Active Filters for Integrated-Circuit Applications
DISCLAIMER OF WARRANTY The technical descriptions, procedures, and...
365 downloads
1384 Views
4MB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
Active Filters for Integrated-Circuit Applications
DISCLAIMER OF WARRANTY The technical descriptions, procedures, and computer programs in this book have been developed with the greatest of care and they have been useful to the author in a broad range of applications; however, they are provided as is, without warranty of any kind. Artech House, Inc., and the author of the book titled Active Filters for Integrated-Circuit Applications make no warranties, expressed or implied, that the equations, programs, and procedures in this book or its associated software are free of error, or are consistent with any particular standard of merchantability, or will meet your requirements for any particular application. They should not be relied upon for solving a problem whose incorrect solution could result in injury to a person or loss of property. Any use of the programs or procedures in such a manner is at the user’s own risk. The editors, author, and publisher disclaim all liability for direct, incidental, or consequent damages resulting from use of the programs or procedures in this book or the associated software.
For a listing of recent titles in the Artech House Microwave Library, turn to the back of this book.
Active Filters for Integrated-Circuit Applications Fred H. Irons
artechhouse.com
Library of Congress Cataloging-in-Publication Data Irons, Fred H. Active filters for integrated-circuit applications / Fred H. Irons p. cm.—(Artech House microwave library) Includes bibliographical references and index. ISBN 1-58053-896-7 (alk. paper) 1. Electric filters, Active. 2. Integrated circuits—Design and construction. I. Title. II. Series. TK 7872.F5I76 2005 621.3815’324—dc22 2005041997
British Library Cataloguing in Publication Data Irons, Fred H. Active filters for integrated-circuit applications.—(Artech House microwave library) 1. Electric filters, Active 2. Integrated circuits—Design and construction I. Title 621.3’815324 ISBN 1-58053-896-7
Cover design by Igor Valdman
© 2005 ARTECH HOUSE, INC. 685 Canton Street Norwood, MA 02062
All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark.
International Standard Book Number: 1-58053-896-7
10 9 8 7 6 5 4 3 2 1
! "
! $
% & &
'
#
'
( (
'
( )
#
( *
+
'
( *
#
* ,
-
( *$
!
'
. / & &
'0
'
1 . ( $ /
'
'
1 /
'+
! / .
#
$
'
-
#
! "
#
1 2
#
$ /
-'
$ 3 2 3( 4
--
3 2 3( 4
-+
'
3 2 3( 4
+0
+
2
'
+'
$
. % 5 ,6
+#
+-
5&
0
$ % & '
(
'
1 "
'
1 8 . $
'
' ''
1 7 / "
+
$
0
$ 3$ % 5
'
$ 5
+
''
$ /32/ ,8 " /
1 $ / $
0
1 1 / $
0
,
1
2 $
9 13$ 2
'#
& 2 28
'#
$/9 / 2
'
-
+
5&
'
'+
/ 6 ' " / " /
#
#
'
'
' " / *: $ 5 ' " / 5 ' $
& '
#
# #'
##
'
'
'-
#
'
'' '#
1 2 $
#'
#
1 *8
#'
#
1 " *8
##
#
1 $
"
##
#'
1 . $
"
#-
##
1 . .
#+
2 ,6
#
#
-'
$
--
// ;
/ "1 /
-
#'
1 /
+0
#'
$ 3 </
#'
1
-
#''
1 * %/
00
5&
#
3
) * % + -
-
+
-
-'
$ & /
1 (& 1 -
-
#
$
(& ,6 & $ &
-
1 , (
-
-
1 3 *
-'
& *
$
''
1 ;
'+
'
5&
#+
# % , +
+
+
-
1 "2$ $
1 4
+
1 ! 5 / $
1 $
+
$
+
1 ,% 5
+'
5 / ! %
$
1 /
-' -+
+
1/ / 2
+'
1/
3
+
$
+
/
+
$ / * / /
!
+ '
0'
5&
/ "1 /
# -
( ., "
./ ( 1
% / $/3$ 5
+
1 *
1
'
1 1 1
'
#
. / 1 1
0
-
4 & 1 (
4 "1 /
+
$ $
/ 5
!
'
2 & 1 5
#
2 =
! 1 ( 1
# - -' +' #
5&
0
/ 6 6
0
0
& 1 ) &
/ (
#
" , ,
$/ $/
" & 1
1 6 & / / / 1 &
000 1 > & " 1 &
/ / =
1
1 6 &
1 / 1 / & 1 & / $ ! ? / / 1 / & 1 13/ 1 1
1/ $ ?
/ 1 /
/ & 1 13& / / ? / /
/ . // ? @ ?
8 1 /
1/ A
.
? 3 * / / / 1 % / ? / 1
& 1 &
1 6
1 / & & 1
1
1 1
/ /
1
1 1 / / & 1 / 1 1 ? / 1 6
=/ 1 /
/ & & $ / 1 / 8 6 / 1
)
? & 1 1 =/
1 Æ 6 / 1 B 1 1
$ ?
6
! & / 1
1 1 & / / 1
? 1 / 6 1 B & / 1 6 / 1
/
1 / / &
1/ &
$ 6 &
C
1 / / & D &
3 /
// /
1
1/ D
* / /? & ' $ # ,6 1
1/ D
1/ /D
1 1
1 / & 1 & D
6
6
- (
! % & & & / / /
(
!D
+ & 1 1 / /
! & @
A / & / &
1 & / //
? 1 =/
& B & 1 0 @ 00 A 1 $/
/ 1 / B 3 1 6 !
1 &
/ /
5% / ! /
/ 1 / ? /
1/ 6 1 " / $ ., 1 B @1 1 1 A / 1 1
3
1& 1
1 %?
1 &% / 3
& ? / 6 & / 1 1 B / ! / & & / /
/? 3
% &% 3/ / / 1 / B @1 ' / #A
/
1 1 / 1 / / /
/ / /
/ / 1 %/
/
// & & 1
/ 1 / / 8
1 3
$ & 3&%
/? / & /
/ / / /
1 /
! / & % / & 1 & 1 1 / B @1 - / +A
/ & /
1 / / / /
1 / 1 & / 1 / &
(
/ 1 1
/ 1 / / 1 &
1/
1 & 1 B @1 A
/ 1 / 1 6 3
. / / 1 1 / / & 1
/
! &
=/ & & ? 1 &
/ 3
/
1 ? / / 1 1 * /
/ 1 1 ?
1 & 1
1? 1 1?
=/ &
/
!
/ / / & / 1 1 / 1 B / /
/ 1 3
&
1 /
1
1 Æ / 1 / 1 / 1 / / 1
/ E6
G 1 /
.
& 1
/
/ & 3
1
F !
/ / / 1
! / & 6 @ ? / 6 / / / 8 / / 3 ? / / //A
/
$1
1 1 1
/ / / @/
/A? / ? / / Æ
/%
/
6
,6 1 B
1 1
? / ? /
1 / /
?
1 / 1 =/ 1 1 1 1 /
1 / 1 / 1 1 $ ., 1 & 1
1 1 " /
1 6 6 / 1
. ?
1 & / / / 71 / & ?
! 1
/ 6 /
1 /
/ / 1 / &
/ ) ? &/ / . & 1 & / 1 / / 1
1 1 / / 1?
/ 6 ? & 6
! / 1 1
/ ?
1 1 &
/ / & !
/ & / 1 / 1 6 / /
1
?
/ / 6 6 & / / 3 / @ ? A 6 ? / 6
?
& 6 ?
// &
!
/ 1
1 6
6
. & 1 , / , & 1 Æ
!
/ % & 1 !
)
? / ) ? 1 !
. // ? .
1 // 1 /
/ 1 /
/ 1& / 1 /
. // ? . 1 ! ? & 71 ?
!
/ 1 /
&/ ! 1 1 1 1 / 1
1 //
1 1 & 6 /
=/ / 1 1 1 % 1 B . 1 1 !
1 1
1 / / 8 / &
/ 1 1
1 6
. / & 1 / / & 1 ) ? ? "! 71? * ( 1? / 5 / & , 1 ? 1&? / . / 1 & 1
1 1 1 3/ & !
& /?
1 / / ? : 4
?
1& / Æ /
1
/
1
1 & 1 6 & 1 ( H
/ $1 ! & 1 B? / .
1 & 1 1 B / !
/ 1
&
/ / 8
1
. // ? .
&? $? 1 1 1 ! )
1 1 & &
6
/ /
3
1 /
71 / 1 I 71 I 71 1 /I B 1
/ 1 ! 1 & I 1
%
/ B / / 1
& /
1 " 1 ! % / =
1 & & 6
* /3 /
& &
3 3/ & 1 / / /
1 / 1 1 / 3 3 3
1 =/ 1 1
& 713 &3
J 6 & 1 / ? ? / 71 / / / 1
/ / & &%
1 /3 // / /
/ / 4/ / ? 1 1
1 ( ,6 " / @(,"A?
1 /
( @($A 1
/
,1
1/ / / / /
1 1 1 3)=
1
1 / / / // 6
1 1 @ =? ? / A
1 1
1 1 / 1
6 / /
1 & 1 & / / / / 1
/ /
71 & 1 / &
1 &
! 1 & / / / / / /
1 &
1 / / &
1 / &
" & /
" / /
1
&? ! 1 &? ! & !
@ A /
$1
1 / ! & 1 & $
// & & ? 1 1 1 1 1
71 1 1 % /
1 1 1 / /
1 / 1 I 1 /
2
D
/ ? 1 / 1 /
& & 1 ! & B 1
1 / 1
/
1 6 1 % / & B . / / 1
1 !
1 1 ?
1 & 1 &
1
& !
1 / !
&
31 1 B
/ 1
/?
6
1 /
1 1 1 /3 8
1 1
/ & / / 1 / 1 / / 1 ! 1 / / D
&
/
3
/
1 ! /
1 / & /
& 1 / /
/ & & /
1 / 6 / !
1 % /
1
. // ? 3 /
1
1 & 1 1
1 ? //? / / /
3/ /
1 &
% ? 1 & / ? / 1
/ & & 1 B
1
& 1 / /% / 1 & ? 1 / / 1
/
/
1 1 1
/
/ 1 3
/ 6 1
1 1
1 ? 1 ? /
/ / / 1 & 1
1 ! 1 1 /
/ & 1 1 & 3
/ 1 / 1
1 / / 1
1
!
/
/ / &
/ /
*& / &1? .
1&
//
1 / / & & %
1 1 // . // ? 1 1 / 1 / &%
&
1
1 1 1 /
&
1 1 / / / / & 1
1 6 &% ?
1 / ! & ?
1
@
1
/ / & 1
? & 1
! 1
@
A?
! &
A? 1 ? !
1
!
? 1
! &
/ / & 1
@A
@
A
0 0
K
K
? 1
@ A K
! &
L L
L L L
L
L
L
@A
/ /
! / 1 /3 1
1
1 / / 1 & 1
? 1 6 &%
&
K
1
/ ?
,% @A 1 &
@ A K
0 0
1 ? 1 / / 1 & 1
@A
K
@
@
A
@A
! & &
0 0
K
@A
K
A
K
C
@ A
@ A
1 1 1 & & &%
% / & &
1
/* & 1
0
1
@'A 1
0
?
!
1 1
/
) ? / B
0 0
0
/
@ A
/*
/
1 6 1
1 / /
&% ?
K
?
/ /
1 @ *A &
1 / & 1
3 &
/ 1 1 / 1 /
/ 1 / / 1
1 1
! &
$ &? 1 / 1 / / !?
7 1 1 /
& ? / ? 1 /
/ / & 1 / / 1 & 1
1
@'A
/ / ? ? 1
/ / &
& 1 ?
,%3
1 1 C
@ A K 0
1
1
/? /
// ! 1
!?
1 1 / & /*
( @#A
/ 6 &
1 /
C
K
K
0
0
@#A
'
+ V2 -
N
V1
/ &
! & ?
@
A
Network N
V1
R1
Sub N
CL
RL
+ V2 -
Rin /
/ / /
#
Rg + V 20 -
V1
/
RL
1 1
Rg
N
+ V2 -
V1
'
1
?
/ ? 1 1
& / ?
/
?
1
/
RL
1 1
1
/
& & &% 1 ! 1
@ A?
@-A / 1 1 & ? Æ 1 & /
@ A L 0 @ A
& & $
0
0
/ / 1 / 1 1
1 1
K
!
K
1 /
0
/*
@-A
/
/ /
0
K
/ '
0
0
K
0
K
@ A
C
L A
@+A
@
! /
/ &
.
/ /
@+AC
L
K
.
1 1 / 1
? 1
1 1
@ A
& & &%
1 ? 1
1 &/ 1 /
/ / 1 /
/ 1
0
1 & & 1 1 /
A?
K
1 / &
@
! & ?
!
.
6 % 1
% ? 1 & 1
0
/ /
@AC
@A
-
45
Attenuation (dB)
40 35
αmin
30 25
Stopband
20 15
Transition Band
10
Passband
αmax
5 0 −2 10
−1
10
0
1
K
0
K
0
0
2
10
ω (rad/sec)
#
1 1
1
10
10
0
@
L
L
L
A
@ A
0
L
0
@ A
@ A
@A
/ 8 & 1
&
@E A / 1 1 &% 3/ / 1 & 1 & ?
@ A?
/ /
/
# 1 1 1 1 / / @*$A ?
1 1 &
,1
1 =/
& ? ? 1 1 / ? ?
6 3
1 B & 1 1
& & &% & 6 1 / / =
? 1 /
&/ 1 / 1 /
6
3
@( A? 1 1 @) A? / @* A?
/ / 1 = % 1
1 /
/
1 /
1 & 1 % / 1 /
3
/ 1 /
& / & 1 & !3 3! % / & &%
+
45
Attenuation (dB)
40 35 30
αmin
25
Stopband
20
Transition Band
15 10
Passband
αmax
5 0 −2
−1
10
10
0
1
10
ω (rad/sec)
2
10
10
- 1 1
45
Attenuation (dB)
40 35
αmin
αmin
30
Stopband
25
Stopband
20 15 10 αmax
5
Passband
0 −2
10
−1
10
0
10
ω (rad/sec)
1
10
+ /
2
10
45
Attenuation (dB)
40 35 30
αmin
25
Stopband
20 15 10
Passband αmax
5
Passband αmax
0 −2
−1
10
10
0
1
10
2
10
ω (rad/sec)
10
/
.
3 % 1 13%
/
1 /
& & & 1 / 1 % & 6
6 & / ? &
/ 8 /
1! 1 6 /
& &? / 1
/
1 1
1 %
1
1 & 3
1 / & =
/ /
? 1
&
1 & 6 ?
6 /? /
/ /
1 & / & /
/ &
1 / .&
E/
71
% 1 1 /3
1 1 / Æ
& &% / . // ? 1 / 1 8 & ! ? / 1 1 / / Æ 6 ?
/ ! ? / 1 & # 1
/ 1 // & / /
/ 6
/
1
/ ? /
1? 61 1 / & 0 )J ?
/
/
1 1
?
1 & 0 0 M?
/ 1
1 & 3
/ ! 1 1 / & 0 "M . & 1 ? & / & 1 & 5( M
M ?
/
. 1 1 / 0
&
/ F &
A
&
1 / & &
G @ ?
1 &
1
/
71 /
% 1 ? 1
1
" 1 1 / 1 /
& 6 & Æ % & 6 / 1 1 1 / Æ
$ / /
,6 / & ? ? / 1 / Æ =
$ // 1 13
% 1 1 1 & 6 / 1 / & Æ @ K A
1 1 1
Æ
/ 1
Æ
00 @NA 00
1
L00 J
.
/ % & 1 /
, %
6
1 1 1 @ / 1 %
& 1
& A / @
!A 1 & 1 / & 1 &
& 1
// 1 & / ? / / 1 /
/ /
/ 1
1 6 / / 1
1 /
1 &
1 / &
1 % 2
1 & E ?
1 & / 5
! /
! & % 1 & 5( @ ?
/
& 1 A 71 1
/ / 1 ?
/ / / 6/ 1
1 1 / .
&
! /
1 ?
/ / / 1
/
& / & E ?
& / &
1 ( /
1 / 1 =
1
0
50
Attenuation (dB)
40 30 20 10 Passive Lossless Active
0 −2
−1
10
0
10
1
10
2
10
ω (rad/sec)
10
. 1 & E
/? = 1
1 1
/ /
& 1 / 1 / E & 1 = . /
/ E
1 &% /
.&
/
1 /
/? /
/? 1 1
.& 1 1
&% 1 / & ? 1 // E 1 1
1 & /
/ & 1 71 1 / &%
? 1
* ? 1
1 /
/ /
& 1
1
/ /
1 3% =
! 1
/ 1
1
" / / 1 & 5
/
! /
1 1 &3
1 / &/ ! Æ
/ 6 / = = / & /
! & 1
/ & ?
& 1 1 ! 1
/ 53
/ ? / 1 ? / 1 4 ? 1
/ / /
1 / 1 % /
&
/ 1
% 1 1 E6
/
.
% /
/ $ &? 1 1
.. .
Active LC Passive
...
Digital Crystals Saws
...
102
10 4
10 6
Distributed: Waveguide, Stripline
108
1010
...
Frequency (Hz) 0 1 &%
& / & /
1 1 / % / &
B / 1 / .
? 1 / 53 3 1 /
/ 1 1 6
. // ? 1 // 1
/
1 &% /
& / /
&
1 1 / /
1? 1
0
1? 1
/ 1 1 &%
1 311/
1
3
? / / 1 % 1 1 % & / % / & 1 $1 3 /
. ?
? =?
1? ? /
/ 1 /
1 &
& //
1
! 1 1 &
1 1 / /3 8
% & D 2 D $ D ' ? & & @" *AD # $ =?
1D
- ? / D + 6 ? / ? /
1 =?
1 &36
1? " *? / 6
/ 1
1 1&
/ /
1 / / 1 & 1
/ 1 % & / B 1
1
1
1.4
+ V1 -
1.4
+ V1 -
+ V2 -
1
0.5
2
(a)
+ 1 V 2 -
(b) (Ω, H,F)
2
1 + V1 -
1 1
0.5
+ V2 -
1.4
+ V1 -
1.4
(c)
1
+ V2 -
(d)
@O/A &
1 1 1 //
/ ? / 1
% & / ? / / / 1 1 6 1
? / 1
! /? 1 / & / ? ? &
1
!
1 /
/ 1
?
! & ?
0 0
& 1 @? ??/A 1
? / 1 &% ?
./ & 1 & E
/ / 1 @( ? * ? / & 1A & 1 $ & 1 / / / &% / / & /
& 1
// /
1 /* ? &%
2
/*
/ /
/
1 &% ?
& 1
03!M /
/ 1
1 1 / 8 /
C / 1 E ? / &%
1
& 1
/ & ? /
/
1 &% / 1 /
/ 6 1 / / # !M & 1 I . 1
? 1 1 Æ @ A
Æ
Æ
& L#0 J ? / 1 1 & L #0 J 1
Æ
1 & L# / 1 1 & 1 & 1
Æ
1 L00
/
1
1 1
0.1
Z
10
5
5
10
in
Ω,µH,pF)
(k
&
Z(s)
1.59
10
Ω ,nF)
(k
&
' / 1 %
/ ?
?
& 1 % & ? &% ?
?
& ( /
& & &% ?
/
/ ? (? /
/ /
?
0I
2
# 71 1 6 & ? 5? / ?
K ? 1 1 1 / 8
1 ? 1
@0A
0
1 &
1
1
? / 1 / / 1 ?
&% & 0 ")=I
? 1
?
'
, 1 1/ 1 / @ 1 A
1 & ?
/ / / 1 / % ? /
3
& ? & ? / & /
1 1 / 1 & / 1& 1 //
1 1
/? 1
1 1 / / /
1 & / 1 = 1 1 !
& 1
& 1
! / / 1
/ / / ? 1 / &% ? /
3
! ? /
! & /
71 / = ? 1 % 5( 1 &
1
6 &% ? P Q
QPQ K P
P
0
Q
@A
0
& ? P
Q PQ?
& ? / P
@AC
Q L PQ L
P
1
6 & 1 ! ! 1 &
Q
/ P
Q
3
/ ? ? / ?
1 1
1 & %
& &
3/ & ?
1 / / = ?
1
6 & 1 ! ! 4(
! #
-
sL
R
R
V (
1/(sC)
Ω)
1 5( 3 &
+
I
sC
v
-
G
1/(sL)
(Ω −1) 1 4( /3 &
1 &
1
@AC
P
1
Q L PQ L
6 &% ? P
Q
P
QP
Q K P Q
@A
& / ? P Q
& / ? / P
Q PQ?
/ P
Q
/ 3
? / ? / / ? 1 1
@A
& & 3/
&
3 / 1 / / & 1
> 1 / & 1
%
3 1 1 1 / / / / 1
/ /
/ /
/
?
?
1 1
R( C
R(
C
0
0
L
#
'
L
L
0
K
K
0
K
0
+
I
s1
Is1
10
v
R1
V s1
i
x
1
20
v
R2
0.2
2
2
v
R3
25 ix
3
100
Ω H,F)
(
,
,6 & 6
'@
0
A
R( C
00
L
L
K
0
K
1 1 % / @'AC
Q L PQ L
P
Q
P
K
1
P
Q
K
0
0
0
0
0
0
0
0
0
0
P(
,% @'A '
71
@ # 0 0#A / &
?
Q
K
0
0
@ # 0 0#A
0 0#
0 0
M
?
0 0
0
0
0
0
0 #
0 #
0
0 #
)
@'A
0 #
1 1
R( ?
3
1 / / 1 @
A
? 1 1 03M / 3
1 /? / / 1 ?
/ 8 ?
/
K
0 #
P4Q
0
L0
@ A
1 /
? / 1 E ?
1 /
/ / 1
/ & 1 / ?
R( C 0
L
#
@
A K
0
1
v1
V s1/10
Is1
v2
20
10
2
v3
0.2 1.25(v 1-v2)
100
Is1
(Ω,H,F) ' / / & /
R(
@ 3 AC
#
@
A L 0@
L
L
A L @
A L 00
K 0
/ $ C
# '
K #@ L
L
A K
Q L PQ L
P
P
Q
K
1
P
Q
P5Q
P
,% @-A
K #
1 1 % / @-AC
/
Q
K
K
K
@#A
0 @
L 0A
#
0
0
0
0
0
0
0
0
)
0
0
0
0
0
00
0
'
#
#
0
#
#
0
0
0
0
M
@-A
1 / 1
# ? 1 /
/ 8 & 1 ? 1
1 & / 1 & # / ?
?
1 1 1 & 1
1 6 1 1 / /
1 %? / 6
/ / 1 / Æ &
/ /
1 1
&
(20+2s)I
10
+ 20
R1
V s1
s1
+ -
24
R2
R3
(100+2s)
R3
R2
0.2
(
1
+ -
+ -
25 I
s1
Ω H,F) ,
# / / &
S 1 / / 1 M3 /J & 1 1 1
/ & /
> & ? 1 M3 /J / & /
. ? 1
? 1 1
1
/
1
/ / &% &
1 / 1 / " !
/ 1 / & M3
/J 1 / 1
& !
1/ &
1 / / / &% % / & 1 / / &/ 1 / 1 /
/ % ( / 1 1 1
/ & & ? / 1
/ &% 3 1 1
/ & /
1 1 /3
/
!
1 &
/ 1 1 /
! /
1 / / 1
-
1
-@A
? 1 1 1 1 / 1 & 1 ?
& ?
/
1 / > ?
QP
P
/
Q
P
K
PQ L PQ L P Q @A
Q
K
Q
P
K
P
1 %
1 1 &
1 1 &
K
1
/ /
0 0
C
Q Q
@+A
1 6 & 1
1 / 1
P
P QP Q
/
P Q PQ L PQ L
1
@AC
P Q
0
I1
I’ 1 N (RLC) [ ZL ]
V1
+ V2 -
N’ (R’L’C’) [ Z’ L]
V1
(a)
(b)
-
+ V2 -
!? @A?
/ / / /
!? @ A
P Q L P Q L
1 / % /
P
@A 1
1 / / / 1
Q
@A
1 1 1 3
/ 1 ? 1
? / 1 /
/ 1
1 /? ?
1
$
/
K
K
K
1
@A
/ ? / ? 3
/ &
/ 1 5(
1&
/? 1
7
1 / / & 1 / 1 1 &
/
!
/
1 1 6
/ /
! 1
1
1
/
1/ & 1 1
! 1
& 1
/ & C
P Q
P P
Q Q
K K
1 /
Q P
P
P Q
P
0 0
Q
Q P
Q K P
0
Q
P Q
@0A
! // 1
/ / 000? 1
/ & ?
1 / / / 8/ 1 1 & &
.&
7 1 /
/
/ /
& / / /? 1 8
//
1
? / 1 / / 1 & 1 & 3 3 3 / 3 3 / / 8/
ω)
H(j
0
1
2
ω (rad/sec)
3
ω ')
H(j
0
k
ω
2k
ω
3k
ω ' (rad/sec)
ω
H(jf ')
ω
0
π
π
ω
ω
2k /2
k /2
3k /2
π
f ' (Hz)
+ / / & &% &%
/
/ ? 1
? 1
& ? / / 1 & ? / 1 / ? 1
&
S
/
1! 1
1
/ 1 8 & / / % 1
B & 1
3
/ 8
+ 1 &% / 1 &
1 & &% 1
1
?
?
1
D
?
/
&% 1
% / 1 & & 1
36
! &
1 &% 1
7
! 1 6 & &
C P
P
,% @A B 1
Q
P
K
K
P
Q
&
@ AQP
0
K
1
1 1 &% ?
@ AQP
Q
0
Q
K
@A
/ 1 / /
! & / & & 1
$ &
1
/ 1 % / &% &
@ A
K K
C
@ A PQ L PQ L P Q
/ 6
P Q L P Q L
K
* 6 @A? 1
Q
P
@A
// 1 / & &%
!C
K
K
K
@ A
? 8/ 1 &% 3
& 1 @ A? 1 (
/ &
? 1
/
5( B & 1 1
K
K
@
1 /
K
K
3 1 1
A
K
@#AC
@#A
6 &
1 M ? / 1 &%
/J $ 1 & 1 & !M / 1 ( 1
%
3 ? 1
&% & ?
/ &
?
1 ( 1 1
1 /
K 0 ?
? 1
? / / 1
/ 1 &%
/ /
1 1
,% @-A 1 ?
1 1 1 C
0 !)=
/ / & M !M )
?
@'A
1
1
K
1 1
%
@'AC
/
& & 1
/
K
K
& / 1 / / &
K
K
0 0 0 #0
'0
K
K
0
K -
K #0
- 0 0#'
@-A
1 / C
#0
@+A
ω 0=2.5
1.68
1
0.09524
V1
1
1
+ V2 -
1
(Ω,H,F)
!
f 0'=20 kHz
33.42
1.0
1.895
1.0
19.89
19.89
(kΩ,mH,nF)
$/
! & / / 1
1 % /
! & 1 /
@'A /
@#AC
K
K
K
K
!
1
1 / 1 6 1 7 1
!
?
/
0
M M
K
-
K ' )J)
0
-
K ' J
@A
/ & &
?
/ /
!
% /
/ / % &
3 71
1 /
/
& 1 1
% 00 / 1
/
1
1 & 0 )I
'
%
3 1 & & / & 1 &
/ 1 / &
00 0
0 0
" /
@'A
C
K
K
-
K
K -
C
000 0
1 & 1
K
-
K -# 0
1 6
/
-
K
0
K 0 0
-
K ++# +
1 &% 1 /
/ 1 / / 1 & /
/
/ & /
1 1 1? /? / 1 1 1 & &% & 1
1 & / / /
6 / 1
& / 8 & B 1 1 & 1
. // ?
1 1 &
/ ? /
/ 8 & & /? ! 1
/ 1 / &% &
1
3 3 &% /
& / / 1 ? ( /
1
/
/
! @ / & / A / 8 &% . 1 &
6
K L 1
&
K
L
1
? ? &% 1 / 1
/ 1 &%
& &% @ /JA? / 1 1 /
,6
/ 1
3 3
@'A / @#A
@( ( A & /
. 1
1 / &
1 & / 1 ( (
1 =/ 1
K
K
,% @A 6 / 1 ? 1 1 & 1
@AC
/ ? 1 &
@A
+
. !
/ & 1
P ass
#
S top
0
1
ω or s
2
...
P ass
S top 0
1
ω' or s'
2
0 1 3 3 ( ) &
& / 5( C 5
. /
/ / & &% ?
K
K
@0A
C
K
K
K
C
K
K
@A
1 % 1 1
@ A
1 &
1 ( / / / 1 1 1 & 1 3
&% 1
@AC
K 1 &% 8 & 1 &
& 1 / 1
/
K
1
/ / & &% ?
5
/ C
A
K
K
@A
0
1 &
C
5
@
K
@
A K
K
K
@ A
-
s
1/s'
R
R'=R
(Ω) Ω
L/s'= 1/(C's') (
Ls
Cs
C/s'= 1/(L's') (
Ω
)
-1
)
, & 1 ( ) &
2
Z(s)
2
1
Ω ,H,F)
(
( & ,6 '
5
@ A
K
K
/ C
%
K
@'A
/
@
/ & 1
!? / 1
1
@
A
A
3 1 /
@A 1 1 @'A / 1
& ? / 1 1 1
A K
3 & ( ) & 1 (
1 %
@
1 &
$
K
1
/ &
! / / 3 @/ &3
A &
C
+
1/2
Z(s)
1/2
1
Ω H,F)
(
,
) / & 1 ( &
C
@ C
@
A K
A K
L
@
A K
@#A
@-A
A
¼
1 & 1 =
K
@
@
L
¼
?
K
3 1 ( ) & 1 &
A? / 1 &% & 1
@
%
3 $
& @AC
@
K
A K
A K
C C
'
L
L
L L L
'
L
K
= =
@+A
@ L A L 'L
K
C
= ? 0 #? D ? 0 #
= ? ? 0D ? 0
K
! &
@A
Æ
0
Æ 0
? 1 &% 1 1 & 1
! & ?
! & C
@+A 1 & /
1 &% &
1 / & &%
1 & &% 1 ( &% /
1 * /
.
3 3
&
1 6?
&
/ &
1
&%
1 1 1
/ / &
1
1 & 1 ( ( / 1 ( ) 1
!
/ & 1 /
?
/1 & 1 & ?
s
1/(s'+1/s')
R
R'=R
L
LA 1/(LA) CA
C
1/(CA) ' , & 1 ( * &
/ 1
1 &
/
&
@ %/ A / / &
!D 1
&
& &
/ 1
/1 1 1 & / &% &
K
1 &
!
L !
@AC @A
/ & 5( C
5
/ / & &% ?
K
. / ( 1C
@
A
K
K
!
K
@
A K ! L ! K L /
K
@ 0A
!
( 1C
@ A
K
K
!
K
@
A K ! L ! K L /
K
1 & 1 &
@ A
! '
1 1 (
1
3 & 1 * & ?
#D /
* AD / 1
0 0
1 1
/ ? / 1
K /J
)
" #
"
& 1
K 0@
L A? 1 (
! @1 ( / 1 / /
! & 1 % / &% & . /3 & 1 /
! $%&
1 + V1 -
+ V2 -
1
(Ω, H) # ( & ,6 -
10
1/10
+ V1 -
+ V2 -
1
(Ω, H,F) - * / / & 1 & #
%
3 > 1 / ? 1
/ &
! & 3
C
C
@
A K
0 0
K
L
K
@ A
C
@
A
K
K
L 0 L K @0 0 # K L 0 L L L
0
1 ( & & 1 3!
@ A
@ 'A
& /
-
1
. //
K 1 &% @!A & 1 /3 ? K 0 1 3/* / /1 & 1 1 " % 1 6 "? ? & 1 %/ ! & ? / 1
& ?
1
#
* %/ & ? @ 'A? & 1
L 0 A
0
4
ω=A(ω’−1/ω’)
3
ω (rad/sec)
2 1
P
0
P’
P’
−1 −2
−A/ω’
Aω’ −3 −4 −2
−1.5
−1
−0.5
0
0.5
1
ω’ (rad/sec)
1.5
K
+ 1 ( * &% & &
&
& / % 0
& & ? 7 /
K
"
&
! 1 ( * &
/1 1
(
1 1
!
K
1
/
/ /
@A / 1 / &
6 C
!1 & @ #A
% 1 /
1 ( / 1 / / *
1
& /3
2
K
!@ A
+?
@ #A
1
/ /
3 / &% & 1 ( ? / 1 36 2 1 1
@ A 1 ! & / 1 /
3 1
3
& 1 & /
& @A / 1 / / 1 1
/ ( 6 &% ?
7 1
,% @ -A 1
K 0
K
K
L A % L
!@
!
!
'
!
1 & 1 &
1 %/ 1
1
/
@ -A
? 1
?
K
?
&
/
/ / 1 (
/ /3 $ / @ +AC
1 /
K
K
K !
K
/1 & 1 *
L 3 & K ? /
K L
&
K
1? 1 * /
'
L
!
L
!
'
@ +A
%$
K
!
K
!
L
!
?
1 &
1
1
/C
L /
'
L
K
1 L 3 & K
@ A? 1 &
!
L
!
'
@ A
/ /C
%$K
K
/1
K
!
/
K
@ A
1 & 1 ?
!?
1 &%
& ? / 1 / / &% 1 1 1 1 1 ( /
/1
?
1 ( * & / / ( 1 / * % ? (
K
!@
L A
! $ &
1 &
! & C
@ 1
&
/
A K
(
! & & /
@
@
& A A
K
@ @
A
! &
! !
@'0A
A
1 ( = / ?
A
K
K
1 1
? 1 (
@
! L !
L
@
@
! & C
A A
& ! L A ! L A
@'A
1 1 = & 1 ( & /
& 6 =
3 1
@
* &% & ? @A? 1 / *
@
! &
! & & 1 1
1 &%
1
& 6 ( 3= / 1
j
ω
'
s’k
j
z k/A, pk/A
ω
+j
z1 /A
p1/A p3/A
σ
0
0
σ
'
p2 /A z 2/A
-j
One zero at 4 One zero at 4
&
1 =
,6 ( 3= * &
/ 1 & & ?
1 ( & =
1 * 1
/
1 & ( @'A &
K
K
!
!
L
! '
/ = 1
1 1 &
*
3C
1 1 (
!
!
'
&
& @ -A?
/
1
@'A
,% @'A 1 1 / * &% 1 1
#
3 1
@
! & & 1 ( & &
A K
0 0
K
0 0@ @
L - #A
L A@
L 0 '
L A
K
@
& 1 & * &
"
A
C
@' A
& # 1
/ = & 1 * & ? / 1 & ?
@ A?
1 0
1 * 1 3/* /
0
1! 1 /
/1 & 1 (
/J
/1 &
60
∆ω=0.5 Null BW
50
α(ω) (dBv)
40 30 20 ∆ω=0.2
10
3 dB BW
Flat Loss=6 dB
0 −0.3
−0.2
−0.1
0
0.1
0.2
0.3
Log10(ω) % & 1 * & & @''A
%
@
@
A
K
K
K
@
A
K
0 0
%
0 @ #@
0#
L 0 -0
L 0+ -
K 0 0'# 1 =
A
1
3 3/*3 /
L A /
L #
L 0 +''0
L A
L 0+ -
1
L 0 -0
L A
? /
1
& 1 /1 #C?
@''A
0'D K 0000 0#0D / K & K 0D & K 0+0D / & K 00
1 & @''A @
K #@
L A L -#Q 00P#@ P#@ L L AQP#@ L A L '0@ L A L Q L A L -# Q 00 P#@ L A L Q P#@ L A L QP#@ L A L '0@ L #-# L #A 00 @# L #0 L '0 L #A @# L L #A@# L '0
1
" % !? @ AC
3 1
A
1 3 /
/13
1 1 1 & 1 ( &
1 - /* E 1 * &% / 1 % ? / & & 0# 1 / &% & 1 (
1 1
'
0.4762
2.1
1 8.4 V1
5
0.119
0.2
0.2
5
1
+ V2 -
(Ω,H,F) 0 * / & 1 ( & &
!
71
1 ( * & ?
@ A?
1
0
7 1 1
/ & 1 * ? ' 0 K ' 0?
? # 0 0 K ' 0
!
& %/?
& #
L A?
K #@
1 1
"
1 1 & 1
1 1 & 3
1? 1
"
% / = 1 *
"
/? 1
1 / Æ
1 ( * & * 1 & 1 / / 1 & &3 ?
!
?
// 1 1 / 1 % &
1 // ( 1 ( 1? 1 1
@ A? 1 &
1
K
* & 1 * ?
!
!
K
!
/ & 1 // 1
& 1 (
/ &
1 ( 1 1
?
1
&
1 /
/ ?
&
K
& ?
!
@
@'#A
/ 1 &%
(
&
1
K
&
@
L
/ & &
@'-A
A
K
!@
L A? / 1
& 1 // 1 1
L A L A L Q
!@ P!
K
/C
@A
& *
/ 1 & //
K
& @!@
@ AC
L AA
LP
#
BP s=A(s’+1/s’) ω 02=1/(LC)
1/(LA)
LA
L CA C 1/(CA) (b)
(a)
5 & / ( 1C
@A D / @ A
/ %
!@
K
P! !
@
&
,% @'+A 1
1
1
/ 1
L A
L
Q
? /
@ L A L @ L ! A
K
@
L A
=
K
@'+A
L A
? 1 * &% ?
1 1 * 1 61
% & 1 & @ A / &
&
& 6 1 & ( 1
&
K
!
@
@ L
?
L A
A@
L
/
K
K
@
K
L
K
L
!
/
K &
!
& / &
A
& 1 / &
& C
!
1
1
,% @'A
C
!
L
L
A
!
!
L
L
'!
L
'!
1
¼
L L
@
L
A
@'A
/
@'A
@'A /
* & 6 /?
L L
1 & &
¼
K
K
!
!
/
@#0A
-
1/(LA)
LA
ω 12
L1
L2
C1
C2
CA 1/(CA) zBP
z BP
ω2 2
Lmax /Lmin = A 2LC = Cmax /Cmin and L 1/L 2=ω 22 Where ω1 2 = 1+ ω0 2/(2A2 )-ω 0[1+ ω 02/(4A 2)]0.5/A ω 22 = 1+ ω02/(2A 2)+ω 0[1+ ω 02/(4A 2)]0.5/A > ω 12 ω 22ω 12 = 1
C1 = AC(ω22 -ω 12 )/(1-ω 12) C2 = AC(ω22 -ω 12 )/(ω 22−1) L1 = 1/(C 1ω1 2) = 1/(AC(1+ω 12)) L2 = 1/(C 2ω2 2) = 1/(AC(1+ω 22)) < L1 L1/L 2 = (ω22 -1)/(1-ω 12 ) = C1/C 2
& % & & 1 // ( 1
. @'A
0 / 1
/
/
& 1 %
1C
K
/
K
@#A
= 1 % & 1 & / ( ( 1 & @ A 1 % / 1 6 1 1
1 &
K
K
/ / &
K
C
!
A A
@ @
!
T 1
!
& /
K /
/
@#A
0.1243
0.0757
13.202
8.0481
+
1
V1
5
0.2
0.2
5
+ V2 -
1
(Ω,H,F)
* / & &
% 1
$ 1 1
(
!
"
& # 1
K
$ ? & 1 %
/ / & 1 & / 1
3 1 % & & 1
3
0? / / & 1 / /
%
3 1
0 / & ( &
K - # & 1 ( 1?
$ 1 / 1 &
K
L
K ? / 1 & &
!
1 1 K #
& 1 % & / 1C
- # @#A
- #
# #
#
L
- # '@#A
- #
K 0 -0-
K
L
K
#@A@
A @ A K 0
K
#@A@
A @
K
@
K
@
@#A
A
L
L
#
'@#A
K -'0'
A K 0'
K 0 '
A K 0 0+#+
1 % * 1 & 1
K 0 0 0+#+ K -'0'? /
K 0 # K
-'0'? 1 & 1 1 'C & / & 1 1 * 1 1
0
! /
& / ? ? 1
% ?
/ 1 61 / 8 1 & 1 / &
1
1 & 0 @ 1 1 1 %
1 A
/
1 1 % / / 1 / 6 ? / 1
36
= 1 &
!
/ /
1 1
1
1
/
! &
! /
1 * / 1
1 / &
/
/ /
1 1 / 1 % 1
61 1
"
/ &%
#
1 & ? ! 1 * & ?
3 3
1 * & ? / ?
1 / 1 / %
& 1
/ 1 1
/
/ 1
/ & 1 * /? / ? 6 & 1 1 ( *$ &% &
&
1 1
% ! ( ) / 1 1 * & 1 ) C
K
1 &
!@
L A
K
!@
@# A
L A
/ & 5(
5
/ / & &% ?
K
. / ( 1C
@
A
K
K
K
K
@
A K
!@
L A
!
L A
@
/
K
!
@#'A
( 1C
@ A
K
K
K
K
A K
@
!@
!
L A
@
/
1 & 1 *$ & ? / 1 & &
!
K
L A
!
1 1
@##A
/
& / 1 / &% 1 / 1
1 ?
& 1 *
1 * )?
!
/1?
1 & 1 * &
1 &
s
1/(As'+A/s')
R
R'=R A/L
L
L/A C/A A/C
C
' , & 1 ( *$ &
1
/ ( 1
) & 1
1
/ 1 * & 1
/ 1
( 1 1 & 1 & &
/ /
K
' ?
/
,% @#-A
/
3 / /
!@
K ? &
C
0
K
K
!
L
!
!
1? 1 / /
/1?
K
L
L
L
36
1 & & 1 (
?
/
1 1 /
L
!
! ' ?
'
K
K L K
/1?
@#-A
A
# / 1
K
1 /
/ &
/ / 1
1 *$ &% & ? @# A? / 1 &
1 ? &
' & 1 ( *$
#
&% 1 C
@#-A &
1 / ( *$ &%
!
'
!
'
@#+A
L
@#A
L
@#A
!?
1 &
B
& C
K K
!
/
K
@-0A
'0
4 3
ω=ω’/(1−ω’2)/A
ω (rad/sec)
2 1
P
P’1
Pass
0
−P’2
−P −1 −2 −3 −4 −2
−1.5
−1
−0.5
0
0.5
1
ω’ (rad/sec)
1.5
K
# 1 ( *$ &% & &
,% @-0A 1
1 1 & 1 // &%
1 1 &% & 1 ( & / /
/1 &
K
@ 1
1 / 7 1 &
1
2
K
K
K K
L
!
!
B
/ & 1
36 A 1 K C
(
& @#+A &
L
L
! K
L
L
!
'
!
'
/
/ @-A
@-A & 1 % / 3
!
. ? /
1
! & 1 =
1 &/ 3 $1 1 & 1 /3 / * 1 1
1 &
/ Æ =
-
1 % 71 1 1
/ ?
1
'
2
V1
1
+ V2 -
1
1
(Ω,H,F) - 1 /3 / *
1
1/(2A)
2A
V1
A
1 (
R3
1/A
1/A
+ V2 -
1
A
(Ω ,H,F) + * / & 1 ( & -
? 1 /
? / & &
? 1 / & )
3 = & 1 (
? 1 * = 1 ?
1 %?
1 6
1
/ &
!
1 1
1 1 / & 1
$% & # ' (
+
* = & 1 (
/ B/ 1 * &% & ?
K
!@
L A
-
1
! & 1 / ? / 1 1/ & " % > ! 1 6 ? 1 1& 3
& 1
/ 1 1
/ % 1 / 1 % / & . 1 1 ! / & & &
1 1 1
/ & / /
3
/
/ 1
! 1 1 / 8 1
/
/
/
'
I
I
1
2
+
+
[Z]
V1
V2
-
1
Ω
-
(a) I
I
1
2
+ V
[Z]
1
I’
2
1:n
+
+
V
V'
2
-
2
n
2
-
Ω
ideal
(b) I1
I'2
+ V
+
[ Z' ]
1
V'
2
n2
Ω
-
-
(c)
3
3?
(
/ 1 /
1 1 1
3 /? @ A
& /
/ &
!
1
/ % 1
/ &
@A
3 & M
/ & /
1 & / / & 1
& 1 1
0
/
1 & 8 1 & / 1 & /
C
0 (0 ( 0 0 0 & & & & ( 0 (0 (& ( & /
K
& 3
? 1
@A
@A , 1 8 & 1 1 1
K
1
&C
/ & /// 3? / @A
3 /
M 1
& 3
/ &
/ /
K K
@-A
C
L
K
K
L
L
/ @- A
1/3
1
R1
V1
x1
R2
1
+
V2
9
x1/3
Q
Q
-
i deal (b) ,H,F)
Q?
/ C @A ?
@-'AC
& (& (& ( &
K
0
0
(
P
Q
/ & ? /
0
0
(
0
0
(
&
& &
&
0
0
(
@-'A
1 ? 1 / 1 /
) 3
/ & 1 ?
'
-
(Ω
& P
K
1
V2
1
1 & / /
1
P
+
V2
1
> / &
P
3:1 +
V1
-
(a)
/ @ A @A
1/3
1
'
6 1
6 & 1 ?
