductors, 18, 23, 32 working voltage, 16 charge, definition of, 6 free electrons, 6,10 holes, 6 on capacitor, 15 circuit, definition of, 11 open, definition, 12 short, definition, 12 labelling quantities, 42 complex numbers, 30, 39, 291 components, standard values, 55 conductors, 10 voltage across, 11 coulomb, definition of, 7

CR circuit, see first-order circuits current, and magnetic field, 7,15 conventional, 7 definition of, 6 destruction due to, 11 direction of, 7 electron, 7 ideal and real source, 44 leakage, 16 speed of, 8 dB, 289 DC, defined, 20 level on signal, 35 decibels, 289 diagrams, block, 12 circuit or schematic, 12 differentiator, see first-order circuits direct current, definition, 20 earth, as reference for voltage, 8 electrons, free electrons, 6,10 holes and, 6 speed of, 8, 23 EMF, 8 equivalent circuits, Th6venin's and Norton's, 45 farad, definition of, 15 filter, high-pass, see first-order circuits filter, low-pass, see first-order circuits first-order circuits, 205 frequency response, 212, 213 instantaneous voltage and current, 209 phase response, 213 time constants, 207 time response, 205 turnover frequency, 212 and capacitance, 32 back EMF in LR, 207 Fourier analysis, 33 frequency, definition of, 28 very low, 28 harmonics, 33 heat, generation by current, 23

298

Index

henry, defined, 17 hertz, definition of, 28 holes, 6 impedance, 32 inductance, definitions of, 15,17 explanation of, 17 mutual, 18 self, 17 inductors, 17 Qof, 78 DC current rating, 18 as chokes, 22 current ramp in, 22 in series and parallel, 18 non-standard values, 57 power in, 37 reactance of, 32 resistance of, 18 saturation of, 18 similarity with capacitors, 18, 23, 32 insulators, 10 breakdown of, 23 integrator, see first-order circuits Kirchhoff, current law, 41 voltage law, 40 LR circuit, see first-order circuits mark-to-space ratio, 35 MMF, 6 Norton's equivalent, 45 ohm, definition of, 10 Ohms Law, 10 defined, 10 in capacitors, 31 in inductors, 32 op-amps, 259 inverting, 259 non-inverting, 261 easy rules for, 259 open circuit, definition, 12 parallel circuits, rules for, 41 parallel tuned circuit, 226 conditions for resonance, 230 dynamic impedance, 229 ideal, 227 practical, 228 Q,factor, 229 resonant frequency for practical, 229 peak amplitude, 27 peak to peak amplitude, 27 period, definition of, 28 permeability, 17 phase cancellation, 31

phase, definition of, 29 effect on power, 37 reference, 29 rules for calculation, 30 phasors, 30, 291 potential difference (also see voltage), 8 power supplies, 8, 20 power, at DC, 23 definition of, 24 explanation of, 23 for AC, 36 Q,factor, see series and parallel tuned circuit quadrature, 30 ramp generator, 22 ramp wave, 34 RMS value of, 37 rectangle wave, 34 RMS value of, 37 resistance, 10 resistivity, 10 resistors, 12 colour codes, 287 in parallel, 13 in parallel, rules of thumb, 14 in series, 13 non-standard values, 55 power rating of, 23 tables for power, 102 resonance, see series and parallel tuned circuit risetime, see square wave RMS, defined, 36 for sine waves, 27 value for misc signals, 37 rules of thumb, resistors in parallel, 14 power, 23,102 sawtooth wave, 34 RMS value, 37 series circuits, rules for, 39 series tuned circuit, 223 Qfactor, 224 bandwidth, 225 explanation of, 224 impedance at resonance, 224 resonant frequency, 224 short circuit, definition, 12 signals, DC level of, 35 fundamental of, 33 vague definition of, 12 very low frequency, 28 sine waves, amplitude of, 27 definition of, 26 importance of, 33

Index 299 square wave, 34 risetime of, 33 RMS value of, 37 suffixes, 286 Th~venin's equivalent, 45 transformers, 18 triangle wave, 34 RMS value of, 37

units, 285 voltage divider, 142 effect of source and load on, 143 voltage, definition of, 8 ideal and real source, 45 reference for, 8 speed of, 8 work done by, 8

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