& & &
% *& 1 3 * ? 1& 1 / &
& @A?
1 & ?
@ A K
1 / ?
@
A K
0
& 1 D K
! & & 1 C
L L
& @A
? 31 / &
0
& @A 1 1
@-#A
@ A? 1 3M M 1
1 & @ A
K
/
> // 1
/ 1 &
0 0
! %
/ 1 1
0
&
@A?
* @ A
@ A
K
)
? / 1 M /
/ / 1 /
0
K
@ A
0 0
? 1 &
0
@ A ? /
1 1
@ A?
$ ? 1 / 1
1
/ 8 /
% & @ A / /
? @-'A? 1
@A &
? & 1
P
Q K P Q L
Q K
P
*
? 1
@A? &
0
0
L
'
C
''
1
3/2
9
+
V1
3
V2 '
1
-
(Ω
,H,F)
0 / / & 1 & @A
? ?
/
!?
1
1 (
P
Q
K
K
K
(
/
0
0
0
0
0
0
0
0
. & @--A &
P
L
&
L
'
& %
0
0
Q
'
@--A
/ 1 0 $ //
0 0 ,% @-+A 1
Q
P
( K C
& 0 / 1 &
@ A
Q
K ? P
K
&
L L
1 1
@
0
1 1 1
1
! & C
A
@-+A
% 1
%
= ? ? 1
/ & T 1
! 1 / & 1 1&3
/
/ & 1 1&3
/
U 1 3 *
-
3 >
& 1
+? /
/ % & 1 1 &
(?
1 & ?
%
1
/ %
1 & /
3 1 ? +? 1 @ / 3
A / / 1 &
Q
P
C
K
Q L PQ L
P
P
Q
P
Q
P
Q
Q
P
1 P
K
K
K
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
! !
! !
0
0
0
0
0
0
0
P
1 5
0
0
0
0
0
(Q K
0
0
0
0
0
0
0
0
0
0
0
1
0
Q K P(QP QP(Q K
!
!
!
!
!
! !
!
!
!
!
! !
0
L
Q L P Q L
0 0
0
0
0 0
0
0
P
0
0
0
0
0
0
0
0
0
0
(
0
0
0
0
0
0
0
0
0
0
P
@-A
0
Q
@-A
B ( ? 1
/ @ & 1 A 1 & ?
& / C
Q
P
Q
P
Q
P
K
K
K
'#
(QPQP(Q K
P
(QPQP(Q K
P
(QP QP(Q K
P
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
! !
! !
0
0
0
0
! (
0
0
0
0
0
0
0
0
0
0
0
0
! ( !
0
0
0
0
0
! !
0
(
@
( ! ! L !A ( ! 0
(?
1
! 0 0 0
!
0
0
0
0
( ! ! 0
0 0 0
@+0A
'-
1 & / 8 1 / & & 1
/
(?
6 / 1 1 &
Q ( P
1 /
( 1 @ A
/ =
1 1 % =
( ?
% /? / 1 1 / ( 1
1 1 & 1/
@+AC
( !
1 1 @
(
!L
@
!
/
1 A?
A
1? & 1 / ?
(
,% @+A
% /
( (
K
!
!
K
K
!
!
!
L A &
/
Q
@+A
! !
0 ?
8/ 1 1 &
P
P
Q
&
Q K
(?
(
!
(
/ &
K
!? P Q
0
0
!
!
0
0
0 +0+
0
0
0
0
0+0+ !
! L ! A 0+0+ !
@
0
0
0
0
! !
0 +0+
0
0 0
0
! &
+ / & 1
0
0
/
/ 8
?
!
1 1 / /C
/ 8
/ &
!
& 1
@+'A
! A
K
!
(
@+'A
? 1
1
1 1 &
1 1 /
! @
!
( 'D / ? 1 &
!
@+ A
!
K
/
+ 1 / 1? / / 1 * & ? ? 1
/ & 1
1 1
1
0
= & 1 & / 1 1
/ 1 & 1
C
0
QC
0 +0+
K
/ P
P
1 / / &
1 @
@+A
L
/ % =
.
! @! L !A
1&
!
1 1
1
!
?
& 1
/ 1 & ? / ?
C
1
R
V1
1
R
1/A
C
1
R'
C3
2
C
1/A
2
3
1
R
C3
'+
1/A
4
R
+ V2 -
1
5
C =[2] A /([2] A-1); C =A /(A -[2] A+1); C =[2] A 1/2
2
1/2
1
3
2
1/2
2
1/2
2
3
( 3/ % & 1 & +
1 1
1 *
/
+ .
1 ( / 1 / /
1 / / / & 1
1
1 1
/ 1
!
*& / 1 1 ?
& /3
1 % & 1 & & (
$% ) $ ( ( &
1 / 1 / / &
1
1 3M / 1
& / 1
1
0
! /
! /
/ /
0
1
&
! / 1
! & &
/ 1
& 3 ?
& 1
/
!
/ 1
! & 3
@AC
C
0
K K
0
& L & & L &
L
@+#A
C
0
K K
0 0
K
0
& L& & L & L & @
A K
/
0 0
& & @ A L & & @ L & A@ L & A & &
/
@+-A
'
I 1
+
V
V1
g
I
1
2
+
[z]
+
V2
-
V
1
-
L
-
(a)
I'
I'
1
+
I
g
1
V'
1
[y']
2
1
+
V'2
I
L
-
-
(b)
@A / / ? / @ A
/
!
1 /
'
!
@ A?
1 1 &
%
1 1 1 & / C
0 0
P) Q
0 0
K
K
K
K
) )
K
) )
K
& &
& 1 / 1 / 1 & /
& &
! &
C
C
0
K
K
0
L
)
)
0 L )
0
L
)
0
@++A
C
)
0 )
K
L )
K
< & ?
1
L
0 )
/
! 1
0
) ) L )
@
A ) )
/
K
A
/
0 0
@+A
! / & 1
! / / ? 1 /
1
)
) @ L ) A@ L )
K
? 1 /
L
!
/
! 1 1 / 1 1
& / 1 ? 1 * *$
6 ? 1
1 / & 1 (
/ 1 1 1 1
/
1 / 1 / 1V U &
1 / / 1 / 1
"
1
! & ?
0
0
?
1 & 1
!
. 1 1
1
%
/ / 1 /
. ? 1 6 &
/ 1
//?
1 1
/ /?
/ /
&% 3 / % & & 1
!
/ /? / 1 / / & & * @ / *$A // %
/ / 1
#0
ω 0=2.5
1. 68
1
1
Vg
1
0. 09524
1
+ VL -
1
+ VL -
(a) ( 1
Ω,H,F)
1
1
Vg
0. 09524
ω0=2.5
1.68
(b)
@A ( ? / @ A
/
!
#
8
0.25
5
0.05
V1
+ V2 -
5
(a) (Ω,H,F) 1
0.8
0.8
+ V2 -
5 1
V1 4
(b) ' @A / @ A & 1 1
1
/
/ 1 & %
/ &
1 & 1 * & & ( / 1 & & 1 * & & 3 / @ MA
!? 1 /
?
1
! / 1
1 1 /
! &
/
/ / & & /
#
$ 1 & 1 ? @A / @ A?
% !M? /
& 1
! & ?
K
0 0
' 1 1 /
/J /*
' ")=
? & 1 & 1 /
2 !
? / / 1 & @ ? ( ? * A $ & 1 E / 1 / & 1
> L 3/*
1 /
1 8 & ? #N & 1
1 ? @A / @ A?
'? / 1
/ @ A & / 1 / / &% 1
#
ω
j
s
j
ω
'
s’
2j
j
-2
σ
0
-1
0
σ
'
-j s=8(s’+1/s’)
-2j
# 3= / & '
1 & 1 ? / 1 8 & / 1
! &%
1 8 & / /
? // #
& 1 / / 1 / ? @A / @ A? '? / 1 / & & 1 / /
. / / ?
//
1 1 / 1 / 8 & 1
/ &%
1
$ & 1
E
/ / & 1
'
& 1 &
! 1 1 3= 1
& 1 & D
"
&
& 1 &
/ = 8/ 1 & ? / 1 @ /
/1A
#
! & $!1 3= & 1 / 1 :
6/ / 8
1 / / = C
@
A K
@
@
L 'A L
L #A
/ 1
#
R
1
1
2
@ s
+
LC
V1
R
Lossl ess
p
Z
in =
(R + j 0)
1
V2
2
-
Ω
- & -
#
1 1 &
@
A K
! & C
# 0-
L - -
L 0
@A / 1 * & & ?
!?
L + #
L'
L
% / & 1 (
& / / 1 3!)= / &% & !)= $ & 1 / &% ? @ A 71
/
1 /
/1 1 /
& -0 /* 1 &% & 1 I
% ?
/
?
$ & 1 &3
1 / 1 -03/* / & 1
& @A 1 &
1
! & & 1 /
K / &
! /
- &% ? 3
+ $1
K
!
1!
1 /
- (
&
%
0 0
1
L 0
M 71
M?
% 1
1 1
!
/
1 ( 3 @ K
$ @
1 & ? / 1
A / 3 @ A / / LA ,6 1 1 $ 8
1 1 1 (
B/ 1 & ? / / 1 / /
/1
1
/ 1
?
+
/
% / 1 1 &%
? / 1
1 1
1 &
1 1 & 1
'## !)=
1 3
1 / & 1 & %/?
? 1 &% I
& 1 & ?
/
3
? 1 /? 1 /
'## !)=?
K ? 1 / /
71 / & & ?
!?
/ &%
#'
70 60
Loss (dB)
50 AS=45 dB
40 30 20 10 0 0
0.5
1
1.5
2
2.5
3
ω (rad/sec)
3.5
4
+ ( &
& ?
?
% / 1 / / & 1
/ I ,6
? / 1
!1 & 1 6/ &
& 1 / / 1 ( 1
- 1 3/* /
/1 & /J
@A ( * & 1 * 1
"
& # 1! 1
@ A ( *$ & 1 & & ? 1 /
!
K 0 # 71
/1 & 1 *$ I 1! 1
0 1 &
/1 & / = ?
K 0
@
L A?
! & ?
@
@
A? 1 3/* /3
K # > 1 / & 3 A / &
1 / = & 1 ? / 1 &
71
/? /
1
1 /
@
1
K /
A K
1 3/* /
/ 3
/1 & 1
/1 1 I
0 -@
L '
L '
L - #A L
/ 8 /J / =
K ' /J 1
& / / /
##
1 / 1
&% 0 !)= 1 & &
1 1 1 /
/1
1
/ &
0 !)= @A 71 & & @ A
% /I
1 &%
1 / / 1 =
I & 1
! & & 0 1 1
1 ( ) &% & 1
@
A
& ? / !1
3=
1
/ / 1 &
3
!1
? ? 1 1 / % ? 1
? 1 1 @ A 1
? 0
#-
1 & 1 1
/ 1 %
/
1 ? &% 3/ / &
/ / 1 8 & 1 /
/
?
1 1
@
3&% /A 3
/ &% 3/ /
& ? 1 / &%
1 /3
1 &% 1 ? /
/% 1 & )
1 3 . /
! &
& / / /
" / / / & 1 & & @ ?
/ B ? / / 1 1 /
1
/ & 1 = & 1 / 1
&/ 1 ! @ A &
/ 1
& 1
5& POQ / 1 / & 1 1
P-Q / / //
1
5&
/ & & ? /
/ 6 : R 5 / 1 /
/ 1 % & 5
8 A
1 / 8 ? 1 1
& 1 &
/ 1
1 & P'Q
// / / & 1 1 ! 1 8 & &% 3/ / & 13
/ / $ 6 =/ 1
/3 /
/1 / 1 6 1
/ @ / & A /
1
1 1 1 13
1 &
1 1 1
1 / & / / &
/3 & 1 & 1 1 1
/ / / & 1
1
/
1 / /
' ( ) # #+
#
I+
V
b
(+V )
(+ )
RL
i
v
0
COMMON
i
+ v0 -
(-)
(-V )
V
b
-
I
1 /
1
& / &% 8 1
/ / . / / / & 1 1 1 1
/ /
1 / &
$ % & '
1 / 3 & ,6 3 /? ? ? 3/ ? / .
31 ? 3
/
1 & 1 1 / / / @.A ! /
E /3 3 @. A ! $ 1 3
/ ! / ! ? / 1 1 1 & /B = 1 & / & 1 $ 3 ! /
/ %/! / 1 6 &
= 1 /
/ /
/ 1 / 1 / 1
3&%
//
/ 1 /
1 1 % / &
1
1 / % / 1 @ ? /
1 /
B A 1 1 /
/ ? 1
1
/
/ / / 1
1
.& 1 / 1 . ! ? 1 1 // / % / ! & ! 71
+
1 1
+
1 ("'# 1
/ & 1
?
1 !
13 .
! ! &
/ 1 #3
1 / 1 1 & 1 !3 3! . // ? 1 1 &
1
% / /
1 / & 00
& 03
@ A &
#
Output Voltage, Vout (V)
20 Room Temp
15
Hi Temp
10 5 Input Offset
0
Slope=150,000 Output Offset
−5 Lo Temp −10 −15 −20 −200
−150
−100
−50
0
50
100
150
200
Input Voltage, Vin (µ V) & 3 &
#0?000C
1
6?
3&%
1 1 /
1 1 1 1 = @ 8A
/ / 1 8 / 3/ / 1 ?
1 1
1
@ A? 1
1 1 ?
, ?
/
8/
/
/B
/ ? 1
/ 1 & &
/ Æ / 1
1 % / " /
& &3 / ? / ? & 1 )
1
1 ! & 1 $
3!M 1
/ 1
K
0
K
0
1
1 00
@ AC
0
K 0 7
? / 0 /
1 1 1 ,1
&
@ A
/ #0 7 &
/ @ & A
@ AC
.& 1 / /
K
#0
@-00A
0 0
& 0 + 0
7
K 0 + 7J
/? 1 1 /
7 K 0+ 7 1
@ A
6 /
/
0
-0
(+)
(+V)
(-)
(-V)
I 0A
0V
Vb
RL
COMMON
+0V -
Vb
I (a) i0 /2
(+) v
RL
i0
COMMON
+ v0 -
i
(-)
i0/2 (b)
@A $ / @ A / & 1
1
@ A & &
& / / / ? / / /
/
1 ? 1
1 1 1 / ? & @/ A &
1
)
? 1
1
& ? / ? *? / 1 ! /
/
/
1 1 / & % / 1 1 1 ! 1 1 /
1
! T 1 $ &?
1 1
71 1
1
/
1 /
/
= ?
1
1 1 1 1 $ / 3 /
/
&
1 = 8?
/ / 1 1 1 1 ?
+
, ?
1 1 /
/ & 1 1 1 1 ! ! $/ E
1 1
& ? 1 & 1 6
1 1
1
& 71 1
/
/ / 1 / % /
-
i0
(+)
+ vi -
+ v0 -
+ Av - i
Ri (-)
COMMON
' 3 / / & 1
// 1 1
1
& 3 / /
1
1 / 1
/
1 U /
' 1 /
/ / 3
1 1 / 1
& 1
1
? 1 /
1
1 / / 1 &? / & / 6 ? 1 /
/ &1
. 1 / 1 & ? 1 1 / & &
/ 1 /
!
T
/ =
$
@ A? /
+
/
1
?
)
A /
/
/ 1
1
? 1 #
1 #@ A
!+
/
1
+
@ A
& 1 /
1
/
@1& ?
1 1 /
/ / 1 1 1 & #@A 1 1
1
? / 3 / 1 / /
#@A
1 / & 1 /
# / /
1 / / /
' 1 &
1 & 1
&/ ! ? 1
1 &
A
@
/
I
! ( 1
/ 1
1
= ?
/ = A & ?
0 K
/ =
1 ! &
/ C
1 1 6
/ &1
K
% ?
1 1 .
1 ! & 1 & /
+ )
1
@ 1 /
1 1
$ & @ & A?
+
/
+ ?
!A
/ 3 @
6 /
-? /
/ 1 & 1 1
3
1 & 1 / / @=
! * % ! Æ !
-
.0 A
+ .0V -
.0 A
(+)
+ v0 -
+v - 0
(-)
(+)
+ .0V -
v0
(-)
(a) #
(b)
/ / / & 1
/ =
@A " / 1
? / @ A 1 / 1
@A
R1
R2
i1
i2
90 A
+ 0V -
vg
+
(-)
v0
(+)
-
90 A
-
& / /
+
- / & R( 1
+
1 A 1
1 1
+
1
K
1 1 1
,
/ @ 'AC
L0
@ 'A
, L 0
@ #A
R( / 1 / @ #AC
+ R( 1
K
/ @ -AC
, L , $ / @ +AC
+ +
K 0
@ -A
@ +A
K
-
R2 R1
(-)
+ vg -
vi R i +
+ Av - i
+ v0 -
(+) + / ! 6 3
1
1
"
/ / &
3 / /
& 1
3&% ? 3 /
/ 1 / & 1 / & 1
1 1
+
/ = 1 & -
1 6 / 1 / &
+
K
0
K
!+
'
* 1
/
!
1
C
R(? /
@+ A L
R( 1 / @
+ !+ A L @+
@
+ A
+ A
& / /
@ AC
. & @ A 1
+
K
+ +
K
1
! + L L AQ L P L @ L AQ !
!
P
1
L@
/
!
@ A
L
? 1
1 1 @ +A & 1 / ? 1 / / / 8 1 & & . 1 6 /
1
/ / / /
8 1 / & / 1
8 / 1 / & / 1
/ 1 1 ?
&/ ! ? 6 1 /
1 1 ? /
/ / & / / % ? 1 /
3
! 8
' & 1 /
/
1
-'
+ 15 V dc
C
b
(+)
+ vi
+
(-)
-
C R
b
v
b
0
-
-15 V dc
1 / &
# (
*& ! 1 B & 1 &% 8 & 1 ? 1 / & 1 /
?
&/ !
/ / /
1 & 1 6 3
1 1
/ ? 1
? ? 1
?
1 / &
1 1 13 1 1 /3 1 1 /
1 1 / 1 6 1 13&% @ / A? 1 1 / / /B 1 ? / 1 1 / 1 / 1
/% & 1 B
1 3 @00 0 % 1 1 / 1
1
"
1 13
1 /
1 =/ & 1 ? 1 / ?
/ ? 1
A?
1
1 1 1 /
// 1 .& 1
% /?
3
1 / 1 ?
?
/ &
8 @ A = & =
1
1
/B = 1
1
1 1
3
1 1
& 1 1 71 1 1
/ 1 ? 1
/ 1 % &
/
/ /
1 & 1 / ? 1
-#
& = 1
/ %
/ 8 1 // 1 / /
1 / 1
1 / 1 /
1
&/ 13 / / Æ
1 6 / 71
1 1 1 / 1 / & 1 ? 1 13
1 1
/ (13
1 // /
/
& 1 1 1 / 1 & @ ?
/ /
/1 1 6/? 1 / A
" 1 1 / 1 1 6/
71 1
& 1 /? 1 / % /
/ 1
/ / 1
1 / 1 / / 1 6 / / 21 1 % / 1 & 1
1
/
1 % 1 1 ! 1 1 1 % &/ &/ !? / // 6 1 % / / & 1 / & + 1?
1
+
= ?
1
+
? 1 ?
! @ / A?
1/
= & = 1 /
1
+
1 1
?
+ ?
?
= 1? 1 & 1
1 1 &/ !
1 1 1
+
!
1/
+
1
1 & / @ A? &/ 1 /3 ? 1
/ 1 ? / ! ! 1 = / 0# $ "1 1 ? 1 ? !? 1 1 1 & L ? 1 /3 1 1 /? ? 1 ! 2
1 / & ? 1 /
1 1 1
/ ?
? /
1
& 1
6
?
/ ? 1
1 /3 & & &% / / 1 /?
@
) ? 1
K ?
@ 1
K
+ 1 / /
A? / 8 @
K
K A? 3
K A & & / 8 %
% & 1
1 1 &/ !
/ 1 / % & 1 1
! 1 #0 000 2
3 ? 1 / &
?
?
?
1 1 ! 1
1
B / 1 / & 00 & /
.
?
/
1 /
/ % 1 / &
+ +
--
& 1 / & 0 .
!
1
/ / / &% 1 8 & 1 1 &% $ ?
?
!
1 /
/ 3 3 1 1
1
1 &% / /
1 !
@ AC
! !@
A K
@ L
! A@ L
A@ L
A
@ A
. @ A? 1 & 1 1 &% / / & 1 & ? 1
1 3 ? / ? ?
!? ?
1 1 1 /3
/ &% / / ?
/ 1 =
L
/ @
1 / 1 &
1 1
!
@ A? / 1
1 A?
1
/ 1 &
# '* + * ,
/ 1
1 1 3
6 /
3 & @ 0AC
! !@ )?
!@
A
!
A K
! L
@ 0A
1 & 1 & & ? /
/ &
+ +
!
@ A?
K
L
L
1
K 0? @ A
L
. @ A? 1 6 & 1 1 1 @ L
A
1
1 /3 ?
K
1
!
1
? 1 / 1 1 3 ?
1 1 1
!
,%3
& * / &
1 3 & ?
1 1
3
1 /3
1 /
/ &
1 & 1 3 / /3 & & 1 3
@ A
6 ? 1
@ 0A / @ A /
1 71
/C
* 1
&
1 =/
1 1 /3
/ / 1 3 & & /3
. // ? 1 1 1 3 /
/ 1&3
/1
/
1 / & 1 3 ? /1?
@1 3 A
& / / 8 / ? 1
! ?
1 /
/1
1 3
/ 1 3 /1 /
/ / 1
1 / 3 &% & 1 1 /3
100
(A )
-+
Open Loop
0 dB
Magnitude (dB)
80 60
−20 dB/decade
40
Closed Loop (G1R2)dB
20
A0p1
0
p1 0
A0p1/(1+G1R2) 2
10
4
10
6
10
10
Frequency (rad/sec) $ 3 3 / /3
/
/1 /
@ L
1 1 1 3 /?
A 1 / 8
1 1 ? & 1
&
3 / /3 1 /
/1
! ?
1 & ?
1/? /
? &3
/ 1 3 3 & 1& 1
7 1
/ ?
/ 1 3 / //
! ?
?
1 ?
/1 & 1
/ 1
& /
1
/ / 1 1 6 &
/
)* + * ,
/ 1
1 1 3
6 /
3
& @ AC
! !@ ?
!
A K
!
@ L
A@ L
1 & 1 & & ? /
$
+ +
!@
A &
!
@ A?
K L
@ L
1
A@ L
A
@ A
A
/
K 0? / @ AC
-
100
(A0)dB
Open Loop
Magnitude (dB)
80
−40 dB/decade
−20 dB/decade
p1=p2=104
60 40
p1=104, p2=107
Closed Loop
20
G1R2=30
0
G R =3 1 2
ω0
2
4
10
ω1
ω0
6
10
ω1 8
10
10
Frequency (rad/sec) 0 ,6 &
L
K L
1
/
1 6
K
K
L
L
3 3
! @ L
L
L
A
1 1 ? K
& @ A
?
! ?
/ & 1 /
1 @ L
A !
/ / & 1 /
,% @ A / @ A /
* / &
K
/ &
0 &
/ 8 & 3
& & 1 1 /3
/ &
&
& 1 3 &
1 1
& 1 1 3
? 1 / 8
A ! ? 1 /
/ 1 1 1 @ L
/ 1 1 1 /3 & ?
1
@ A
1? / 1 /3
1 3 /
/1
? 1 /
/ / 1 3
1 & 1 3
/ /3 & . 1 ? 1 3 3 / 1
/1
! A
K @
? 3 /
& 1
1
/ ?
/1 & & &
C . / K 0
3 &% @
1 6 ?
K - 0
& 1 1 & /
A / 1 3 ? 1
3 / 3
/3 1? ? 1 13&%
-
1 1 =/ !/ ? ? / 1 & 1 6 / 1 &/ ! / 1 3 & 1 1 ! / / &/ 1? / & 1 /3
3 1/
3&%
/3
1 13&%
71 1
%? 1 3 / 8 '0 /*J/?
" 6 / A $ 1 3
/ 1 13
"
K
1 /3 @ ?
1 /
6 ? 1 / 8 0 /*J/ / 1 '0 /*J/
1 1 / ! &%
"?
6 1 1 !
1 1
& 0
1/
1/
1 1 ? 1 !/ 1
& & 1 ?
1 3 3 /
. 1 1
/ 1 /3 1
/1 @
/
1 / K
! A
71
1 1 3 ! ! 3
& &% 1 /3
1
3 /
1/ &
/1
1 /
/ & /3
% 4 ? / 1 3 1 & 3 1 @0 /*J/A 3
/ / 71 1 1 1
1 / & / & & ?
1
? / 1 1 1 /
/1
/
/ 1 / 1 / / / & B & &/ ! .& / / / ?
1 1 / & //
? / 5
/ 1 & / / 6 ? 1
K
/ /
1
/
!
3 3
1 1 5 & ? @
L
A @
L
A?
1
" & /
1
/ / & 1 / 1 1 / *&
/ 1 /
/ 1 /3
1 13 6 ?
/ & 1 %/ & & @ A
$ & 1 = 3&% & 1 / & @ A / 1 /3 ?
?
@ 'AC
K
1 1
L
@
A
&
!
L
1 1 1 1 /3
1 ?
@ 'A
!/?
? / 1 &31& & 1 63&%
& & 1 13 6 //
! ?
/
1 &
1
/
/ &
+0
100
(A )
Open Loop
Magnitude (dB)
0 dB
80
−20 dB/decade p1=104, p2=107 p3=108
60 Closed Loop
40 20
G1R2=30
0
G1R2=3
ω1
2
4
10
6
10
8
10
10
Frequency (rad/sec) ,6 & 13 3
$ * + * ,
6
1
1 / 1
/3 & 13 / & 1 6 ?
1 1 /3 1 ! @ 6 A 1 13&% 1 3 / 1 3 / 3 /
K
1
0 ?
/1
! A
K @
1 & 1
@. 1 / 1IA
1 1 / 1 3 / 0
/ 1 /
1 1
?
1 /3 & 1
3 6 ? 6 1 1 &
0 @# /*A
& /3 % 1
0 @& 1 A 1 1 * / / 1
.
(
#
K
1 /3 & ? @ A? / @ #A &
+ +
K
K
1
"@
A
K
11
/ 1 &
/ 1 / & / &
1
/1? / ? 1 ! !
1 /3 1 1 1&3 &
&
/3 . 1 ? 1 3
3 6
/1
1
D 1 ? C
# # A@ L A@ L A@ L A ! #! @ L # A"@ A ! @ L A@ L A@ L A L L# L @ L
@ #A
$ & @ #A &
"@
+
A K 0 / 1 ?
K
& 1 1 / & 1 ?
#
1
? & 1 /3
! @ L # A?
131&3 1 ? ?
1
1 1 / !
1 1 % " & @ #A & / ) /
? ? 1 B 1
1 = (
1 &
K
& 1 1 ?
36
/
% C 0
A L @ L
K
@
L
A@ A
L@
L
P L ! @ L # AQ
L
/
L A@ A @ -A
,% @ -A? 6 1 ? 1 @ ?
"@ A
1
% = A
1?
1
36 & 1 /3 &
/ @ +A & & @ #AC
! L#
& 1
K
L
K
K
0 #
K @0 '
-A0
#
@ +A
"@
!
K @+ - L
1 1
1
#
K
1
& /3 &
/
/
K
1 & 1&3 ?
/ 71 # K /*? #- A0 ? /
1 & P &
K 0
A? @ #A? / 1
1 1&3 1 /3 /
/3 ?
& 1
K 0
1 / &/ !
K # /* & 1
/ 1
!
9
K 0 /*9& 1
/ 1 /3 &
? / 1 6
& @ -A 1
0
L
L L A
@
"@
@ #A 1
! & AQ & &
. 1 / & 1 1
& " 1
1 / 1 1 ?
! ?
1
/ /
! "# $% &&$# ''' ## ( # /
1& / /
! & & " 1 ! 1 !
+
100 80 K=1
jω (Rad/sec)106
60 40 20 K=1
0
K=100
K=100
−20 −40 −60 −80 −100 −150
−100
−50
0
50
6
σ (Nep/sec)10
#
41 & & & /3 ?
4 ? / // @ 1 3 /
/1 1 1?
1 / &
/ &
& 1 1? 1
&
A
& 1 /
1
/
1 1
/
6 &/ !
? 8 1 &
/ &/ ! / &% %
& % & ' (
1 / / @$A
/ & / 1 =
/ 1 ? 1
@A? 1
1 ?
/ 1
+ ,?
= 1
1 / @/
Q . // ? 1 ?
/ / / 1
+ ?
A
1 1 / & / ?
1
& 1 @ A
1
1
?
1 8 1 & & ?
1 &
+ ?
! / P ?
+ +
1
/ / & 1 /
1 /
@$A / / & &
?
1 % =
/ / 1 1 1 $1
. 1 ? 1
/
1 1
+
R2
R2
R1 i=0 + vg -
R1
i=0
+ vx -
+ vg -
+ Avx v 0 -
+
ix
i=0
+ v=0 -
(a)
+ Bix v0 (b)
/ ! / / /C @A $? / @ A $
, ?
?
/ 1
/
?
1 =
+, ?
= $ ? 1 /
1
& 1 & & & 1
1
$ 1&
)
?
! / ! / 83
/ / 1 &
& @ A / @ A & 1 & @? A? @AC
+ +
K
A !
@ A
$
@ A
L @ L
@ AC
+ + / / ? @ A
K
L
1 @ A
& & @ A 1 &
!
/
$?
1
K 0? / @ A
1 / 1 &/ ! ?
1 &/ ! *? 1
&
!
/
& ? 1 1 @ A? 1 /
. 1
$
@ A / /
/? 1 1 &/ !
1 1 1 1I 71
? % /
1 / / 3
/ 1 1 & 1 &% ? 71
1
/ 8 1T 1
1
?
1 / /
1
1 =/ 1
& 1 /I 7
&
1
1 6/ 1 / U 1 & 1
1
=/ 1 1 B & @ A 1
1
1 /
/ 1 $ ?
/
&
%
1 &
1 1 1
1 1 /
1 1 &? @ A
? 1 / / / /
+ +
1 6
/
&/ ! 3 / / &% I
1
'
& /
3 &
1
/ &
? /
@ 0A & 1 & & & 1
+'
R2 ix
R1 + vg -
i=0
+ v=0 -
+ vy -
Bix R
+
+ - 1v y v 0
-
' / &/ !
+ + . 1 ?
K
1
L $
@ 0A
1 8 1 &%
1 1
& 1 /3 & &
)
? 1
1
8 1 1 & 1 &% . // ? 1 / 1
+ +
8
1
/ 1 /
1 8 1 &%
)? & 1
&% 1
1 1 $ ?
'?
1
/
/ & 1
/?
1 1
/
& - . / !0
1 /3 & @ 0A 1 &
0 AQ
C $
K L
1 6 1
/3 ?
L
$
K 0
0 @ L 0 A@ L 0 A 0
0 L 0
#
? P@ L 0 A@ L
# & / 8
K 00 !M? /
/ 0
&
K
@ A
" / &
/ & / 8 &
1 % / 8 & 1 1
0 / & 1 / /3
. 1 6 1 1&3 3 / & 1
/
K "M?
@ 0A / @ AC
+ +
+ +
/ @ A?
/
/1 1 /
1 /?
/1 / 1
/ / &/ ! ? 1 1&3
? / 1 3 /
/1 1
1 1
/
/1
1 1 &/ ! @ /3
A ,1 & &/ ! 1 / &
/ / 1 $
3&% / /
1
+#
70 60
Magnitude (dB)
B0=103, p1=104, p2=108
G1R2=103
−40 dB/dec
50
G R =102 1 2
40 30
G1R2=10
20 10
G1R2=1, R2=105 Ω
0 −10
2
4
10
6
10
8
10
10
10
10
Frequency (rad/sec) # / /3 6
/ /
/ 1
1 $
/ & >) 3
/ / 1 / 1 /
8 & 1 13/ 3 3/ 5 ? 1
/ / / &
1 1 =/ /
1 / 1 1
1 1 &
&/ !
/ &% 3/ / 8 / / & & / /? /
1
3
1 ? /
/ / & &% 3/ / 1 1 6 / 1 1 1
1 /3 /
% 1 / /
/3 1 1 13&% 1 / / / 1 1 / 1 &/ ! */ 6 // &? 1 $ &/ ! / 3 / $ &/ ! / 1&3
/
/1?
1
/1
1 / 1 / / / U 1
1
1 / / / &%
1
1 %
/ 1 / &/
1 1 / /
1 &% &
1 / 1
! & / / &
@ ? ? &/ ! ? 3 A
71 1
+-
B
B
1
& & /
1? 1
/% 1
5
/
1 ' & P'Q?
/ 1
1 ' & PQ
$!1 @ A?
1
3 ? 1 & 1 & 1 /3
? @ A? & & 1 ?
3 3 &
1
#
K
!
K 0 ?
K
K
K 0?
0 ? /
#
&
00 5 13 3 & ?
0 ?
K
K
0 ?
/
K
0
5 13 3 & ?
0 ?
K
K
0 ?
/
K
0
1
!
K 0 ?
1
!
K 0 ?
' 6 & 1 / & 1 ! & 1 /3 1 /*
0? / 1
1 1 / 8
K / 0
# 2 * / / & 1 /3 ? @ A? & 3 & /
K 0
(
> 1
/
1 /
K / 1 6
1
K
!
K 0 ?
3
K 0 ?
1
K 0 I
1 / ?
1 1 3
1
- / 6 & 1 /3 & 1
K 00?
+
( 1 / / @
1 /3 / 1 / / @ /*A
K 0?
K !M? /
K 00
+ 1
/
!
& / / 1
K 0
@
L
1 /* )
1
0 0
1 /* /
K &
/
/
&
00A / 1 / / @ A K @ A .@ A? /
/ 1 / & ?
&
I
// & 1 1 = ? 1 (
1 &% /
1 1 1 / 1 / / 1 &
1
A? /
/3
-
.
K @ A @ A /* 3
/1 & 1 /
1
/ 1 71 8 / 1 1 1
/1 &
I
5 + & 1
K 0 0
/ & 1
0 5 1 6 /
# /B
00 M 1 1
#
/ 1 /
K
++
0.2 µ F 1 kΩ
100 Ω
i=0
+ vg -
+ vi -
+ v0 -
- Av i +
1 kΩ
- & +
(+) + vi (o.c.) (-)
-+ Avi
(-)
vi +
v0
v0 ZTH
(+)
vin
(b)
(a)
+ & C @A /? / @ A 8
> 1 / 1
+@A / / 1 1V @ A
/ & 1 8 1
+@ A
/ & 1 3 P ? % / & 1 71 ! / &
1
!
K
! @
> 3
AQ
L
/ & 1 & /
/ I . 1
/ 5? 5(?
5(I / 1 8 /3
!
)
/ ?
?
/ 1 3 8 1
& 1
/ I
/ 1 1V % / & 1 1
(
!
K 0
@
L
#0A
% / & 1 ? /
1
$ & &
/
1 /* /
71
1 8 & 1
/1 /
3&%
& 1 1V I ' . 0?
3
!
/ / &/ !
+
R2
+ Ri +- AV1 V0 -
+ V1 -
I1
Zin &
vx +
Vg
R0
(-) (+)
+ -
Avx
+ V -
Thev=?
&
+
I
1
1
+
R0
N
V1
I
2
2
+ V2
-
Vg
-
+
0 & '
1 & 1 >
! & ?
) 3 ? &
0 0
)
K
# 1
1 /? 1
/ ?
@
A K
0
?
&
@A 71 1 / = & @ A 1 &
@
A
@
36
>
! K ! @ L A? / / 1 ! ? /
AI
0 /
!
1 1
@0AI
@A 71 & ? ? 1 1
@ AQ 0I
P
= & 1
1
71 / / ?
&
?
/
+@A?
1
0
1
I
!
3 ? / / 1
) 3 D
0
/ 1
) )
)
71 1
1
?
/
% / &
/ /
?
K
0
R
1
I
-
+ V -
+
R
2
R
4
R3
& #
) PQ R ? * ?
! ?
-1 /? > $// 5 ? :C
)? PQ "1
!? . ?
"# ! $ % & ?
> $// 5 ? :C
)? P Q " ? : ?
' ! ' ( # ! () *?
* ?
"C ) 1 " W ? P'Q 5 ? : R?
+ ,-"# ?
S !C 7 3
? +# P#Q 5 / ? " $?
$ ?
& ''. (
. !
5/ ? "C // 37?
P-Q ? 4 ,? 4 ? : 4? / ) ? ( ?
* ?
S !C "4
P+Q = ? ? ( / ? :? / ) 1? 4?
& #?
+ ,-
3) ? +
'
.,,, $ ? ( / ? , /C
* "#
(/? 0 PQ 6? : 4?
! ! #?
S !C "4
3) ? ##
1 1 1 =/ 1
1 &%
&/ ! / 8
8 / / / & 1 / / // ?
1
1
1 1 1 1
/ 1 00 /* & 3 .
/
1 1 /
1 //
/1 / 8 &
* 1 1 /
@$A / / @$A / /? /
1 1
1 & 1 1
1 / 8
1
/ ? ?
1 / / & & /
/
/ / &% & 1 13
? 1 ? / 1 & 1
8 / / 1
1 / !
1 1
1 6 / 1 / ! 1 1 . 1 !
% ?
//
// & 1 /
/ ? ? / &
1
1 / &
1
1
/ 711
/ / /
/ B
$ *
1 /
1 / & 6/ 3
1 1 &
/ /
1 ? 1 1 1 /
1 / T
% / / / / 3
1
/ /3 E @
A & ? 1
'
.
% / 1
IR
IM
+ VR -
R
'
(+V)
/
+ V E+ -
+ V
Q1
I R+
R-
Q4
V (-V)
R1
2N3906B Q2
R+
I R-
+
αMIR
Q3
I M+
IW+
I
I
M-
Q5
+ V B-
Q6
R2
' * / &
1 & ?
" ?
W-
2N3903B
/
1 1
! ! / '
& / !
1
/ / & 1 /
/
3
1 1 1 3
/ 1 /
1
?
1 1
1 /
& 1 & & / / // 1 &
/
' @A 1 ! 1
1
& 1 1 & 1
/ 1 1 1 3 ?
* ?
1 ?
1 / 1
/#
@$ / 6 ' &
,-.
Higher P otential S ource
I
R
I
R
R
I I
F
I =I C
Q3
M
+
M
α )I
2(1-
V’ I
I
B1
B-
Q1
Q2
Q1
+ I
Q2
+ I
V
E1
E
-
B2
I
E2
B-
I
V
E
B-
-
-
(-V)
(-V)
(a)
E
(b)
' * 3 C @A ? / @ A ,
/ & / & 1 B
A 7 1 1 ' @A / 1 3 3 ?
* ?
/ 1 & / 1
/ ? 1 &
?
" C
/
K
/ /#
K
/
K
/ $ / /#
R( 1 /
/"
K
/
K
"
K
0% & 00? /
1
/ 6 & 1
/
K
0% /
K
K
/
$ $
0% L A/
K @
@'A
" C K
0% /
0% / L / K @0% L A/ /" 0% K / 0% L 0%
@'A
1 1 / & N
1 E &
1 ?
& / 1 1
1 1 & ' @A 1 1 1 / 1 1 ? / 1 1
' @ A
1 &% / . &/ & @,A 1 & / 1
/"
1 / &
/
/ / & / 1 C K
/
K
0% /
'
K
/
K
/ L /
"
K
/" /
? &
0 0N
/
/
1
0% L
0%
0% /
K
L
/ 0% L
0% @0% L A 0% @0% L A L
K
K
0% @0% L A L / 0% L
@' A
0%
& 00? 1 , /
1
% / & 1 & ?
/ ?
/
B 1 & 1 // 6 ? &
/"
K & 1 ,
' @ A
" / 1 / / /
7 1
/
/" ?
K
*
K
1
1 ?
1
/ 6 'C
/ /
0 *@0
A K 0- 0
1 / 1 / & 1 3 &
/ 1 C
/ / Q K 0 *@0- 0 A K P+-
P
/# ?
& R( 6
" C /# P
*
/ / Q
/
K
K
1
K
/" /
/# A K 0'-
1 1 /
/ C K
/ L /
K 0 - /
K 000
*#
K
* L *
1 1 , / 6 & D
"
K # #
0 *@* A K P0 ++ #Q /
$ ? ?
1 &
0 *@
K
& R( /
1 1
Q
K 1 1
? 1
1 % / 8 / / 1
/ /
0%
K
0%
K
0%
K
/ /
K 0 0
K ++
"
&
1
$% 1( 2
1
'
1 1
1
1 / & 1
& & &
1 3 / & 1 &
/
#
IR I M=mIR IB1 I B2 Q2 ++ 2N3903B VB1 VB2 - IE2 R
Q1 I E1
(-V) '' 1 7 /
1
?
& ?
&/ 7 / ? 1 / & & 1
& 1 &
. /
? /
& &
2 1 & 1 / /
*
P
/ /
Q
/#
*
,1 6
*
!
.& 1 & ?
R( / @'#AC
/"
K
''? 1 &
/ AD
0 *@
K
0 *@
K
/
*
K
@
/ ?
/
L L
* C
*
/"
/#
1
@''A
/ /
/#
K
/ L /"
*
/# ?
/#
1
@'#A
/# A
@'-A
/ /
/ 1 1 & 1 / / 3
? / & & / / % # "M
/" ?
1 / % / 3
K 0 *@
1 /
K 0
/ 1
6 1 1 ?
A
1
/ R( %
7 1 % / 1 / /? &
1
* * A /#
1 % / & ? ?
/" C
K
K
1
/ &
/ 1 & % / @ /A ?
/
1
1 & 1 %
K ? @''A /
K # -# !M
1 # 1 0
' /
-
&
! 1 % 1 &
1 1 / & &
/&
3 1
/ &
K '0
%
'? / 1 1 &
*
K # C
3 1
1/
/
7 / /
*#
/
/
*#
L
/
K
*#
/ / Q /#
/
L
/
"#
1
&
/
*
/ / Q /
P
/
* /
*
/ / Q
P
/#
1 &
A K P# #00Q
/& A K 0#''+
0-*@
K
0-*@
K
/ L /
K
@
K
/ L / L /
L
K
@#
K !M
*#
*# A K P0+
K 0 +
*# A /#
*# A /
0 0Q
/"
/
/
K #0
/
K #00
0 *@
K
/
K
1 / 1
C
/ A K 0-0
0 *@
K
K
/ 1 & 1
K
K
K ' ' - !M
/ ? /
K
/
/C
K
/
/
*# A /
L
*#
1 / & 1 ! &
"'
D
/
L
/" A K 0- '+
*#
P
K 0
1 1 ?
@#
0-*@
*#
"
/
K
K
K
D /&
K #00
/ L / L /
Q
/
/"
K
0-*@
/ /
"
K
P
K
/ / & 1 !? 1 /3
/ D
1
/"
1 ? 1 1&?
/ 7 1 / 1 R( /
/ 1 %
1 /
* A K P+ +
#00 0Q
/
* /&
K '0
/ A K 0#0+
K
0 *@
K
0 *@
K
/ L /
* A K P'+
K ' '+
'0 00Q
"-
/
1 6 1
*
* A /#
K
@
K
/ L / L / L /
K
@#
* A /
+
K -'# !M
K ##
K + 0 !M
1 /
? // 1 & & 1 / 8
1 3
/ 1 3
/ 1
/ 8 8 1 & % /
/ 1 / /
$ (+ & '
7 1 1 1/? 1 / 1 @ A? 1 1
3
. 1 / /?
? & ? & //
/ 3 @ ? 0 A
1
/
/ 1 1 1 ? 1 1 1 1 1
1 1 & 1 71 / / 13
/ /
1
% / 1 &
,6 & / / 1 / / 8? / / ? / 63 1 / 8 1 / /
/
/ / 1
1 B & 1
/ 8 / &
/
1
1 &
1 / ? 1 /
/ 1
& & / ? 1
1 & /
'# 1
, ? "
1 1 ?
1 / 8 & 1 & / 1 / 8 ?
+
"
+
/
?
1
1
. 8?
1 / $ 1 1 & / ? ?
,
+
/
/
7
+
/
? /
1
1 1 / /
1 / /
1 & 1 / &
1 ?
/ & / 1 1
/ 1 1
1 R( 1 1
C
/ +
* 1
+
?
1 1
/ / 1 1
K
, L ,
, L ,
@'+A
1 & 1 13 ? 1 / 8
=
1 &
1& ? &
?
/
? 1 % / / / /
,
K
1 &
' '
C
(+V) 2N3906B Q3
Q4
α Mic1 -ic2)
i0=( ic2
ic1 ib1
ib2 Q1 ie1
v
2N3903B
Q2
ie2
v
g1
g2
I
(-V)
'# 1 / 8 @$A
, , ,
$ 1 &
+
K
*
L
1 &
+
' ' '
' ' '
@'A
/ 1 / / % ?
/
,
K
/ ,
+
&
K
*
+ ?
/
,
, ,
L
K
/ L ,
1?
1 & 1 / & 1 C
/
+ L +
+ + , ,
#
#
K
' ' ' ' ' '
K
K
K
K
K
K
$ $
* L 0 +
+
K @
+
& 1
A
$ ' ' $
+%
# '
K
@'A
& 1 / 8
* $ & , C
& /
,
,
&
& @'A
K
" , ,
@
K
&
/
/
# '
@'0A
" # '
@
#
@
1 /
L A
? 1 1 1 /? 1 ?
,
.
@'+A &
'
, ?
A
L A
/
/
K
, @+ A
@'AC
@'A
Output Current, i0 (mA)
Polynomial Model µCAP
1
0.5
0
−0.5
−1 −0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Differential Input, vd (V) '- 1 / 8 & C / 3 /
1 / &
,
@'A @&
1 1 &
1, 1+
K
, ?
@
A @
"
L A
# '
&
K
"
@
A
/
/
L @
#
A
?
"
@
@'A
L A
+ ? +
& 6 & @'A /
,
/ &
C
/# ' @#
1 1 & 1 ? 1
+ ?
1 1 / ?
!A
L A
'
1 / &
K 0C
+ L
@' A
2 * L 2 A / " K 0 @0 L A 1 0 *? 1 , K / K #00 ? * K 0 *@, A K 0-0 ? @# A K #0#+? / 1, 1+ @0A K ' J 1 & 1! 1 & 1 / 8 1 3
#
1 @
'-
A K @
$ & 1 & 1 &
? 1
1 ?
& & ?
3!
/
1
/ / &
/ $ /? 1
0 0 # # 1 ) * 2 3 #
0
& ?
" /
L
,
/ 1 / 8
&
& / 8
+% ?
?
! !
1 & & &
/
/
,
3 1/
& / 8
,% @' A
+% ?
?
& & & 1 &
)
1 1 / 8
1 1 & ?
&/ 8? / 1 / 8
+
A
1 % ? 1
1
+
?
/
+ #0
1
11 1
, /
+%
+
K
"
@
K
K @
+
/
1?
1& /
,% @''A 1
K 0C
" #' #' L
K
+%
1 / 8
1
6 & @'A /
6
?
1 / 1
1 1
1I
A
@
"
"
@
L
"
" L A #' L A
@ @
L A
' L A
# A+% L @0A
@
@
#
A
+% T
L
+% T
@''A
5% 1 3 / 1 1 1 1 /3 / /
+% @# A? +% '- #0#+ K 0 ? 1 & + & 1 & 1 13 / // ? / ? @' A
/ 6 1 3
1 & 1 2 B 1
/ & 1
1 1 / 8 // / /
1 1 1 / / ?
1& / &
# ' $
/ 1 1
'+ .
$ / / &
/ 1 / & 1 / 8
1
/ & ? / 1 / / /B 1 8 = 1
+ ,
K K
,
L
@'#AC
*
' ' $ $ $ ' ' ' / # ' + * / , / / # '
&
/
@'#A
# K $ / / 1 & + K * # 1 & ? # ? / / & 1 / 8
1 1
K
+
/ /
(+V ) I i0=I-ic ic
i
b + v
2N3903B
1
-
Vg
V0
'+
1
1 6 //
,
/
K @
C
# # ' +
/ A /
@
#
A
L @
6 & & ? & @'-A?
+
#
L @
T
A
+ T
'
L
1
/
1 @'-A
? 1
& &
1 &
#
A
& /
@'-A
K 00
? 1 / 8
/ 1 & 1 &
& @'-A
/ & / 1 13 / ? @
&
/ @' A
1 / Æ ? / /? 1 7
+
1 8
= ? / 1 3 @ Æ & 1 A
& & )
A
1
? 1 / 1 1
/ /
% /
1
1 / & 1 / 8
+% '- @#
.
+
A 1& ? 1 / & 1 / &3
& 6/ 1 & 1 0 @ '- A K
' ++ /*? 1 1
1
1 / / & / 8 / / / & 1
& 1 3
(
/
1 8
& 1 / 8
/01 C
/
K
3/ 3
K
"
@
A
"
@
A
/
1
3/ 3
K
0
@
L A
3/ 3
@'+A
200 I=I0=100 µA
Output Current (µA)
150 100 50 0 −50 −100 −150 −200 −0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Input (Vg) ' $ & & & 1
1 / / & 1 ?
" ?
/
@'+A
3/ 3
1 1 & 1 & 1 / /
/Æ
1 8 & 1
* ?/ A?
? @
/ 1 &
/
1 1
1
1 1 / / ? 1 1
@'A
3 C
/Æ 3/Æ 3 1 1
K K
/ / 3/ 3
1 @'A
1 1 / 8
1 1 / / * 1 / 8 / 8
& / 1
1 1 & 1 1 / ? 1?
/
& ?
0
. /
1 ? 1 8 1 / & & 1 / 8 3
1 / &
/ 1
& 1
? 1 / 8
& 1 3
.& 1 1 1 / &?
1 8
// ? 1 / 8 1 1
3/ 3 ?
1 / 8
1 ? / / 3&
1 1 / 8
0
.
1 & 1
αMi R
i0= αmi R-i C
cµ + v1 -
iR
cπ
rπ
cµ
iC
gmv 2
gmv 1
rπ
cπ
+ v2 -
+ vx -
v g1
v g2
' $ 3 / & 1 / 8
# *#' - . /
*& / 1 / / 1 / & ? ! 1 3 &% & 1 1 & 1 / 8 1
/
&
1 1 &
1 1 / 8 1 1 & 1 &
/
1& ? &% 1
/ 8 &
/ 1
/
/ /
3 / & 1 / 8 & '# ' $ / 1 /3 $
/ / &
/ & 1 ?
/ 1 /3 1 /
/
"
/
"'
$ PO#Q 1
"
/
"?
/
&
1 @ A /
1
1 % / 5 1 /
" / " 1 4 ? 5( ? / ) 1 & 1 " / " $ 1 & " / " 1 @ ? 1 * 1 A? 1 1 ) 1 / 8 & 1 ? 1 1 ) %? 1 / ! / & 1
1 ? / ? 1
% 31& & 1 ?
/ 1 1 1 / 8 1 &
/
1?
! ?
& 1 3 @ / 6
'A > & & 1 ?
/?
1 &
/
/ & 1 1 / /C
# C
,
K
#00
/
+
K
0 *@
, A K 0-0'
'
P
, , Q 5(
4
(
)
+ A K P+-
K
0 *@
K
@
K
@
K
+
K
#
, A K -+# 2 + L 2 A,
' ++Q
!M
K + "1
# C
+
P
, , Q 5(
4
)
1
K
0-*@
K
@
+ A K P# +
, A K #- !M @2 + L 2 A, K --
+
K
'' 0Q
"1
K
- +'
K
0-
1&
/ /
R( / 0
0-*@
K
( 1
, A K 0- ''
K
/ 1 / ? 1 (
)(
K
4(
+ ? 1 ( D 1 ?
L
/ @'AC
)( @+ + A 4
+
+
K @
,
1 &
+ + A 4
+
@
L
@
+ A
/
, @
+ A L )( @+ +
A @'A
@'0A 1 1 1 & R(
1 /C
1 ? / 1 & ? @
,
,
K
4
K
@
,
K
4
K
@
, ?
1
6" AC
" , ,
K
@
4 ) A+ +
@
4 +
+ A ) +
4 ) A+
4 +
@'0A
1 / R( 1
K
4
+ + A ) +
@'A?
1 1
6 / 1
, , A 6" ,
@
)
+
A@
+
A
6" P@4 ) A+
1 8 & 1 / 1
4 + Q
1
@'A
6"
0?
1 3 1 / / 1 / 8 & 1
1
1 /
/ /
@'A
/ & 1
1 / 8
& ' C
1 /?
,
+
+ ?
K L
6" ) +
K L
/
@'AC @'A
) 1 =
#
/ 1 3 ?
6" ?
/
0
*2 & /3 1 ' C
1 /?
+
+ ?
K
/
@' AC
,
K
@
@
6" A@4
4
) A+
) A+
)? 1 1 / ?
@' A
0
1
/ 1
& 1 / $ / / ?
5 ?
1 1 13&% & 1
4 & ' C 1 1 /? + K 0? / @''AC
,
K
P@
@
4
6" A@4
. 1 ? 1 / 8 /
)
1 / 8
&
@
) A+
6" A)
AQ
+ @''A
6 31& 1 / & 1
? &% 3/ / 8
1 1 & 1
&% 1 /
,% @'A 1 1 @''A / / / =/ & '0 1 1 /
0
/ 1 / ?
=/ 1 3= / 1 /
1 1
/* & 1 & &
4
1 6 &% ?
/1?
4 )
/1?
$% 1?
4 ) ?
K
4 )
?
/ 1 / / / 8
1 & 1 / #00 = /
K
1 1
?
1 3
& / C
K + 0
# 0 @ A K 0
1 1 / 8 /
4)=
/ / & 1
& & .
& 1 / 8 1 & 1 3
1 3 /
& '+
/ 1 &
4 5( ?
R( / 1 ?
, .
/ & 1?
6 !
/
1
' & 1
1 1 1 / %
, ?
@'#AC
4
K @
/
K #0
) A+
@'#A
1 1 %
& 1 1 / ? /
1 & '? /
1 1 & & % 1 & 1 1 / 8
/ & 1 / 83
1 /
1 1 / 8 / &%
&
1 / 1
Normalized Magnitude (dB)
-
60 |I0/(gmVg1)| 40 20
+20 dB/dec. Balanced Input
0
Unbalanced Input
−20
Common Mode Input
−40 log10|ωCµ/gm| −60
−2
0
10
2
10
10
Normalized Frequency (rad/sec) '0 8
cµ
v g1
+ v1 -
rπ
cπ
g mv1
i0
' $ 3 / & 1
Q6
2N3906B
+
Q5 + 10 V V
Q1
-
+
1
8. 7 V
Q2 -
v g1 + -
Vg1
Q3
-
3093. 7
+ 10 V
Q4 47. 04
-
2N3903B
'
& 1 / 8
1 / 1
/ 1
/ / 8 ? /
& 1 +3 / / 1 1
1 1 &
/ /
' K ' +'
3&% & 1 / 1 1
&%
@' A
1 / 8
/ /
4
1
1
/ ) 1
L0 /*J/ &% 1 1 / 1 1 / / / 1 /
?
/ /
1 / &
0
/ 1 &
1
/1 1
4 )
/J
.
/1 & / 1
/1 & 1
#' /
1 1
& /? &/ ? ?
/
/ 1 1 1
1
/ /
&%
" / / /
1 8
/ 1 &
/ 1 & /
+ + /* & 1
.
' / 8 / ? /
+% ?
/ 1
@ '#A 1 @'-A
?
+
/ 8
& 1 (
+
/
+
2
/ C
+%
K
+
K
+ + + L +
@'-A
Normalized Magnitude (dB)
50 |I *103| 0
45 40 35
Text Model
30 25
µCAP
20 15 10 5 0
6
8
10
10
10
10
Frequency (rad/sec)
'
1
& @'-A
&%
@'+AC
1 1 / ?
+
K
+%
+
K
+ ?
L
+%
+
L
+
@'A & /
@'+A
1 & 1 &
' % 1
/ & 1 1 / 8
1?
1
/
/
? / 1 & 1 1
//
& 1 & '0
+
+ C
K L
$
@'-A / 1 &
+% +
2
/
+
+ C
K
$
K
0
K
+
C
1 & 1
@'-A / 1 &
+%
+
K
K
0
+
C
2 / 8 /
+
K 0C $
1 & 1
@'-A / 1 &
+% +
* 1 /
K
+
K
0 #
+
( ! '0? -- /*
$ 1 /
1 ? / / %
1 1
/ = ?
?
C
1 & 1
/ /
/
1 / 1 / 8
1 1
/ ? & 1
1 / 8 / & &%
1 3 1 & 1 3= / &
/ 1 / 8 / ? 1
/1 & 1 &
& / 1 0 /*
& 1 & &%
/ ? 1 / / 1 / 6 1
1
+
# (*+( !3 2 (
1
& 1 /
1 !
1 . ! /
1
1 & 1 / / . 1 3 &% B /? 1
& '
/ 8 & 1
/ / & 1 & ' 1 1 1 / / & 1
$
& & B & & / 8 & /
?
1 1 / 1 ?
&
/ / / / ?
6 / 1 / / ! 1 / & & /
1 /
/ 6 /
/ /
1 / & /
$ ., 1 1 & /
/ / & E 1
1
1 3
1 / 6 1
&% & 1 3 / 8 1 & '
" ?
/ ?
& 1 / 1 & 1 / 8
71 1
/
+
+
/
+
/ / 1
+
"
+ ?
8 & /
/ / /
/ &
1 / / / 1
1 ? R(
@
"?
0 1
1 1 /
R(
'' //
///? 1 &
/ ?
/ /
@'A
+
/
/ @'AC
L
,
K
0
K
) A+
K K
" + " + 4 , ) +
L
@
+ L ) @+ + A
4 ) A+
4 +
/
@'A
00
αMi R
ZM cµ + v1 -
cµ
iC
vR
cπ
rπ
i0= αmi R-i C
iR
gmv 1
g mv 2 c π
+ vx -
v g1
v g2
'' $ 3
1 1 131 / / & @'A @'0A 1
1
/ /
1 1 % &
/ 1 & 1
& 1 / 1 R( & 1 ? 1 / 1& & @'0A 1 ? @'A
+ v2 -
rπ
1
,
1
, ?
+
0 /
"
,
1 / /
& / R( 1 /?
/C
,
K
" , ,
K
"
"
@
4 ) A+ 4 + " L ) 4 ) A+
P@
4 + Q
1 / 1 & ?
@'A
, @
/ / / 1 1 /
A? & & 1
/
1 1 / 8
1 1
/
+
& ' ?
+
1
K
/ /
$ 1
@'A / @' 0AC
, *"
, '
K
K
L
,% @' 0A / 1 A /
"
1
'
"
" " )
@
L
4
/
&
1 &% 3/ / 1
! 6 @ ' A?
&
) A+
@' 0A
"
@ 1
1 !
1 1
"
/
"
1 & / .
1 / / 1 1 / & C
"
K
4( L 4
/ &
? 1 1 &
(
L @
L
) A
0
"
4
K
@
. & 1 1 1
&
&% ? /
) A
"
@' A
1 1
?
/
3
? 1 &%
3
$ ? 1 / / 1
" ? 1 0 @0 L A?
?
?
& &%
"
8/
1
D
&%
1 1
/
K
L
K
4(
L
4
4( L 4
)
(
L @
L
) A
)
L@
1
'
@' 0A / @' AC
@
L
( L 0#) A L @( L ) L ) A
4
@
4
) A+
) A+
@' A
@' A 1 &% 3/ / 8 & 1 ?
/ 1 & 1 % /
4
4( L 4
1 !/
$ ?
1 1 & @' 0A 1
/ $ & @' A
, *"
.
) @( L ) A
& 1 1 &% .
1 1 / 1
1
& / & 1 ? /
1 1 / P @' AQ
' $ & & 1 / ? /3
/ & 1 6 ? / 1 1
'#
& 1 / & @' A 1 & 1 / /
1 1
7
/ 1 1 / / /% 1 3 / &3 & &% 3/ / 1 " 6 /
/ / 1 13&%
$ !
$ &? 1 / 1 / / / / 1 1 & 1 1 1 7 & / 1 1 / 8 1/ / / 1 1 / 1 /
/1
&
/? & / /
1 1 ?
, ?
1 / 8
/
,
+%
/
, +% /
?
+%
K
+ +
/
2 *
@
L
, ?
K
0
,
?
*
1 3
% /? / ? 1 @' 'A 1
& 0
%
+
K
0
C
@' A
/ / / ?
"
2 A
1 & 1 / 8 ? /
& 1 ?
P @''AQ 1 /
6 @' A
& 1 / 8
% /
/ 1 1 / 8 /
1 /
@00 /*AC
/ @2 * L 2 A
"M
@' 'A
0
Normalized Magnitude (dB)
50 45
|I0*103|
40 35 µCAP
30 25
Improved Model
20 15 10 5 0
6
8
10
10
10
10
Frequency (rad/sec) '# 5 / &%
1 1
"M & $1
1 ? / ? &
/ /
/ % & /
/ 1 1 / 3 / // ? / 1 1 / 1 1 1 / & 1
/ / /
& /
1
'- & /3 1
/ !?
/
1 / ?
/ / &
1 3 ? 1 , ?
/ 1 "M
"#
"- . 5 ? /
/ /
/% 3 3 & 1 & 1 ?
,
1 / 1 1 1 13
1 1 / 1 ?
/
? / /?
1 / 1 !3 3! & 1
?
/ & /
1 /
/ 1 1 & 1
1 /
? / /
/ ? / 1 ? 3 / =/ / /
/1 1 1
71 1
?
& 1 / ?
,
K
*
/ /
*
K
*L
* ?
K L
1 1 /
1 &
"-
1
0
(+V)
Q5
2N3906B
+ v
EB
-
β
+ i
R
V
S
0
Q6
ic/
-
ic
S
iL
I
2 RL
2N3903B
(-V)
'- /3
, K / L , ? R( 1 % / & 1 / 8 71 1 , K * , 0% ? * K * K * ? / 1 & 1 / ? ,
K * "- 1 , K / L , 1 / % / & 1 / 8 1 , K * , 0 . ? & "-? %
1 1 ?
1
+
K
,
K
, ,
X
X
2
1
/
2
*
1 @' -AC
+
X+%
1 .
?
*
0%
? /
X
K
K
/ 0%
% X
+
0%
/
2 * L 2 AX+%
@
@' #A
1
2 * L 2 A K !
@
X, ? 0%
K
1 /
/
@' -A
1 1 1 1
? / 8 1 . 1 1 &
1
@' #A 7 1
1
1
0%
0 !M
K 00?
/
K ? / / / ?
/ % /
3
@' -A 1
!
"-
K 0 ? @' -A
, ? 1 / /
$ 0% 0 ? 1 &1 /
1 % / / 1 & ? / % / / 1 1 1 1
/
/
/1 1
0'
2N3906B
Q3
Q4 i0
Vg
VS RS=10
0.624 mV -offset+
2N3903B
Q1
Q6
6
vL R L=105
Q2
I.1 mA
-Vg
I2.500 µ A
Q8
3101.9
Q9
Q7
149.75
47.04
-
.3 mA '+
1 / 1 1 / ? ?
/
& 1
/
8
, ?
/ 8
,++
K
K
* *
K
71 1 = ?
= ? / ? 1
*
+
/ 8 % /
1 ? R( 1
1
10
3
& / &
, '
+ 10 -
Q5
"-
*
% 1
/ @' +AC
/ 0% @' +A
8 % / 8 &
1 1 1 8? @
" A/ ?
/ 1
/ 1 / 8
@' +A 1 % /
8
1 @' AC
,++
+% ++
K
@
A
1 8 1 &
@
"
A
'
#
@
@
"
*
L
/
/ @"
A
/
L A
'
/
#
@
0
%
L A
1 /
3 6
+% A++
A@
" A @" L A @
@' A
&
1 &
1
/ / / 8 & 1
1 &
/
3
'+ 5& '+ & / / 1
C
1 &
K 0
M?
/B/ &
K "M?
/
K ? /
& 0 + M
/
K 0 #
'
& 0 M ?
+ ?
0#
,
, , Q
P
0
,
* 1 ?
"#
K
0-*@
K
, ,
"-?
, A++
@
+ A K P#
#00 0Q
K ' #0
1
/ ? 1 3
8 &
+
K 0C
+
K
0
K
*
$ & 1
,
K ''
@' A / & 1
+% A++
? 3
K + 0- ? / 1
K 0--#
1 / 8 /
?
1
+ ?
1 1 ?
K
/ 83
C
@
+
71 1 /
/ 1 / 1 / 1 8
*
1
, A K 0- '+
0-*@
% / 1 = ?
1
/
/
K #00
K
/
/
K
+
/
/ 1 ?
= ? 1 ?
+ A++
@
+% A++
K 0 #@
'+ &
1 / 8 /?
K 0 #
1 / 8 1 / / / ? & 1
/ / 0 # ? 1 1 1 1 1 6 & =
1
'
& 1 8 1/
/ 1 & 1 &
% ? 1 /
1
= . & / 8 ? 1 ' 1 / & Æ
& '+?
1 1
/? 1 1 1
Æ
+
/
/ 1 / 8
/ % @
/
/1 & 1
& / ? / 1 /
.& 1 /
, ?
+ /* / 8
1 1
1 8 / 1
/1 0 !)= & 1 ? 0 /
1 1 8 1 & 1 ?
1 / 1 / 7
/ & 1 / 1 / /
1 A )
/ / / ")= 5 1 1 00 ")=
3
' & 1
3&% / 8 3 & 0' /*
1 1&3
1 1 8
JR
& 1 / & @' -A & 1 1
/
6 0
1 6 % ! 1 3 / 1
//? 1
1
E = 3 3 /
/1
0-
Output Voltage (V)
10
5
0 =50o
−5 =0o
T=25o C
−10 −150
−100
−50
0
50
100
150
Input Voltage (µV) '
3 & & & &
120
Gain (dB)
100
A0=104.1 dB
80 60 40 20 0
2
10
4
10
6
10
8
10
Frequency (Hz) ' 8 3 &% & 1
3
0+
µ
c'
+ i
0
v
+
b
R
S
π
π
r'
L
c'
R
v
m b
g'
-
v
L
-
'0 $ 3 / & 1 /
3 1 1
1
'0 & 1 /3 .
D 1 1 / / / ?
1 1 D / 1 1 ?
1 1 /3
/
?
/ & // 1 1
/ / ? 1 / & &
"#?
1
R( %
R( 1 / @' AC
0
K
+
K
+ L 4 + L ) @+ + A
@ L ) @4 )
& R( 1
)(
K
,
4(
K
@
+
,
K
L
+
)( A+
L
) @+ + A
/
@) 4 A ) ( L @4 ) L @( L ) A A
71 / 1 /
@' A
/ @''0AC
(
L
A A
/
L
@4(
@''0A?
/ / / 1 1
4 (
4 (
1 1 1 &
) A
( ) ' @4( L A ( ) @
(
L
A
@''0A
& / 1 1
@''AC
L
/
@''A
6 & C
4 ( @4( L A ) 4
K
5( ) 0
L
@''A
0
1 /3 / / 1 &
/
& 1 C
5(
(
1
"1
K
# - !M
K
- +'
+ ! J # !)=
'# 4 J + # ")=
4
K 0
"1
/
K
/
)
K - - "1
/
0
K
K 0-
1 1
1
3
' 1 / @''A & / 1 @ /
) ?
1 1 ?
0?
1 1 8
1
1
1
&/ 1 " 8?
B & & &/ !
/1A & 1
1 3 ?
1 / & 1
1 1
0 3
1
/% / / 6 ? 1 ( # 1
'0 )= 1 ?
1 % /
1 &
/ &
K @ L
K 00 !M
/
0
K 00?
K '00
. & ?
1 6 ? 1 1 1 /// @ 3 3
C
5( A 0 0
1
1
)
/// 1
// 1 B ? 1
"-A / / 3 3 /
& 1 & 1 .& 1
1
/// 1 ? 1 1 % / 1
1
.
?
1 1
/ / // 3
1 % / / / 1 3 1 / & 00 /* 1 / / 1 & 1 /
/1 & 1
1 3
/// 1 3 & 1 & / 8 // / 1 ? / 1 8
8 / 1
/ / 1 / ? / % ?
8/ 1 / // 1 1 1 & 3 1 1 ? 1 1 ?
/ ! 1 1 / ?
/
1 1
/ ? /
& 1
1
$ $!
7 1 / & B / / & / / /
/1
$ &?
1 / / 1 % / 3 /
1
/ / & /
0
(+V)
2N3903B Q7 i
i
S
e
i
L
I3
REF
R
L
(-V)
' &
7
1
! 1 1 1
/ & 1 / 71
/
/ 1 ? 1 B /
1 1 1 1 / $ ?
1!
1 / 8 & ? 1 / & 1 & & ? / 1 3 &% * & 1 % ? 1 1 /
& &
&
@
A
1 =/ 1 1 1
/
1 1
8 1 3 1 &
1
& 1 1 ? 1 1 &
/ ?
?
?
/ /
/ ?
/1? / ? 1 1 / 1
! & & 1
'
& 1
/ 1 !3 3! &
1 1 Æ & 1
1
/ &
1
// ?
"+
@
/
,
8?
/ 1 /
K 0A /
+
K
/
K
*
/ /
*
1 1 /
= ? 1
/ & @
L
* *
,
K
/ ?
A %
?
"+
,
/ ? ,
K
/
* /
7
"+
/
71 1 1 1
/ 1 @%
/ ?
K
/
*L *
/ @
"+
/
K
/ 7D ? & 1 / / ? 1 / A/ 7? 1 1 / = ? /
%
6
/
,
1 1
1 ? 1 1
/
/ 1 Æ & 1 /?
/
A
*
K
1
/
7 ?
*
K
/
K
*
@ &
"+
/A
/? / 1
*
K
* ?
/ ?
0
+V0 βDCi b
ib
Rp B
E
V b0
vS
i0
RL
+ vL -
-V0 ' / & 1
/3
6 /3
* / *
.&
/
K
& C
* / * /
K
@'' A
/ ?
& 1 ?
1 0C 1 1
?
1 1 % / 6 / 1 8
/ 1
/3
"+
1
1 1
/ 1 1 & ?
* ?
&/
1 /
/1
& / & & 1
'
/ 3
1
/ 1
@1 1 A / / & & / $ & 1 1
/
1 ! 1
1
1 /
1 1
/ 1
,+
1
1 ?
/ //
> & R( / 1 /
@'''AC
@
0% L A, ,
/ L +
K
@+
K
1 / 1 & 1
@0% L A
/
* + A +
/
,
@'''A
@''#A
1 / 1 & 1
+
K
,
K
,% @''#A 1 @ A? / ? 1
+ * A / L
@+ * A L / L
@
1
+
K 0? 1
@''#A
/ 8
)
*
?
L
/
1 1
8
&/ 1
?
// 1 3 &
A?
1
? & 1 ? 1 % &
& , 1 1 8 @, K 0A 1 @+ * A K / ?
& 1
@
L
/
8 /
& 1 ?
@''#A 1 1
1
/
1 1
&
1
3&%
& 1 ,% @''-A 1 C
1
/
K
0% L
1 1
@''-A
1
1 & 1 /
3
? /
?
/ 1& ? 1 U 3 ,% @''-A 1
1
1 1 1
1 &
% / 3 1 1
1
1 1 / 1 8
1 3 & 1 1 / 8
/ 1 8 B / /? 1 / Æ
$ / /
1 . /
1 1 / / // 6
1 1 1 13
8 1 / 1
& 1 . / 1 1
& 1 / &
/ & B 2 / 1 & ? 1
1 /
& *& / / 8 ? ! 1 3 3 & & 1
'
' . /
& 1 1
K #0 M?
/
K 0 "1 7 1
& 1 ? & 1 0 *
+
P
, , Q 0% 5(
4
(
) ?
+
K
0 *@
P0 0# Q
K
, ,
K
@
1
&
,
K
0% 5(
0 @
+
/
0 ?
/
K 0
K 0 ?
K
, A K '-
M
K + ' "1 @ 1
+
1
, A K 0+ --
K
/
! = ? / ?
1 % 1 ? (
3 /
1 ?
1
1 TA
&
+
A
/ / & 1
0 # -4 - & ( 5 6 7
b-
+ v
B
E
r
π
+ i
S
v
+
c
π
S
-
c
R
L
L
v
-
µ
m vb
g
C ' $ 3 / & 1
1 ? R( 1 / ? ? / @''+AC
)( ,
K
0
K
+
+ + , 7 1
4 ? 1? 1
L
(
) +
L
)( @+
+ A
/
+ @)( L 4 A@+ + A )( L 4 )( L 4 L
)( L 4 L
) @)( L 4 L A L )(
K
K
&
/ &% / 1
1
K
K
) P
L@
)
4( @
) @ )
@''+A
4( L 4 A (
L@ L
4
L
/ / 1
1
+
&
/
@''AC
A ( ) L 4( @( ) AQ
L 0 0 A
L
L L
L
+
L 0## 0 A
L 0#- 0 A@
1
6
1 / &
+ ,
/
& 1 ? 1 1
K
4(
K
- .
/
@''A
1 @4( L 4 L A ( K
) @ @0% L A L 5( A K ' - 0 ? / 1 0 0 J . 1 ? 1 0 3 & ) 1 / /1 ,% @''A
0## 0
1/ & 1
1
&
@''A?
7 1 1 1 ? 1 /
/1
+V0
Q7 iL>0
VS
iL<0 Q8
+ VL -
RL
-V0 '' &
0 0
K ' - !)=?
1 /3 /
/1
/
/ & / 1
/1 & # !)= 1 /
1 / 8 1 / /
1 1
/1 & 1
/1 & 1 1 1
/
0 3&
/ //? / ? 3 /
7 1 ! 1 / 1
)
? 1
/1 /3 8
/
/ &
& & 1 / / / & 1 & 7 &
! !
/ 1
&1
/ 1 Æ /
! / $ & 1 B / /
6 / /
/ / & 1 6
. ! + #'
1 1 &
1
"+
@ 3 A
1 / 1 ?
/ ?
& '? / 1
1 / / 1
"
/
& = 3 / @ ? 1 8 & = A
/3 3 6 /3
)
/
1 / Æ
1? 1
'' !
"
= ? ! 1 1 1
? 1 ?
/ U 1 & 1 ? / ?
/ 1 1 1 6 1 / 1 7 &
1
& & )
1 1
! 1 & & & 1 /
/ / 1
1 & &
/ & 1 & 1
'
15 10 Q7 On
VL (V)
5 −V’b0
0
+Vb0
−5
Q8 On
−10 −15 −15
−10
−5
0
5
10
15
VS (V) '# $ & & & 1 &
/
71 1 /
? 1 / & '
/ 1 @
/
K 0A 1 ? R(
+
@''AC
+
?
*
K
@
1 1 /
L
A
+
@
* A
&
+ 0
@''A
? ' ?
1 1
,% @'#0A
1 / &
/ C
+
K
@
L
A
1 & & 1
*
*
/ L
+
@
L
/
. &? 1 1 1
&
+ 0
'#?
1
1
$ ? 1 1 1
& &
1 1
& /
&/ 1
?
/? / ? / / 1 1
1 1 &/ ! / &
@'#0A
1
& 1 71 1 F// = G
&
1 1 / / / & 1
3 B & 1 Æ / 1 8?
* A
$1
1 /
1 / Æ /
/3
#
+V0 I3 Q7 ie 0 A
Q9
.0 V
ie
+ Q10 VS -
IS
+ RL V L -
Q8
I'3 -V0
'- / 8 & 1 &
1 6 1 / & / / B / 8 1 ! 2 1 /
+
1
1
/ 1
& / 8
'- 1 1
// @ 0A . 1 ?
/
1
K
/
&
/
0
K
+
0
1 / @'#AC
1 1/?
/
K
,
K
, L @0 L A, K @0 L A, 0L 0 L @0 L A, K / K / 0L 0 L
! 1 1
K
?
/ & 1 1 = &
/
/ 1 1 7? 1 1
&
//
1 ?
/ 7 /
1 /
%
@'#A
1 1
1/ 1
1 / & & & &
, L ,
/ / / 1 / 8 1 /
/
/ ?
?
/ 1 1 / 1 1
=
1
1
/
1
1 Æ 1 1 3 //
/ 1 % / 6 / 71 + " 8? / / 1 "+ 1 @0 L A 1 ? @0 L A/ 1? /
/ & Æ ? ? 1
"+
1 6 / 1 / / 1 /? / ?
/ / ? ? 1 !3 3! 1
1 / 1 & 1
& / /
'+ & 1 & & ?
'-
C
*
K # ?
*
K !M?
* ? & 1 / K / K 00
-
15 10
VL (V)
5 0 −5 −10 −15 −20
−15
−10
−5
0
5
10
15
20
VS (V) '+ $ & & 1 / /3 / &
1 / 8
& 1 ? / 1 // =
/
1 1 1 3 1 & 1 & ? 1 8 1 / /? 1
"
/
/ &
/
"?
K
4
"0?
/
/ /? ?
"+
"
& ? / 1 3
'
1 /
3 /
/
1 1 /
71
? 1 / E ! / & 1
1 1
* 1 &
1 1
1 1
3 / / /
1 //
& 1 &
/ 4
+
0 K 0? "+ /
/? 1 /
/ 1 3 1 1 / & ' /
) L ) A / (
1 @
& @''+A 1 / @'#A & 1
+ ,
K
1 & /
) L ) A
@
L@
4(
L
1 @
( L ( A
1
)
/
/ & C
4
L ¼
L
A @(
¼
L
L
( A
@'#A
¼ ¼
/ & 1 0 * / 0-* 3
1 00
/
L
1 '
/
%
/ & 1 1
+
gmva cµ
cµ
cπ
cπ
rπ + va iS
+ vS -
c’µ
RL
c’π
+ vS -
iS
+ vL -
+ vb r’π RL
c’π c’µ
+ vL -
gmvb (a) Q7 Active
(b) Q8 Active
' $ 3 / & 1 & '+ @A
"+
"
,
K
00
K
#'
K
+ ##+
K
"1
K
'
)
K
#
,
K
00
K
0
K
+ 0
K
- "1
K
0
K
0#
? / @ A
563 C
0% 4(
4
(
/
+
K 0 #-#
+
K 0 -0+-
"1
56 3 C
0
%
4(
4
(
)
/
"1
1
0
K
0C
5.5 µCAP
5.0 Model
Log10(|Z|)
4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0
4
6
10
8
10
10
Frequency (Hz) ' 1 /3
$ & 1
+ , 1 & 1
K
/ /C 1
@'#A / @'# AC
@) L ) A @
@
L # # 0 A
L # 0
4 (
/ / ? /
?
= '' ")= 1&
/1
/
/ ? 1
1
1
/ & '
1 /*
1 1 / / 1
& 1 & '- / 1 /
1
/ & @''A 1? 1 /
/ / / 1 &% & '?
@'# A
A
L --- 0
- !)= / '+ ")=
7 1 1 ? 1 1
/ 8
1 & 1
1 / 8 / / 1 % ? 8 ?
/ 1 1 /3 !
/ 1
1
1
& 1 3 / 1
1 & 1
1
1 & 1 / /
// . 1 / / 1 1 1 / 1 ?
/ ? / ?
/ 1 ?
,
/ &
71 / /? 1
6 / / Æ / ? / 1
1 1 /
1 . 8 E 1 1 /
1 6
/1 & 1 1 8
/1 8
1 /
/ 1 / 7
234.63
2N3906B Q3
Q1 + 0.622 mV
Vg
Q4
Q5 106
Q2
2N3903B
Q11 Q7
Q9
1250 Q10
47.04
149.75
547.2
+ 10 -
+ 10 -
Q8
Q15
Q13
' 0
Q12
Q6 9323.0
Q14 3082.4
Q16
& 1 13
! ! 1 & & 1 & 1
& 1 /
"
& $ ,& $- %
. 1 ?
E ! 1 & /
1 / / 1 1
' 0
/ & 1 / /
1 1 8
1
/ 1
1 & & 1
1
*
K 0
1 1 0- /
1 & 1 1 / / & 1
/ /
1 1
3
Æ
' & #0 3
$ & / & 1 ? &
Æ
# ? 1 / +'
& 1 # !M / 1
/ 1 & 1 ? 1 1 // = 1 / / &
"
"+ / "?
/ 1 ? / ?
/
"0
1
/
/
/
1 /
$ /? 1 1 / 1
1 / 1
1 /?
1 1 / // 8 ? /
1 / / & 1 8 1 / & 1 1
'
6 L
JR
& 1 / /
/ 1 / & 1
/ 8 / 00 !M
3
1
1 // & 1 1 / 1 & / 1
/ % & 1 / #03M / 1
1 // / 1 1 & & 1 3 & 1
' & 1 3 / /3
0
Output Voltage (V)
10
5
0 o
=50
−5 =0o
T=25oC
−10 −250 −200 −150 −100 −50
0
50
100
150
200
250
Input Voltage (µV) ' 13 & &
1 1 /
+ !)= @0 !)=
1 /
/ 1
/ / & 1
0 ")=?
/
6
3 A? / 1 /
1 3
00 /*
@L0 A % / 1 / B 1 /3 / 1 8 1 &
"
6 //
/ /
1 # M / 1 #0 M /
1 1 /
7 1 1 1 ! 1
1 ? 1 /3 ?
/1
!
/ / 1 3 /
3 &
"-A
1 8
$ ? 1 1
1
//
1/ 1
/1 @// 1
''@A
&
1
1
1 1 / / 1 ? /
K 0?
1 1/ / & $
1 &
2 &
/
/
1 3
1
/
1 1 1 / &
/ / & &1 / 1 B? B !
1/ & ? 1 1 ("+' / & 1 3 / /
1 8 //
/ 1 % 1 6 / 1 6 ?
K #00 M & / D 1
1 1
' / '
$ % ?
& #00 M ? 1 - /*? / 31& 5 1 1 /3
K #00 M
/
1 1 /
/1
3&% / /
100 Open Loop
Magnitude (dB)
80 60 40 Closed Loop 20 0 −20 2
4
10
6
10
8
10
10
Frequency (Hz) ' 2 3 / /3 & 1 13
/ 1 / 1 @
A
& 1 1 / / ? / /
=
/
/3
1?
1 ? 1 = 1 3
/1
1 6 /
% 1 1 /// 1
1
1 1 / 8 1
1
1 / 1 1 1 1 /
1 /?
/ ? / ? &
/ >
/ ?
3 ?
1 / 1?
///
/ & = 1 8 & 1 & 1
&
1 / & & 1
8 . 1 / & @ 1 8A & 1 / ? / ?
1
$ 4 + +3
1 ' 1 / & 0
#0Æ ?
0 - 8 1 = A
1 1 3 ? ? /3 8
JR
? 1
1 1
1
1 1 6/
@ &
/
1& & 1 / &?
1 ? 1 1
1 / / 1
.
$ 1 8
I/2
I/2
V0 Q2
Q1 v
g1=0
v
g2 =0
R∆ I
' // & 8 / &
1 & / / /
1 3 ?
/
1 & 1 / &
1
* 1 3 1
/
% 31& 1 ?
/
"
/
"
1
1 // & ?
' ? / 1 8 % / &
@'#'AD
+++
1 / / @' A & 1
* 1 ?
?
/
1
1
+++
&
!
?
1
3 C
/
@'#'A
+++ ?
1 / / & 1
@'##AC
*
K
K
X
X
/ X
K
*
1 / / & 1 / & &
/
X
'
1 3 ? 1 &
1
P @' AQ? 1
+++ X/ X X X+++ X X/ X 0 K
/ /
X
D 1
@'##A
JR @
/ X ? /
1 ? X
K# A? & 1 / / 1
$
Æ
@'##A 1 / &
C
JR JR
K -' M
@'#-A
T=25oC
10
Output Voltage (V)
=50o o
=0
5
0
−5
−10 −250 −200 −150 −100 −50
0
50
100
150
200
250
Input Voltage (µV) ' ' 1 13 & &
1 3
& 1 8 / &
1 6/ 8
* 71
/ 1 6/
K
1 1 / &
+++
/
* ?
&
"? * ?
%
' ' 1 1
K 0 - -'@0 #A K 0
1 1 &
1 // & 0 #0
&
?
/ 1
1
/
C
JR
1 & ' 0? &
1 1 8 / &
1 #0
JR 1
/
1 / / 8 & 1 8
& 1 / & 1/ ?
"
@'#+A
1 1
/ 1 / & 1 / &
1 1 / 1 // 6 & 1
1
' ' 1
Æ
1 1 3 1
=/ / 1 1 #0 / & 1 & 1
$1 &
& 1 / 8
1 ?
1 / 8
/ 1 / 1
1
1
& 1
?
"
1
1
/
"?
$
/ /B 1
1
B &
1 / & & 1
1 / & 1
1 / / 1
8 / 1 /3 1& ?
/ /?
1 / /
'
Q3
Q4 αia
Q1
Q9
Q4p
Q2 ib
Q1p
Q2p
Vg
Q8
Q6
α MIR. 5 mA
Q11
+ vL RL=1 k G2 vL + 10 -
2N3906B
V+
R1 A
.0 V 1800 G1Vg IR R11
+ 10 -
. 5 mA R9 1819 Q5 Q7 V2N3903B id iL
ααMia
ia
V+
Q10
. 5 mA
Q12
Q13
G2 vL
V-
R2 2k
' # / 6
8
1 & 1 / &
1 1
/ 1 & & / / &
/ 3
1 /
1
1 1 / 1 / ! / 1 1 & / 3 / / // 1
1
& /
7
/ / / 1
&
1 ! !
/ / 1
! /
&
1
1 & / 1 / & 1 3
/ / 1 ? / / 1 / 8
&
1
B & 1 1
#(.5 ( +
. 1 ?
= / &/ !
1
/ & / / & / 1
1
' #?
1 / 3
? & & 1 & 1 / & 1 & /
PQ
.
1 / 1 1 !
&
? /
6 &
1 6 & & 1
1
6 1 3
/ 1
/ 1 1 /3
1 &
" 1 1 " & 1 1 1 / # "0 / " / &
1 1
"
/ $ #
/ /
1 / 1
"#
#
"-
/
1 // = / / / & 1 ? 1 & 1
"+
1
?
1
, ?
/ 1 / ?
1
,% ?
1 ?
/ 1
"
/ 1
1 / / & 1
,
? / 1 &
1 1
/
0 3&
0
?
1
1
"#
/
"-
1
@'#AC
#
,,
# 0
1 1 &/ 1 &
,% ?
1 1
,% L
,
0L
,,
, @0 L A
#
0 L
,%
,
"# / "- & 1
K
,,
1 / /
/ / ? 1
/ 1
@ A
0
0
@'#A
0
00? 1
& 1 $ ?
1 1 1 1
1 &
1
/
#
& / / /
"
! 1 1
0L @ L A+
@0 L A
1 6 / 1 1 & 0 /*
?
@'#AC
K
0 L A
@
@'#A
"
1
"
/
"
/ 8
1 & ' # 1 1 //
"
1 1
"'
& & 1 / 3 / / 1
, ? " & 1 ? , ? " 1 1 , % 1 & "? 1 &
" "' 6 , 1 1 / 1 & "' @ / "'A 1 & ? " ? / / R( " / " / , C 1 1 ?
7 1
1 1 /
"
/
! 1
!
"
,
K
K
,
K
1
,
" L A, 1 0 0 / " K 0L 0L 0 , 0L
@
/
3 ?
,
% 1& ? 1 3
/ ? 1 /
!?
"
/
"
1
/ ? 0 .
! ! 1 /
1 / & 1
@'-0A
1 3 /
-
. 1 / / 1 @'-0A
/ / 1
1 / 1
. ? 1
/ Æ
1 ? 1 / / 1 / 8 & 1 / / 8
0/
A P@
0/
0 L AQA / 0 K #0?
/ ,
L A@
K 0
/ 8
6 ? @'-0A
1 1/
,
@'-0A /
K 0 -#
-0 .
,
,
, @0/ 0
K
0
/ 1 1 ?
,
K 0 #+
&
0
1
K 0? / 1
1 / 8
1
& & &
/
? 1
1 R( 1 3
/ 7 1
,
,
!
1
?
#
K
/ +
"'
,%
K K
+
!K0
@'-A
,% ? 1 "'? / ? ,% & /
/ 1 ?
/ 1
R( 1 &
1
!C
"'
/
"
" @, / A
" P@ A/ @ +
+ AQ
@'-A
@'#A / @'-A 1 & & & 1 C
L
L " @0 L A
1 1
+
K
+
+
@
+ L / 0 A @" 0 @0 L AA
L @ L
@'- A
1 1 1 / 8 / / 1
& / 1 6/ &/ ! ? &
A/
/ 1 / /
1 1
1 3
1 1 /3 /B/
?
?
/ 1 1&3
/
/1 1 /
1 1 1
& ' #
' 1
/ &
1 / & ' ")= @ A / & 1 1
/
& 1 #0 /* /
1
& 00 !M !M 1
& 1
% !M 1 1&3
&%
#
M 1 &
/ / !M /
8 1 1 / & 6
& 1 ?
6 +00 M & 1 @$ 1 03/* /3
&
K +00 M
' -A
7 / / / 1 ?
1 /
1 6 1 & 1
#
*
1 1 1 // 1 1 / 1 / &
/
" 1 /
//
+
70 60 50
Magnitude (dB)
RL=1 k
R1=1.7 R1=5.4
40
R1=17
30
R1=54
20
R1=170
10
R1=540
0
R =1700 R =100 k 1
L
−10 −20
4
6
10
8
10
10
Frequency (Hz) ' - /3 & 1 / 6
S 1 ! & / 1 T 1 & ! 1 1 / / 1 &3
7 / !
1
/ ? /
8 ? 1 & /? / 1 ? / ? /J &% ? / & 1 1 ? / 1 1 &
/ & 1
1
/ 1 / 1 !? / & 00 /*
! ? / 1 & & 1 / &%
& 1 / 1 & 1 !?
1
/ & &% 3/ / @A &% /
/ 1 / 1
.
/ /
1
1 % &
&
11
1 ! / & 1 1
& 1
' 1 3
/
"
1 &
' @A 1 / &% ' . 1
6 ? @''A? & 1 ?
? / 1 6 / &
+%
1
, ? & 1 / 8 3
& /
+V
R
αM R I
V
R
I
(a)
µ
αM R I
µ
c'
R
I
c'
0A + V
+
R
π
c'
π
r'
b
v
m R
g'
-
v
+
π
c'
π
r'
g'
-
L
v =0
m b v
-
(b)
' + & ' C @A /? / @ A 1 /3
3
/
/ 1 000 & 1
+%
/
/ / ' /
"
+%
& 1
1
1 1 &
@'-A
/
"
& 1 3
' + &
/ / '' 1 & 1
1
/ & 1 3 / 8
'
1
1 / 3
/ 1 6? / 8 / 1 1 1 1 & ?
1
6 3
1 & / 8
/J , 1 @A / @ A >
/
K 00
+
& 1 / 1
&
/
K 0
1 / & 1 / & /
+
& 1
&
@A 1 / 1
/
/
1 % / /
3
/ 1 1 /
/ / & 1
+ 15 V
Ω
600 k
v
0
Ω
600 k
R
vg
R
1
-15 V
' & ''
'# 5
/
1 ?
&
/
# ? #
' / / 1
!3 3! 8/
K
*
? 1
K
*
)
' ,6 1
1
#
13 / 1!
&
1
$ ., 1 3 1 / 0 /* & / /
/3
1 6
/ 3
! / / &
'+
*
# I
/
&
'- $
*
&
&%
/ 61 0 /*J/ 8 3
1 / 1 / 1 / !M
' > @ '+A /3 / 8 &
7 1
1 &/ ! 1! 1
1
K !M /
1 1 6
/
1 /
' 5 ' &
K !M? 1! 1 &% &
1 ?
K 0 /
1
/ & 1 /
/1
'0 2 1 / & 1 ("+' / 6
/
@A 1 /
1 1 &U 1
1 1 / I
0
V+ I3
i IN R1 R2
iL
+ KV + E VE -
I3 V ' & '-
@ A 5 @A & ()00' @A 5 @A & (''' ' 1 / 1 1 ()00'
''0 / 1 / 8
/ / = 1 /
& / 6 .
1
/ 1 8
& 1 1 7 / & ' @ AI ' ( 1 ?
@
A K
@ L A?
/ 1 8
&% ? 1
?
3 & & &% ?
1 1 8 &% &
/
/
0
0@
A
' 1 & ' 1 ? @'- A? & 1 /
)
/ 1 & &% 3/ /
/ 1 & &
+ +
0@
A
1 1
& ' -I ''
1 &
% & 1 '' . !
1 1 & 1 00 )=? / @A 71 % / &
/
0
K 00 & 1
/ / /
& 00 /* & 1 3!M /I @ A / 1
/ 8 & 1
@A 1 / 71
&
/ 8 ?
1 6 &
)
&
K 00
? "I
/ 1
M
I
R
R
I
V-
''0 & '
@/A
)
'# $
/
)
K # ?
1 & ///
1
1 00 )=I
K 00
1 & '' /
/ 1 3 &% &
&%
0 /* 1 3 &% '- 1 1 / & ' # 1 / 8? / / & 1 8
1
/ / 1 /3 /I '+ >
/ 1 3 / & 1
''
1
0 @A 71 / 1
/ &
I @ A / J6
1 1 3/* /
/1
/ /
1 & @1 1 1 ''3!M A
' . 1 & '' ? 1 3 /
,
K
,
@ ?
,
&
,
, 0A
K
,
L
,
1 1 1 3
/
,
> 8
K
0
,
/ & 1 1 8
C
S
1 /
0
,
0?
,
K
,
, / , & 1 , ? / ? 0 ? / 0
&
' % 1 1
&
/
'''
K 00 & 1 / 1 1 &
!M
1 / / 1
+15 V Q2
i0 RL2
vg
I1
1 kΩ
80 µA -15 V
'' & '' / '#
14.4 k
I
V
15 V
2N3903 '' & '+
V+ i IN
Q1 i1
+ 1. 3 V
iL
i2
-
I2
Q2 V-
'' & '
65 µA
15 V
+ vL -
5 mA
g v
0 g
vg
Ω
R L= 2 k
15 V
''' & '
@A 71
)
1 @ A & 1 I $ & 1
&
+ ?
/ / 1
/3 3 6 /3
/
& 1 & 1 @1 / 1 #3 A @ A / 6 & 1 ? ?
3&%
1
+ ? / 1 ? + 1 1 / & 3 0 ? 4 ? ? / 1 3 1
* / 1
? / / &
4
1
> 1
/ &
00 /* & 1 @A / 6 ? & 1 ? & 1
8
% / & = ? / & 1 % /
4
K 0
1
"1
@/A & 1 & 1 % / $3 1 & 1 / / &
'0 1
''#
.
& 1
K #0 !M?
K
/ / & 1 / &
/ // 3 & 1
K -##
S B
(
/
K 0
?
1 3
& & 1 1 / 1 /
1 6
/ 3 @A > 1 / /
*
/ 1 3
3&% 1 &
*
/ & 1 & 1
71 8 / 1 1 1 / & / / 8 & 1 I @ A >
@ $ ., &
&% 1
A
3
/ / ? /
& 1 &/ & 1 / ) 1 / 1
/ / & 0
?
'
(+V)
I0
T1 +
v in
RL
T2
v
L
-
''# & '0
@A > 1 1 /3
/ / / 1 /
1 1 ! & 1 & & / & 1 @/A / J/ J 1 1 // =/
1 1
3
1 / 1 3 / 8 3 1 6
) PQ = ? ? ( / ? :? / ) 1? 4?
& #?
'
.,,, $ ? ( / ? , /C
* "#
(/? 0
PQ /!? 4 7?
"# 3 7 " ?
...? 5/ ? "C
// 37?
P Q 4? .?
& # 3 " ?
* ? 25C ! 6? . ?
+-
P'Q 4? ,? ? F 1 , / " / & @ "A?G
!((
?
P#Q $ ? * 4?
?
S !C 7 ? -'
! ! ( *8 ?
> $// 5 ? :C
)? 0
P-Q *!? 5 :? ( ? ) 7? / * ? ,?
! ?
&+!
S !C .,,, . ?
* . .
!
& .
#
!/ & ! !
!
1 $ .,?
?
/ 1 6 1
1 & / 1 B @*: A / 1 / / 1 /? &
1 ?
/ / & /
1
/ & / / ? / ? 1 / 6 1
" / / & 1 & *:
1 &
1 /
/ 1 1 / 1 & 1 /
/ /
1 / &
& 1 /
1 1 / /
& /
&
! 01 )
1 /
?
1 &3 /? /
/ & ? 1
* +
7 1
0 '
'
,
? / / & @
0 1 /
1
,
A / @
A
'?
& 1 / ? 1 1 & 1
1
1 3 1 1 & 1
ic
2N3903B +
ib V1
V2
v
ce
+
-
v
be -
ie
' &
,
> " / 3% 1 @
A /? 1 &
&3
& /C
"
K P
Q K @+ @, A A K P-#
Q
@'A
1
,
1
K
'
K
P
+ + Q
K
@'A
-
0 −2
Model
−4 −6
Loge(i)
Loge(ic)
µCAP
−8 −10 Loge(ib)
−12 −14 −16 2N3903B at Vce=2 V
−18 −20 0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
vbe (V) ' / / & 1 0 *
,
/3 / / / 1 @
K P
2 2 2 Q K @+ @, A A K P+00
A /C
# 0 0 #--Q
@' A
1
,
1
1 & ' /
1
*
K
K
P
' '
+ + + Q
"
,
, " & ?
@''A
/ 1
+ 0
0 '
@'#A & 1 0-* / 1
1 &
K
1
''
K
P '-0#Q
K
P' +-' -' + +-Q 1
K K
'
/
/
' '
"" ) *'% / " )!*'%?
@'#A
&
3
/ & & & 3 C
!
ic
2N3906B ib V1
+
-
V2
ec
v v
eb +
+ ie
' &
0 −2
Model
−4 −6
Loge(i)
Loge(ic)
µCAP
−8 −10 Log (i ) e b
−12 −14 −16 2N3906B at Vec=2 V
−18 −20 0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
veb (V) '' / / & 1 0-*
0.8
+ + + + + + + +
," $" $($ "" ) *-( , " ) * "" "$ ," % $$# ( .%$ - -( /# % ,# 0 0 1 $& $ 0. "# %# 202 0 34 5 6 " $( $ "$$(
," $" $($ "" ) *-( ()')! (. '
) . '7) ' ) . '! ! ( ( ( $(6- (-( $6- -( + + + + + + +
," $" $($ " )!*-( , " )!* " "$ ," % $$# %$ .( - -( /# % ,# 0 0 1 $&$ 0. "# %# 202 0
," $" $($ " )!*-( ( '))) (. '8! . 8'7!8 !8')7 . '7 ! ( ( ( $(6- (-( $6- -( 1 / & 1 " &
1!/ / 1
1 & 1 & & 1 3 1 1
' / ''?
/ 1
1 1 / @1
/ @1
A 1
/ @3%A 1 / 1 & & & 1
*
K
*
K
+
/ A
+
1
! 120
βdc=ic/ib
100 80 60 40 2N3903B at V =2 V
20
ce
0 0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
vbe (V) '# & ?
1 1 /
0?
& 1 0 *
/ 1 ?
/ & 1
0?
& 1
0 K , , ? 1 '# 2 1 1 ? + 0+#? 1 / 6 0 & 1
?
0 -#
1 & /
& &
/ & 1 / / /
1
@'A? & 1 0 * ?
/ &
& 1 3 3 3 3
1 C
,
1
/ 7
7 1 &
K
'
K
K
K
*1
K
K
'
/ ' 0$
K '' #+ /
@ -#A0 0-
K -+
@'-A
& 1 0-* C
/ 7
K K
K
* 1
K
K + & /
@ A0 0-
K 0
@'+A
1 & 3 3 . / ?
1 1 / & / R 11 8 U %3
% / / 1
1 & @ ?
/ 1 3 & / 1 A
1 &
+
'0
ln(i)
ln(i )
ln(i )
2
1
v
2
i =i
c x
d
1
d2
ln(i )
x
v
'-
1
0. 01
v2
x
v
v
1
be
/ & 1 &
/
@
+ A
& 1 /
& 1
/
/ & 1 / / / 1 & ( 1 / !
+ 0
, +
@
, #
C
,
@
A
K
0
K
+
K
, # C
,
/
A
/ / /
K
+ L
K
@ @
2
+
,
A
A
@'A
2 + L 2 + L @2 @, AA
C
2 + L 2 + L 2
.
3 1 / / 1 &
& 1 ? 0 '
, # C
1&
1 &
2 '2 @2 @, AA @2
. %
/
A
@'A
/3
, K , 1 / @'A + & , 1 ? , K , K , L , 1 , 6? + K + 00 , K , L , & + 1 1 , D 1 ? , 1 , ? 1 '- $ 1
& 1 /
1
'- / @'0AC
1
1 " & ? &
C
?
+
K
1
K
1
K
$"- ) *'%
1 + 1 + 1 1 @, A @, A
,
@
/
,
A @
$"- )!*'%?
A
@'0A
& 1
! + 9"- "$ %# , 4 : ) * + -($"- ) *$ +34 4 ( "4 ," $ % ;4$4 +$ $ #$# $"# 4 ( .%$ - ' +< , $" ,# 4 5 6 + "## " 0= 0 - + ( ," + %$ ," + ," ," $" -($"- ) *$ ()')! (. '
) . '7) ' ) . '! ! ( ( ( $ 2 -($.( ( $ = - $ ,'82- > -2' -(,& - - .$ ,'82- > -2' -,& - $, $- "" ) *- #$,$-.$ - -.' $, $- "" ) *- # $,$-.$ -(- #.- # #.# "# + 9"- "$ %# , 4 : )!* + -$"- )!*$ +34 4 ( "4 ," $ % ;4$4 +$ $ #$# $"# 4 ( .%$ - ' +< , $" ,# 4 5 6 + 4 "## " 0= 0 + ( ," + %$ ," + ,"
'
'
i
i
b
c
ideal
+
v
+ g(v
be )
be
v
ce
i -
e
'+ 1 / 1
-
+
/ / &
*
," $" -$"- )!*$ ( '))) (. '8! . 8'7!8 !8')7 . '7 ! ( ( ( $ 2 -$.( ( $ = - .$ ,'82- > -2' -,& - - .$ ,'82- > -2' -,& - $, $- " )!*- #$,$-.$ - -.' $, $- " )!*- # $,$-.$ -- #.# - #.# "# $ &? 1 / /
/ / / 1 3
1 / / &
/? /
/? 1
'+? & 1 1 / /? / 1 / / '
//
/
/ / & & 1
/ / & 1
1
! i -
i
b
c -
ideal v
'
g(v
eb )
eb i
e
+
v
ec
+
' 1 / 1
+
/ / &
+
1 @ A / / 1 8 &
1 & 1 1 1 1
1 &
/ 1
*
'
? 1
8 1 / 8 1 / ? 1 8 1
1
/ // 1 , 8 ?
1
'0 1
& 1 1 1 /// / 1 1 / .
/ 1 8 &
*
/ 1 , 8
/
// //
1 B
K
&
* 2
* * 2
K
1 / !3 3 ! 1 3
1 // / / ? 1 / & 1
1 1
3
/ 1 & // 1? 1 , ?
* ?
1 / & 00
&
! ( )
71
?
& 1 & ! 1
/ 1
1 /
1 / / 1 1 1
1
/
/ 1 & 1 / &
& 1 ? ?
/
'@A?
'
. 1 ? 1
1 '@ ? A 1
1 & 1
/ / ?
P '@ ? AQ & & R 11 8 U
,+
1
3
? ?
?
* 1
/ / 1
/ 8
' / & 1 6 & '@A?
1 1
&/
1 ? / / 1 ? 1 / / 1 / ? 1
'@ A? / 1 / / / 3 @ A / 1 .
1 /3
/
,3. --8 9
&/
''
−2 Vce=2 V Vce=12 V
−4
Loge(ic)
Loge(i)
−6 −8 Loge(ib)
−10 −12 −14 −16 0.4
2N3903B 0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
vbe (V) ' $ 1
i
1 8 &
*
i
b
i'
c
+
ideal
v
c
g(vbe )
ic(v ce-2) VA
be
+
v
ce
i
e
-
i'
e
(a)
i
i
b
-
ideal
v
i'
c
c
g(veb )
ic(v ec-2) VA
eb +
(b)
'0 ,6 // / &
ie
-
v
ec
+ i'
e
* * 2
K C @A ? / @ A
!
∆i c
I' +
c
i +
b
∆ib + v b+∆ vb -
v g+∆v g
R
'#
L
+ vce+∆ vce -
+ - V2
2N3903B
(a)
i'
c
i
vg
b
+ vb -
+ v ce -
R
∆i c
L
+ - V2
∆ib ∆v g
(b)
+ ∆v b -
+ ∆v ce -
R
L + 0 V -
(c)
' $ / / C @A ? @ A ? / @A /
'-
c
c
i
i'
R
L
b
i
g(v
+
g
v
v
b
)
b
R
+
+
0
V
2
V
cal
-
(a)
∆b ∆ g v
∆c
µ
c
i
i
+
∆ b v
R
π
r
c
π
m∆ b
-
g
v
0
+
∆ ce v
R
L
-
(b)
'
$ / / / & 1 & 3
'C @A /? / @ A / /
!
'+
> & / 1 /? / / / &
5( 4
@
+ ,
X
*
K
@2 + L 2 AX+ , K X+ X+ @2 + L 2 A, * , X
K
1
X+ ' X+
K
X
&% AC
K
,
@'A
' ' @'A @' A
1 ,
1 & 1 / / 3 & 1 & .& 1 !
/ &
(
/
)
? 1
1 1 / / & 1
&
(
) ?
/
/
! & 3
& 1 / /? '@ A 2
1 &?
K X
+ X+ ?
K X
/ 1 1
/ 1
1
)
L
K
@
K
X
K
@
L AX+ A
/ ?
8 C
8
K
)
K
?
) K
+ C 4
L
+
X
L
)
+
@X
+ X+
X
4
K
+
AX
)
)
L
4
@''A
L
/ & &
?
K L
)
L A
@
L A
@
4 L
)
@
@ A
K
8
/
@ L AA 8
8
@
8 8
4 @ L A
&
4
&
@'-A / / & 1 & 1
= / @ ?
A
4
L )
A
1 ?
@'#A
@A /// & @'#A / 1 &
+ A
X
)
4
4 @ L A 1 /
+
K
&% 6 ?
1 1 &
L AX+
0
+
X
@ 7 1 !
, X+
/ & 1
1 & ? ! R( X
@
/ ?
! & / 1 1 / @ /A
/
L @'-A
1
'
' & & 1 0 *
+ @A ( @!MA ) @ "1 A ( @A ) @A 0 @!MA
( !
?
0#0
0##
0-#
0+0
0+#
00
# '0
0
0
''
-+-
0
0 0
0
-0
'+0
-0
-00
-'
++
'##0
+0
'#-0
'0
#0
'
# 0
#
#
-
-
+
+
''
--
00
00
+
#-0
-0
#0
0
#-0
0
0
'
1 !
/ / &
& & 1
0-0
, C
,
K
4( X+
+ ?
L
(
$ @''A & X
/ 1
,
L
?
) L ( A
K
P@
K
@
K
K
(
4( AX+
K
(
?
, +
X X
K
(
+
' 1
4(
) L
L
)
)
+
@X
)
)
)
L
)
L
4
4
/
5(
&
X
L
+
X
L +
A K 9 L + L
@
@'+A
1 ?
L L 4 A) @) L L A
L L 4 P@ L A
@
&
@'A
( C
L A L ) Q
A@
@'A
& & 1 ?
& / / 1 1 & 3
K 0 / * K - 1 1 0 ) / 0 1 1 / / + ? 1 / / , / , ? $ / 3
/
/ & 1
4
L 4 A) @) L L A
@
+ )
+ A
X
3 & 1 0 * '@A
/
@
@'A / 1 &
K
? 1 1 /3 1
L
( L 4(
K
L
+
X
4( QX+
L
9 L + ,%
) ? (
@ A
? R( X
X
X
/ ?
/
1
'
& &
+
@ ?
/ /
1 'A
!
'
10 R0
Rπ
5
Log10[ ]
βac gm
0
−5 Cπ
−10 Cµ −15 0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
vbe (V) ' 3 & 1 0 *
1
4
/
5(
0
/
1
0
K
,
K
X
X /
1
/
@
/
, X, 4 X+ X
+ 5(
K
X
K
4 5(
@'0A
1 1
A
1 1
/
! & 1 /
$ ? 1
'#? '-? / '? / &
1 / &
&
C
'' / / & 1 3
/ / / 1 1
,
0
/ / &
! & &
1 1
&
1 /
1 / 6 " /
// / 1
1
6 / /
/ // & /3
/!
1 / /
/ & / 1 13
1 1
1
// 1 / /
#0
10
µCAP Model R0
Rπ
Log10[ ]
5
βac 0
−5 0.4
gm
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
vbe (V) '' " / /
& 1 0 *
10 R0
Rπ
5
Log10[ ]
βac 0
gm
−5 Cπ
−10 Cµ −15 0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
veb (V) '# 3 & 1 0-*
0.9
!
#
' & & 1 0-*
+ @A ( @!MA ) @ "1 A ( @A ) @A 0 @!MA
0#0
0##
0-0
0-#
0+0
0+#
00
''-0
+'0
-#0
0
0#+
0 '
00'
0
0
#+
-0
0
# 0
00
+0
+#
#0
'--
0
+
#00
0
0'
0#
0-
0+
0
0
#'
+
''
0
0'0
+#
'''
00
' 0
-0
##0
+#0
''
10
µCAP Model R0
Rπ
Log10[ ]
5
βac 0
−5 0.4
gm
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
veb (V) '- " / /
& 1 0-*
#
// 1 &
B /
Æ & @ /A / / 1 1 6 / 8 / 1 /
1&
/ /
/
1 / 1 / / / / / / 1
1 1 &
" / & / / ? / 1 &
& " ! 1 / "
B / / / T
1 & 1 1
/ ! / 1 /
/ & & &/ !
6
7 / 1 1 1 13
1 / 1 1 !
/ / & 1 1 / &
&
"
/ &
&
// ? /
1
/1? /
& 1 ? ?
1 / / & & / )
?
/ & & 1
#@A
1 / /
?
1
1 / &/ ! 1 1
1 / / 1 &/ ! %
& 1 =
% & 1
&% 3? 1 3? / 3 3/ / 1 / & #@ A
/
1 / 1
&
/ /3 / /
&% 3/ / 8 & / /
/
3
@= A91 / ?
1 1
& 0 1 /
& & 1
/ 1 9 @ 3
A 1
0
& & / ?
1 3 / 1
&/ ! 8
/1
1 / 1
1 / / / /
8 1 ? / & / &% 3/ / 8 71 1 / 1 1/ / / /
1 1!
/ 8? 1 1 & 1 / 1
1 // / 1
/
? & / 1 / =
1 / /
.& 1 1 0 /? 1 1
/ / 1
& @ / A &
#
!
/
#'
+
0A
-
0V -
I
0
+ V0 -
+
(a)
I0
(+) +
Vx
+
Ri
-
-
+ V0 -
A(s)Vx
(-)
(b)
#
$ / / & / C
@A 3
/? / @ A /3 / / /
1 1 .& & !
? 1
& 1 / / B
1 % / & / 1 & &
! ?
1
& 1 1 & /
? 1
1
1 & !
"
$ %
1 /
& F G 1
/ . /
1 1 / // /
/ / 8 % & / /
$1
1 &
& 1 3 ! E
/
$% 3 '
#? 1 /
? 1 / / E
3
& / / !
0 0 K
@= / A 1 1
? & /
? 8 ? 1 ?
/ 1 E
1 1
0
1
1 1 & 1
0A
-
+
0V - +
+
V1
##
1
V1
+
V0 =V 1
V0
-
-
# &
R2
R1
0A
-
+
0V - +
+
V1
K
V1
+
V 0=KV 1
V0
-
-
# 8
$% ' 2 . ' 3
# 1
1
/ R(?
1
&
#
0
K @ L
A
0
& 1 1
$% ' #
' 2
1 3 1
0
1
K L
? 1
0
R( 1
0 (
Y
K
K
0
1
0
#' / 8/ ?
0
,% @#A /
/
#
/
1/ & ?
K
#
0
0
L L
L /
K
L
K
# @4 L 4
0
L
L / L L / L
0
L
/
4
L 4/
0/
K
0/
@#A
Y
A
@#A
#-
R
(K-1)R
0A R
V1
-
+
0V -
1
V1
V0
+
R2
V2
R
VN
g
1
V2
g
VN
g
2
K
Σ
V0
N
VΣ
N
#'
* 1
#
/
4
/ / & %
/ & 1
1 / 1 1 / / &
1
/ 1 &
C
0 #
&
1
0
0
K
Y
0
L
L /
K
K Y
.&
0
@# A
1/ & 1 /? 1
/ ? / ? 1
0/
#
/ /
? / & 1 1 1
/ /
/ 8
1
0
/
$% & ' #
' 2
1 1
## / 1
1/ & 1 /
0
L
K
1
? 1
/
& 21 /J ? 1 1
0
0
/ 1 ?
0
K
K
1 1
R( 1 @A /
0
@ L
K
/ 0
0
L
L /
A
1 & ?
@#'A
?
/ / & %
/ & / 1 . 1 ?
0/
1 1
?
0
/ &
D 1
? 1 /?
/ / 1 1
/ / 1
/ / 1
0
?
##
R1
V1
I
+
1 E
/
1
)
? 1
?
K
&
(
%
##?
@##A
1
#'
#'
1 1
A
L
% / 8 &
@#-AC
L
0
L / L /
L L
0/
/ / 1 /
1 1
1
/
1
@#-A
0
&
/
? 1
/ !
0
1 ? & 1
0
K
1
0 0 0 0 0 0 @
K
,% @#-A 1 1
0
K
? & 1
)?
K
1
1 / / 1
& 1
/ 1 / @0 A 1
1 & 1
1
V0
GN
1 C
? 1
-R0
Σ
1
?
1 &
G2
V2 VN
##
/
G1
V1
V0
0V - +
RN
VN
R0
Σ
0A
R2
V2
#+
/
?
&/
/ /
? 1
1 1
% ? 1
1 1
0
3
/?
/ & /
1 1 ?
? 3 C 1
$% & ' & '
1 53 1
0
/
0
#- /
1 6 &% /
0
K
K
0
@#+AC
@#+A
#
C
IC R
-
+
+ V1 -
0V - +
0A
+ V0 -
#-
-1/RCs
V1
V0
. 1 / ? 1 / @#AC
+ @ A . / ? 1
K
+ @0A
+ @ A
1
1 /
@#A
//
K 0
.& 1 1 1 / 8 1 ? / 8 1 1 &/ !
1
1
?
& 1
?
1 1 1 & .
1
/ 1 / 1
1
? / ?
?
& /
/ /3
? 1
.
=/ &
&/ ! ? 1 &
"
1 1
6
& % * 2/
/ / = & 1 &
/ & C
1
+ @ A
1 + 1
L'
1+ 1
+
L 0'
+ @ A
K #
/ 1 ?
+ @ A?
@#A
& & ?
& / @#A
1 + 1
@1 1 1
/ AC (
+Z
#+
K
1+ 1
/
1 + 1+ K #+ @ A ' 0'+ 1
1
+[ K 1 1 ?
1 1
/3 /
1
@#0A E
/
1
% / 1
!
v
5
g
2
Σ
d v / dt
2
#
dv / dt
- I dt
v
- I dt
4
4
-26v
-26
#+ 2 & /3 / / &
1 / ! / / ?
1 E
# 1 1 P1 ? @#AQ
0
/ / 1
@ A K #
1 / & 1 1
0
@ A '
0
K ' L ' L # K
0
K
#
K
#
0
#
0
1&
'
'
0
0
3/ % & @#0A
@ A 0'
0
@ A
@#A
0 Y
@ A?
L '@-A
@#A / 1 1
0
K
0
#
0
'
0
0'
@#A
# 1 /
& / / & . 1 1
@ @
A 1
1 / /
@
A K
K A? 1
0
0'
? 1 ? @#A? 1 1 % 1 1
/
# 1!/ 1 1
& 1
? ? Y
/ & #+ 1 53 & 3
0 0
@ A @ A
0 /
K
1
! & @# AC
# L'
@# A
L 0'
/
I 1
@#A
? / &1
& 11 1
/ %
#
/ /
1 % / / / / 7 1 ? 1
! & / / C % /
/ ! / &% & 1
1 /
. 1 6 ? 1
1 & ?
. / ?
1 &
1 1
@ A 1 1 @ A ! & 1 .& 1
-0
1/4 1
Vg
1/5 + -
1/4
2
V1
s
-s
V
1
1
V
1 -
-
V2
+
+
V3
V (s)
12 1
26 1
V
-
-26
(
V4
Ω F)
+
,
# 53 = & 1
#+
? 1 / & 1 8 71
& 1 / ?
1 1 1 ! ?
61
&% 1 1
/ ? 1 & ?
0 0 0 0 0 0 0 0 0
K
0
0
K
-
1
1 &%
@
@
K
K
K
@A
0 0 0 0 0 0 0 0 0 K
K
/ 1 / / ?
@ /* 1 A
&
A? &
A
@
A
@ A
@
K -
/
1
C
A
@#'A
-
!
K
0?
0
/ 1
K 00 @'0 /*A 1 1
? 1 / / / /
! 1
7 1 / ? 1 1 & 0 /
1
/ //
/ &
K L 0 @0 L 00A? 1 K 0 1 ? & K 0 ? 1 @ A K #0 1 #0 1 / 6 &
71 1
K
@
?
/ 1 &
! 10/4 1/10
Vg
100/5
-s
-
V/10
1 +
s
1
1
V
2 /100
V1
-
1/10
-
-
V2
+
V3
+
V (s)
0.45 1
104/100 1
V
-
-1. 04
(
Ω F)
V4
+
,
# 3/ & 1
#
1 A 1 //
1 %
& 1 ? 1
0 0
0
/ $
1
& & 00
1
/ 1 /
0
/
0
1 ! &
0
@ A
K
# 00
0
@ A
0
' 00
@ A
/ / / / & @##A ? # / #? /
@
A? /
00 1 % = 1
,% @#A 1 &
00
1 / / / /
0' 00
C
0
1
@ A
/
@##A
#
* 1
/ ?
1 ! / / ! / 8 & & 1
0 0 0 0 0 0 0 0
K
K
K
K
# &
0 0 0 0 0 0 0 0
K
00
K
0
K
0' 00
00
0
@
@
1
C
A
A
@ A
K 0'
@
A
@#-A
7 " 1! 1 / & 1 .&
/
1 ? 1
// 1 1
/ / &% / / &
/
1 " & 1 / / &
C
-
30 V1=s2V(s)
Magnitude (dB)
20 10
V4=−26V(s)
0 −10
V2=−sV(s)
−20 V3=V(s)
−30 −40 −50 0 10
1
2
10
10
ω (rad/sec)
#0 3 / & 1
#
; ?;? ; 4 4 . 4 48 . ! 4" 4 4 4 48 4# 8 8 6- 4#?; 8 4 (6- 4"?;' "# %"$ % 4& ;% ;$ 1 / @ / A 1 1 / / / & 1 ?
#0 &
1 / / 1 1
1 1 1
!
&
6 ? 1 1 / & 0 1
0
K 0
0
?
0
& 1 1 & 1
6 @L /*A? &
K 0 0
1 ?
K #
/ / 1 1
1
1
$ 1 1
0
K 0 0
K #
!
-
−10
Magnitude (dB)
−15 −20
V1=0.01s2V(s)
V4=−1.04V(s)
−25
V3=V(s)
−30
V =−0.1sV(s) 2
−35 −40 −45 −50 0 10
1
2
10
10
ω (rad/sec)
# 3 / & 1
1 6
0
K 0
? 1 6
# K 0 0
? J001 & 1 !
1 / / ? 1 1 &
#
! & 1 /
C
4 ' 4 .' 4 48 .'8 4" 4 4 4 48 4# 8 8 1 / /
# / 1
1 !
1 1 1 ! @ /*A 1 & ' 1
0
0
0' @L0 ' /*A 1 & ? / 1
/ 1 /
K 0 0
1 & 0
K #
1
0
1
K 0
?
1 1 /
/ / /
/ 1 1 / / 0 1 1 / 1 0C? 1 !
1 1 -#3& / / ? 1 / /
)9
1 & 1 2
& 1
-'
1
499 0A
1
s 2V /100
-
+
V0
0V - +
V5
1/4
V
# . 1 & & =
(( ' $ 6
3 ? 1 1
1 6 ? / /
! & 1 1 =
/
1
1/
1 1 6 & 1 / /
6 ? 1 &
0 0
K
#@
@#+A
% /C
L '00A
L'
@#+A
L 0'
1 & 1 1 1 6 // =
& @
K 0
,% @#+A
A? & 1 6 &
0 0 1
#?
?
0 0
K @
L '00A
0
@
00 /
C
A K 00
0
#
0
L'
00
1 1
! & 1 1
! & ?
0
@#A
// 1
/ /
/ Y
& 1
/
# 1 1
K #? 1 ? RJY
0
0
?
/ 1 / /
K 00 %
#
1/
K #00 &
$ ? 1 6 = & ? 1 /
/ / / / % ! " 1 1 6/ 1 '# /* @ & & 00A? / ? 1 & 1 / ? 6
71 1 1 1 /
? 3 3 @$ 5A
& 1 1 ! 1 1
1 / & 1 E & 1 1 ? 1 / /
0 0
K
#@
! &
L '00A
L'
L 0'
#00@ @
1?
00 L ' A L'
/ % =
L 0'A
@#AC
@#A
0 # & '" & #
! 10/4 1/10
Vg
1/15
-s
-#
V/10
1 +
s
1
1
V
2 /100
V1
-
1/10
-
-
V2
+
+
V3
V (s)
15.4 1
3
104/100 1
V
-
-1. 04
V4
+
+
V0
V5
3/4
-
2/3 1
(
Ω F) ,
# = /
& 3
1 ? 3 & /
0 00 1 1!/
"
!
0
#00
K
00
@#0AC
' 00
0
0' 00
0
@#0A
# 1 & 1
1 1 &
/ & 1 C
4 ' 4 .' 4 48 .'8 4 ' 8 4" 4 4 4 48 4 4# 8 8 1 &% 1
#'
1
1 ! @ /*A 1 / / &% & 1 . 1 / / 1
! 1 & 1 /?
1 1 8 % = 1 1 1 %
8 ? 6 = / / / / $ 5 & 1
--
Magnitude (dB)
40 30
V5
20
V3
V1 V2
V5
10 V2 0 V4 V3
V1
−10 −20 0 10
1
2
10
10
ω (rad/sec)
#' ,% =/ & 1
&
7 1 / 1
/ /?
/ 7
@
/ U !
"
3
. 1 6 ? 1
1 1 1 $ ., A / /
& & 6
0
1 /
!
/
#
/
@ A & &/
1
0
@ A?
0
@ A?
%
@ A & 1 @ 1 / & 1
! 1
% A?
/ 31 = 3 / 3 &
//
/ 3
1 =
! & 1 3
= 1 = % / & / ?
1
/ 1 1 1
= / & 1
3
! ?
1 / 1 1 1
1 1 =/
%
Æ
1 % / 3 &
1
(13 /
1
3 1 &
-+
6 & 1 / / / 1
6 & 13 / / & / @#AC
0 0
@ A
-
K
@
L 0A@
L
L +A
-
K
%
L
L'
L
L #'
@#A
L +0
3 ? 1 3 & ? / @#A? / 1 =
1 & 1 / & C
0 0 0 0
K
K
0
K
-
L'
@'
0
L
L
L #'
L +0
L #'
L +0A
0
1
@ A
@#A
3 / ? 1 1 =/
1
/ 1 Æ & 1 3 & / 3 ? 6 & 1
?
1 1
/ / -
0
@ A " 1
/ ! & 1 &
C
; . ?;? ; 4 4 .8 4 ! 48 .8 4 7 4!. 7 4" 4 4 4 48 4 4! 4# 8 8 7 6- 4#?; ! 4 (6- 4"?;' "# %"$ % 4& ;% ;$ 1 6
/ #'
0
D
0 0
4 / +0
@
L +0A
0
0
D
! 1
&% & / -
1 /? 4 1 & 4 / ' 0 D 4 / - 0 D 48 D / 4! / & 1
1 / / / C
Æ 1 /
#
1 ! /
/ 1 / /
@ A? / 1 1 / & 0 /*
1 / /
% ? /
1 # 1
/
/3 & 1
& ! ? 1 ? 1
-
# 3 4 & 1 & 5% /
#
! 4
@/JA
@/*A
'
0'
'00
00
+
+
'
'
-#
#
0
-
'00
'
$ /3 4 2 $ & 5 & 1
5% /
3 4
/3 4
@/*A
@/*A
0'
0+0
00
0'
'
+
+
-
'
-#
0
#'
#
0
30''
+0
-
'
'
00
@
L +0A
/ / & 1 & & % L0' /* # 1 /*
2
0 0 0 0 0
% L#' /* / & '
1 1 / / ? 1 /3 1 !
1 = 1 ?
/ /
&
1 & / 1
0
K
& ?
/
/
K
'?
0 ?
0
0
1
# 1 // &
@'
L
L #'
1
L +0A
0
@# A
## &
? 1 / 1 6 ?
/
1 1
/ 1 !M $ 1
K 0 1 &% &
1 1 1 & 1
& 1 1 &
K
A
K @
1 1 1 /
@# AC
1 / & 1 / & 1 /
'
1 !
/ /
0
0? /
J
K @ A
1
K #
1 % 1
1/ &
kR
3*kR Vg
kR
V+
V-
V8*kR/3 kR
-18s Va
+6s 2V a
-4s 3Va/3
kR/4 kC
H1
3*kR/4
-
VBP
4*kR/18 kC V+
H2
V-
kR/3 H3
V+
15
15
V-
kC 54*kR/170 kC V-
H4
V-
V+
24*kR/31
kR
H5
V+
+170Va/3
4*kR/3
V-
-(31s 2+170)Va /4
V+
H6
.define kR 8e3 .define kC 62.5e-9/pi
V+
*** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) ##
1 & 1
& 1 * 6
& 1 & 1 /
#- / / 1 / / &
"
1
6 & 1 / / 1 &%
& 1
.& 1 &% & 1 /
/ & /?
/ /
/ / 1
/
1 & 1 / ? 1
1 / & 1 / / / & /
! & . 1 1 ?
/
& &
/? /
/? 1 1 / &% & 1
1
.& 1 / % = !
& / %
!
& 1
&
1 ? 1 1
!
& 1
& &
1 1
) ? 1 1 1
1 / ? /
// 8 / 3
! &
1 1 /?
& 1
/
& / /
/
/ / 8
"
*! $ !
< & / / = * / 1 = & &% & 1 @/3 % =? /
/
!A & ? 1
* / 1 =
/
+0
10 o o µCAP
Magnitude (dBv)
5
VBP=H3 Out
0 −5
H5
−10
H1
H6
−15 −20 −25
H4
−30
H2
Theory
−35
H3
−40
H2
−45 2 10
H1
H4
H5
3
H3
H6
4
10
5
10
10
Frequency (Hz) #-
&
1 & 1 *
6
&
! & $1
! & 3
=/ / & / = / 3 / / 1 ! & 1 * / & 71 1 ! / = / & & ? 1
! & / 1 1 =/ 1
1 / 1?
/ & / 1? 1 &
1 1 8
/
& / /
$% (
&
/ & / & & &
/
/ / & & / 1
1
/
Æ
1
4 ? 1 /
&
@ A 1 & = 1
1 ?
/ = & / /
! &
1 1 8 1
/ & ? 1 & &
0
K
0
/ =
#+
1 1 & &
C
0
K K
0
K
0
0
1 & !
N
+
N
1
+
+ -
V0
N
2
-
+
+
+ -
V1
n-1
2
-
-
+
+ -
V
V
n
V
n
-
V ol tage source output
#+ 1 /
Z +
V
0A
1
+
Z
2
V
+
+ 0V -
+
k
V
k-1
-
-
0 0
V -
K
K
? / @ A
1
@#'A
#
/ / &/ !? &% ? / 1 / & #@A
1
0 0
3
K
! &
K
0 0
K L
&
1 1
7
*& 6 ?
@##A
! &
&
/
@#-A
1
!
/
1& 1 &
1 /
. / 1 1 / & = /J
! 6 1
/ & / / &
@##AC
K L
?
1 %
? / / 1
/
1 1
/ & 1 ? #@ A? 1
5
k
+
? 1 6
, 1
+
-
(b)
# / C @A
@#-AC
2
-
(a)
Z
0A
1
+
-
0V -
k-1
Z
!
1 / 3
1
#
? / 3
1
! & ?
+
No.
Circuit
Z(s)
R C C
2. Rb
3.
RA
RB C
4.
R
a = G/C Z 6 aR/s as s 6 4
R (1+s/a)
1.
Ra
Comments
C
# $ 5
a = Ga /C b = 1/(Ra+Rb)C < a Z 6 1/(Ga+Gb ) as s 6 4
Rb (1+s/a) (1+s/b)
(R A+R B)(1+s/a) (1+s/b)
(1+s/a) Cs
/ &
a = (GA+GB)/C b = GB/C < a Z 6 RA as s 6 4
a = G/C
/
)
?
+
1 1 5
/
? 1
1 13&% 1 / 1 1
1? 1 /
/ & & /
1 1 13&% / & 1 5 1 /3 8 1 = /
/ /
1
1 J/B 1
& /
1 *
&
:
K
! &
/ 1 &
& / /
* / ! & / / 1 ?
;<4 @ AC 8%
K
0@
: 0-0A9@: 0-0A '0@: 00 A9@: 00 A L0@
/ 1 /
: #0#A9@: #0#A
@#+A
! & % / / / 1 13
/ / / /
%
3 1 8% & & & & 1 : 1 & L0 /*J/ @1 & : // A / 1 & '0 /*J/ 5 = 1 1 / = & @ A / 1 & ? ?
@#+A / @ / = A 1 &
@ A
?
! / & 1 0
K
L
' L
! & & @#A
L
A K
K ? / 0
@#A? K
1 1 ?
C
'A@ L A
A
@ L
K
@#A
6 // 1 6 &% ?
@
K ' 0
@#A
@ L
' 8 "! ! > 5
/ @
/ 1 / /
@
@ 1 1
A
K
K
@
1
A
A
#A? 1 & #0
1 L &
@A
@ L A / K @ L A @ L A L @ L A @ L A
K
& & 1 1 5
/ 1
/ 2
& / / &
C
1 3
1 1 1
1 1
/ 1 1
@# 0A
1
! ?
+'
+
R1
R2
R3
R4
C1
C2
C3
C4
V0
+
-
7
V2
+
#0 &
/ & 1
-
3 ?
C & ! / @
& $ 3
/ /
UAD
1
? 1 1 / 3
1
! & ?
1 6
? 1
/ /
1 1 !
1 1 ! ? ' ? / $ 3
$ ? / /
1 & 1
/ 1 ! % 1
@ A
?
! & ?
1 / /
1 1
K 0 0#
&
11
/ 1 ?
K
/ 1
/
@# 0A
K K @
A K @
K A
K 0 #
@# A
K ' . @#A? 1 / / @ A 1 & $ 3? 1 1 $ ? 1 & $ 3 1 / 6/
K '? & 1 $ 3
8 @ &
K
&
1 //
K 1 ? ?
8 @ A
& @#A
K D / 1 ! & $ 3 1 / 6/ 1 ! 3
& 1 1 !
1
?
1 / 1 / / /
/ /? ? 1 & 1 1 !
@ A
+
A K
K 0
@ L @ L
! &
@# AC
'A
A
@# A
&
K
1& ?
K '
/ 1
? /
K
8 ?
8 @ 1 /? &
K
A K
@# AC @ L @ L
A
A
@# A
? & K 0 K 0# K & 1 !
1
K
@
K
@
A K
A K '
/
/
1?
+#
kR
kR
kR
kR
kC/32
kC/8
kC/4
kC/8
V2a
VVg
H1
V-
H2 + 15 -
+ 15 -
V+ V-
V+ .define kR 2e3 .define kC 2.5e-6/pi *** Wide bandwidth JFET i/p opamp
.MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) #
1 /
& 1
K
K
'
@#A
@# 'A
3 /
1 1 ? 1 & 1 1 &% & /
! &
?
1
# & 1 3
1 /?
1 1
$1 / & / / /
! & / 1 & & &%
@ A & 1 / 1
1
1 / 8 /
/
'8 "! ! 2
1 1 / 1 @ 1 /
/ A 1 =
1 1 1 / / &
# . // ? 1 ///
1
/
1 1 / &
1 /
& 1 % 1 1
/
/
1
& 1
/ /
& 1 & @
/
1
A @
&
L
A?
1
& 5
A?
/
/ ? 1
/ 1
@
! .&
! 1 & ?
1 @
#
A / 1 ?
/ 1
1 1
&/ ! / 1 1
L
/ &/ ! @
/
A & @#A 6
1 = 1 / /
@
A
1
+-
C2
Ra2
R1
R b2
+
V0
Rb3
L
@
/
K K
?
8
@
A K
@A
/
A
@ L
@ L
K
K
K K K
K
K ' K
K
'
K K
K
K
K
V2
A
-
3
!
A @A @ L A @ L
@# #A
# , & / &
K ?
/
1 ? 1 / 1 & & $ 3
K /
1 / 1 &
/
A ?
P @# AQ? %
+ +
# &
1
R4
+
-
? 1
C3
Ra3
@
L
K 1
K ' /
K
C
A
K L
K L
K
K @ L A K L K
K L
K K
1 / ?
?
1
K
# 1 1
/ 1 / ? 1 ) 1 / 1 D /? /
& 1
1 /
/D / 1 /? 1 /
/
&/
1 1
1 1 1 /
)
/
1 1 &
? 1 /
/
! ,. + ! ! 1 @ # # A
1
% / 1 1 % / / 1 & ! / 1 * / & & @#A / &
1
++
kR/3
3*kC/32
kR
kR
kR
kC/8 kR
kR
V2b
VV0
V-
H1
H2 + 15 -
V+
+ 15 -
V-
V+
.define kR 2e3 .define kC 2.5e-6/pi *** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) #
/ & / & / /
! &
@ 1
//
A K
% /?
? 1
1
@ L
@ L
?
/
! &
/
A
A
K / K ?
K
L
A
1 1 ?
. / &
1 6
1 !
&% ? 1
1 &
K ?
A
1
& 1
1
K % /
K K K K
K '?
1 / ?
1 / & 1 &
'
@ L A K L K K @ L A K ' K K L K K
K K
/ /
/
K #
C
/ ?
K ? /
? / ? /
K /
1
@# -A
! & ? & &
1? 1
?
1 1 1
#'
A
@ L
@ L
K @
@#A
@# -AC
. / @#A?
K
K
& 1
&
+
C1
R a1
C2
R a2
R b1
+
Rb2
V0
+
V2
+
-
2
#' & 3
K
1
K
K
K
K
K
& ? / 1 @1
K
@#A
K
@# +A
##A
1/
&% ? 1 / 1 & & 0
1? 1
1 & 1 1 /
1 / K 000? / &% & ?
( #? /
1& 6
/ ? 0 !)=? 1 !
K 000 ?
1 1 1 / & 00 /*? / /1
1 1
/ & ?
& 1 1
'0 )=
! K ' 0
1 3
K ' ")=
1 & &%
#- !/
1 1 / /
1 / / 1 /
1 1
/ &% 1 U 3 / @ !/
/
#-
/1
1 6UA 1 1 @ ! A 00 !)= &
/ @ !/
1 % / /
1 !A?
8 & 1 % 1 / 8 & 1 / &
? 1 /
?
1 /
1 3
/
2
1
/
1
/1 / 1 3
/1 1 1
/ &
2?
1 ")=?
/ % 8 & 1
! & . ? 1 /
&
1 / @& &% A
6/ &
1 /
1 & /
/1
.
1&
/ &%
1 1 / / &
& 1 & & 1 1
1
1
&%
%
?
1
/ 1 /
/ 2
1 & 1 1
1 & 1 3 /
1 & 1 6
1 &
?
/
/ ? & /1 /?
!/
1 / 1 /
kR
+
kC/8
3*kC/32
kR/3
kR
kR
V2c
Vg
15 +
H1
15 +
.define kR 2e3 .define kC 2.5e-6/pi
*** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) ##
2
& 1
! &
@#A
10 8
Magnitude (dBv)
6 4
Bode Asymp.
2 a
0 −2 −4
|H(jω)|
−6 b
−8 −10
2
10
4
10
c 6
10
Frequency (Hz) #- & &% &
? ?
/
2
0
//
1 / / 1 .
1 /
% 1 1 / = % /
1 1 1
/ / 1 1 6 / ? / / / /
3 / & 1
! &
3
/ 6 =
#
! / 1 &
& 1 /* /
! & 3
/1 & 1
@
%
3 / / /
A K
1
#
@
L A
@# A
#+ .
/ ' = 1 & 13 / % /
#
/ &
. / &
/ / 1 (
*
1
# !
& & 1 & #+
* @
A
K
K
1
# #
1 K
K
#
# #
@
L A
/// & @#'A?
@A
1 1
K
K
#
K ? @
%
A
@
L A
#
@
K
1
! /
@#'0A
L A
!
A? /
& & C
# L A
K
@
@
# L A
K
@#'A
K - /*? 1 &% 3/ / & 1 &
#
( !
- /* &
? 1 /
1 /* % & 1 ?
/ 1 # 1 # K # 1 # 1 1 &
6 ? / 1 # 1 6 & 1 / 1 / / 1!/ & # K 0? # K ? K 000? / K 000 1 / 1
.&
#
L A @
#
A K
1 / % &
/ 1
#
#
L A @
% /
! & & $ 3
- /* &
L A @
@# A
1
# @
@
K L
K @L- /*A
1 & $ 3? 1 1
/ ! ? 1
#
1 1
1
/ +0 /* @L0 #0 /*A? 00 !)=
%
1
K1*kR kR
kC
K2*kR
kC/K1
kR
kC
kC/K2
VVg
V-
H1
H2 + 15 -
V+
+ 15 -
V+
V-
.define K1=20 .define K2=2 .define kR 2e3 .define kC 250e-9/pi *** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) #+ / & 1
! &
@# A
V2
20
Magnitude (dBv)
10 0 −10 −20 −30 µCAP
−40 −50 −60
|H|dB
−70 2
4
10
6
10
10
Frequency (Hz) # % & 1 /
/ 1
@ A @
C
K '0
/1 & 1 1 / /1 1 A 1 ! 1 / /1
1 1 /* @
1 & / &
#
1 3 / 1
%/ 1 3/* /
#+?
A
/*
#
K
#
K
A @ L A @
A
@ L
K
K
L
%$K
# @ L A
K
@ L
K
@ L
K
0
K
K
K
K
#
@
A
#
A
A
1
0 #'#- 1
K +
K
#
C1
Vg
R1
V2
R2
V1
V0
+ -
C2
R4 R3
# 1 $ 3R 63
# '* 7(
< & ?
1 / / 1?
/ 1 3
& / 63 %/ & 1 $ / R @$3RA?
1 /
1 1 /
/ /
! &
& /
/ / / 6 P? Q / 1 ! R( %
: C :
0
@
@
0
0
#
/
A L
0
1
/
0 0
@
A L
0
@
K
0
0
?
1
0
K L
A K 0
C
0
0
@ L
! /
K
K
A
K
@#'A
L A
@
L
0 &
0
1 1
L
L
@#'A
1 & / & * / ?
'0 /*J/ & 1 ! ? / / &
0 0
R( @#'AC
0 0 1 / &
A L
K
/
/
1 ?
/
?
C
K
K
K
1
A @ A @ L L L @
A
@#' A
'
1
K
1 &
" ? / " 6 ?
/ ! & 1 &%
?
K
0 0
C
@
A
1 & & ? @#'A?
K
K
"
@#''A
1 / / & 1 ? ? 1
"
/ 1 3
1 ,% @#' A 1 ?
.
1&
!
/ 1 1 $3R 1
= @ A
/B/
!
/ / &
/? & 1 B
? 1
/3
/ ! 1 !
/
1 3
/
"A
K 0 @
@#'#AC
K L
@ L A
@#'#A
$ 1 ,1& + > / & 6 / 1 &
& 13 /
% $ & 1 & 1 & ? /
1 / /J !)= / M !M
@
%
3
A K
#
@
L 0 +-#
$3R /
* 1 1 ? /
L A@
L '
@#'-A
L A
/ = 1 /
1 1 &
@
A
% / / 3
C
K
K
K
'
K
0 +-#
K
# 1
"
3
@#'+A
/ 1
! & 1 & 1
1! 1 / & 1
1 1
?
1
/ 1 !
& & 1 1 6
& 1 K ? 1 &
% / ?
K
K K
K
1 ?
K K
/
?
& 1
(
#
kC
kC kR
kR kC
Vg
kR
V+
kR
H1
V+
kC
H2
0.152*kR
V-
V0
V1.235*kR
15 +
kR
kR
V+
- 15 +
.define kR 2e3 .define kC 250e-9/pi *** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) # 0 / & ,6 '
6?
1
, &
K ?
?
? /
C
/
K
K
@#'A
1 1
1
1 & 1
/
& 1 % / / C
#
K 0 +-# K # M
K
K
K 0 +-# K #
K
K ' K 0 # M
K
K ' K #
K
1 /
K @ #A@ #A K #+# @ # /*A
# 0
1 1 ?
?
1 1 &
1 1 $1 & * @/ / 1 A? / 1 1
$ / 1
1
1
# / # & 1 &
1 $ 3 / $ 3 1! & 1 1 & 1 1 1
1 1
"
3
1 / /
"
3
1
-
20
Magnitude (dB)
0 −20 Stage 1
−40 −60
Stage 2
−80 −100 −120
2
4
10
6
10
10
Frequency (Hz) "
# % & ,6 '?
/ 1 &
3
$ 3
?
1 1
1 & 1 ? & 1 ? 1 @0 /*J/A 6 / 0 !)=
/
1 ? 1 &
/ / 1 ? / 1 / / &% /
1 / & 1 / #- /*
& &% # ")= 1 / & 3 *
1 & 1 /
& & 1
/
1 / . 1 / / 1 / ? & 3 & ? 1 / /
/ 1 1
/
1 / 8 ?
? B & & 1 /
$% $ *$
: / 1 6 & 1 / / 1?
& 1
1
!
! &
1 1
36
= $1
# 1
// 1 1
/ 1 1 &%
1
& / / & / & 1
! 1
# ' 1 &
/ 1D 1 & & 1 ? 1 1 / 1 @ ?
)
K
)
/
% /
3 1 &
!
)
1 3 / 3 K
) A
6? 1
1
!
+
20
Magnitude (dB)
0 −20 Stage 1
−40 −60
Stage 2
−80 −100 −120
2
4
10
6
10
10
Frequency (Hz) # % & ,6 '? 1 13
"
$ 3
N
R
1/Ω 0
I
1
V
g
1
-
#
/
=
I
2
+ V
1/Ω 0
1
1
1/2
2/Ω 0
R
+ V2
I
L
-
3 /
36
3
1
1
1V
+ (2s/Ω0+1) A 2s/Ω A 0 V1=2s/Ω 0+2
1/Ω 0
1A
1V + (s/Ω +2) A 2 A 0
+ 0V -
2/Ω0
-
V1=2+2Ω0/s -
(b)
# '
?
/ @ A 3
/ /
+ 0V -
1/2
(a)
1 3
1/Ω 0 s/Ω0 A
! / = 1
1 3
3 C @A 3
) 3 // & 1 ) 3 & 1 / ) 1 ) 3 & 1 3 6? ? # ? 1 & !
? 1
)
! (
/
1
& & 1 /
!C
C
0 0
0 0 ) 0 0 ) 0
K
@
K
@
K
@
L
0 0
) L ) L) /
A K
A
0
) L A
A @
@#'A
C
@ L
0 0 0
) A
K
K
K
0
@) L )
K
0 0
0
A
) / ) @ L ) A
@##0A
,% @#'A / @##0A / 1 / / &
/ 1
0 0
!
K
K
? 1
) 3
# ' & 1 1 & 1
! &
0
) ) L A ) ) @) L L ) A@) L ) A K
@
& 1
! /
@##A
& 3
1 1 1 1 3 / @
0
K 0A 7
// @ /
AC
)
K
0
) 3 C
K
@ L
M A
K
M @
L M A
!
)
)
K
) @ ?
K
)
6? 1
0 0 0
@
M
K
K
L M
L M A
L M A M
@
K
@
K
@
L M A
@
L M A
M @
L M A
@
K
& 1 /
L M A
M @
@##A
L M A
! / //
K
)
)
K
)
)
L M A
L ) )
K
K
L M A
M @
K
L 'M
@
K
?
L
@
K
L M A M
L M A M
@
K
K
) 3 L ) AC )
M @
M L M A
@
M @
L M A
/
@## A
@
L M A
@
L M A
L
L M A
@
M @
L M A
L M A
@##'A
L M A
1
) 3
@##A 1 / /
! & C
0 0
P'M
1 1
L M
L M AAQ
L M A
L@
L M AQP
K
K
M @ L A M
L
A
L M A M Q
1
@###A
3 / 1 1 = 1 &
1 1 /
1
@ 3 . & 1
1 / /
3
! & 1 1
% / 1 /
/ / =
%
@
3 > 1
L
@ L M A @ L A@ L A@ @ L AM M
! & 1
?
L M A @M @
@
P@
L
K
L
K
36
A K
@
3
@
L A
@##-A
L A ! & ? @###A? 1
= ? 1
1
!
/ ? / 1 M
// 3
1 % /
@
A 1
0
Ra
Z
R +
T-T +
-
-
-
V2
# # /
& 1
3
K
/
)
-
.
?
1
# #?
1 1 / 1 &
K
/
1 1
K
K
@
L
/
@ A@
L M A L
A@
L
K
A
&
/ ?
@
L
A
@##+A
L A
A L @ L A A
@
L
1 1
! & & 1 /
! & C
@ L A@
@
1
#@
@
1 @
A
L A A
K
M
K
/
K
K
-
L
L @
M @ L A
1
1 / 1 &
3
A
%/ 1 / /
@ L
K
& & C
1
1 &
%
1
& & / /
1 = 1 / /
1
& 1
V0
3 @3 A / & ,6 #
1 M K
K
+
+
/ 1 /
Rb
R
Vg
C
K
K
L AM
/ / % & 1 1 !
K
@ @
L A L A
/
1 &/3
! 1 / 1 / C
A
@
K
L A A
@@
@ L
A@ L A
1 / /
K
-
K
K
K + MD
K - MD /
K # -
kR
kC/3
kC/3
kR
kR
Vg
kR
V- 36*kR A1
2*kC/3
kR/2
5*kC/216
7.2*kR
+ 15
15
V-
V0
-
.define kR 2e3 .define kC 0.25e-6/pi *** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=1M IOFF=5P SRP=13MEG SRN=13MEG IBIAS=10P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) # - / /
36
3
1 1 1 % & 1 $ 1 1 ? /
/ / 1 1
/
0
1
1
# # /
1 &%
# + & 1 /
1 1 /
# - ,1
/ &
1 / 1 1
/ ? / 00 !)=?
3 /
/ /
1 &/ ! ? 1
1 1
=
1
K !M /
& 1 / / 1
1
/ 1 & 1 1 3
8 > &
/ /
/1
1 / /
1&
K
")=?
/ 6 / 1 & 1
/ ? % ? /
/ 1 1 / $ # / # '
$% -(
& ? / %/ @1 & %/ A? / /
@
A K
// 3
! & & 1 & 1
0 0
K
2
@ @
L L
1
A A
L L
@##AC
@##A
20
|H(jω)| (dBv)
10 Theory
0 −10
µCAP −20 −30 2
4
10
6
10
10
Frequency (Hz)
# +
/ & 1
1 1 1 % & 1 /
?
1
1? 1 =
!
0
@
A 1 3
1 8 1
1 3 & ? & 1 3
K
@
0
#
L
L
C
@##A
A
// / 6 & 1
1 @A 1 1 1 / / &
1/ / / 1 / & 1 / &
& @##A 1 & ? @ @
AC
L L
@ L
. =/ 1
1/ & / 8
1 3 &
! &
1 / & 1 %/ /
/
?
% / /B
,6 #
L
L
A
A
@
L
A
0
K
0
K
0
K
1 1 & ?
#
@
#
@
0 0
A
L
#
@
0
@
&
A
L
K @
L
0
A
L
L
A
@#-0A
A? 5 # / /
! / &/ ! /
? 1
1/ b
1/ a 1/ K
1
1
1
1
+
1
-
Vg
s
+
Va
-
-
+
(
Va
-
Va
+
-
Ω F) ,
# / 1 %/ 3 & ? @##A
1
& 1 ?
& 1 3 & 1 ?
? ?
#?
/
& 3 ? 1
1
0 0 0 0 0 0 0 0 0
$ &
/
/
# ?
2
K
@
K
@
2
?
3
1
/ /
1
C
0
L
2
A
L
0
/
& %/ &
0
# 1
2
0 0
0 L
L
2
0
A
2
@#-A
/ @#-AC
K
K
P
2
L
@
L
@
2 L 2
L@
& @#-A 1 / / & ?
1 / ?
2? 1 ?
2
/
?
2 A@# A L A
/
2 2 # A L @2 2 # AQ @ L L A
@ A & @##A / 1 @ A =/ 1
1
2
K
2
1
K
2 2 #
K
2 2 #
&
@#-A
/ 3
@A
@#- A
? / 8 &
!
&
3 C
K
L @
L
L
A
@#-'A
'
1/ b
1/ a
Vg
1/ K
1
1
1
1
1
-
s
+
Va
-
-
+
Va
-
Va
+
1 1/ c
1/ c
0
V0
1/ c
1
2
+
(
Ω,F)
# 3 %/
1
/ @ / % / &
1 &
2
C
2 K 0 C =
A
/ 1
1 1 & @#-A? 3 3 ? K 0D
2 L 2 #
K L ?
2
K
# D / 2 L 2 #
K 0?
/
?
/
C
K
@
L
3 3 / 1 &
2 L 2 #
K 0?
2
K 0D /
L
@#-#A
A
/ &
2 L 2 #
K L ?
2
K
#
C
2
K 0D
; # C
K
@
L
3 3 / 1 &
2 L 2 #
K 0?
2
K
# D
L
@#--A
A
/ &
2 L 2 #
/
K 0?
C L2 2 K #
K LD
1 1 /
8 3 C
K
@ @
2
L
L
A A
L
@#-+A
#
3 3 / 1 &
2 L 2 #
K 0?
2
2 # D
K
/ &
2 L 2 #
/
8
C
K
@
L
3 3 / 1 &
2 L 2 #
K L ?
1 & ?
2
@
K
?
A A
L L
@#-A
/ &
# D / 2 L 2 # K ? 1 1 1 1 ? / / K
1 / / & 1 1 & ?
C L2 K L2D 2 K @ L 2A #
1 1 /
C / 1
L
2
2
K LD
K 0
1
! & / @#-A
1 / / 1 1 /
3
/ / & 1 / 8 & . // ? 1 / /
0
0
1 %/ . ?
"
? & 1 13
)
3 > 1 %/ / 1
@ $ &
1
1 & # ? 1 / 1 1 ! 1
#
A K
L
L 0A
L A@
@#-A
L A
& 6 1 1 ! 1 3
1 1 /
%
#@
@
! & @#-AC
3 7 1
K K
#'0? / 1
0 0
K
! & 1 1 / & ,6 #
#?
K
1 %/ ! 1 & 1
! & ? @#-A? = @#+0AC
# P2
L@
2 2 A
@
"1 @#+0A @#-A % 1
L
2
L@
2 2
AQ
@#+0A
L A
K ?
2
K ?
2
K ? /
#
K
# @
LA
$ / ? 1 1 1/ ! 1 @&
2
0
A &
1 1 /1/ 1
/ & L
#'0
0
1 1 / /
1 % &
5
!
1
# / 1 # / K # ?
K
#'
. / 1! 1 % ? 1 /
K 000 /
0
K
#'? / 1 / #'
1
/
1
#
/ 1 ? &
K ?
1 / 1 1 /
& 1 6
. 1
?
/ 1 ? #'
#
K
'?
&
/ 1 1 !
#
1 1
/ 1
! & / & 1
6 1 / / & 1
36
3 /
=
1 / /1
/
,6 # 1 &% 1
-
1
1
Vg
1
1
1
1
1
1
+
s
Va
+
-
Va
-
Va
+
K
0
1/ c
0
1/ c
1/ c
1
2
+
(
Ω,F)
#'0 & ,6 -
K
1/K
#' 5 = &
#
&% 3/ / &
V0
+
kR kC kR
kR
Va
kR
kC
VVg
kR
kR
V-
H1
V-
H2 V+
kR
H3 V+
kR
V+ kR/9 kC/K
V+
+ 15 -
+ 15 -
K*kR V-
V-
.define K 1.0 .define kR 2e3 .define kC 0.25e-6/pi
V0
H4 V+
*** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) #' / & ,6 -?
#
K
20 10
|H(jω)| (dBv)
0 −10 −20
µCAP
−30 −40 −50 Theory
−60 −70 2
4
10
6
10
10
Frequency (Hz) #' 1 & ,6 -
1 &% ? 1
1
1 ! 1
&
#
3
/ &%
3 7 / 1 1 / /
1 3 /
@##AC
0 0 .
1 /
/ 1 / 1? 1
1 1
K
# L A
@
L
1 1 & & 1 %/
/ 1 %/ &
,
1 1
+
1 /3
/ & 1 %/
%
3 $ &
1
0 0
0
& 1 3 & ? / 1 =
C
#
K
0
1 /?
& 1 = & 1 3
1
#''
@
L
A
0
/
0
/
! & 1
/ 1 / %/? 1
# ?
1 % // / 1 & %/ & 3
)
? 1 & / / Æ
1/ b
1
Va
+s
1/ a
-
VBP
+ 1
Vg
1/ K
1
Va
s2
1
-s
1
Va
Va
1
1
-
VHP
+
(
-
Ω
-
+
-
VBP
VLP
+
1
,F) 1/ c
1/ d
V BS, V AP
1/ e
+
2
-(cs -ds+e)
Va
#'' 1 / & %/ &
1 1 1 %/ & 1
# .&
/ / 1 &
1 ? 1
#''
# 1 & // &
/ 1
/
1 / A ,1 1 8 &
3 C
K
0 0
K
#
L
L
C
K
0 0
K
L
#
L
; # C
K
0 0
K
#
L
L
3
@ 1
! 8 &
00
83 @2
K ?
1
K 0AC
8
@2
K ?
K
@
0
K
0
K
L
A
L
A
0
#@
K
@
0
#@
L
%/
1
1 Æ * ? 1
& 71 L
. 1 1
Æ &
A
/
/
1 1
1?
! ? 1 / ?
/
1 !/ / 7 !/
1 1 / = 1
!
1 1
1 1
! &
1 / 1 / / 1?
! &
/ / &
& 1? 1 &% /
*
? 1 1 & 1
& &/ ! 1 1 / /
1 1
! &
/ 1 &
/
L
L
1 @= A
/ 1 1 / 1 1?
/ / =
1&
! & &
/ &
& /
L
. 1 / 1 1 & & 1 %/
1 1
L
1 K ? K AC
#''
A L L
L
! 1 / 1
1 1 &
!
/ / & 1 1 &
! & 1 $3R / %/
6 & / 63 & . 1 6 1?
! !
! & 3
/ 1 8 & ? / 1 1 61
/
1 ? &/ 1 & ? 1 1
1 3
1 1
""
# 1 / 8 ?
1
#'#?
/ J
/ + @7*1 A
K
4 + ?
1
0
1
1 / 1
@ A
1
&/
> 1 6 ?
/
0
,
@ A
1 / / /
! / # 5 = & 1 &
! &
3
1 1 1
$ & 1
& 1 & #'-?
0
?
/ ? 1 & @A
0
A
0
K
0 L
L
L
1
0
@ ?
0
&
K @LA
0
V+ V+
i0
0A + V0 -
C0
+ Vi -
0A
+ V -
+
i
-
C0
Ik V-
Ik V #'# & #
V1 V2 V3 V4
1 1 1
1 0A +
-
0V - +
1
#'- & #
0A
gk
s 3Va
+ V0 -
0
# 1 & & 5
& & ? &% ?
B
% /
/
! = 1 % / & & 1 / 1 /
/ / !M? / 1 &% & /J 1 /
/ !)=
1
% ?
$ /
&
/ /
S B
/ !
1 1 1
1 & 1 % % = !
1 /* 1 1 %
/
1
& & ? / 6 1 1 / / / &
@
#' 5 = 1 &
0 @
A K
@
L0
L 0 #A@
0
/ & 1
1 6
0
@ A K
L'
L 0
## & 1 & ?
@
A K
0 0
#- . 1
K
L
L #
L
L
#'+? 1 ! ' / 1 1 /
/ 1 %
1 1
#+ 1
! &
@ A#
/ & & ' @ /*A ./ &
1 / / & 1
& ?
1
1
L #-#A
! & 1 1 / /
0 0
L 0 #-#
=
/
L 'A
L 0 -'A@
1
! &
#' 1 / / & 1 &
! & &
0 0
71
1 1
!? / 1
/
= 1 % / & I
0 0 1 &
@
(
A K
K
@
A K
! &
0@ @
L -000A
L 000A
& # / C
# 0-
L - -
L 0
L + #
L ' 0
L 00
@#+A
0
1 + -
1
V0
3
s
A1
4
1
1
-
A2
+
1
-s
1
1/4
-
V0
A3
2
s
+
1 -
V0
A4
+
-
V0
2
V0
1
1
-s
1 A5
4
-
(
Ω,F)
+
Vg
#'+ & #-
1
1
1
1
1/6
1
1
+
1
-
-
+
+
+
V2
V1
-
-
µ
( F,k
Ω)
#' & #+
0'
# * & 1 (
"
& -
! & ? @#+A?
K @ ? * & ?
&
? /
&% & !)= >
A
/ & !M /
/ " 1! 1 &%
/ & / # 1
/ 8
*
1 31& 1 & / # M O /J & 1 ( & 1 1 & ? &% & ?
K
L ?
!
K
M O /J *
$ 1 1 & / 1
1
@#+A % 3
6? & ( 3 3*
#? / 1!
1 1
1
/ ( @ /A 1 & & 1 / 1 &
1 1 / & #? / / 1 (
! &
@
A K
& #0 /
@
L - #A
0@
#0 * & 1 (
"
& #
L 0 #A@
L #A
! & ? @#+A?
K @ ? * & ?
&
? /
&% & 0 !)= >
@#+A
L0 '
A
/ & # !M /
/ " 1! 1 &%
/ & / # 1
/ 8
1 31& 1 &
*
/
#0
M O /J & 1 ( & % 3 1 1 & ? ( 3 3* &% & ?
K
"
K
1
#0
1 1
1 / ( @ /A & & 1 /
6? &
L ? M O /J *
$ 1 1 & /
/ 1! 1
@#+A
1
1 1 / & #0 / /
1 # > / 1 /
1 $3R / 1 &
! &
1 1 / & 1 1 1 1 1 6
1! 1
$ &
# @
A K
K # !M /
0
K
# @
L
# > / 1 / / 1 &
L0 #
L A
3 / 1 &
1 $ & # ? / / 1
1! 1
# !M / /J !)=
L 0 #A@
1
!
K
1
0#
1 6 $ & 1 & &% & 1 B
1
1 /
1 / 1 / /
@
A K
#@ @
L 'A
L A@
L A
#' 5 # / 1 &3 % & 1 1 / & &% @ 1 1A ## 1 & 1 3 / / & 1 &
! & C
0 0
L -
K
'@
L A@
L
L 'A
@A 3 & 1 % /
! & ?
/ " / &% & 1 $ & 3/ & 1 1 1 ! 1
1 0 ' /* & 1 ! / /
1 &% & @ A / /3 / @ A 2 / & 1 /3 1 1 / / /
/J !)=A >
$ 1 1! /
2
0
K # !M /
K
@ ? M # !M /
&% & 1
1 &% / 1 &
/ 1 % I #- 5 ## & 1 &
0 0
K
@ @
L
! & C
L - #A@
L #A@
L #A L
#+ %/ / 1 &
L - #A
! &
$ & 71 & @ ? ( ? * A / 1 & I ,6
@
#
@A / 1
A K
! &
& 1 @ A $1
1
@ @
L A
L
L #A
1 & / 1
#'
/ / & 1
1 & / '
! /*
1 1 1
/ 1 1
! &
0-
1
1/2 +
Vg
-
2
A1
1
1
-
1/2 -
A2
+
1
1
(
1
+
1
1
A4
Ω ,F)
A3
V0
+
#' & #
# > / / / / & 1 &
/?
! &
1 / & 1
1 / 8/
@
A K
0@ @
L A@
L A L
L #A
#0 = 1 & ! & C
0 0
K
@ @
1
/ 1
L A@
3
L A L
L A
@A 1 1 1 1 6
/ 1 ! &
1 & 1
! &
? 1 @L A @ A >
1 0 / - /* & 1 //
1! / ( # / /
& 1 / /
1 &% &
1 !)=? / 1 3M / # !M
0 ")= 1! 1 /
/
1! 1 ! & 1
5
3 3 &
1/4
A1
+ -
0+
1
1
3
1/2
1
A2
-
-
+
+
1
1
1 -
A3
2
A4
+
1 -
A5
+
1 1
1
1
V
1
A6-
1
+
Vg
(
Ω,F)
##0 & #
@A % 3 1 / / & 1
" ? / 1
/
/1 & #0 !)=
@/A # . 1
##0? 1 ! ? ? '? / - 1
/ // - /*? # $1
1
1 8 1 /
/ / & 1 1 %
# &
0 0
&
@ A K
#@ @
L
C L A
L A@
L
L #A
@A > 1 1 / / % / = 1 &
@ A 71 1 & & 1 %
#
/ 1
5/ 1 1 !
1 0 / /* & 1 !
#
&
1 1
I 1
1 1
/ 1 / / /B 1 & > 1 /
1 1 1 0 /* & &% @A $ 1 1 1 1 / 1 !M / 1 /J &% 1 &/ !)= >
1 &% 1
"
# 1 13
! &
&
0 0
K
1 / /
C
L 0 0
L
0
@A = 1 & $ 1 / / ! 00 )= & & 1 >
1 03!M /
1! & &
C
? N @( A 5 ? / 3
&% & / / 1 0
& & 0
Æ
0 )=
K L# > " 1 % &
1 1 0 1
1 1
Æ
Æ & L #0 J 1 /
Æ 00 J 1 / / 1 & 1
& 0
Æ
+#
2 &% & 3
! & 1 &%
Æ
& # & 1 &
> 03/* & 1 /
C
S
/ / & / 1
1 1 ( / Æ & 1 1
!?
3&% ?
/ 1 3 /
/1?
$% ?
3
@ A 5 1 $3R = 1 #' > / 1 / / 5
/
! &
!? / /
1
6? / 1 &
% /
& 1 & ?
#?
1 /
/ >
!
/ " 1! / / 1 1 1 /J &% !)=?
#
K 0
1
/
/? /
1 / Æ ? / 1 / /
1 / 1 1 ! 1
@
A K
0 0
K
#@
L #A@
L A@
L A
L ' #A@
L A@
L A
L # 'A@
## & 1 &
& , 1 @L A
/ /
.
/
L #A@
@
! &
/?
3
/ ! & 1 / 1 1 & % /
1 /
@
A
K
@ @
L
@
K
L
L -A
L A@
! & ?
@
A K
L #A
L -A
L
L+
#- > %/ = 1 &
L
L#
/ @A
@
A?
L
L
L
/
0
#+ 5 = 1 & 1 & / 1 /
* /
> &
/ 1 / &
1 3= & = 1 / & & 1 @ ? 1 1 !3 3!
A >
1
1! 1 / &
1 / ? / 1 /
: K ;<4 @ A
& 1 ? /
%
@A
%
1=
: #A9@: #A L 0@: A9@: A
K 0 0@ 0@
@ A
K 0@
: 'A9@: 'A L 0@: '#A9@: '#A
: #A9@: #A 0@: A9@: A
0@
: A9@: A L 0@: 'A9@: 'A
# / 1 & &
=
/*
/*
& &
$ 1 / 1 1
0 !)= / M !M
>
1! 1 / & &%
@
L 0
A K
@
L #A@
L
L A
# > 1 1 / / / & 1 &
& & C
@
A K
0 0
K
L # @
L
L A@
L
@A 1! 1 ! & 1
1
?
L 0A
/ / 1
1 1 1
1 ! / 1 / 1 - /* @ A > " @ "1/A ? / 1
1 &
/J !)= / M !M 1 / 1 / / 00 ")= 1! 1 8 & / 1 / & # 0 " / & 1
## / 1 1 1 &
? ? / '
& & ' @ /*A
1 / & &
$1
1 ! 1
% / / & 1 # 1 1 /
##
!
//
&
!
& /
/ &
/ 1 1 13&% 1
/ 5/ 1 / 1 1 3
/
1 / & 1 1
$ &
0
0.5
V0
1 +
Vg
-
1
A1
1
12
-
1 -
A2
A3
+
0.1
1
+
1 1
(
A4
Ω ,F)
1 +
## & # 0
1
1
1/8 -
1/4 -
A1
A2
+
+
(
Ω F) ,
## & #
R0
1
1
1
1 +
Vg
1/2
R
2
VT
0
-
(
Ω,F)
## & #
# 1 &
! & 1
01 0
## C
K
@ @
LL
3 1
$ & 1 & /
!? / /
3
L A
A@@ L A
@A % 3 1 1 1
' /J
L A
36
=
K
! & & 1 /
/ & 1
$ &
@ A > 1 & $3R / / & 1 & &
/ /
?
! &
C
.
1
1 1 /
@
A K
0 0
K
L @
L A@
L
L A
# > 1 1 / / & 1 /
! &
,6 #
# ' > 1 1 / / & 1 & & & C
0 0
K
#@ @
L
L 0A L A@
L A
@A 2 / ? / & 1 6 & 1 6
3
#
& 1 &
1 & & 1
1 % / & & /
/
&% ? / 1 / / 1 / / $ !M / !)=? /
@ A 5/ / 1 /
1! 1 /
1 B
/ & 1 1 1
$ 1
1
1 A1
+
V0 1
-
Vi
1/2
1
+s3
4
2
A2
-
-s
+
1
1
V0
-
1
A3
+s
+
V0
1 +
1
V0
-
A4
1 2
1 -2s
V0
1
Ω ,F)
A5-
(
+
##' & # #
# # 1 & ?
@
##' = / (
A K
0 0
1
# - 1 1
L
$1
1
/ & 1
& 0
###
@
A
1
/ 1 &
# + > 1 1 / / & 1 & & & C
0 0
@A > &
@ A K
!
1 //
& /
0 0
@ A K
$1 L 0A @ A & 1
! & ?
K @
#@ @
3
L 0A
L A@
L
L ' #A
? / & 1 6 &
& 1 & 1 6 & 1
#
1 &
1 1 /
@ / A &% / 1 / / 1 / / >
1 1
1! 1 / & >
! / !M / !)= / / & 1 /
&% 3 & & 1 @ A 5/ / 1 / / 1 1
1 B
$ 1
1 & 63
> 1 / 1! 1 /
1
# 2 / & 1 & 1 * / &3 % ? @A / @ A? 1
##- > &
? / 1 % & 3= = 1 / & & 1 /
1
1
1/ 2
1
+
1
1
1
2
1
1
3
-
-
-
-
+
+
+
+
1
1
1
1
1
+
V1
(
Ω,F)
### & # -
|H| 10
dB -20 dB /dec
0 1
-10
10
100
f (kHz )
(a)
|H|
dB
10 -20 dB /dec
0 1
10
100 f (kHz )
+ 20 dB /dec
-10
(b)
##- 5 ? @A / @ A? & #
V2
'
1
1/ 2
1/ 4
1/ 3
1
1
1
1
V1
V2 -
-
+
+
(
Ω,F )
##+ & #
# 1 1
& ?
@A ,6
0 0
1 1
##+
/ / / 1 3
C
0 0
K
A@ L 'A
A@ L A
@ L @ L
/
@ A 5/ 1 / 1 & & @ L A /
@ &
TA #'0 & 1 &
/
% = & & ?
@
A
/B & & 1
? / 1 /B 1
@
A K
L
@
8
A
L L
#' > %/ / / / & 1 &
!
##
& $ &
@
A K
-@ @
L A@
L #A L'
#' 63
L 0A
1
/ 1 $3R ? / &/ ! / = 1 ?
?
&
/
! & ?
0 0
?
&
1 %/ & ?
? / / / &
/
/
/ #' 1 $ 1
1
! & ? @#A? & ,63 /
1 6 ? /
#
R2
R1
R3 +
+
V1
C2
-
C1
0A 0V -
+
+
V2 -
(
Ω,F)
## & #'
1 / &
2?
1
/ & 1 / #'' 2 & 1 &
A
>
?
! & & ,6 # @
/ 1 &% 1 /
& 1 / 1
3
1
36
= 1
/ & 1 /
K
@ @
L
L 0A L A@
L A
) PQ : 1 ? ,? / ) ? : (?
< * % 8 ?
S !C 7 3. ? +#
-
! " . 1 1?
/ / 1 1 /
1 =
! & / & / &
1 6 &% ?
$ &?
1 //
1
&/
! / & .
1 1?
! & / & 1 & / 1
1 ? / & ? 1 & & //
!
/
2 ?
3
/
/ = & % / 1 / /
!
&
#
& ('
-
1
1 ?
1
= ?
?
?
&
@
! & ?
& 1
!
0 0
>?
A? 1 1 3/* /
/ / 1 ?
:
=/ 1 ? 1
1
/ /
/
/1? ! ? 1 1
1 1
? 1 1 &
@-AC
1
-
K
:
/ 1 & ?
N 1 N 1
:
K
X: :
X
K
:
/ &
: X:
1? 1 / ?
/ /
X
-
:
3
+
3:
/ /
@-A
:
1 ?
@-A?
1 & / 8 %
1 @-AC
.
X
& E 1 1 / 1
-
?
/
1
@-A
Ek
Vg
-
0
+
V2
N
-
1
1 / / 1 & 1
% & ? &% /
% ?
1 1 / 8 & 1 1 &
-
K
?
=
@- A?
3 @ A K 3 C
/?
3 @ @ AA 3 @ @:AA
@- A
? 1 & / / & / ! / 1 / . ? 1 &
!/ & . ? 1
-
1
/ /?
1 / & 1 / C
3 3:
K
:
@-'A
1 / @A @-'A 1 / 1 / 8 &
1
@-#AC
1
K
1
K
= 3 ?
3 3 1: 1: 3: 3: 3
3:
L
L
1:
@-#A
1 1 6 @ A 1
1
= 1
% 1 1 / /B/ 1 1 = C
= @1 A
K
1
1:
K
0 &
1 &
1
3 1:
3:
K 0
@--A
/ % @-#A / C
1 K
3 3 1: 1: 3
3:
3:3
3
@-+A
1
1: 1:3
6 1
/ / & 1 1 @1 A?
1
& = 3
K
&
K
: 3 3:
K
3 L : 3:
- 1 - 1
@-AC
:
3
K
:
3:
3 3: L
- 1 Q L >P- 1 Q
:
1 /
/ / / ?
K
,% @-A 1
@-A
1 & 1 / / &
@A - 1
: 3 3:
! &
- 1
1 / &
-
1 & / 1
! 1
@A
:
/ /
/ /3 7 1
1 1
1? @-+A / @-AC
3 1: 3:
&
K
= &
1 1
:?
3 3:
P
- 1 L -
K
- 1 Q
K
P
K
>P- 1 Q
/
@-A
! & / 1
& & 1 /
3 / 1 / / 1 & & 1 &
! &
& 1 / /
%
3 7 1 1 &
- 1 3 3 @A - 1
- 1
K
K
K
@
3 3 @A
L
/
@
L
A@ L A
L @
1 L -
L A @ A L A
L
@
@
-
C
L A
@A K
L
A
L'
1
1
0
1.6 1.4 α (Nepers)
1.2
[]
1.0 0.8
S|T| 2a
0.6 Sθ2a
0.4 0.2 0.0 0 10
1
10
ω (rad/sec)
- ,6 ? / &
-
1
- 1
L A A L '
@
K
@
@ L A
K
@
L
L
A
L'
& / & 1 & /
1 1
! @ A &
-
1 & 1 / & 1 & & ?
K 0
? 1
1
1 1
$ / / 1 / 1 1
& &
1 $3R 63 ? 1 6
1
& 1
0 0
//
K
K
K
K
- ? / / /
! & / / &
1
1 1
@
A K
@ A
L L
L
L
L
K L
L
1 C
C1
V1
R1
R2
V2
+ -
R4
C2 R3
- $3R / /
1 ?
?
1 /3 /
/ & ?
@
A
1 Æ ?
(
K
$ ?
?
&/
1 3/* /
K ? /
K ?
#
/1 & 1
1 &
!
/
& 1 C
K
K
,% @-0A / 1
$K K
L
L
@-0A
% & & !
? / ?
/ & 1
K K ? & 1 1 K $ / " K K $ & 1
K
&
1
$
1 1
3
?
? / 1
1 ?
-)
/ 1 ?
K
K
1? 1 3/*
3 @A 3
/ 8 1 1
$
$
K
"
K
"
/
"
& K
1
/ / 8 & 1
/1 3 & & 1 1
7 1 1 1 &
/1?
C
1 % & 1 3
% & /3 1 13
/
1 & 1 3/* /
1 &
/
C
K K
L
$
K
"
K
"
K
L
0
K
"
L
K
L
"
1 & 1 1 &
-)
K
K
L
"
K
L
$
@
"
" 1
1 1
L
K
"
C
A K "
L
"
L
1 1 & ? 1 / 1 3
1
1
/1
/
% =
?
1
"
# . . 4 $ (
$
/ / 1
& & / /
/ 1 1 1 1 = / &% 1 &%
! & ?
@
&
A K
0 0
?
1 1
6 @ 1 /A? 1
71 1
& ? .(?
/ @ 1 / A? 1 &
! 1
! &
. &
D 1? 1
1 % = &
1 1 / 1
1
! 1 &
1 & =/ 1 1 1 &
/ & 1
& / / 1 U 3 -' /
?
1 1
/ / / &% ?
1 1
/ 71 1 ? 1
3
1 /
@-AC
3
1 1 & ?
K 0
1 ? @-A
&
K 0
@ A?
? 1 & &
3
/
K 0
3
3
&
6
C
3
! $ ?
/
3
K
K 0
K
1
3
K 0
1
@-A
( !
?
@-A
1.5 Loss at ω = ωp
Loss (dB)
1.0
0.5
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
kth Element Value (L/Lk or C/Ck) -' " / / &% ?
1
1 / ( / / &
/
&
C
1
-
1
-
# 1
K
K
! 1 /
? 1 / / 1
! / 1 &% ?
3 33
3
?
1 /
K 0 /
K 0
@- A
$ 4 &$
= / & 1
? / / 1
&
/ /
! &
!?
1
& 1
1 PQ 1
1 &/ & 1 & 1
-#
//
! / ?
1 1
13
& / / / 1 1?
1
/ / / 1 1 2 6 1
/ 1 Æ
1 / 1 1
'
I
1
I
3
Y1
+ V
Z2
1
V
+
Y1
I1
+
Z2
% & 1
/
Z6
V
4
V
6
-
-1
+
V
I3
Y3
2
-1
- V6
+
Z4
V
+
Y5
4
- I5
I
5
! &
K K K K K K
Z6
V
6
-1
& % & //
0 0 0
+
-
-1
-- 1 E
1 1
Z4
2
- V4
-I3
+
! / 1 /
-1
-V2
T=0
I
Y5
-
-# //
1
5
+
-
V1
I
Y3
!
C
0 0 0 @
@
@
@
@
@
0 0 0 1
A
A
A
A
A
A K
@-'A
1 & 1 &
1 & % @-'A =/ & & 1
1 E
& &
1
!/ 8 / 1 E ?
1 1 1
-- . 1 1? 1 !
/ .
/ 1
1 8 1 1 /
1 1 & 1 & & 1 3
1 B !
/ 1
6 ? 1 / &
0
K
& 1
0 0 0
&/ ! 1 1 1 & @
@
0 0
A
. 1 E
B / ! @ A &
&/ ! & 1 / 8 ?
( !
? /
1 ?
0
! !
A
1
1 1
? / & 1
1
#
I =0
2
5
I
3
+
+
V1
V2
1
V4
1
1
-
-
(
-+ 1 /3 / *
?
1
?
1 (
1 ? 1 ?
/
Ω,H,F)
04
/
/
5
?
1 /
? / =/? 1
/
/ & & &
1 % @-'A 1 / 1 1
1
7
@-#A &
C
04 0 04 0 04 0 1
0 0 5 0 6 04 5 0 6 04
K K
@
K K
@
K
A
A
@
A
A
A
6
A K
04
@-#A
1 ? 1 / 3
/ 1
--
& 7
0
0
A
E
1 1
1 & @-#A !
1 / &
! 6
3 & = & 1 / / (
1 /
@
1 @ ?
0 04 0 04 0 04
5 @ 6 @ 4
K
-+
$ 1 / !M / !)=?
1! 1 & &%
? 1
& 1 1! 1 / & 1 =3
%
3 1 & & 1 &
0 4 0 04
K K
K
@
0 0 04 04 0 0
@
@
A
A
A
C
-
+V4
-V2 kR V+ +V kR I1 kR
kR
kR
A3 V+
kR kC
kR
V-
A2 V-
V1
kR
V-
A1
kR
kR 2*kC
kC
V+
kR
V-
V-
A4
+VI3
A5 V+ + 15 V- + 15 -
V+
kR -VI3 2*kL
kR Vg
kC
kC
.define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
kR
- / &
0 1 & 1
/
-
1 /
!
04 1 ?
0 0
A?
!
04
@
1 1
1 E
0 04
L A
04
1 / 1
!
!
@
04
@
L A
04
1
0
!'
?
04
K
0
@
L
--
1
1 &
@ L A
1
? / & 1 1 % /
1 1 K
A
? 1 ?
/
A K L
? % /C
@
& L
&% 3 1 &
0
? 1 1 L
/ / & E
K
@--A
0 0
A
@
% / / &/ !
0
/ 3 / &% 3/
0 0
@
1 1 1 & 1
@--A
1 & -- 6 ? 1 &
A
B /
1 &
0A
? 1 & 1
K @ L
0
@
L A
1 / 1 %
% / &
04
K
C
04
1 &% 3/ % / @--A
1 1 & 1 1
1
1 & / 1 &
+
Magnitude (dBv)
0
−50 Leapfrog
−100
Theory −150
2
4
10
6
10
10
Frequency (Hz) - % & 1 &
1
/
/ &
.
! &
1 & & & 1
! 3 3 1
1
/ 1 & 1 / &% & 1 / &
1
1 / / &
- 1
& // /
1 / 8 &% / & 0 /* ) 1 1 &% ? 1 &%
? &
/ ? 1
& 8? / / ! / & +0 /* 1 & #0 ")=
? 1 / /
& 1 ? -0 /* 1 / /
$ ?
& 1 / /
. 1 / / 1?
1 1
-? 1
/ 1 E @- /*A & 1 & / 1
1
! 1 / & 1 & ? 1 -3/* / 1 1
%
! 1 & 1
!
1 ? $ ?
!#?
71
-0?
/ 1 ! ?
/ % = 1 / ?
/ 1 & & @- /*A / / 1 / 1
-
1
0
'
#
# 3 3
Magnitude (dBv)
0
A1
−20 A2 −40 −60
A3
−80 −100
A5
A4
−120 Theory −140
2
4
10
6
10
10
Frequency (Hz) -0 & 1 &
/
1 !
0
!#
1
?
?
. /
1
1 / / & 1 1 1 / / 1 1 1
0
1 % / /
& 1 / / 1 % ?
-
! ?
? 1 1 & 3
1 & 1 &/ ! & 1
0
K
L
0
0
L
0
@
C
A
71 1 3/ &/ !
? 1 & 8 1 1 1
1
!
& ?
1 1 1
1 Y
1 1
/
#
K Y
?
1 1
/ &/ ! 1
% 6
1 & 1 3/ / 1
-
1 ?
/
!#?
1
/
- @L- /*A 1
1 & 1 & 1 1 &
8/ 1 / ? 1 1
/ 1 1
1 /3 & ?
& 1
1 & ? 1 1
1 / / /
% 1
1
/
&/ ! 1
- -
/ / 1
Y
1 1 / .
1 /
1 &
!#?
& -0
/ 1 1 1 ! &
-V2
+2*V4
kR V+ +V kR I1
kR
A3 V+
VkR kR
A4
.define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
kR
kC
- 1
-
1 /
1 / 1
V+ + V15 - + 15 -
V+
-VI3
kC
1 1 / 1 ?
/ 1 &%
VA5
kR 2*kL
Vg
V- kR/2
+VI3
V+
kR kC
kR kR
V-
A2
kR
!?
kR
V-
A1 V1
2*kR 2*kC I Σ
kC
!#?
/ &
!
+0 /*? 1 1
/ - /* 1
1 1 /
1
.
8 *& / 1 1 1 6 ? & 1
& 1 & 1
-+ / &
& @ / 1V U % A 1
1
/
-
04 0 .
K K
K
K
@
L A
1 ?
1
1 & 3 /
0
04 04
@
0
L A
1 %
@
@
6
0
0
04
@
A
A
0A
@-+A
& 1 / 8 & 1 & 1
1 /
3
@-+AC
04 0
1 1
1 / /
1 & 1 /
1
1
@-+A
-#
/
-'
1 &
1
&
1 & 1
/ @&
A 1 1 1 / /? 1
1 /
@ /*A 1 & 1 /
$ ?
0
Magnitude (dBv)
0
A1
−20 A2 −40 −60
A3
−80 −100
A5
A4
−120 Theory −140
2
4
10
6
10
10
Frequency (Hz) - & 1 3/ /
I =0
2
5
I
V
1YI 1
3
+
+
1
1
V2
1
-
(
-
1
V4 -
Ω ,H,F)
- 1 / / &
-VI3 kR
kR
2*kC
kC -V2 kR
kR
V-
VkR
- 15 +
Vg
kR A3
VA4
V+
V+
2*kR
kR/2
V-
+VI3
A2 V+ + 15 -
VI1
kR
V-
A1
kR kC
V+
+2*V4 2*kL kC
kC
.define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
kR
-' 1 3 & / 1
/ /3 8 1 1
1 @
3 A %
1 / 1 / 1 / / 1 &
1
6 / 1 1 1 1 &
/ /
"
4 ' !0 4 # . 4
*& 1 6 B?
!
& & & = & 1 1
-'
13 3
/
/ 6 & 1 / 5 1
/ / 1 / 1 1 & 1 & 1 3
? ? 1 & =
1 1 @
1 6 A . 1 6 ( ? 1 1 /? --
1 1
? / /* / 8
& 1 @ 1
* A
-' 1
/
/
--@A
/ @
Æ
/ @
A
1
A
1
1
// 1 L #0 J Æ 1
Æ #0
1 ? 1
? 1 61 1 1 1 & / / / A
1
1 & 1 @ /A
1 = / / 6 & 1
* 1
6
/ / !)=
Æ
# ? 1
/ 1 / /
1 / @ -# & / 8
1 ? 1
? 1 / ! 6?
Magnitude (dBv)
0 −20 A1 −40 −60 A2 −80 −100 2xTheory −120
2
A4
A3
4
10
6
10
10
Frequency (Hz) -# & 1 3 & / /
1 = 1 / &
--@ A 1
Æ
1 1
1 6/
& # & 1
&
1 1 & 1
!
&%
6
1
1 / 0N ?
1 1
1 1
6 &
/ / @ /*A 1
& &% / 1 /? ? 1 = 1 / & 1 $ /
1 1 1
/ $ 1 8 1 1? 1 1
1
!
& / &%
& 3 &3 / &%
? --@A 1
? 3
? 1 3 / & 1 #0N? / 1 ? 1
!
1
? 1
/
1 1 & &% / $ / & 1 1
1 1
1 ! 8 &
&/ ! / 1 & 1 1 1 ? 1 7 1 1 / & 1 & ? 1
& . / / 1 ?
/ 1
0.5
(a) 0.0
∆dB
T=25oC
T=0oC T=50oC
−0.5 4.0 2.0
(b) 0.0
2
10
3
4
10
10
∆dB
R=1.6 kΩ R=2.0 kΩ
−2.0
R=2.4 kΩ
−4.0 0.1
(c) 0.0 −0.1
2
10
∆
dB
2
10
3
4
10
10 4
4
4
A= 5x10 , 10x10 , 15x10
3
10
4
10
Frequency (Hz) -- 4 3 & & C @A ? @ A ? / @A 3
/
'
kR
+2*V4
kR/2 kR
V+
kC
kR
A1
V-
V-
VA4
A3 V+
V+
kR
kC
kR V-
A2
5*kR
kR/2
kC
kR
kR
kR
V-
V-
V+ + 15 -
- 15 +
A5
Vin
V+
2*kL
kR kC
.define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
kR
kC
-+ 1 = & 1 &
! & & 1 6 1
/ 1
-+ (// & 1
@-AC
0 0
K
/ & @-A
1
L
L
@-A
L
-+?
1 1
1 /B/ / 1 ! 1 & & & 1 1 / / & 6
+ /*?
1 1
!'
1
!
1 1 1 3
/ @ #0 !)=A? 1 / & 1 &
-
/
1 / & 1
? 1 &
& 1 / $ ? 1
/1 1 / 1 /
& 1 &
1 & 1
1!/
& 1 1 1
/
1 &1
/ & 1
- 1 ?
Æ
L #0 J Æ ?
1 ? 1 &/ ! / 1 Æ
!
1
1 1/
1
1 1 / & 1 &
1
!3 3! / @ /A
1 ? / 1 / 8 1 = 1 !
0.5
(a) 0.0
∆dB
#
o
T=50 C
T=25oC
o T=0 C
−0.5 4.0 2.0
(b) 0.0
2
10
3
4
10
10
∆dB
R=1.6 kΩ R=2.0 kΩ
−2.0
R=2.4 kΩ
−4.0 0.1
(c) 0.0 −0.1
2
10
3
∆
2
10 4
4
4
A= 5x10 , 10x10 , 15x10
dB
10
4
10
3
10
4
10
Frequency (Hz) - 4 3 & 1 = @A
-+C
/ ? @ A ? / @A
-
I3
R
I
L
+
C
+
I
1
+
V
-
-
V4
V2 -
3
R
2
L C
(a)
-
(b)
. 1 /
C
@A ? / @ A
1
. -@ A? 0N 5 /? / 1 & 1 / D 1
? 1
? 1
@
/ 1 /
! A
/ 3
1 1
1 /
1
& 1
& = 1 1 / ? 1
-@A?
3 / &
/ @ #0NA 1
!
1 &%
/ 1 / 8 /
/ 1 1
1 1 .
1/
1 1 1 1 1 ? / 1 1 1
& 1 / & 1 & / 1 , 1 / 8 ? / / &% / 1 1 / &
& & ?
*& ! 3 &
/ & /
"
$% ! $ '.
1 / 1 / / & / 3 (
1 / /
&/ & / 1 &/ ! & 1 E
1
1 & / 1 & / / / 6 // 1 / 1 ( / ? 1 1 / 1 1 1 1 / 1 3 / 1 =/ 1 / @ -
36 A
=
1 & 1 /
= 1 1 1
-@A
1 / 1 ( / -@ A 1
/ 1 1
?
( /
/ @
A
1 1
1 1 & 1 1 / 1
71 1
/
/
1
L
1
C
1
-
V
+
+
1
+
V
-1/Ls
-1/ Cs
I
R
1
1
I
-
1/R
Y
-(Cs+G)
+
C
V =T V
1
L
+
1
1
1
-(Ls+R)
+
(a)
V=T V Z
I
+
(b)
-0 = & 1 . 1C @A ? / @ A 1
@ =
&
A ?
1 1 ?
A
/ @
1 1 / / 1 1
( !
?
1
1 /
1
/ 1 1 & 1 /? / ?
/ / 1 1 % &
C
# # = 5/1> C
1
K K
@
0 L
0
A
L
@-A
#
# = 5/1> C
0 1
1 1
/
K K
@ A L L
@-0A
1 1 & / =/
1 3
& 1 /&
/ = & @-A / @-0A 1
& & 1 & 1
04 0
/ 1 /
5
6
K K
-0 1 3
@-A 1&
/
-0C
0 6 04 5
& 1 & 1
K
L
L
K
L
L
@-A
1. 68
0A
I
3
V
1Y
1
I
1
+ V2 -
1
1
0. 09524
+ V4 -
1
(Ω ,H,F) - 1 /3 / (
1 =
3 1 & 1
1 (
/ /
- 1 1 =
K # / 1 1 1
&
C
04 0 04 0 ,% @-A
0
0
K
K
@
L A
K
A
L - A@
@
@0 0#
K
04 04
@
L A
04
@
0
0
A
0A
=/ 1 1
!? -0@A?
1
S
/ 6 1 & 6 . 1 %
@-A
-
1
/ = 1 ( 1 1
?
/ ? 1 ?
/ ? / ? 1
& 1 1 71 1 =
!-?
/ 1 1 !
/
0 5
6 1 1 & ?
? K
/
L
1 ' /* 1
?
=/
1
1 1 1 & 1 & - 1 / / & 1
/ &
1
/ (
1 /
- /
1 1 / /
1 !
/
00 !)= 1 ! 6/ 1 / & 1 & /
1&
/
/ 1 1 & 1 0 0# 2
1 8
/ /
7 // 1 1 !
/ & 1 ?
!'
1 1
!
)
1 / 1 I 1 % /? 1 / ? & 1 00#3 1 = ?
K #?
'+ M 1& ?
03M / & N & 1 % / &% 1 1
- ?
& 1
1 0
1 / / / ?
/
-VI3 kR
kR kC kR
kR
kR 1.68*kC
kR V-
VA1
-VI3
A4 V+
kR
+ 15 - + 15 -
V+
1.68*kL
Vin
VV-
A6
kR
A5
kR
(V2-V4) 0.095*kC
2*V4
V-
V+
V+
V+
kR
kR
A3
A2
V+ kC 2*kR kR/2
V-
V4 kC
kC 0.095*kC
- (& = & 1 (
!'
1 1
1 1
V-
-
1 1 !
1 1 1 1 /
1 1 1 / 1
"
kR
.define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
kR
/ / 1 ?
kR
& 1 6
$% * $ '.
1
/ ?
1 / /
! & ( 1 &
! * % ?
3 / 1
1 1
1 ! 1 /
=
1 & / 3
1
1
?
! 1
-' 1
1 / & 3 ( 3
1 1? /
? 1 1 1? 1 /
= 1 1? 1 & / & 1 1 ( !
1 1
/ ? / 1
?
1 1 1? 1
/ 1
1? 1 1 / &
1 1 1 % &
# ! 3 # = 0/1> C
K
0
@
0
A
C
1
'0
10
Magnitude (dBv)
0 2xTheory
−10 −20
Initial
−30 −40 −50 −60
Modified
−70 −80 −90
2
4
10
6
10
10
Frequency (Hz) - 5 & 1
1 1
I
3
R
L
+
!'
-
+ V
-
(a)
-' .. 1 / @A ? / @ A 1
3
1
V4
-
/
I
I
C +
V2
& 1 / / /
-
2
C
L
R=1/G
(b)
& / 3 C
1
L
1
+
- V 0/Ls
Vi
R
1
1 C
+
'
V0
1
z
+
- V0
-# * %/ ? ..? = 1 1
1
K
@
L
L
K
A
/ ? @-'A
@
L
L A
@- A
@
L
L A
@-'A
# !# 3 # = 0/1> C
0
1
@ A
K
K
@
L
L
K
A
* 1 1 1 ? @- A / @-'A? & 1 & / =/ %/ 1
0 0
! & ?
0
?
?
0
6
/ &
@
@
-#
1 = 1
& 1 1 1
C &
L
0 0
0 0
L
L
K
A
K
A
K
1
K @
1 1
3 /
L
A
/ 1
1
6
K K
0 0 0 0 0 6 0 &
@
A
/
@
L
L
@-#A
A
-# / 1 & ?
& 1 1 1
@--AC
?
AC
@
1
K
! &
& /
K
?
K
?
/
5 ?
1
'
1/2
2
I
1
I =0
2
3
+
+
2 1/2
V1
V
1
2
-
-
(
Ω ,H,F)
-- $ /3 / 3 ( & ,6
1/2
2
I
1
20
0.05
0
+
+ 0.1
10
V1
V
1/2
2
2
-
-
(
Ω ,H,F)
-+ * & & 1
5
$
K
@
L
--
"
& 0
@--A
L A
3 & 1 /3 / (
1 1
"
-- *
& 0 > & 1 = 1
%
3 1 * -+ &
/ / /
1 1 & / % &
04 0
K
K
0
5 @
04
6 @
0
A K @0
L L 0
0A K @0
L
C
L 0
@ A
A
0 0
04
A
@-+A
1 & - / / & 1 -+ 1 ..
1 1 &
/
! /
1
& 1
/
1 5( / 1 4(? 71 1 &
!
-
1!/ & / ? 1 !
1 1 6 6/ 1 ?
!-?
kC/20
'
kC/10
kR
V-
VA4
kR kR
V+ A1
A2
10*kC
!?
6 ?
! 1
V-
V-
A6
A5
V+ + 15 V- + 15 -
V+
1 / & & @L- /*A /
*
/
/ 1 1
!#
*
/ L
!?
!-
/ @
71 1
*
/
0
1 /
0 0
&
& 0 #? & 1
Y
kR
1 ? & 1 * -+
?
1
kR
2V 2
.define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
+ V2 1.414*kR -
kL/10
1 1
/ 1
10*kC
-2*V2
- /* 1
0
V+ 1.414*kR
V+
V+
- (& = ?
1 1
A7
VI1
A3
1.414*kR kC/20 20*kL
kR/2 V-
V-
kR/2 (V 1-V2) kR
V1
kR
20*kC
V2*kR
kR
V+ 0.707*kR kR
kR
kR
&/
A? 1 & &
1 ! 1
1 &/ ! /
!
1
% / 3/ / 1 &% & 1 & / / / % / /
+# /*?
-?
1 &
/ / / 1
/ 1 / & / % /
-
&
.& 1
1 003 03!)= ? 1 1
/
/ / & 1 & / / 1 1
'03/* / -# ")=
711 1 /
1
1 1 & / & /
1 1 / & 1 &%
1
// & &% 1
1
/ Æ = 1 / /3& " 1 &
!
6 1 / 1
1 1? / // & / /
/ 1 /
''
0
dB Magnitude
−10 2xIdeal
−20 −30 −40 −50 −60
2V
−70
2
−80 −90 2
3
10
4
10
10
Frequency (Hz) - % & 1
"
$ '. 4 % $ 6
1 1 /
-
! &
* =
1 6 & 1 * = & 33
1 ( 1
/ /
-
1
.
1 ? / & & & 1
1 % & ? 1 * & 3 ( 1
& =
/ 1
/ =
& .@A & 1 1 / ..@ A & 1 1 1 & /
/ / 1 & 1
/ 1 &
&
1 * & & 1
/ /
/
6
3 > & / / = 1 * 1
- 0 1
1
1?
-? / 1 %
1 @ A &
"
& # 1
- 0 / / & 1 1 /
%
3 1 & / / / 3
1 / % - 0 1
1
% 1 &
04
K
C
0
& 1 ?
1 1
1 % / &
'#
ω 22=1.6404
ω1 2=0.6906 1. 308
I
V
0
1. 254
+
V2
1YI 1
0. 797
3
1
5
0. 765
+ V
(
0 04 0 0 0
1
V
4
,H,F)
K
@#
@ #'
K
@#
"!
K #
A
A@
A
L 0 ++ A
K
0
@0 +-#
- ?
04 04 0 0 0 04
@
A L 0
LL#
K
-
Ω
- 0 * & 1
// / ?
5
0.2
-
1 / /
+
-
3
0.2
LL#
A
04
@
0A
@-A
1 1 1 ?
? / /
? & 1 /// 1 / 6
& 1 / . 1 / & 1 6 1
1 /
/ & 1 13 / 1 1 1 1 %
@-A
/
1 & 1
- 1 % / = @-A
& 1 ( & 1 * ? % 0 / - @-
/ = 1 -3
? 1 ? /
A )
!
1
! & & 1 .
3
1 1 /
! &
?
/
1&
/
/
! & & ? 1 //3
- 1
1 & 1 & / 1 /
// & &%
1
&
1 1 1 1! & / & 0 ")= 1 1 ! 1 3/* 6
/ & 1
/ & 1 / / / & 1
/
1! & 1 ! ? 1 & - /*
!
/
? / /
!
@
0
1 !
? 1 / / A
1
/) 0
'-
kC/5
kR
-VI3
kR
V-
A2 kR
+V2
5*kC V+
kR
kR
Vin
kR
V+ kC/5
kR
kR
kR
5*kC V+ kR kR kR V-
V+
A11 V+
V+
VA7
-VI3 V+
kR 0.797*kC kR
V-
VA9
-V3 kR
A13
kR VV+
-(V2-V3 -V4)
-V4
V-
A5
V+
V-
kR
V- 1.254*kC kR
V+
kR
V+
A4
A3
A12
A6
kR kR
V-
VA1
-VI3
kR 1.308*kC kR
V-
kR .define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
kR VA10 V+
V+ kR 0.765*kC kR VA8
- (& = & 1 * 1
V+
- 0
'+
0
dB Magnitude
−10 −20 Passive −30 Leapfrog
−40 −50 −60
2
3
10
4
10
10
Frequency (Hz) - & & / & ,6 #
1
! & T
/ ? 1 @
! A
1
"
1 13
&
!?
!
L' /*
!-?
$ 1 1 1
$ !
L- /*
!?
& & +' @K 0
A & /
1 / 1 &
0
! &
!
0
?
L# /*
!0?
L' / 1 !
& - /*? 1 1 / / L /*?
1
/ 1
1 1 1 1 1 ! 1
( 1 1
& / L' /* / L' /*
1& ?
/ 1 / 1
&
1 1
%
1 / 1
?
1 /
1 ! 1
1 7 1 1 / ? 1 & / / = & 1
#
! & & 1 * @L /*A
1 6 /
/ & / / 1
1 / / / & 1 & & / / 1 1
! &
% /
/ / 1 & 1 / /
1
& D 1
/
/ / /
? 1 1 / & 3
1? 1 / / & 1 1
'
1/ 2
V0
3 s
+
1
1
1 1
1
1
1
R
4
0
-
-s
+
-
V0
2
s
+
-
V0
-
+
V0
1
-2s
1
2
V0
1
1
(
Ω,F)
+
Vi
- & -
/ & 1 & /
/ 1 % &
1 1 / 1 & 1 1 / & !
!
/
1 / 1
% & 1 & 1
1? 1 &
/ 1
? 1 1 / 1 / /
1
1/
1 / / 1 &
1 1 ? 1 &
1/
1 6 1 /
/
/
1/
/ /
#
- . 1 & /
- ? 1 &
1 & 1
A -
@
A K
- 1 & 1
0 0
K
Æ 1 ?
@ ?
# L
L
L
2
? 1 ! &
?
1 $3R / 1 ! 1 & @ / A 1 $3R @A & 1 & $ &
#?
! &
/ 1 1 Æ & L#00
'
Z(s)
1
2.5/ π
1/π
(kΩ ,mH, µF) - ' & -' / -#
Æ
Æ
J / 00 )= /
1 L 00 J $
K M # !M
% 1 03/* /
Æ
>
K /J
1! &3
/1 @ ! A & 3
Æ
0 +# > / 1 1 & / 8
@
@ A = 1 / / & 1
# L 0 L
A K
L
/
1 1 @ ?
/ / 1
-
/
/1 3
- A
& &
- ? 63 ? %/ / / / 3 &
Æ
J ?
.& 1 Æ & L#00
1 Æ
1 Æ &
K
% / & 1
= I
L
-' . 1 / & - '? 1 / &
Æ
& # 1
/
1 & / / % 1
#N / /
1
3 & 1 & 1
/3%/ 6 & 1 / & & 1 / 1 1 / 1 "
"
& 1 % & 1 6/ & & 6 $ & / 1
1 1
-# 5 -' & 1 =
Æ
1 1 1
Æ
L00 1 Æ &
Æ
L#00 J D
Æ
K # ? 1 & #0
Æ
K 00 J D /
Æ
C
K L'00 J
K
#0
1
1. 529
V1
1. 838
1. 159
1. 159
1. 838
1
1. 529
Ω ,H,F)
(
- # & -+
-- " / & 1
/ ?
/ ")=
1
1 1
- 1
/ 1 1 1 3
5 1 & 1 1
&% /
/
,6 / / / 1
1 & 1
% & I -+ 1 & 1
1!
11
&
1 1 / 1 &
1
!
/
( & #N 1 @A & & 1 ( @ A / 1
! & & 1 ( 1
- # - #? /
1 & / @A 5/ 1 1 & / @A / @ A 1 E & - /* / 1 % D / 1 ? 1
! ' !M / 0 !)= 0 "
& 8 / & 1 / ? / 1 00 )= 0 !)=? /
1 &
.
/* !3 3!
- & & 1 ( - -
3
$ 1 / 0 !)= / 0 !M
5
1 & 1 N ( &
/ 5 0 ? / 1
&%
& 1 / 1 " 1 & U /
- / & & 1 $ 1 1 &
- +
- /
1 &% & / "
& 1 ( ! &% 0 ")=
#
1
1. 618
1. 618
0. 618
2. 0
(
1
0. 618
Ω,H,F)
- - & -
Ω2=2.76
0. 905
1
0. 145 1. 910
1
1. 910
Ω ,H,F)
(
- + & -
/ 1
1 / 1 / /
1 1 13&% 1 (A % /
- 1 ?
&
@
&
& &
- > 1 / / 1 % E
A
1
71
& 1
1 1 & 1
I
@
/ / 1 1I
-0 / 1 & ?
1 & 1 ! @ 1 1 I )
A K
0 -
L
L
L '
L
1 *
1?
- 1
1
- ? 1
1 % & = & 1
- / 1
! & ?
-'0? / 1
1
>
0 0 /
? & 1 5( 1 1 1 &
K K
?
"?
K
/
K @ L A
/
3
/ / 1
A
K @
"A
K @
&
#
I
I
2
+
+ V
V2
10
1
20
3
1
0.05
0
+ V3 -
0.1
+
V4
1
-
-
-
(
Ω
,H,F)
- & -
V 1Y VI1
+
Σ
-
1/(10s)
V2
V I3
-
V I2 10/s
1/(20s)
+
- ,% E
Σ
20/s
-
1
V3
-
1 & -
Out
V4
#
R1 C
Vg
L
R2
-'0 & -
@A , 1 / & 1
/
& 1 3
1 ? 1 ?
/ 1 & @ ? /
1 A C
1 /3
1@A / 1@ A ? ? / 1
/ 1 % & 1 Æ & = I ,6
.
1 / 8
@ A 1 &
& 1 &
/ 1
- 1
1 $3R
& - 1 $3R ?
1
/
1 1
?
?
?
/
1 &
& 1 @A / 1
1@A
/
1 & 1 &
.
@A
K
@A
K
1@ A
& 1 & ? /
& C
K " K K K "
K K
/
/
"
K 0 # K
"
1 Æ 1 1 / 8
= I ,6
@ A 1 &
& 1 &
/ 1 & 1 . 1 1 1I ,6
-' > 1 ? / / & & 1 -' . @ 1 1
1 // 6 A
1 / & 0 /*
-# & & 1 -- & & 1 5( 71 &
-'
!
-'
// 1 I ,6
-+ & & 1 1 / &
-'' $ &
1 1 /
#'
1
1
1 +
+
V
2
V
1
i
o
-
(
Ω,H,F)
-' & -'
1
1
1
+
V
+
0.1
V
1
in
1.6
-
(
out
-
Ω,H,F)
-' & -#
2
1
1/9
1/8
V1
1 1
(
Ω,H,F)
-' & --
1
V1
5
1/5
+
10
1/10
1
V4 -
(
Ω,H,F)
-'' & -+
##
I
1
1
1
+
I
3
I =0
5
3
+
V1
V2
-
2
-
(
+
4
V4
10
-
Ω,H,F)
-'# & -
V1
Ω 0=3.279
0.929
1
+
0.101 1.965
1.965
(
V4
1
-
Ω,H,F)
-'- & -
- & = 1
-'# - & & / % & 1
"
& 0
-'-
/ /
@A / 1 % / *
1 &% /J?
/ 1 * 1 ( ! 1 3 &
( ! / /
1
$ &
& 1 @ A / & & 1
!M / !)=? /
$
1! 1
& / & 1 1 / * -0 & & 1 3/* 1 /3 / ( -'+
$ 1 / & M # !M / /J
!)=? / 1! 1 /
S 1
/ 1 1 @ /A & 1 8 & 1 / 1 1? @/ 8 A 1
#-
0.865
1
0.214 1.852
1
1.852
Ω ,H,F)
(
-'+ & -0 / -
- > 1
-0 / / 1
/ & / & 1 / > 1 / &% &
"
& 0?
/
-0? / 1 &
1 & 1 1 6/ - > 1! 1 / &
Æ
# 1 & 1 ? / 1
/ /?
530
1 & 1
1 ? / & 1 3
1 !
/ -
1
/ 8/
1 & I
@A > 1 (
-'+ / &
1&3 / 1 1 / 1 !)= > 03!M
"
& '' /
/ & ? / / ! & L /*
1 / & 1
1! / 1
/
1
Æ
@ A > L#0 J Æ & B 1
1
/ & 1 1&3 * ? / 1! 1 & 1
Æ
L#0 1 -' & & 1 / 1 -' ,6
1
/ & 1 %/
1 1 / & /
1 1 &
&
0 0
K
K
0
0
L
L
3
?
1 1 /
& % @ /AC
K
K
/ ?
/ /
I
1
#+
1
I
+
V1 -
I
2
0
3
M
+
+
C
1
V2 -
L
L
1
2
C
4
1
V4 -
Ω,H,F)
(
-' & -'
) PQ 21/? ) :? F. / ?G
( ?
? $ --
#
# 1 "2$ .3& 1 1 / 1 & 1 &
3
? &? 3 /
Æ ? ? / /
?
3
1
1 / 1 1 / & 3 !
! 1 1 1 & &
& ? / ? 1
1/
/ /
1 % & 1 & & 1 & 1 1 / 1
1
/ 1
6 / 1 1 1 / & "2$ /
1 /
6 !
.
&/ 1
& "2$ /
/
//
1 1 B 1
?
(
E
1 1 1
0 0
0
K
0
& 1 &
?
/
1
/ . +?
/ E
( !
1D
?
7
0
/
1
/ ? 2 ? 1 ? 1 / % / 1 /J
1 3 3/ & 1 2 ! 1 @ ?
1
1
/ 1 & 1 "2$ /
1 "2$ /
1
+
/ 1 / & 1
/ / 1 & 1 "2$ / ?
1
1
& + / 1 /
& 1 ?
&
PQ
+ 1 / & "2$
& &/ ? /
/ 1
&
3
1 1 & 1 /
$ *% $ 5
1 1 .
1/ % &
1 1 /
1 / &
K 0 !M & 1 2 A
1 1 1 1 3 3 11 / ?
1 "2$ / 8 /
1 2 1 3 3/ 3
& 1 2 1 / & & 1 @ ?
#
7
K 00 "M &
-0
+Vdd PMOS D
S G +Vdd
A
-Vss
I nv
B
Vgate
Source
Load
G S
i + v -
D NMOS -V ss
+ "2$
1 1
A
B
Source + Vgate + $ /
E
i Load
@ $ .,A / & 1 "2$
+ v 1
+
1 2 A
1 & 23 32
-
0
1 0
0 /* 03/* / ! & / 1 !
/ 1 1 2
? 1
1U 2
?
K 0
1D 1
?
& 1
/ /3
( 1 & 1 / / 1 1 1 & / . / &
0
1 "2$ / ? 1
+? @+A
C
0 0 01
0 0 01 0 0 01
K K
& 2
& 2
@+A
1 11 / & 1 /
?
1 1
0
@+AC
0 0
0 0
L
@+A
$ & 1 & 1 @+A / / & 1 &
C
0 0
01 0 01 0
? 1 / 1 ? / 1 /
0
0
/
0
& 1 1 1
L
& 2
& 2
@+ A
/ "2$
0
1 &
& 1
. // ? 1 11 /
1 "2$ / 7 1 1 &
&
/ 1 / &
C
+ C
0 0
0
01 0 01 0 01 0 L
& "2$
& "2$?
L
+ C
0
0
0
?
0
/ 1
/
0
01 0 01 0 01 0
L
L
& "2$?
& "2$
@+'A
01 0 0 0
1 1 1 ?
1?
0
0
K L
/
L
K
? 3 ?
1 1
/
& & 1 "2$ ?
-
50
R v
Ω
10 k
S
R
Ω
50
on
R
+
S
C
C= 5 p
v
v
Ω
ΜΩ
100
S
R
off
S
+ C= 5 p
v
-
(a)
+
C
-
(b)
1/ / C @A 2 ? /
@ A 2
&
01
1
K # /
0
K 0 ?
0
#
% / 1
1 1 / 1 3 3/ & E
& 1
1 )
/
? 1 /
1 % 1 1 ?
0
/ & 1
/
0
& 1 7
1 1 / & 1 3 3/ "2$
/
8 1
$% # % / ( # ' 1/ 1 / / 1 8
1 & 1
=/ 1 1 & 1 1
/ 1
1? 1 %
/ &
1 1 /? ! / !
1 1
1 1
1 + 1 "2$
8/ ?
1 1 / 1 ?
?8/
71 1
1
?8!! 1
K
2?
/ 1 ?
8!! 8/ ?
& / 1 1 . + @A? 1
?8!!
1 1
K #00
/
L
8/ A
2 ? / ? 1 K #0 ? & 1
#0
+ @ A? 1
?8!!
K
K @
1
?8/
K @
?8/
1
?
L
@+#A
8!! ?
1 1
& 1
8!! A
K #00
1
@+-A
1 / & ?
1/ % 1 @ A /
1 1 / 1 1 & @ / 1 % A? 1
+'
. / % 1
1 / /
1& & 1 ! /? 1 1&3 / 1 / 1 1
-
3.0 vC
2.5
Voltage
2.0 vS
1.5 1.0 0.5 Hold 0.0 −0.5
Acq. 0.0
Hold 0.5
Acq. 1.0
Hold 1.5
Acq. 2.0
2.5
t/TC +' 1&3 @ 2A
1
1/
& % 1
1 2 A / 1 / 1 % / & 1&3 @
1
-'
#?8/
0 #
8/ ?
1 &
K #@
/
L
8/ A
% / & 1
1 ! C
08/ #00 ? ")=?
1 ? % 1 2 1
% /
1&3 /
% /?
/ 1 /
& 1 / 1&3
1 1 1 1/ 1 1
3& & 1 1 6 1
*
1 1 @+A
* * ?8!!
/ / & 1
1
1& ! / &
X
@
@++A
&
*
C
@
@+A
/ & 1 / 1 / 1 2 &
1
71 @++A / @+A /? ! /C
1 &
1
8/ @8!!
1
0
. 1 ? 1
8!!
/
@?
/ 1
*
X
* /
8
1
1 1 1 & 1
/ 1 ?
@
@+A
1 / & ?
@
/
8!! 8/
#8/ 8!!
@+0A
1 / & 1
1
# % ' (
1 "2$ / 8
@$ $ A
/ / !? ?
1 & ? 1 3 3/ 31
/ 31
@ A * 1
&? 1
1 / 8
@$ A / / 3 3 3 3 31
1 1 % 1 & 3
1/ !? / / 1 & @1 31
1 %
& ?
31 !? 1
+
K
A
/
+
K
A
1
A !
+# & 3
1 & 1
? & 23 32 2 3 32?
F !3 & 3 !G @ A
1
1 F"!3 & 3 !G
@ A % & 1
8/
&
& .
1
1 / / 1 & &
/ 1 $
&
1 / / 1 1 1 1 1
1 ! 6 ?
+-@A 1
1 1 1
1
+ /
+-@ A /
. 1 ? 1 $
1
1
1
vg2=φ2
vg1=φ1
5 4 3 2 1 0 0.0 5 4 3 2 1 0 0.0
-#
VH
VL 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1.4
1.6
1.8
2.0
VH
VL 0.2
0.4
0.6
0.8
1.0
1.2
t/T +#
1/
1
31 !
1 / & & 1 1& ! 1
& 1 / 1&3 1 1 1 1 1
1
1 // 6
1/
$
1
1
1 ! / 1
& / 1 1 % &
1
1 /
1? 1
++
/ 1 / & 1 1&3 / & 1
! 1 /
/
&
1 / 1&3
1
/
+
+ @ A? / + @ A K + @ A
1 1&3 1 % 1 1 1 / 1&3? 1 /
/ 1
5 1 1 & 1 %
@A? / ?
1 1
/
1/
1
1 / /
&/
1 /
3
/
1 1 1 / P?
?
1
1 1 @A & 1 ? /
1 / & 0N &
1
1 1 @A & 1 ? /
1 / & N & 1 ?
/
1
"2$ 1 3
-'O--Q + "2$ / & E ? /
3
& 1 1
1
1
1 ?
1 &
1
/
/ &
1
/ / 1 / /
--
G
vS
φ1
G
1
2
φ2
C
Load
(a)
v
Load
C
S
(b)
+- $ 6 C @A 1 & $ / 1 & $
1 ? / @ A
1
1
3 C
2
4
++
+ v1 -
C
$
1
v2 +
+ /
-+
C CT
CB
+ / & "2$
+ v
φ1
v1
C
CT
φ2
+0 $
C-
φ2
CB
v2
φ1
1/
1
1 / 1 & & / / ! 1 1 / /
1
/
1/
1
/ / & 1 1 E
+0?
1 & $ $
1 / & 1 1 ! 1 // /
1 & 1 71 /
/ /? /
+
6 1 71
A
2 /
1 1 1 ?
A?
/
A
2 ?
A
+ ?
2? / ?
/
@ 1 / / A 1 ?
+
1
& 1 /
A
+
@ /
2? 1
1 /? /
1? 1 1 A?
/ &
/
1
/
/
1
/ 1 /
/
1 6 1 1 ?
8/ 1 &
1 1
1
1
+
@ /
1 ! 1
1/ ? 1
1 1 / /
7 & 8 6 / 8 1 ? 1
8
1 6
$% !- /
7 1 & 1 ! /
1 % & 1
/ /
+?
1 ?
/ & 1/
?
/
/ 8
-
1
2 q
+
v 1(t)
v
C
C
-
+
/
1/
/ 1 1 &
1 /?
2
1 /? / 1 & 1
/ ?
v (t)
R
1
3 / 6 1
// 1
1
+ @ A
@ 1
/ /
1
1 A
/ / ?
1 1 ?
1
1
1
1 1 &
1 ? 1 / 1& & 1 ?
1 1 &
+ @ A
1
1 1 / 1 / / ? 1 1&3 /? ? 1 % 1 1 @8/ A ? 1 1 E & / / 1 / / & C / 1 1
X
"
K
K
X
@+ @ A + @ AA
?
/
> 1 / & ? ?
+ & 1
,
@+A
K X
" X ?
/ % 1 /
/ / ?
1
1/
% C
,@ A
K
K
" @+ @ A + @ AA K + @ A + @ A K M X
X
@+A
1 1 % / 1 1 1 ,% @+A & 1 &
+
1
1 / 21 U
& 1 ?
?
1/
1
1
& 1
?
3
!
1 / & /
*/ 1 ?
+ D
1
1
+ /
1 1 1 1 1
1
% 1
+
1 /
-
4.0 3.5
v1(kTC)
vC (V)
3.0 2.5 2.0
v2(kTC)
1.5 1.0 0.5 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(t/TC−k) + 6
1/ &
+ v1 -
CR
+
+
v2
v1
v2
-
-
-
R =1/(f C )
C
C R
+ 3 / % &
1 /
+
1/
+0
ix
swmod
swmod v1
1e-9 +
-
-
1ix
+
va
1e-9
vb
.IC v(6)=-6.25 .MODEL swmod VSWITCH (RON=1e3 ROFF=1e7 VON=1 VOFF=-1) .MODEL V1 SIN (F=1000 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL VA PUL (VZERO=-5 VONE=5 P1=0.1u P2=0.2u P3=24.8u P4=24.9u P5=50u) .MODEL VB PUL (VZERO=-5 VONE=5 P1=25.1u P2=25.2u P3=49.8u P4=49.9u P5=50u) +' / % 8
3 1 1
+'
% 8 & / /
1
&% & 1
1 !?
+
K 0 !)=
?
+ ?
/ @
1/
+
/
+ ?
+ ?
1
/ 1
/ 1 /
+
& 6 1&3 /
1 / & 1 / 1&3 ?
A
1
6 /
1 1 1
/ 1 / & 1
1 & / 1 ?
1 /
71 1
+
1 &
/ /?
//? 1
/ 3
/ 3 / 1 / / - 1 1 / / % & 1
,+
1 1
1 1 // 1
& !M / 2 & 0 "M
/ 2
1
*
+
3!)= '3
1 & 1 1 / 1? /
*
+
+#?
@& / & - # A?
& 1 / /
1 / & 1
1
+
/
1 / 1 1 6
+
/ / @ 1
1 1 1
Æ
& 1 &/ 0 ?
1 A . & !3 3! /
/ 1 % ?
K
1 1 &
0
K '
C
2
+
V =4.0 V 1
1
pp
V2
0 −1
1
2
V and V (V)
−2 0.0
0.2
0.4
0.6
0.8
1.2
1.4
1.6
1.8
2.0
1.2
1.4
1.6
1.8
2.0
V =12.8
5
v(6) (V)
1.0
pp
0 −5 0.0
0.2
0.4
0.6
0.8
1.0
t (msec) +# 7& & 1
0
1/
K
K
K
0
* 1 ? % / 1 /? 1
0
K
0
K
0
K
K 0 '
K ' 0 0
0
0#N
1
?
> 1 ? @+A? &
K 0
1 / 8 & 0'
1 ? /
%
& / & 1 % ? / 1 % & 1 8/ 1 ! / & / 1 2 / 2 $
/
8
1 1 1 & 1 6 / /
& & 1
8
1 / & 1 / / /
$. / ( -
1 % & * 1 / ?
+
1/
/
+
&% ?
?
?
/ 1
1
1 1 / 1 1 6 &% ?
/
/ 3 / / 3
? & / 1 ?
/ 1 ! /?
?
1
1 Æ ? / 2 3
! > / 1 6 &%
1 & 6 6 ?
+ @ A
K
1/ ? 1
0 @ A
@+ AC
+
+ @ A + @ A 1
?
1
0 1 0 1
K K
/ @+ A
! ?
1 1 / 1 &
&% ?
1? ?
/
1
K 0
@ ?
7 1
&
K 0 ?
1/ ?
K 0 "M & / /
&
1 / & 0
A
K
/ &
/ / ?
/ / & 1
1
K 0 !M
K 0 ?
/1
1
1/ % /
1 / & /
/ 3 3 ? 1 / 1 3 % 1
& &%
1 /
/ ! 1 /
? 1
/
1 &? / 1 / ?
& 1 ! &%
& 3 @#
1 ? 1 1 3
?8/ A?
/ ? /
/
1
/ 1 & / & 0 ")=
,% @+'A 1 & 1 1 & ! &% ?
8#
1 1 1 1 / /
1 1
8/
#
@+'A
?8/
? #
6 ? " / 1 6 / 00 !)=? /
?8/
1 #
")=?
? 1
1
&
K
C
")=
& / & 71
1 ? 1 / ?
8#
/1 1 / &
1 &
00 !)=
C
! / 8
/ &1 1
1 & 1 ! &% / 1 & % / & / *&
1/ 6 ?
1 / &
& 1 ! 1
1
/ 1
!?
1 ! &% // /
1&
/
1
/
1 //
+-?
/ & & 25 1
/ & E 3E ++
! 1
31 !
A ?
7& & 1
1
/ &
A
B
1
/
1 /
31
A ?
/ 1
3 /
,$ $3. ! !
p
φA
φ1
+-
Offset Waveforms
AB A+B 00 1 01 0 11 0 10 0 NOR
φ2
q
7
+
31 !
q=φA
6 5
p 4 3
φ
2
2 1
φ1
0 −0.4 −0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
t/T ++
31 !
&
1.6
+'
R
C
1
C
2
0A
+
+
V1
+
-
0V -
+
0A
+
V2
V1
-
-
-
C
+ 0V -
1
1
B
/
C @A ? / @ A
/ & &
/ / & 1
A
B
A
/
1 1
1
V2
+
(b)
1
A
/
1
A
K @
1/
& ? /
. / ! 1 E 3E 1 ?
1 1
+
-
-
(a)
+
2
1& 1
LA
1
A
A? /
? /
A
B L A A?
K @
1 1
& 1
1
6 1
& ++? / 1 ! 3 / & 1 1 1
1 1 25 . 1 ? 1
1 1 /
A
1 1?
A
1 1 1 /
/ ? 1
/
A
1
/?
1 1
1
1 / &
B
1 ?
B
/
1
B
A
/
1 1? / 1 1 // / & 1 1
B
1
1 1
A 1 1? 1 1 1
A
1
1 / & 1 % /
/
A
1 1
A A
B
1 /
1 1
1? 1
7 1
C
1 1 1?
1 6
1 1?
/
A ?
31 ?
/
A
1 1 @2 A
?
K 0 #
//
7 1
? ?
1
.
$! * ! & %
*&
1
! 6 ?
A
1 1
1 1? 1 &
A
?
1
A
71
A
&
/ 1 1 /
A
A
/ 1
1 / /
1
/ & 1
1 1 / 1
/ /
B
/ &
?
A 1 ? A 3A
1 & 1 1 ! 1
/ 8 ? 1
1 & 1 1
/
B
&
1/ % &
' 8 ' 1
1/ & 1
7 1 1 &
! & & 1
1
C
+
R
V1
V1
1 C
I
V0
R0
+#
+
V2
2
C
V0
-
2
V
2
-
+ 0 V
0 V -
C
I
1
+
C
0
-
(b)
(a)
+ $
/
+
C @A ? / @ A
1/
C
! #
0 0
1
K
K
1 ! &% ? /
1/
& 1
C
0 0 0
K
K
1 ?
//
0
@+#A
+ @ A?
6 &% 1
& 1 % /
1/
1 / /? +? 1 /
@ A
! ' 1
! & & 1
B
+ &
B @1 A
1 / 1/ & 1 1
C
! #
0
K
C
0 0
K
K
1 ///
1 &/ ! 1 1
@
0
1
0
L A
/
@ L A
0
0
@+-A
+-
+
V1
-
V0
R
1 C
I
V2
2
+ R
0
+
-
+
C + +
V
2
-
0 V
1
-
+
V0
(a)
+0
2
V1
0 V -
C
I
(b)
$ /
C
@A ? / @ A
1/
7 1
K
K
?
1
&
& 1
1/
C
0
K
@ L
0
0
A
@++A
! ' & 1 % 1
+0
/ @ 1 /A
1/ / % 1
1 1
/ 1 / 8 ?
/ 1 1
/ 8
C
0 0 ! #
K
K
0
@
0 0
A
&
K
K
C
0
K
K
*
0
L A
@
1 1
1 1 1 & & 1 &
@ A @ A
0
0
0
0
@+A
? 1 / 8 /
1 1 1
1 1
/ // / &
1/
C
C
1
++
2
V1 C
C
1
2
V2
V1 R
R
1
+
-
C
C
R1
2
V2
R2
-
+ 0 V
0 V
-
+
-
+
(b)
(a)
+ /3
!C @A ? / @ A
1/
1 & 1 .
+
/
C
0 0 C
0 0
K
K
@
@
@
@
. & 1 6 ? 1 6 &%
A L A L
A L A L
@+A
! & / 1 1
! & / / &
$ ! ? 1
1/ / / %
& 3 &
/ 1
! / % = /
! #
&
1 / & / =3
/ & = &/ !
1 ! &% 1 3
? & 1 / ? 1 & & & / .
? 1 & 3/
1 &
!
1 /
+ @ A
0
K P
1 Q
@ A
1 1 3 / /
/
/
+ @ A
3/ ?
K P
0
1
0
@ A
@ A /
1 Q?
0
@ A
/ / @ ? 1 3
A
3 1 & 1 6
& 1 3 1 1 1
K 000
/
+
J @#00 )=A?
1/
1
% /
1 #003!M % /
1 '0 !)= . // ? 1 1 / / @ A
& & 1
+
C
V2
V1 R
R
-
+ 0 V
+
-
+ 3
%
3 1
! & & 1
+
/
3
0 0
@
K
1
K
1/
1
K
K
?
@+0A
/ 1
K
0
K
0
! &
1
1/ % / & 1 % & C
K
K
K
#0
31 !?
0
#00 !M K
K
'0 0
#00 0
+ / + ?
K
1 #3
0
0
/ % /
1 1 1 1/ 1
1 1 / 1 1
L
& 1 3
1
/ &
& 1 '03!)=
K
1 /
#00 !M
A
1 / #00 !M 1? / ?
1
+
L
L
@
&
A K
1
1 & & 1
1/ $ 3
& 6/ @/ / A !? / / & % ? / ? / & & / & 1
3
1 ? 1 1 1
+
2e-9/pi vsw
vsw
50e-12
V1 a V2
vsw
va
vsw 50e-12
b
b
a
vb - 15 +
V3
+ 15 .IC v(5)=0 v(8)=0 v(9)=0 .MODEL VA PUL (VZERO=-5 VONE=5 P1=0.1u P2=0.2u P3=12.3u P4=12.4u P5=25u) .MODEL VB PUL (VZERO=-5 VONE=5 P1=12.6u P2=12.7u P3=24.8u P4=24.9u P5=25u) .MODEL V1 SIN (F=200 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL V2 SIN (F=2040 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL V3 SIN (F=10040 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) +
1/ 3 /
0
&
&%
& 1 / / &%
1? /
1 / & @ A & 1 / 1
71 & & @ A
& 1
?
/ 1
1 1 &%
6 1
@$ / 3
A . ? 1 / & &% ?
A ? / 1 % = ? 1 &% // ? 1? & 1 ? 1 000 / 1
K @0
1
1 &% // X
K
/ #?
K '0 0
000
1 &
& 1
K '0 )=? / ?
1
1 &%
3
& #? #?
1 &% C
K
# '0 K 00 )=
K
# '0 K 0'0 )=
K
# '0 K 00'0 )=
1 1 &%
1 /?
1 /? /
1 /
?
1 1
?
& 1
/ & 1 / 1 & ? 1 =
/ & 1
1 / ?
K @
$
A
1?
/ / 1
1 / / &
/
&
& & & 1 3 1 1 1
& & '+#
'- 6 = &
1
1 / 1 /
. ? & 1
1
K '0 000 K ' +# ?
& 000 & 1 ? 1
000 & 1
& 1 / /?
1/? / 1 1 1 &
/
" 1
3 / 1
1
& / 1 / 1 1 & / / 1 8 & & 1 P'Q
# # 7@ 8'# . $$ + ' 3$% 0$" 0, % A" ; : B8 #B : # : . & 0A ' ? + 0 $", $" % $" ; - 0#(#( (0A :. & + C$" ,(# ;$"#;
;'7 $ $"$ :'D + ", ;$"#; + ;"$E -$"# 7@ 88))! -, # 7@ 88))! 09: -$"' ; : 0A13 -, ' ; : $, ,( . #(09:: ''' . !' "$E&..&$# $ B . ' . 6 (&9", #*-&&B" $E&8 ,( . #(0A13: ''' . 0#(&..&$# $ B . ' . 6 (&A, , #*-&&B" $E&8 (&B,"6 FE&&B" $E&8 B % $% $" % $, ,( -$"$# $ .7' 7' 6 (&9", 0&&B" $E&8 ,( -, $# $ . ' ' 6 (&A, , 0&&B" $E&8 (&3$% %&&B" $E&8
1
& &
/
- A?
1
1
& & 1 1 &%
+' 1 1 & 1
1
/ 1
% / @0 / & 1 003)=
1 1 0?0'03)=
! 1
1 & 1 1
1 003)=
1 0'03)=
? 1
/ 1
/
/ 1
1 3/ 1
/ 1 1 / & #
/ 1 13 ? 1 / 1
/ 1
1
.&
1 1
/ 1 &% @ / = A
& / / &%
Input (V)
5 0
Output (V)
−5 0
5
0
5
10
15
20
25
10
15
20
25
5 0 −5
Time (msec) +' . 3
& & 1 3
1/ 6
Input (dBv)
10 0 −10 −20 −30 −40
Output (dBv)
−50
0
2
4
6
0
2
4
6
8
10
12
14
16
18
20
8
10
12
14
16
18
20
0 −20 −40 −60 −80 −100
Frequency (kHz) +# $ & 1 3
1 / 1 1 ! & !
1 1 & 1 1
1
1/ 6
1 1 & +#
? / 1
/ / 1
/
& 1
3 / 1
?
1& ? / 1 /* & 1 1 C
0
0 1 /1/ 1 1
1
/*
Æ
K
0
K
L- 0
1 L- /* & & .
1 1 % / 1 & / 1
1
/ 6/ 1 / @
/*A & 1 / / 3 @ A 1 1 &
0
K
1 / / & 1
/
)
C
0
L
#00
K
@ L
/* 1 / 1
. /
#00A
1 1 6
/ 1 / / 3
.& 1 8 &%
/ 1
/ 1 /
1 &% ? 1 3
/1 @
& / & 1 2 6 6 1
A
1 / &
'
V
1YI 1
I =0
2
5
I
3
+
V2
1
1
-
(
+
V4
1
1
-
Ω,H,F)
+- 13 3
1 / 1 / / 1
1
&%
3 / 1 &
& 1 3 13
1
1/
+-
1 / &% 3/ & /J #00 )=
3
1
. // ? 1 =
1 / 1 & / / & 1 / / @ ? 1
%
*
3 1 & 1 % 1 / / &
0
K
04
K
0 0
1/ 1 / =
A
/
0
K
04 04
@
@
L A
0
@
@
L A
0
04
@
A
A
0A
@+A
% 1 3 + ? /
! 1
+
04
0
,% @+A / / / / /
/
/ & / 8
1
0
1 &/ ! &
0
K
04
K
0
6?
K
@
L A
@ A @
L A
04 04
0
04
@
/ & & 1
1 6 ?
1 &% ?
0
?
0 0
1/
1
1 / / @
C
@
@
04
%
/ &
1 /
% A 1 % 1 &
C
0
A
A
0A
@+A
1/ =
K '0 !)=?
/
1 1
Vi3
Vi1 a
Vg1
vsw
vsw
b
v-
15 +
a
vsw 100p vsw
Vg2 Vg3
#
v+
v+
b b vsw
50p vsw a
a
vsw
v- 4e-9/pi b
X2
b 2e-9/pi
X1 + v15 -
a
a
vsw
X3
vsw a
v- 2e-9/pi vsw
2V4
vsw 50p
a
++
1/
vb
vsw
v+
2V2
va
b
b vsw 25p vsw vsw
100p
vsw
b
& 1 3
3
+-
/ & ?
M
K #00 !M 1
K
#00 C
K
0
K
'0 0
0
K
K
0
1 ?
0
04
@ 1 1 1
1
M 1 & & =/
K #0
K
1 / A 1 1
04
/
0
/
1
6
K
? 1 / 1
? 1 / 1 & 1 1
/ /
1 &/ !
1 1 / ++A
04
04 04
=/
%
1 / 8 ?
0
0 04
/ 1 &? ? & 1
/ & 1 / 8 ?
1/
=/ 1 3
% 0# M / 5
1
/ /J #00 )= 1
& 1 ? / 1 ? 1
0
@+A 1 =/ @
++
?
1& ? 1 & & 1
1 %
1 &% &
1/ ?
1 #0 C
/ 1 &
0
0
/
0
?
1/
1 &/ ! @+A ?
0
% 1 &
& 2 1
3
++ & 1
1 = &
/ 6
& 1 &
(13 /
3 /
. & & / /
-
Input (dBv)
0 −20 −40 −60
Output (dBv)
−80 0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0 −20 −40 −60 −80 −100
Frequency (kHz) +
"/ & 1
13
1/ / &
1 / / 6 1 1 / 1 6
1
1 /? 3
/? / / & 1 / & ! / +
1 &% /
1
+
+ / 1 &% / 1
1 6/ & 1 / 1 6/ ? / 1 &
0 0 0 0
K
K
@
L
L
L A
K
@
0?
?
L
L A
/
@
L A@
L
L A
1 " / / & 1 6 1 6 ?
L A@
0 0
C
1 / / 1
& 1 6/ & 1
1 1 / A
''' # : . ? 0 ' ' 'D 0#*#( (0 '''
0
@ /
+
Input (V)
5 0 −5 0
1
2
3
0
1
2
3
4
5
6
7
8
9
10
4
5
6
7
8
9
10
Output (V)
2 1 0 −1 −2
Time (msec) + "/ 3/ & 1 13 6
1 & 1 ? 1 1 +
/ 1 6/ 00 /* / 1
1 & 1 /
/
/ 1 1 0 !)=
! /
/ 1 / /
% ? 1
3 1
1 & 6/
1 / & 1 / . ? 1
/*
1 / /
& 1 @/ A &%
1/ 1 / 1
& / / &
3/ / 1
+ & 1 13&%
/ 1 /
1 / / & 1 0 1 #3 &
@5 1 1 '-
000 X /
K #
/
& 1 A
/
3 / 1 1 1
1
1 13 1 / B &
1 1 3!)= / 03!)= / 1 3 6 1 / 1 / & 1 13 /
/ 1
1 /
/1 /
/
8
# %( *
71 1 6 1 / /? 1 6 1
/
1/ /
/ / & 1 1 /
*
1 & / ? / 1
/ 1 % &
/ /
/
1
& ?
! &
/ 3
6 1 & / = ? 1
1
1 %
! &
$ 1
1/ 6 & 1
& / 1? ! /? 1
3
/ 3 1 1 3 8 1 & & 1 & 1 & & ?
?
1 &
1 1 / /
? &
/ 1 /
1/
A ( 1 1
0
1
K
0
+@?
@L
A
1 & 1 1 // ? @+ AC
0 0 0
@ A
K
@ A
K
@ A
. @+ A? 1 / &
0
@+ A
1/ % 1
1
1 /
& &
/
1
& 1 % & +@ A? 1
1
1 1
+ @
L
A
K
" 1
X X
1 + @ A + @
,% @+'A 1
1
L
1
1 1
1
L
+ @ A
A + @ A
?
1
1
1
/ 1 &
+ @ A 0Q
P
+ @ A /
C
L
+ @ A
/
+ @ A
1/
% & & 1 / !
1
?
@+'A
1 ?
/ 8
K 0
& / 3 3 1 %? 1 / 8 % & / 3
3 % 1 &
?
1
&
K
@
1 C
0 & 0 & 0 &
& A
@ A
@ A
@ A
& 1
& 3 & &
K
K
1? @+'A 1 /
@& A @& A
0
& & ? @+ A / @+#A? 1
/ / & 1
@+#A
1 &
C
& K 1
@+-A
1 1
& 1
/ @
1 / /
K
K
L
1 / / /
L
L
/
& &
A
L
T
1
L
T
@
L
T
L
T
A
@
A
/ & 1
/ / 1
1
1
@++A
0 @ ? &
13
&% A
$
3 /
& 1 (
= / / 1 &
0 0
1/ / 1 3
- 1 1
K
@0 -
@
L '
@+A
L A 1
/ & &
1 &% & '0 !)= 1 63
/ 3= / / 1 / 3 1 / &
3
L A
L '
$ 1 /J / &% 00 )=? 0# "M & 1 ? /
36
! &
/ /
/? = @ A? / /
& 1
%
3 1 3 / / / / / /
36 =
?
1 1/ 1 &
-? 1 ?
K - ) 1 1 1 &
@ L @
L
A
04 0 0 0
K K
A
K K
04 @ L @
1
@+A 1
L A
K K
K
0 0 0
K
A
?
K K
? E
1 %3
1 1 1
/ ?
C
0
04 04 0 0 04 04 0 04 04 0
@
L A
P
@ L @
L
0
@
@
04
L A L
L
A
0
AQ
A
P
L
Q
A
04 0
P
@
/
0
L A
@
0
0
AQ
/
@ L @
A
K 0 0#' @
A? /
04
P
L
0
Q
@+A
K - ) 1 %
1 1 / / / & 1 3 & /
0
C3
V2 V i3
C3+C4
1
1
-
+ 0 V
-V 4
+
-
+ 0 1 // & &
0
?
0
1 & & /
1 1 1
/
1 1 1
+ 0 1
1
1
1 / / & & + 0
&
0
@+A
7 1 1 / / 1 % 1 / /? 1
1/ 3
1 /C
0 # "M
K
K
K
K
K
1
K
00 K - 0 # K 0
'0 !)=? 1 M
0
0
1
1/
K #0 / & 1 ?
- -
K
K
0 0#' 0 0#'
L
K - #
K 0#' 0#'
1/
?
/
K ' #
K +
1
+ 1 1 /
0
? / &
1 =/ & L
0
1 1 1
$ ?
?
1 & ? 1 / 1 ,6
1 % /? 1
& L
04
? / 1 1 &
0
& 1
? 1 1 =/ & 1 13 /
1
#3 #
6 ? 1
/
/ '-
3 000 1
1
1 X
K '0 !)=J0
1 / &
K '0 )=J
1 1 &% / //
@ +A?
&%
K 0'0 )= @ #A? / M
K -0'0 )= @ #A
K #@00A K 000 )= & 1
36
K 0 )=
1 6/
= & 1
!
Vi1 Vg1
a
Vg2 Vg3
b
v15 +
Vi3
vsw
50p
a vsw
va 50p
vsw vb b 37.9p - V4
vsw
v+ + 15 -
X1
v-
b 435.8p 50p a
v+
+
vX2
b vsw vsw a
V2
1 &
vsw
50p
vsw
668.5p
37.9p b vsw
vsw
vsw a
vsw vsw
50 p
vsw
b v+
vsw
X3
a
b
V2
435.8p v-
b
vsw vsw
50p a
- V4
1/ / &
"
a
vsw
36
=
/ / 1 3= 6/ &
1 / / 1 / / / / @+-AC
# # 7@ '# . $$ + ' 3$% 0$" 0, % A" ; : B8 #B : # : . & ? :. & + C$" ,(# ;$"#; ;'7 $ $"$ :'D -$"# 7@ 8))! -, # 7@ 8))! 0 -$"' ; : 0 -, ' ; : + .E ,"$ #, %$" #$ $" G'! !' H '8 '8 E G H ; $ 3 B EE ; ; E$%E 3. 3 $% 3. 3 GE'! 6E$% ;
jω
15
Zero−s Zero−z
10
krad/sec
5
Pole−s
Pole−z
0
σ
−5
−10
−15 −6
−5
−4
−3
−2
−1
0
1
2
kNep/sec + 3= 1 & / & 1 / 3 / &
1/
HE6$% ; F6- G' 6- H FE6- GE' 6- HE 1 3= 1 1
+ 1 /
1 / 1 = 1
/ = // 1 / 3
1 1
& 3 & 1
& / % & = 1 1 / 1 & & 1 6 1
36
!
1 1 3
= ? 1
? 1
1 1 & 1 / / 1 &/ ! J 1 & 1&3 $1 1 &
1 = 1 / /
36
/ 1
8 1 6/ / /3 & 1 $ / 1 / /*A & 1
+
1
+ & 1
1 1
? / 1
1
1/
1 / @
1 /3' 1
1 1 /? 1 1 / & 1 /? / 1 1
1 /
1 / / /
3 / B ? 1
36
Input (dBv)
0 −20 −40 −60 −80
Output (dBv)
0
1
2
3
4
5
6
7
8
0 −20
z−Distort
−40
s−Proto Measured
−60 −80 0
1
2
3
4
5
6
7
8
Frequency (kHz) + "/ 6/ & 1
= 1 1
+
1 / ? /
1 / 1 1 1 / / & ?
/ / &% ? 1 1 / 5 1
& 3 & /
// 1
1? 1 /1 & 1 6 &% @ ? 00 !)= &%
/ 1 / 1 1 &
1
13 1
1 . / 8 1
1 1 / 6
? / 1 /
% / /
1 &% & / 1
36
=
1 / 1 / 3
&% / ? @++A? & ( / 1 @++A / 1 &
1
@
&% 1 &
A
1 6 ?
1
/ &
1 / =
/ 1 1
/ & '0 !)=A
1 /
1 &?
$1
& 1 / 1/ 1
?
36
- L
K
&% ?
@+ 0A
? / K -00 ? 1 1 3 K 00 K +' J 1
K #
6
? 3 / 6 ? 1 1 1 & 1
& 1 /
K
C
+ 6/
5/ 1 ! / 1 8 /
1 1 & $1 &% 1 &/
1 & 1&3 /
/ 1
1 6 1 8 $ +- 1! 1
'
?
1 / / 1
1
8 1 / & 1 6
?
/
1
1
/ & ? (
& 6/ 2 1 % / / & 3M
. 1 6 1 2
// 0 "M? / 1 3M
/ 0# "M &
& 0C @- /*A 5/ 1 & #0 !M / & 00C? 1
1 / & 1 1
$ + 1! 1 &
3/ / & 1
)
? 1
+ 1 1 !
/ / & 1
! 3=
% & 1 / 3
& / 1
1
% % & 1 / /
8
(
1 6 1
/ 1 1
/ / & / / 1 &
1 / /
1/
/ 1 / 3 & 1 &
/ /?
/ & & 1 / 3 1
1
$ 1 /
K
1 ¼
K
1
! & ? @+#A?
0 0
0 0
K
K
&
K
@
& A
@& A / K .
1 ! /?
? @+-A 1 &
?
! & C
1/
C
.
1 1
. ,6 '?
7 1 1 / ? 1
&
,% @+ A B 1 /
K
1 / 1 &
@ A
@ A
&
@+-A . ?
1 1/
' 1
1
1
3= 1 &? /
8/ 1 & 1
/ 1 @/A 6 &% ? 6 & & 1
36 &% & /
K
.
@+ A
! & 6 1 /3
! &
/ / /
/ @ ?
! & %/
36
= / 1 A .&
1 1 / = & 1 / 3 / ? 1
1&
/ / = 1 3
% ? 1 & &
/
/ 1 = / 3=
1
1/
/ / )
? 1 3= !
? /
! 1 / /
#
1 &
1/
/ 1 % 1 3E 1 / 3
! / 1
+ ' &
1
'
6
1 / %/ 3 3 / / &
! & & 1 !
C
3 C
0 0 0
0 '0 '0 '
K K K
K
'
K
'
0 0
@+ A
# C
0 ' 0 0 0
0 0
K
K
K
' L '
0
$ 1 & ?
L
0 0
A
L
@+ A
' L A
C
0
0
0 0
L @ ' L ' L A
K K
0 0 ! & ? @+ 'A?
0
L @ ' L ' L A
@
0
6
0
"#
1
@
L
' L ' L A @' L ' L ' L A
@
K
@+ 'A
1 / / & & %/ ?
1
'
?
?
/ 1
'?
@+ 'A? / / 1 &%
1 /?
?
1 / ?
?
/
1 / / & 1 > 1 / 1 K # K @'0 !)=A / K -00 K 5<< @P ' ' QA K 0 0'00 00+#? / K 5<< @P 0 -#QA K #00
/ & ,6 '? &% &% 1
&
/ & 1 1 & / %
1 / & @+ 'A = & 1 & 1 1 &
1 /
?
& / % 1 = & 1
1 /
&
1 / / 6 1
/ & & 1
/
& 1
/ 1 1 & 1 1 6 ? 1?
1 =
'
K 0 -
% 1 &
! & &
@
/ 1 &
K
/ /
1
'9 % 1
A 0 -
K ? /
-
x (-b2)
"V g
V3
Σ
V2
1/w
V1
1/w
Va
1/w
x (-b1) x (-b0) x (a1) x (a2 )
+ ' 3E
&
&
&
K
"
% QP
P
/
%9 QP
P
' '
' ' '
Q K
Q K
'
'9 '9
V0
& 3 1
1 / ? 1 &
Σ
1 & / 3
K 7 1 1 &
1 /C
x (a0)
K
?
K
' '
'
'9 '9
/
& ?
' Q
K P
@+ #A
P'9 Q
@+ -A
K
@+ #A / @+ -A /
/ Æ & 1 /
K 0 -
1
K 0 '-
K 0 D
K #-0
/ & 1 &
K 0? /
! & C
K 0 0-
" C
3 8 ;! $ '! '8 '8 E !' ; ; 3. ; 3 ;EE ; 3. ; 3 I ;'D ; " IE ;E " (.$"-I ;'D . $"-IE ;E'D
/
! &
1/ / 1
@+ A / @+ 'A 2 1
1
-w 3Va
"Vg C1
+ 0 V -
1 +w 2Va
+w Va
1 C1
+
+
+Va
1 C1
+
+
+w 2Va C1/b2 C 1/a1
C1/a0
C 1/a2
C1
+w Va C1/b1 +Va C1/b0
-V0
1/10
+
+ # $
+ # 1
/ 1 1 % /? / 1
0
/ / ?
?
1 1 / /
1/
/ 3
/1 & 1
/1 & 1 / /
1 1 1 / 3 ? /
/ 1
1 1
'
0
/
/ 1
1/ %
'
1 &/ ! & 1 13 1 / /
&
1/ &
1 &? 1
0 1
7 & / 1
'
/ / L
0 ' 0
/ / L
1
/ 1
0
1/
? / / ? 1 L
0
&
1 3 1 1 + # Æ & 1
/
D 1
0
?
&
/ @ ?
% / ? 1
& & 1
&
'
0
/
A 1 ? / 1 / / 1 /
1 & / / /
1 /
/ & 1 6 /
1 1 1 & 1
& & 1
1
1 !
1 & & / 1 / 3 &%
@+ 0A . // ?
1 /
1 /
/ &% ? / 1 1 ? 0 6 ?
1
& -03/* 1& ? & 1
/ & ?
?
& & 0 &
#0 !M 1 / & 1 6 ! & &% / &
K
#0 !M
K
'0 !)=
K
-00
/J
K K
#0 0 -00 K 0
K
K 0' '
K
K '#
K K
1
K
'0 0
#0 0
K
K
K
#
& 1 / & - /*
K 0 0
K -
K '#
+ -
1 /
-? /
@+A
1
+ +
1 / /
1 6 ?
/ 1 / / &% ? / 1 1 &%
1 6/ 1? 1 / 1 / 1
1/
3 / 1 & / / /
36
/ 2 32 & 1 & 1 1
! 6 1
=
1? 1 /
1 8 1
36
= $ &?
1 1 / & 6 /
&
/
+ & ! 1
1
/ / 1 & &
1 / / 6
8
J
/ 1 % 1
/
K #00
1 6 / & /
% & 1
+ #C
K
& &
& 1
1? 1
1 /
1/ / /
$
# ( ( (
1 ? 1 / &
1
1 &% ?
& ?
?
1
1/ ?
& 1
?
.
/ / & 1
/
?
1 / 1 / 1 3
& M /
& 1 1 &/ !
b
a vsw
V1 Vg1 Vg2 Vg3
vsw
vsw
b vb
+sVa
vsw 904.4p
a +Va
v-
15 +
vsw
X2 b
b
vsw +sVa
v-
a
a
v+
vsw
3979p
500p vsw
vX3
b
+s 2Va vsw
vsw 445.3p
vsw
+sVa vsw 80p
a
vsw 62.3p
a
b
b
.MODEL VA PUL (VZERO=-5 VONE=5 P1=0.1u P2=0.2u P3=12.3u P4=12.4u P5=25u) .MODEL VB PUL (VZERO=-5 VONE=5 P1=12.6u P2=12.7u P3=24.8u P4=24.9u P5=25u) .MODEL Vg1 SIN(F=280 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0)
b
b
+Va
v+ vsw
b vsw
3979p
vsw
vsw vsw
vv+ + 15
a
500p
3979p X1
b
a vsw
vsw
928p
vsw 500p
a va
b
vsw 495.9p a vsw 500p
vsw
a 397.9p v-
V0
X4 v+
.MODEL vsw VSWITCH (RON=1e3 ROFF=1e7 VON=1 VOFF=-1) .MODEL Vg2 SIN(F=2000 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL Vg3 SIN(F=6040 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) + - ,6
1/ & /
00
Input (dBv)
0 −20 −40 −60 −80
Output (dBv)
0
1
2
3
4
5
6
7
8
0 Desired
−20 −40
V meas. 0
−60 −80 0
1
2
3
4
5
6
7
8
Frequency (kHz) + + $ & 1
1
1/
1 &% 1 1 //
1 / & 1 ?
1
1 6 &%
% / & 1 1 1 @& 1 1 A 1
/ &
/ 1 1 2 & 1
1
/ 1 1 & )
? 1 1 1 1 1 /
1 % / 1 1 3 / 1 &
/
/ / 1
3 3
1 6 &
1 / 1 1 & / 3
&
/ 6 &
/
: ?
1
0 C A 0 & 0 @ 0 CA 1 / / ?
1 / &
1 0 00 & @
/ 8
. // ?
? & 1
/ & 1
& & / / & $ 1 @& 1 ? + A & M
/
&
& /? 1 1
& ? /
1 / 1
K
C
1/ / ?
@+ +AC
:
1/
@+ +A
. // ?
A
K @
/
2
& 1 ? / 1 & / @+ AC
,% @+ A
:
6 ?
1 1
/
@+ A
1 &% 1 / & 1
&
1 1
:
1 1 1 &
1 &%
/ 1 1
$'?
$'
/ / 1 / 3
& 1 & 1
/ 1 1 /
:
K -00
? $'
0 # 0 !M
0 0
@+'A
# 0
C
0 # 0
"M
1 &%
: K # ? / 1 K 0? /
K ' ")=?
#0 0
K # ?
&
/ & 1 /
& 1 & 1
>:
>,( $%
%$
K 0 !)=?
-00
1 ? ? / &
0 ,% @+ A / 1 &
K #0 !M
C
/1?
1/
6 ? / 1 / & 1 & 1
/
@+'A
1 &% / 1
/1?
&
@+ A? 1 1
:
@+'0A / / / 1 &
1
@+'0A
/ 1 & @+ +A
1 / / /
>:
C
> &
$% ?
/ %
&
:
&
@+ +AC
@+ A
: ?
:
:
&
K
C
/ &
&
1 ? 1
0
-00
K
+ -? / ? / & @+'0AC
0
V
1YI 1
L
C3
3
I3 I
L2
1
C
2
5
3-
IL4
+ V
+
V2
I
L
+ C
V
2
4
-
L
4
4
-
+ 3 / 1
.
>:
0 0
>,(
'000
0 !)=
1 1 & '0 !)=
>,( ' 0
#0 0
' 0
' 0
' ")=
1 1
/ &
/ . // ? & 1 6 1 1 & 1 & / / 1 & @+ AQ
/
1
@' "MA P&
. // ? 1 &
8/ / 1
/ 1 1
# 0
1 / / &
1 2 / 1 1
* 1 & 1 / / /
/ 8 &
/ 8 / / 1 & 1
K
?
1
1 3 /3
+ ?
1
K
/ & 1 & MO /J @ 1 A 1
1 % & &
04 0 04 04 0 0 04
K K
K
K
K
K
K
/ &
0
@
L A
04 04 04
@
C
A
0 0
@
0 0
A
04 @
04 04 04
A
0 @+' A
V 16V I1
0
V I3 C1 + -
C1
VI L2 C2
C1
C1
CL2
+ C1
+ -
CL3
+ C1
V3
C1
V2
V4
+ & 1
// & 1 1
1/
@ ? 1 1
&
/ /
/
1/
/
/
1 1
1?
/ / &
"? 1 ? ! K " ? " ? % 1 6 (
/
& 1
? 1
/ & 1?
/
1 1 ? 1 * ? 1 6
?
"
1 1
" (
K
/ & 1? 1 1 & & ?
K
"
1
& 1
. // ? 1 /
+
1/ %
!
A
?
1
1 /
&
1/ /
@+' A
& 1
C3
"
/
"
"
"
C
" @1 A & 1/ @+ A / / @+''AC
"
1 / / 1 & % 1
K
/ ? 1 &
" :
1 &
%
@+''A
"
1 & 1
C
" "
:
:
@+'#A
0'
,% @+'#A & 1 6
1 3 / 1 & 6 ?
:
K 0
/
" 1 /
1/
K D 1 ? & @+'#A
1 6 /
"
& ?
1 1 13
"
K #
1 / 1 /
"
!
1 / 1 / 1 / /
& 1 1 & /? / /
1
36 = ?
1 ? 1
1 / 1 / @+'#A
7 / 1 1
@+'#A
1 ! &
/ / & & / %
.
+ 1 & 1
+'0?
1
/
/ 1
1/ & 3
1 / 1 1 & 1 1
1 / /
@A > 1 1
1/ / & % ? /
! & &
+
+
& & &% ?
& 1 1 % /
1 1 &% / 8
*
&
&% @ A 1 1 ! ")= 5 1
! 1
& & & 1 ? / / 1
! & @ /A &% 1 1
/ 1
+ 1 ? 1
1/
1
.
+
S
+'? &
/ / & & 3
1 ? /
&
/ / /
1 ? / ? / & 1 /
8 @, A
1
& 1 @
A?
1 1
/ &
/ /
& %
? /
1
1 1
71 1 6/ 1 & 1 / 1
1
1 1 / / / 1 I & 1
6 1
1 1 / / / &
1
,
+ // %/
1
+'
? / /
>
1/
1/ &
1 %/ ! / & 1 & 1 % / &
1
& /
1/ /
$ &
0#
vsw
ix
vsw
-1ix
100p
v1
100p
.Ic v(6)=0
Vb
Va
+ vC -
.MODEL VA PUL (VZERO=0 VONE=5 P1=1u P2=2u P3=49u P4=50u P5=100u) .MODEL VB PUL (VZERO=5 VONE=0 P1=1u P2=2u P3=49u P4=50u P5=100u) .MODEL VSW VSWITCH (RON=1e-3 ROFF=100MEG VON=4 VOFF=1) .MODEL V1 SIN (F=1e3 A=1 DC=0 PH=0 RS=1M RP=0 TAU=0) +'0 & +
v+ b
a q3
v+ v-
v1 a
v+ vq1 1e-8 va
+ 15 -
q3
b
v15 +
ix q1 vb
-1ix
1e-8
.IC v(8)=0
.MODEL VA PUL (VZERO=-10 VONE=10 P1=10n P2=20n P3=490n P4=500n P5=1000n) .MODEL VB PUL (VZERO=10 VONE=-10 P1=10n P2=20n P3=490n P4=500n P5=1000n) +' & +
0-
1/b
1/a
Vg
1/k
1
1 1
-
s
+
1
-
V
-
+
BP
LP
out
V
1
-
V
+
out
+' & +
1
1. 108
2. 251
0. 8015
(
0. 5058
1
0. 1735
Ω,H,F)
+' & +#
+' 1 &
&
% / & 3
. / / = 1 &
/ & 1
1/ /
! & ? / 1 /
1/ & 1
/ & ! &% 1
0 0
K
K 00
00A
000A@ L 0 A
L00@ L @ L
+# 1 &13 / 4 1 1 !)= /
/ & ?
+'
% /
1/ = 2
/ ? / & ! &% /
00
& ? 1 1 1 0 1 1 4 3/* /
+- .
/ /
& 1 &
/1
1/
/
=/ /J
1/ = &% 3/ 1
& /J # !)=
+''@A 1 / /
0+
1
V1
V2 1
1
+
-
0 V
+
-
15 V + -
+
(a)
V1
-15 V
-15 V
-15 V
φ2
C
φ1
C
-15 V
φ1
R
φ2
-
R
C =5 pF
V2
-15 V
+ +15 V
(b)
+''
& +-C
@A
? / @ A
1/
@A > 3")=
1 / / 1 &/ ! ?
% / & 1 1 1 1
+''@ A?
1 1
1 /
1 & & 1
A
/
A
1/ & &3
% ? #? / 0 !)= > 3 ! / &
&
3
K #
@ A > "2$
1
?
1
/ / 3
0
1
1 & 3
@A > / /3 ? / 1 6/ ! &
0
& 1
&% ? / 1
/ & 1 @/A 71 1 ?
& ?
! ?
1 /
!
1 & ?
&
1/
I
++ . / / = 1 &
1
1 1 1
& # #
1 1
@
A / 1
1/ 1 . / = 1 &
1 ? 1
+'#?
1
1 1 / %
0
=s3V 0
I
Vi
1
1
1
V
0
C
C1
+
1
C
0.543
C
+
+
1
-s 2V0
-sV 0 ISC C
0. 543
+'# & ++
/ / 1 / / & 1 & 1 &
1 =
&1 1 &
1 1
1
1 % / 1
/ & 1 1 1
1/ 1
?
?
1 ? 1
&
@
0 -@
A K
L '
L - #A L '
L
$1
1 % / / 1
/ & 1 / / 1
+ .
/ /
1 / 1
1/ / / 3 1
"
" "? 1
1 &% !)= /
1 1
1/ / M
/ /? / ?
1 1 0
/ 1 / I 71 1
1 % /
1 ! /
1 6
" 1
/ & I 71
& 1 ! &% I
+ . 1 & +'-? 1 & M
/
% / 1 1 & 1 / 1 /
00 71
1
1/
:
/ %
1
/ / !
1
% / / # !)=? 1 & #0 1
/ & 1 / / 1 !
&% 1 / / 1 @/A +0 71
1 & & ?
+'+I
1
0 0
? & 1
3
1/ % / / M %
1 ! /
0
V1
VI3
I
C1
C1
+ -
+ 2
C1
5
+ C1
3
V2
V4
+'- & +
C
1
Vi
0. 5
C1
C1
+
0. 4
C
1
V0
+ (F)
+'+ & +0
0
V4 C2
C1
V3
+ -
CU
V1
CU
-
V2
+' & +
+ 5( /
1
1/
1 6 / ( % # / 00'? . &1 % / &% 3 1 &
/J ' !)= & 1 &
$ &
/ & ?
1/ ! &% ?
00
1 & 0
+ $ & 1 & & 1
?
?
/ 1
1
1 / 1 &
1/
+'
+ 1 / 1 & 0# / M ' M? . 1 &
K /J
1/
K # !)=
1 1
! &% ? / & 1 &
/ /
1 &% 3
1
#0
1/
/ &
1 %
/ & 1 & ! &% I
+' .
/ / 5( /
1 6
"
0
1/
1
"
/ 1
1 6 /
M / 0# M? 1 / 1
1 0
>:
& 1
00 & 1
/ & ?
&% & ?
?
// 1
+# .
/ /
1/ /
?
"
/ 1
1
03!)= /
/1? /
/
1 & 1 3!)= /
"?
& &
/ 1 / 1 6
>,(
1/ 3
1 * %
1 ( &
0# 0
!
/ &
00 !M
@A >
K 00 !M? &
= 1 @ A $ & 1 6
1 &% 1 /
1
/ +-
/
1 / & ,6 '? 1 /1 1 /
1
/ & 1
1 &% 1 1
! &% & 1 / & / & ,6 ' & '0 !)= 00 !)=? / / 1 1 /1?
& ,6 / 1!?
3 / ?
1 / / /1
++ 5 +- & ! &% & 00 !)= + 1 / & ?
?
,6 '
& / & 1 6 ? / 1
/
+ / / & 1 /
1 / 1 1
& #0 !M
/ & #00 !M 5 1 /
1
1 6 / /
+ -? 1 ! 1! 1
1 2 32 8 1 /1 @ 3 / A 3
/ & 1 1 1 00 "M & 2 1
& 0
1 2 32 0 M & 2 /
/
C ? '0 /*? / / 1 1
/
1
/1?
&
) PQ *!? 5 :? ( ? ) 7? / * ? ,?
! ?
&+!
* . .
S !C .,,, ? . ?
&+!
PQ ? ,? / ) ? 5?
* ?
7 1?
HC ) ? 5 1 / 7 ? + P Q )
? 5 7?
* ?
/ /? > $// 5 ? :C
)? P'Q 2 1 ? ? / $1&? 5 7? / 5 ? :C )? +#
* !
? > $/3
$# % 6
! $ !
$ &
1 / / 1
/ / / &%
1 & / / & 3 /
! & " / / 1
D 1
? 1 3
1 / U % / 1 % /
71 1 1 ?
& / / ? 3
! & ? / 1 % / & & ? &
/
1 6 &% ?
1 6 1 1 / 1 / 1 / /
?
!
&/
/ / 3
! & / /
1 / / / &
9
&( %
1 / &% / & &
.
L /J? / /
& &% ?
1 / 1 / 1 1 1 & ?
-
& / @A?
1 &
/
1 & 1 &% /?
1 1
/ &
& 1
.
? 1 /
/1 & / / K @ L 0A K
1
= D 1?
& / 1
>
@ A?
/ /
/ 1 &
& C
@ A
;
K
K
0 &
K
&
; 9 P
@
L A
9@ AQ
&
@A
!
#
!
# - ) - Æ 1
" !
'
1.5
|H(jω)|
1.0
0.5
0.0
−0.5 −2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
ω (rad/sec)
% / &
8@ A
K
K
K
1 ;
?
& 1 6 @
@
1
2.0
A
?A
?A
@
!1 & 1 1
/ 1 / ?
/
1.5
@A
@
?
1 6 /
1 1 /
K 0A? / ? 1 3/
/
/ ? 1 = ? 1 7 /? 1
? 1
& 1 &
& Æ / & ?
??
0
/ 1 = ?
1 1 = 1?
& & / 1 / 1 3 / / / 1
/ / /
& @= 1A?
1 / & ? ! & 1
1 1
? / @A
@ A & ?
K
/
@ A
K
1 = /
1 1
.
/ & &
& ? 1 & / / 1
?
1 1?
;
1 ?
@ A ! ? 1 =
K @M A 1 = 1?
/ / / .
1 8 1 1 / 1 1 & 1
"
#
0.40 0.35 0.30
τ=2π
0.25
h(t)
0.20 0.15 0.10 0.05 0.00 −0.05 −0.10 −3
−2
−1
0
1
2
3
4
5
6
t/π (sec) . &
1
@ A
!
/
1 = / & & / / 1 1
/
1
& &
/ 1 &
@A
K
@ A L @ A
@ A 8@ A
K
8 @ A L 8 @ A
8 @ A
@A 1 1
/ &
@ A
1 &% / &
@ A
& 1
= 1 ?
8 @ A
8
K
K
K
8 @ A
K
8@ A
8 @ A
1
/
&
1
'
1 1 &
@M
A
@M
1 1
@
1
A @
@ A @M A @M A L
A
@ A
1 / &
/
C
1
@ AC
1
A
" !
-
1.5
H(jω)
1.0
0.5 a 0.0
−0.5 −2.0
ΩS
−1.5
−1.0
ΩS
−0.5
0.0
0.5
ω (rad/sec)
/ /
1.0
1.5
2.0
&
10 b=0.1
dH1 / dω
5
0
−5
−10 −2.0
−1.5
−1.0
−0.5
0.0
0.5
ω (rad/sec)
' % / & 1
1.0
&
1.5
@ A
2.0
"
8 @ A
@M
@M
K
@@M
A
L A @@M
@M
K L
?
8@ A
K
8 @ A L 8 @ A
8@ A
K
Æ @ A L
1 1
@ L
0
& @'A /
1
A @@ L A
A @
A @ L A
?
?
// /
0? 1
@#A
/ &/ & 1
K 0
8@ A
@#A 1 & 1
& 1
& @A? & 1 /?
/ & 1 1 1 1
/? & / /? 1 1 1 1
/1
1 / & 1 1 1
0 /
@'A
0 1 /// /? ? 8 @ A? / 8 1? @ A 1 1 1
@A # 1
A @@M A
A
@M A
L A
L A
&
?
/ &
A
1 1 1 1 1 /// 1 1
1 / 1
&
A
1 / 1 /
7 1 ?
/
A @@M
L A
&
&% ? M
@ A K ? 1 1 ? 8 @ A K Æ @ A? / ? @ A 1 @#A 1 1 /
1 ? 1
+
1
1
?
K 0 # /J
1
/
8 @ A
1 //
#? 1
1? /?
??
/
/ 1 1
1
! 1 & 1 / &% 1 / = 1 & . 1 / /?
1 1 &%
& 1 1 / / & ? 1 & 1 1 &
1 &%
/ 1 1 1 . ?
1 6
/ (
61 /
9
- ( #(.*# /
1 & & 1
! & /
@
A K
&
08:1
!
@
A
@A
1 / = &
/ /3 &% & @ A
K
K
04/
K
?
08:1 04/ @
A
7
@ A 1 @ A & 3 1 &
@ A K
K
@ .@
.
A A @ A @ A
1 C
/
) % %
" !
Impulse Response
Impulse Response
0.4 Nonideal 0.3 b=0.25 rad/sec 0.2 0.1 Ideal 0 −0.1 −20
−15
−10
−5
−45
−40
−35
0
5
10
15
20
−30
−25
−20
−15
−10
0.05
0
−0.05 −50
t (sec) # . & 1
@A
K
K
1 &
/ / / &% &
@A @ A @ A @
.
@ A. @
@ A
A
@
A
@
1 = &
K
1 / K
?
K
/ K
? 1
@
A?
@
@
A
K
#
@
A
K
#
1 6 &% ? &
@
.
?
@ A 1 @A 1
.@
A
.
@+AC
.@ A / 1 @ A K 1 3
1 .@ A 1
@+A
1 1
36
C
@
.
@-A
A? / 1 1 &
A 1
/// &
// ? 1 1 / /
@A
A
@
.
.
A /
.
A @A
@= A &
#
.
@
@ A ,% @ A
A 1 & 1 &
L
.
A
@A 1
@A
1 1
"
7 // / 1 1 / & ?
36
?
@
A?
/
1 &
@
A?
1
6 C
A
K
@ A @
A
K
@
A
K
@ A @
A
K
@
L @
L A@
L @
@
A
K
@
@ A @
A
K
@
K
L
L A@
L
L
L
L A K
L
L0
L
L
L A@
A K
L
L A@
0
A K
L
L
L0
L
L
A
L
? 1 & ? 1 / 3
1 / 1
& &
1
@A
1 !
K
! 1
@-A / 6
/
(
9
$% % .
/ 1
! / & @AC
@A 1
@A !
K ?
@ L
@A
A
*
@ A
1
(
K 0 # &
U ! 1
/ ( 3
- 1 1 / 1 /
1 / /
3 / 6 1 / &
& ? 1
&
K
0?
/ / *
1
(?
1 / ?
! ?
@
&
(?
/
1
1 6
A /
.@
A? & / &
@A ,% @A 1 & / / K
K
C
@A
K
.
@ A. @
@ A
A
@
A
@ A
K
@A
@ A @
A
K
/
.@ A.@
A
K
L @A
1 & 1&3 @1A 1 (
&
.@
@-A?
K
1 &
L @
A
L
@0A
@0A / &
.@
A 1 1 &
L @A
&
K
0
A? / C
@
A K
" !
0
1.2 1 Ideal
|T(jω)|2
0.8 0.6 0.4 n=2,4,6 0.2 0 −0.2 0
0.5
- *
1
1.5
2
(
1 6
.@
K K
1 1 ?
K
@A
K
L &
(
//
K
&
(
3
1
&
K
(
.@
A
K
@
.@
A
K
(
1 ? K # / -
36
& / &
A
(
( K ' -
@A
(
1
5
.@ A & 1 (13 / * 1 .@ A & 1 / / ! &
+ &
4.5
K @A
&
A
4
/ ( &
( ( ( ( ( L
1 / / ? 1
3.5
A
1 / &
3
ω (rad/sec)
1
2.5
(
1
//
A
K
@A
(?
/ 1
1 ? //?
1 *
1 ?
1 1
@ AC
L A
/
,% @ A
@
@
L @@
L @@
L 0#AAA L A
L 0#AAA L A
& & 1 *
&
(
&
(
//
@ A
1 & &
(
"
jΩ (rad/sec)
(a)
(b)
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
−0.5
−0.5
−1.0
−1.0
−1.5
−1
0
−1.5
1
−1
Σ (Nep/sec) + ,6 *
1
/
1 & @A
" 1 1 1 &
/ @1 1
@A
7
( K #?
/ @ A
"- & ?
1 1
1 &
! 6 1
1
1
K
0
K
L0 L
0 C
0 @A K 0 /*
K C
K
0 @A K 0 /*
C
0
@A
K 0
!
& ?
1
!
C
@A
/
(
@'A
1 @* /A & 1 * 1
(
/ D 1
7 1 1 &
&
&
@A
/* &
/
1 / &
1& / 1 1 & 1 * & (
( K -
@0A? / 6 1 (
1 / %
1
,6 A
-? 1 *
& & ?
0
Σ (Nep/sec)
& / 8 &
(
1 &
1 1 / 1
: K @ A 1 1 8 &% ? K ? ( / 1 // & 1 / 8 ? 1 0 /* & 1 1 ( / 1 1 1 & ( & %
1 ?
1
&
K 0?
3 &
1 &
(
& *
3
1
( & & &%
& 1 / 6 / & /*
K 00 )= / / & #0 /*
K 00 )=
" !
90 n=4
80
Loss (dB)
70 n=3
60 50
n=2
40 30
n=1
20 10 0 −1.0 −0.8 −0.6 −0.4 −0.2
0.0
0.2
0.4
0.6
0.8
1.0
x=Log10(ω) & *
%
1 &
3 1 / / % !1/
&% &
3 / / % 1
,% @#A
A
0 @ L
A
K @
@00 00A
(
1 &
(
?
K '
$
/ 1 &
A
0
(
1
#0
0
0
0
K &
@'A
(
C
@#A
(
1
0
0
K
K 0 1 %
6/ 1 % 1? / ? 1
&% &
1 1
1 / &
A
@
0 @ L
(
1 1 /
& 1
? @#A
1 % &
C
K
@0
A
K 0 '+
( K 0
"
50 dB
Relative Loss (dB)
50
Specification
40 30
nth−Order Butterworth
20 10 f1=100
1 dB 0 0.0
0.5
*
f2=200 1.0
ω (rad/sec)
:
K
@0
A
K
0-
/ #03/* 3/* /
K ++
K 0
1 1 1 13 / *
1
/1 & 0 ?
1
0 1 2 1 K
& &
0
2.0
1 / ( %
:
1.5
f (Hz)
& 3
% &
/
K 0 0 /
K 0 & 1 13 / 1 / &% K 00
& / & 1 &
K
& 1 / 1 Æ
" C
," $" J( ; 4" 4$$ " $%" J + " $ ## ". J"-J $" 4$4$ "# J + " $ -" ". J"-J $" 4$4$ "# "#
" !
'
( K 0?
1 &
/ & 1 *
1
& 1 / @ AC
. @
A
K
@
L 0
@
L +0
K
L A@
L A
L +#'
L 0 ' +
L -' '
L ' 0
L ' 0
L ''
L A
L -' '
L 0 ' +
L- # 1 % /
L 0 00
L A@
L - #
L+' '
L A@
L 0
@-A
1
! & ?
@
. @
A K
A? /3
/ 1 1 1 & 1 / 1 0 / =/ # $3R @# AD # %/ @# AD 3 @0 A &
? 1 ? /
& &
& / 03 *
1 (
/ 1 1 & 1 & / &
1 1 1
/
9
1 &
$% %).% .
. 1 ?
// 1 *
(
/ / ? 6 1 & 1
(13 /
K
! & ?
0? 1
K
@
K
/ & / 6 &
1 & 1 7
/ C
(AA
:A
@
:
(
&
@A L & / 8 &
1
:
:
&
(
* @:A * @:A L * @:A /
* @:A
(?
? 1
/
1 /
:
/ & 1 1
* @:A
1 1
1
:
/ 1 1 // & &
// / & &
/ /
A?
@+A
1 / % 1 &
1 1 1 &
@+AC
6 * @ AQ
1 1 1 1 1 &
A
1 1
3 &
P L
* @:A
1
1 1
1 1
1 1
.
1 / 1 1 1 & 1 1
@A * @ A
1
/ 1 / U & /
/ / 1 / @A
( L AAA @(AA @AA @(AA @AA
K
@@
K
@@
K
@
K
( AAA @(AA @AA L @(AA @AA AA @(AA
:* @:A
:* @:A * @:A
@A
9 ) : ; :
0
"
#
2.5 2.0 1.5 n=3
Vn(x)
1.0
n=4 n=1
0.5 0.0 −0.5 −1.0
n=2
−1.5 −2.0 −2.5
−1.0
−0.5
0.0
0.5
1.0
x (
0 1 1 1 & / 8 &
7 1
* @:A
@A
K /
* @:A
K
: 1 & ( K 0 / ? ?
/ 1 /
2 1 // / & & 1 & // ? 1 % %
:
K 0?
: K ?
(
// /
1 1 // % =
:
K 0
1 1 1 1 / /
1 & ? 1 1
!
A
.
/ 1
1 &
:
. 1
1 1
& 1
/ ?
/
1
1 1 & 1 / 1 % / %
1 // & 1 1 1 &
/ & 1 %/C
*
* 6 ?
@ :
':
:A
@
K
K
(AA
@
@ L
*
:AA
@
: :A K -: ': L : L : L A *
K @'
1 1 1 1 1
*
@
& &
A
(AAA
@ L @
@0A
% @ L
! & ? @+A? &
1& ? 1 / & 1
/ & 1&3 3 & & @+A?
/ & 1 *
* A K
1
@
A /
" !
-
4 / & 1 1
(
5
*
0
' # +
:@:A :@: A : :@': :A @: A :@: : L A @': :A :@-: 0: L #:A @: :
L A
/ ? 1 3 1 1 ?
6
/
(
: : ': : : : L -: 0: L #: : ': L :
. / / / 1
! & 1
1 1 ?
/ 3
1&
! 1 1 & 1 & & 1 1 1
! &
?
@A
?
. // ?
1 /* & : K /
1 & 3 1 1
K 0
@A
K L0 @ L
* @A K
/
6 * @ AA
0 @ L
6
@A
A
@A
1 1 6 / & 1 ( 6 &
1? 1 ?
6?
/ / &
1 1 /
& 1 / & & 1 / /
1 /?
(?
/ / & 1 / % 1 & 1 / @ 1 / & 1 /A * / ? & &
(?
/ 1 3
1 1 C
:
K
*
0 @ L
6
0 @
:
K
6 * A 0 6
(
A L 0
&
1 & 1 1 1 1 1 / 1 *
6
? 0 @
1 ?
A
// ?
/ /
8 & = 1 3
/* 1 1 1 ? 1& ? 61 1 8
@ /A 1 1 * 1 1 1
@ A
&
1 & 1 1
(
K - /
6
K 0 #
3
1 8 1
0 @0 # A K ' 0 /* 1 8 1 1 3
1 & 1 / & 1 / & 1 1 * &
1 @ / = A
/
&
1
3
. 1 /? 1 1 1 & / %
/ / 1 &
6?
K 0 @ L
6
A
"
+
80 Chebyshev
70
Loss (dB)
60 50 Butterworth
40 30 Asymptote
20 10
0 −1.0 −0.8 −0.6 −0.4 −0.2
0.0
0.2
0.4
0.6
0.8
1.0
Log10(ω) 1 1 @
3 / 1 1 1 ?
(
/
( K - 6 K 0#A
6?
& 1 ( % 3
& ,6 / & 1 &% & & 1 / . // ? / 1 & 1 3 & / & 1 3 ! & ?
%
@
# .@
A K
A
3 7 % 6 & /* & &% 1
00 )= / & &% 1
K
K 00 )= $ 3
K ? 1 K K 00 / K 1 6 / K & 1 1 1 & ? / 1 / / 6
7 1 1 1 ? 1 / /
/
1 /
6
K
6
K 0 #0
@0
6
0 @ L A
A /*
K 0 #0
& 1 %
1
/
1 /
/
K 1 1& ?
6 * @AA
0 @ L
> 1 &
* @A
* @A
#0
@0
/ 1 &
- '#'
A
(C
K ?
6 K - '#'
1 3
K 00?
1 1
" !
80 70
Loss (dB)
60 50 dB
50
Specification 40 Chebyshev
30 20 10
ω1=1
1 dB
0 0
50
ω2=2
100
150
ω (rad/sec)
200
250
300
f (Hz)
(13 /
1 1 1 1 ( % 3
$
(
(
% /
@-' 0'A
@A
?
5 1 13 / *
-' 0'
1
(
1
K # #'
K - & 1 / 6 % / 1
& ,6 1 & ? 1
(
/ 1 1 1 &
1 / 1!/ 1
(
?
/
K - 1
1 1 / ? @A?
1 &
* @A K @-
&
* @AC
@AA K # 0
* @A 1 - '#? % / 1 // & & ( & 1 6 1 / @ /A? 1 &
(
1
&
@A 1
* @ A
1! 1 1 & 1
/ & /
6 K 0 # K
/
( K -?
L0 #
K
@
K
0'
* @ A
'
&
K
* @ A
L 0 #
L
0+
& 1
C
A
L '#- + L '0 -
L
"
K
&
@
A
K
@
@
A K
AC
.@
A
.@
A
1
.@
A
.@
A
K
L 0 #@0' L+
K 1 1 &
0--
.@
#-
L +-
L 0+
L '0
A 0 0-
L '#-
L -
L -'
L A
L ''
L 0#
L
L #
0'0? 0+ 0+++? /
1 1 / 1 / /
0 '+
! & 1
@'AC
@ 1
.@
A
A
K
K
.@ -
A
L # 00
L# +' 1
/
L 0'
L ' 0
L '#
L 0
1 1 1 & 1 &
'%3C + ," $" G4(6" :- ! + " 4 " 4 # <4(64- 6"%$ ," $" G4(6" - +0 - +0 ". - "- -. - + ,$- $" - - -- "# G- & + 5 % 6"%$ % " %" <4(64- KG $ ' "! 0"4(6" 0" "-0"0" JJD 0" E " +6"%$ $" ;D + 4 - 4 " & JJ 4 ;D .D JJJJ " JJJJ .D. "#
@'A "
" !
0
E JJ # E$"# E2 J6# JJ 1 ?
6 K 0#? ( K -?
1 1
1 1 & 1 6 1
6A
(K#
! & & @'A?
1 / @3
1
1
/ @
?
6 & A 1 / 1 ?
1 /3 8
/ 3
1 & 1 /
1 / @- /*A 1
% ? /
1 & 63
$ & 1 /
&
1 / & / 1 1
'%3 / /
1 1 (
9
1 &
6 / (
! &
& ( %).% .
. 1 ? / %
/ 1 1 / 1
1 / & ( 1 // 1
3 1 *
1
1 1
/ / / . / 1 1 / 1 1 / / 1 *
1
1 & 1 @#AC
@A
K
/ 1 1
L
< $
1 1 & 1 ?
& &
31 1 & ? / 1 1 / & 1
@'A
1
& 1 &
3
1 1 1 @ 6 EA / &
* ?
@#A
/? 1 1
1 1 1
3
/ & ( &
1 & 1 /
/ &13 / 1 1 0
/
1 1 & 1
1? 1 / / * @ A / 6 / 6
* @ A / 8 /
/ 1 % &
( 6 ? /
7 1 1 /
K & 1
/ 1 1 ?
1 1 / /
K & 1 1 1
3 > 1
/ 1 1 & ? @#A? /
& & 1 ,6 / $ & 1 &
"
25
V5+2(ω)
20 15 10 5 0 0.0
0.5
1.0
0.5
1.0
1.5
2.0
2.5
3.0
1.5
2.0
2.5
3.0
25
V5−2(1/ω)
20 15 10 5 0 0.0
1
%
/ 1 1 &
3 . 1 6 ? 1 /
&
1& ? 1
/ &
8
K #
K 0
L
K @1 & 1 /A?
K /J
( K #
1 3
K
K '00
1? 6
K 0 # 1 1 & ?
@A
K 0
1
K 00 )=? 31& &
C
$ ?
/
1 ? 1 / & 1 /
?
ω (rad/sec)
8
@-A
* @ A
& /
8C
K
#0 0 @ L
8
@0
A
8 A
/
K - -
1 / 1 / / 8 1
1 / % / / & 1 1
( K
& 1?
@1 / & 1 /A?
K
0
8 * @A
@0
1 &
L
A
8 * @A
/ C
" !
* @A
@0
7 1
(
/
K
(
?
@A
L
A
* @A
$ & 1 &
* @A
8
K - -+
/ 1 / / / C
K
P8 @0
8 @0 A
Q A
@A
1
( K - 1
& / & ,6 ? 1
? 1
%
1 1
K # ##
(
1 1
/ / 8 ?
K #?
/
1 !
1 & 1 /
7 1 / /
8
(
K # /
K - 1 / /?
/ / 1
! & / 1 /
7 1 &
C
' L
* @ A
K
* @ A
K
@A
K
1
@
A
8
1 & 1 1 & /
@
A?
L
<
< L
L@
L '
L
L '
'%3
"
L A
Æ
Æ?
1
//
8 K #
@
A
K
.@
A
K
@
/
L
0'?
A
@ A . @
A
@ # 00
A
&
36 ?
1
1
Æ
1 &
1 /
! & 6 /
1 / / 1 &
L A
A
L +
/ 0
L 0 ' ''
L '# +'
- +? 0 ''? 0#? /
0 ''
A
1
& 1 &
L '
.@
0 +
@ .@
A
( K -C
L -
1 = 0
K
1 ? / 1
1
! & &
@
! &
% = 1? 1 3
A
* @ A?
@
/ 1 1
1 ?
/D 1 ? 1
@
L A
3
1 & 1
/ / / & /
/
@
K
K
L
A
<
$
L
K
@
' L
L
L -0 '
0 # ? / 0-0 '#
0
L 0000A
1
"
+ 5 % 6"%$ % " %" + $"- # <4(64- KG $ 4 "! 0"4(6" 0" "-0"0" ::0" "#. + 3," 6"%$ "#.."# JJ4D E " :: + 6"%$ $" ;D + 4 " & :: "# JJ 4 ;D .D :::: JJJJ " JJCJJ .D. ::C:: .D. "# E ::C " E$"# E2 + 34 ,% $" 4 4 $ + % 6 " ; 6 ( , 4 ?. $ + , #, ' 9 6 4 4 $" 6"%$ + $$" ' 9 46 " 4" + % ", 4 : ;$ 4 - ( %#' 9" + 46 4 :: " 4 ?. $ ;$ 4 ' JJ # $"# 2 :6" :: J6# JJ 1 &% & 1 & 1 & 1 * /
1 & ?
1
1
'
.
& 1
/ 1 E @ 3&A /
1 / 1 @1 & A 1
/ 1 1 1 ( 6
= & 1 ( 6
9 "
, 4 % $
1 1 6 & 1 / / & & & 1 ( &
! &
1
@
A
,% @+A / & & 1
& &
1 1 & / 1 1 & 1
@A 1 1 6 ?
K
L
@
A
1/ 1 &
,6 C
A K
@
.
? 1 &%
3
@
@ A . @
@ A
A
@
A
&
(13 /
*
@+A
1A
@
AC
" !
'
70
Loss (dB)
60 50
Specification
50 dB
40 30 Inverted Chebyshev
20 10 1 dB
0 0.0
0.5
'
1.0
1.5
2.0
ω (rad/sec)
2.5
3.0
/ 1 1 & 1 6
,6 C
A K 6 * @ A
@
@
(13 /
1 1A
,6 C
5 1 1
@
A
K
8 * @ A
* @ A K @L*
1 *
@
(13 /
@
AA
/ 1 1A
1
Æ
1 / 1 1 & / 3
/ 1 1 / =
1
/
1 ? / / & ( ? 1 / &% & 1 ? 1 ) ? * ? *$ $ & 1 & ? @+A? / 1 P / & ? & 1 ?
@
AQ
7
& ( % ? 1 &% 3
/ / & 1 / /
1
/ / * 1 / 1 / ( & " / 8 & / &
A
@
7
! 6
/ * / 1 & ? / 1 / 1 1 / 1 / 1 6 &
$
3 * & &/ * A 1 6
@ ? 1 /
/ 1 / 1 /* 1 1 /
" 30
#
ω−2
ω2
25
F(ω)
20
LF Asymp.
HF Asymp.
15 10
F(ω)
5 0 −3
−2
−1
0
1
2
3
Log2(ω) @ A
# /
& /
8 '0 /*J/ & 1 /
1
0 /
%
3 7 &
1 !
1
# &
A
@
!
$1 &
6@
&
@A
A@
? /
A
@A
1 6 & & ? / 1 1 &
6
1
1 / /
6 K C
@ A K
@ /3 / =
1 /
1 / & / &% / !1/
3
A
/ =
0
@ A
1 / /
# 1
1 1
/ ! 1
1 /* . &
A K 0? / &
1?
K
/* 0 @ L
@A
@0
K 1 & 1
1
?
K ? 1 / 1
C
6
/ / 1 6 &
/ 1 1 @
= / & &
6
K
$ ? 1
& 1 & & &
?
A
@AA
" !
-
$ & @A &
@A
K
6
6 .
'@0 @0
6
K
6
@A@ 'A
A
A
K 0++
K 0 & 1 &
K
@ A
$ A
@
K
L
@
@ A @ A
?
K
L @
1 1 / /
A @
A
! & & 1 1
& C
A
@
A K
L @ L
A @ L
K
A
@ .@
A A
@ .@
A A
? ? / / 1
1
C
@A
&
6
1
&
6C
1 / &
/
.?
@AC
@
A
K
.@
A
K
@ 1 &
@
A
L
@ .@
K
A
L 0
L
L 0000
A
@A
A
@A
K 0 -0
1 &% &
1? 1
0-+'
1
/
K 0 #
-
1
#-
1
/*J @ '0 /*J/A? / 1 /
1 % /*? % /
1 & 1 /
1
/ 1 1 Æ
1 & 1
1 1 1
1
3 ? / ? % ( & / 6 &
@
A
1
1
/ / / // ! / 8 1 P ? % &
@ A
/ 1 1Q
1 / & 1 6 &
@ A
1 1 1
- /* 1 /
/ 1 1 6
@ A / %/? 1 / = / / 6 / / 1 1 / & 1
@A 6 ?
1 1? / 1 6 1 &
@ A
1
/
1 / / / @ / //A
1 ?
1 / / / 1 / & /
& 1 * 1 1 &
1 / 1 1 3 ?
. // ? 1 6 1
/ / &
/ 1
1 1
/
&
1 / % /
"
+
45 40 35
Loss (dB)
30 25 20
Design
15 Asymptotes
10 5
1 dB Specification
0 −5 −4
−3
−2
−1
0
1
2
3
4
Log2(ω) - % & 1 / 6
! & & 1 / 8 1 1&
/?
/
1 / / & 1 6 ? / & / 1 / 1 1 1 / / 1 1 6 / / 1 & &
/
/ & &% < & ? / ? 6 &% 1 & 3 ? 1 1 ? % = ? / 1 ?
&
/ 1 / & 63
&% %
6
5 $ !
//
1 ? 1 1 / % /
/
! & & % 1 /
3
1 & 1 6 / & / 3& % 1
1 /?
1 1
/ / ? /
/ 1 ) & 1
& /
/ 1
1 1 / 1
! /
% / 1 & 1 1 / 3
1 1 /
! & & 1 /
1 / @ A 1 / / & 13 / / @ / A &%
" !
4
-
-1
-π
0
- π/2
ω =tan(φ/2) φ =2tan -1(ω )
π
π/2
0
?
+ " & &% ?
9
4
1
/ ?
A
# #
1 1 / 1 // ? / / @ B A & &
/ ? 1 % &
/ ?
/ & &
1 / 1? 1
3 3 ? / ? & ? 1
/ 1 /
= % ? 1 1 1 &
Æ
1 1 / Æ 3 1 /? / 1 1 1 ? 1
?
! & / 1 &
/
1 1 3
/ / 1
/ /3 / /
1 & / / . / ?
/ / &
1 & 3
@ 0A / / & & 1 &%
1
A
/
1 &
A?
A A
K @
?
/ %
& C
=
1? 3 & ?
@AA
1 / &
@ AC
@AA K $ & @ A? &
!
=
A C
1
A
K
L
@ A?
AA
/
@
@ 0A
+ ,% @ A
1 1 33
@ A
/ & 1 &
!
1 / 6 & & 1 6 & &
A
?
!
L
? @ A !
@ A K
!
=
@ A
& &
/ /C
@ A
& / 1
1 1 ?
A
@ A?
/ 6 /
"
6 &%
@ 1
! & ?
1
@
!
AC
@ 'A
L
A? / 6
1
1 1 / 1
A K
@
?
/ /
@A
1
/ 1
@ 'A / / 1
@ AD / & 1? 1
1 1
1
1
/ / 1
!
/
1
/
*& / & 1?
& 1
AD /?
! ?
/ 1 / / Æ
/ !
= 1 / /
@
! & ?
/ 3 & & / & D 1 /?
K
/ &
1& !
1
/ /
! & & @ 'A 1
& / 1 1 3
3 / / 1 1 & 3 & & ?
1
1 / 8
6 @$
& & 1 3 / A ? 1 / /
!
/ / & 1 3 ? 1
1 & 1
/?
1
1 & 1 Æ3
? & 1 % / & / & @ 'A 1 1
! ? 3 & 1 3 / @A 1 & 1 Æ ? ! ?
1 ?
3
6
1
/ 1 / 1 . // ?
1
// 1 /
/ 3
/ @
A 8 1 & 1
!1 & 1
/ 1 / / & & 1
1 /
3
& 1 ?
. // ? &
/ 1
?
&1 / 1 1 @/ A / 1 1 /
K
1 @ 3 A
L
C
:$C
@
L
A L
/
0 0 L
K
0
K
: C
L
0
$ &
@
K
K
K
0 0
R( /
AL
L
0
0 L
&
(
" !
'0
+Vc1 +Ve2
R2
C
αi e
.0 vk
ie R1
.0
iC R
v k+1
.0 -V c2
-Ve1
,6 3 3 /
1-s 1+s v
1/A0
1-s 1+s
1-s 1+s
1/A1
1-s 1+s
1/A2
1/A3
1/AN
R
Connect for A k > 0
0V
R
-
R
+ 0V R
Connect for A k < 0
3
0V
R
+
& 1
-
+
vout
R
! & ? @ 'A
"
P
@
'
0 0 A L Q
K
0 (
@
&
K @ L
A
K
P L
? / 1 @
$
1
@K
1
/
1 1 &
K
L
K
K
L
3 1
/1 & / 6
/ / /B
E @ A
1
/ 1 1 / & /
&
1 /
1 ? ? & 1
@
K
@ #A
@ -A
/ /
/ 1 / / C
0 0
/ & 1 6
&
3
A? @ 'A? 1 / ? 1
1&
/ &
/
1 #0 ? 1 00
1 1
6 3
/ /
1 1 & / .
1 % & 1 )
? 1
/ & #0
& ? @
% & / & / .5
A
@ L @ K L @@ A L
0
0
K
C
0 0
,
0
A / 1 P L @ A Q @ L A L @ A
K
L
Q
@ L
/ /
00A
1 % &
L
1 1 6 1 1 & 3
? & ! / @/B A
/ 1 ?
Æ % & / 1
/ & ?
? 1 1 1
/ Æ 6?
/ 3 & & /
@ A / & /
1
& / &
!
? / &
& 1
1 / /
C
@A @ A
K
K
@A
@ +A
" !
'
* 1
@ A
@A
/
1 1 /
/ 1
D
/
@A
K
-
@ A
K
D @ A
K
1 /
= 1
0A
@
7
K
L 0 C
@A L D @A
0?
1 1
@ A
/
0A
@ A
@A?
/? 1
@ A
/ 1 !
K
@
&
1 &
1 &
1 6 &
1 1 / 1 1 ?
! ?
1
& &
?
.
% /
= ? @1 A?
!
& 1 ! ! & 1 / / 1
1
1
@ = A / /
/ = /
1 1 % @ 3 A
1 6
. 1 / / 1 /3
/ 3
1 1 / 1 / 1? 1
1 /
& &
K
1 1 &
1 1 &%
& &
0 @ A K
?
/ & 1
@ A
1E
@E A EA
@'0A
@
1?
1
@ A
@AQ
K P
1
@ A?
/ & ?
0
/ ? / ?
0 @ A
/ 6 / / /
1 @ A
0 @ A
/ /
/
% / Æ
1 / 1
1 1 / 2
& /
1 1
&
&/ % =
1 = /
// 1 ) & @ PQ?
-O 0AC
,% @'0A 1
!
! / 8 1 /
&
@ A
!
/&/ &
/ 1 & 1 Æ ? 1 1 /
1
A
0?
K
@ A
@ A
@'A 6
K
/ / & & 1
. & 1 6 6 ?
@AA
1 1 / &
A
K & 1 6
@AA
@KA
5 = = 1A A ( 1A A A ( (
1
5
K
K
@
(
AP @
@
A
A
1A@AA @AA
K 0
@AAQ
?
K
"
'
R(φ)=Re[T(jφ)]
5 4 3 2 1 0
−1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0
φ/π=(2/π)tan−1(ω) @AAQ
0 1 P
/ / 1 ?
1
5
(
@AA @AA?
K
1A@AA @AA
/ 1 1 1
1 // & ?
A
@ A
@'A
&
/ = 1 6 &
@AA
1
/ & & 6 / 1 / / 1
AA K 2<
@
@AA
@KA
AA?
@L
1
5 = L
K
5
5
=
L 5
5 L 5 = L 5
K
5 L 5 @ = L
5 L 5 @AA L 5
& @'A
K
=
A L
5
= =
L
@
L
5
=
L
=
5
5 = L
L
=
A L
5 @ =
L
AA L 5 @ AA L
@
1 @ A / 1 &
=
A L
@'A
& 1
C
!
!
1
!
/ ! 1
1
/
K
5
K
5
&
K
/ 1 Æ & 1
@' A
?
1 1 8 & 1 @!
A 6 1
1
1 & 1
" !
''
6
/ 1 / / 1 8 & /
6 / &
& / /?
&
/ ?
1 &
&/
3 ! 1
@AA?
/ ( & ?
1
@AA
0?
B & / 6 & 1 0 1 C
@AA
9@A L A L 9@A AQ
= ( =
K
'P
@KA
1
K
(
K
K
1A
A A
@ @
0 &
1 R ! / & ?
%
1
@AA
K
1 &
1 1
Æ
/
K 0
1 1 %
3 1 & 1
L'
@A
(
&
Æ
@AA
/
&
//
1
K
1
/
K 0
!" #
@''A
/ 0 &
K
C
=
@'#A
K 0 / 1 B ?
/ 3 ! ? 1 6 ? & /?
1 & / / &
/// 1 ? 1 / &
1 /? / ? 1 & 1 1 1 1 ? /
1 / ? &/ 4 U
1 ( = PQ / 1 1 1 !? 0 1
?
!?
1 ( = U
1 1 / & 1
1 /?
K 0
L A . 1 6 ?
( = / 1 / 1/
1 1 / / /
(
@
1 /? &
@
? 1 / &
K
L
/
1 1/ &
L A? & 1 /?
& C
1 1
= ( /
= ( /
1 @A
/
1
@'-A
"
'#
Partial Sums
5
FP(φ)
4 3 2 1
FS(φ)
F(φ)
0 −1.0 −0.8 −0.6 −0.4 −0.2
0.0
0.2
0.4
φ/π (rad/rad)
0.6
0.8
1.0
/ 1 /
$ &
?
1
K
K
K
K
K
1
1
1
1 &
/
1/ Æ C
@ A
K
@
L A
= ( /
/
1
? /
= ( / / =( / / 1 / = ( / / = ( / ( / / / = / / = /
@
L A
@
L A
P
@
@
L A
@
Q
L AA
@
A
@ L AA @ L A
@
@'+A
@ A &/ ( = 1 & ? / 1/ @ # A K 0 & K L ? 1 /?
1
& 1
" !
'-
5
α(ω)
(ω ,a ) 4 4
Loss (Nepers)
4 3 2 (ω1,a1)
1
(ω2,a2)
0 −6
@ A?
&
−4
(
0
ω (rad/sec)
2
4
6
? 13 ? / / & 1 & ?
K ' !
1 &
?
?
−2
(ω ,a ) 3 3
1
/ 1
?
@AA
1 1
? 1 1/ &
1 1 / 1 1 1 //? 1
$ 1
/ ? 1
?
1
/ / / .
? 1 1 & 6 / / / & 7
! 1 ) & ? @'0A?
1 1?
0 @ A?
// 1
1 &
? 1
(
0
@ A
& ?
@ A K 1
?
@ A
& &
& &
L
! 1 0
@ A
1 =
@ A
/ / &
2
P@
A9@ A L @ L A9@ L AQ
2
& 1 / / &
2
1
1/
@'AC
1 1
/ & &
1?
/ 1 % & &
1 Æ 1
1
.
1 = 1 / / 13 /
1 &
& & ?
@'A
1
? 1 / / & 1
1 & &
@ A / 1 &
&
@ A
&
"
'+
dα/dω b =0 nk
(a)
bk=(ak+1−ak)/(ωk+1−ωk) −6
−4
2
−2
2
d α/dω
∞
0
2
∞
4
∞
∞
(c ) 2
(b)
(c3)
(c ) 1
∞ c1=(b1−0) −4
//
∞ c =(b −b k
−3
−2
−1
∞
)
k−1
(c4)
c =(0−b nk
0
1
C
)
3
@A 1 /
/ @ A 1 / /
∞
nk−1
2
ω (rad/sec)
1 / &
3/ / ?
k
6
4
3
1
1
3/ /
& 1 // ?
?
1 1 / /
= 1 &
&
2
?
K
2 L 2
K
@
0
L
0
A L @
/
K
K
1E
A L
L @0 A
@E A EA
@
K
= =
L
@ A? @ A ? ?
1 1 & &
1 1
1E
/
0
@
= C
E A
P E Q
P K #
#
% /
1 1 /
/ 1 1 1 /
K
2 ?
C
@'A
0 @ A
1?
2 L L 2
1 ) & 1
?
1 & 1 & &
/ &
0A L @
/ /
1 = ? 1
=
=
Q
@#0A
" !
'
A
7 / 1 // E @ 1
! 1 &
6?
/ 1 1?
.
K
?
/
K
K
1
@
1 1
C
K L
A9@ A
L
1E
E A9@E A @ E A
@
& & / 8
1E
A 9@E A @E A
@
L
. /
P@
K
# =
P
P@
&
= ?
K
=
? & 1
/
1 1
0 @ A
K K K
@ A?
A
Q
A9@E AQ
? / 1
1? &
P
L@
Q
K
1
@ A
1 1
A =
L@
A
=
1E PE L @ A E QÆ @E A
L@
1 1 / 1 L
E L @ A E A9@E AQ
K
K @
K
# = P
L@
1
P
L@
A =
Q
K 1 / & L A9@ L A?
# =
@#A
B
L A L
L@
L A =
Q
@#A
/ 1 1
/ &
@ AC
2 P@ A9@ ' A L @ L A9@ L AQ
2 P L Q 2 @ A L @ L A L P= L = Q
#
1 1
0 @ A?
1 1
/
/ / 71 1
0
@# A
1 / 1 & ?
/
&
0 @ A?
"
'
1 / 1 = & 1
@ A
K
0 @A
K
2
1? &
A
@
0 @ A
2
1?
P@
A
L
$ %
2
L@
L A L
=
#
P
=
L
Q
Q
$ & @'A /
0 @ A K
2
P@
A
L A L
L@
Q
@#'A
2 K 0 1 = & 1 1? 2 ? 0 @ A ? & 1 ! ! 1 1? & ? 0 @ A = & C
/ Y =
0 @ A
K
1
!
/
1
2 $ %
@
L
A
2
@
A K 0
@##A
/ 1 & & / & ?
! 6 / 1
! 6 3
1 /
)
3 > 1 6 1 / 1 % 3
& & / / 1 ! ?
K P0 # #Q /J /
K P0 Q & 1 1 / 1/
& 1 & ? 1 1/ &
(
( ?
% '? ? / -
K '? / 1 1 1
1/ & 1 /
%
3 1 &
" /
& / 1 1
(
! & 0
1 / 3
13 / & @ A
#0
" !
+ 5 % ! . $"# B,$ $$" $-" + $$# ",%( $" % ; ' ' + ,"6 ( # + ", $" : "" 4; + 4,# ( % " 4 $ " 4 L " &" 4 '"' " 4;& "# "; + "' ,"$ (? $- ," $" #$ "; $" ..";& 4$$ ; "4$ + (? $- $%$E$" ,"6 2;2!'88 " 8 + ",%( $" % $" $ ' + , ", $" - ,"6 ;2; " ;=;" ". ;; ; ; . ;.; ; .;' ;=;.;=; "# + F,;$ E %$"$%,% 4 @ ". ( . ' ;.; + B$ #$- $- (.@ + C"# #$- $- @( "# (" ".(". ( E";& " ,; ( ( ;.,' (;.,''' ;,' (;, "# ( .( $ M;. ' ( + J$# N3N ,.? 4$ " " " 9$" 4$M;' . 4$ + $",# J< % 9"; $ + B,$ $$" "" $ $
"
#
"# "$E, + 4 J< % K K + 4 ;$4 # $$" " " K; $"$ " $ " +K "E ;$4 K"" K; +;$4 # $$" " ,'D K K K" ,'D "# . ( K. ( K 1 /
1
1 ! ?
00 &
5
'
1 /
1
1 !?
/
? / / @ A & 1 & ) ? ' / 1 1 / 1!/ 1 6? 1 ? # & A? / / / 1 6 Æ ? 5 ? & / & @AA 1 A # & 1 1
1
/
1 1 /
/ &
@& 1 /A? 3 1 1 ! / / 1 1 & ! 0 -' 0 6? 1 ) 1 / 1 6 / / @#'A & 1 & Æ ? 2 7 1 0 @ A 1 / /? 1 / 1 / / @ A @ A ? 1 Æ ? 5 ? @' A? /
&
1 & ?
/ 1
& 1 / / & @ A & &
@
1
A
6 1 / & 1 & 1 '? ? / -
'
? 1 61 3
1 / / 1 1 / 61 / / / 1 1
1/ 1 1 B &
1
// 6/ 1 1 & ?
A
' / 1&3 / & 1
1 1 = 1
&% 3/ 1 / & 1 & 8 Æ
1 1
/
3
1 1 1 / @ ? & 1 /
@ A
K A
/?
% 3
1 & 1
& &
1 /
*
K
1 / & 1 6 % / / 1 & 1
/ 1 & & 1
! & ? @ 'A? & &
2 & 1 / &
/) %
" !
#
F
|α| (Nep)
3 2 1 0 −1 0.0
P
nt=4 FS α(φ) 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
nt=8
2 1 0 0.0
0.1 nt=16
2 1 0 0.0
0.1
Φ/π (rad)
' 6 & 1 6 ?
& & / 1 & Æ ?
5
K
@' A5 C
?
1 &
& 1
5
K
0 #+ K
5
5
K
0 0 K
5
5
K
0 0# # K
5
K
0 00- # K
5
5
K
0 000--# K
5
5
1 Æ / 1 & &
1
#?
1
?
0? @' A 1
5 ?
1 1 Æ ?
1 1 Æ 1
2? 1
1 3 ?
1 1 Æ / 1
&
1
1/
1&
#N 1
/
1 &
! 1 &% 1 ? / &% E 0 ")= &% ?
1
K K
?
K 0#
E
1 3
. / 1 6
/ !M
7 1
/ /
"?
K !)=
1?
K
0
& 1 6 ?
"
#
+10 +5 +10 +5 +10 +5 +10 +5 1.05*kR kR 1.05*kR kR 1.05*kR kR 1.05*kR kR Q1 kC Q2
Vg
Q3 kC
Q5 kC
Q4
Q6
Q7 kC
Q8
kR -10 kR -10 kR kR kR kR -10 kR kR kR/0.408 kR/0.0127 -5 -5 kR/0.211 -5 -5
kR/0.358
kR/0.0181 kR -10
kR .define kC 250e-9/pi .define kR 2e3
kR -10
NPN - 2N3903B PNP - 2N3906B
A1
A3
-10
+10 +10 kR Vout A2 -10
kR
kR +10 *** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-18 VCC=18 VPS=14 VNS=-14 GBW=4MEG)
# / 1 6 1 /?
# 1
1 /
1 & &
1/ 6 1 / &
& & / &
/ 1 1 / /
? 1
1
1 / /
1 /
1 &% & 1 1
( K '
#
@ A
1
1/ & & /13/ ? &
-?
@ / A / 1 1 3 1
1 1 6
1 1 1 / / / / / / & & &% #00 !)= 1 1 / 8 / 1 // 1
K &% & !)=
/
1? 1 // 3
")= & 1 3
1 & 1 1 / 1 & 1 1 & 1
/ 6 /
1 3
& 1 & 1 / & ! 1 6 / & 1 13&% &% / / /
9
1? 1 / / 1 & 1 Æ &
3
/
!
( ' . /
1 1 / 1 1 3& 1 1 3 6 1 1 / 1 / / ? ? 1 % 3
& / / &% & 1 1
/ / 1 / 1 1 /C
/ ?
" !
#'
0
α(ω)
Magnitude (dB)
−2 −4 −6 −8 −10 −12 −14
|H(jω)|
S
−16 −18
µCAP
−20 −3
−2
−1
0
1
2
3
4
3
Log10(F/10 ) - / 1 & 6
1 / / 1 @ 1 Æ A? / 1 / / 1 & & 1 &
/
1 6
1 //
3
1
/% & 1
% 4 PQ
1 &
1 1 6 1 1 1 /?
// 3 ?
3
1 1
13 /
&
/A
. & 1
@
$ &? 1 ?
/ & 3 & 1 /
1 6/
1 1
1 = 6/ K ?
& 3= 1 1? = /
A
@ 'A
7 1 1 1
A 1 % / & =
/ /
@
A /
& 1 / & 1 Æ ?
@
1 1
Æ 1 1 &
! & 1 &/
1
K @ ?
! ?
1
1 3
// (
K ? /
? & 1
1 1 /
! 1 / /
Æ & 1 1 / 1 = (
6 1
! 1 / / 3 /
! &
1 / 6/ & 1 1
1
/ 1 1
/ 1 ?
7 1 /U
! & ?
1
" Æ
!
##
? / /
! & ? 1
= 1 Æ @ 3= A / 1 / / / 1 1 / &
. &? 1
1 / & = 1 / 1 0
1 ! / & & 1 /
/
1 1
/ &
1
1 &
/ =
1 / & 1
.& 1
@ 1 / = A? /
& 1 1 ? /
1
! 1 / 1
/ 1 @1
& 1
!
A? 1 1 = & /
1 / 1 1 / &
1 /
/ 1 1 /
B 1 1 &
1 & =
6 ?
?
/
% ? 1 & 1
1& / / 1
! / / / & 1
& / = @ A ? 1 /
0 @ A?
& ? 1
1
1 1 3
7 / !
1
& @'A
1 1
& / 1 1 @ A &
/ 1 1 / / 1 Æ & 1
1 & /// ! 1
1 ) 1
@ A?
& @#'A & 1 & ?
/ !
/ 1
/ 1 ? /
1 & P Q
/ &
1 & ? 1
1
! & 1 3
! & 71 "
!
1
! 1 3
& 1 1 1
#
?
3 > 1 &
! & ? 1 & ?
0 > &% ? A K @ A? / 3 0 : & : K A ? / 1
/ 1 & ?
1
5 1
! 1 1
1
%
/
0
3 (
K
A
K
"@
A
K
@ "@
A A
K
L
"@ A "@ A L#
L#
L
L
@#-A
& 1 / /3 &
& / &
@ 1 &
@
C
@A
K
@ A
K
@ A - "@A - @ @ A "@ A A
0 @ A
K
@
/
-
1
K
@ A
"@A
-# 1
/
A
@#+A K
?
1
" !
#-
50
α (dBv)
40 30 20 10 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
Angle (rad)
4 Bp
2 0
B
q
−2
B
−4 0.0
0.1
0.2
0.3
0.4
0.5
0.6
x=φ/π + ,6 + / 13 & &
B 6 ?
0
1 &
61 / 1
/ / & 1 /
3 ? :
1 1A 1 &
"@A
K
0 ? 0 ?
/
0
K
&
1 1
"@ A
/?
0
&
1 / /
1 1 & &
1
/ @/ /
1 1 = / 1 & L
. 1
1 1 1
L
"@ A
? 1
=
1
1 & L ? 1 B
/? 1 & 1 /3%/
1 1 L
/ & 1
0
1 & 1
1 1 1 / %/ &%
/ 1
A ?
"@ A
1
&
1
2 1 1 &
& L
@ AC
1 1 1 ?
& 6
@ A & 1 /
@ A
& 1 &
1 / Æ
1 / 1
K
1 / / =
7 // 1 1 1 /
/ 1
A
1 1 6 & 1
+ 1 & 61 ( 1 ?
1 & /
K
@ A K @ >P @ AQ P @ AQA
K
& 1 / 1 /
0?
:
1
&% ? 1
1 1 1 & 1 %/
. 1 &
?
/?
1 &13 / 1
(+−)Real−Imag. Parts
(+−)Real−Imag. Parts
"
#+
2 1 0 −1 Re(Q) 0.0
0.1
0.2
0.3
Im(Q)
2BQ/π
−2 0.4
0.5
0.6
0.7
0.8
0.9
1.0
2 1 0
2BP/π
−1 Re(P)
Im(P)
−2 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x=φ/π 1 / & ? 1 & 1 /
@ A
/
"@ A?
/
" !
#
1 L
/
1?
0
& = ? 1
# & = # 1 FG
&
1 /
& & !
3
@' %/ A 1
= 1
1
&
0
K
"@A
K
0 A
&
1 & 1
"@A
@
L
#
0
0 -+
@ A "
3
1
1
1
L A L A
1
>P"@ AQ P"@ AQ L
@
L
#
L A
L 0 -+A@
L ' 0A L ' ' A
0
@#A
= ?
' ' ?
1 =
& @#A !
1 3
'
L 0 'A@
?
1
1
L#
L A L
# #
@ @
1 1 ? 1
L#
@
K
1 / %/ /
K
/ 1 6
C
@
K
1 1 &
/ /
@
! 1 & / ! 1
K
1 1 1 &
1 / 1
1 / ?
0 '
1
/ & 1 1 & ?
& 1
1
/ / 1 1 &
"@ A / / 3 6 @ A K "@ A
1 &
1 /
1
1 ? ? & .
/
*&
/
1
1 @
A // &
1
0
1&
@ %/ A
? 1 1
1 1
' 0? 1 = ? / 1
?
? 1 1 1 1 %/ / ? /
K
L
/ "@ A
K #
/ ?
1
1 1 / & 1
/ %
1 %/ &% B / / 1 &
?
C
% :
P0 ' 0 -+ ' ' ' 0Q
K
P0 ' 0 #0 +- 0+' Q
K
A
K
P0 -0 0 '' 0 ##+ 0 +'0Q
K
@
% A
K
1 1 /
3
/ & 1
:
K
A
"
#
& 1
0
1
1 1 / &
1 1 6 / 1 & 1
& 1 ?
"@A
1 1 1 / 1 1 61 1 1 &
&/ ) / 1 )
= & ? &
&%
= /
? & 1
! & ?
@
$1 1
A @ PQ? -?
& / AC
1
@ "@
A
K
@
A
K
K
=+ P @
"@
A
A
K
L
K @
AQ L
B
=+ P"@
K
1
A
@
C1P @
AQ
B L B
K @
AQ L
(
711
L L A
B L A L @B
B L B L A
L
AQ
@#A
! & / /
/
L
/
L
C1P"@
L A L @
L
1 1 1 1
// /
1 1
? //? 1 1 1 13 / 1 ? 1
@
C1 " #=+ "
& 1 )
0 A
P
K
1
(
0
&
1 1 1 %/
"@A?
A@
L
L
A@
A@
L
L
A
A
@-0A
(13 / 1 3 % & 1 / 1 % 1 &
& 1
@-0AC
& 1 ?
1 )
1 1 &
?
& !
?
%
0
@
& 1 &% ?
1
@ AQ
@
&% ?
&
&
@ AQ
P
0
= & & 1 C
= &
0 ? & "@ A
@-A
1 ?
@A
1 & 1
@#A /// & 1
/
$
1
& / & / & 1 &
& @ L A 1 L L A 1 / / 1 = & 6 B " & 1 /
0
1
( L
() & 1
& 1 6 ? / @
& /
L
1 Æ
1
" !
-0
10 8 6 4
tan(Bq)
2 0 −2 −4 −6 −8 −10
0
1
2
3
4
5
6
Bq/(π/2) (quadrants) $1
1
1 & /
/ 1
/ 1 ! // 1 1 1 1 &
@-A? / 1
% & 1 1 /
& 1 & 1
0 A 1 )
1
1 1
/ &
(
$ &?
0
& ? 1 & &
3 / / =
1 1
1 / 1 )
/ 1 1 & 1
/ /?
/ & 1
&
/
(
& ? @-0A 1 1 &
@
0 A
K
=
&% 1
2 1 &
1 / 1
1 // & 1 & 1
(
1
= & & 1 ? /
& 1 1
&%
/ 1
,% @-0A 1
& & @ 1
1
1 1 & 1 / //
?
,1
1? 1 X
#
/C
A@
@ @
L
L
A@
# @X A@ @
0 1 1 X
A@ L
L
A
A
A
A
& 1
&
"
-
5.0
β/(π/2) (quadrants)
4.5 β
4.0
q
3.5 3.0
βp
β
2.5 2.0 1.5 1.0 0.5 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x=φ/π (rad/rad) 0 / 1 &
#
@
0 @X AA @ A A @ A
1? 1 1 &
1 !
& 1 ? 1
@
A K
@ "@
A A
K
1 ?
! &
@
L
@
L
?
1 1 / 1
> 1 )
A@
L
A@
L
! &
A@ A L # A@ A L #
= &
C
@
L
@
L
A@ A@
A
A
@- A
& 1 1 3
/ / & ? ? 1 /
&% ? 1 1
@-A
@X
K 0 1
1 1
1 /
1? @- A
& / / & &
! &
1 &
1 1 ? / & 1 / 1 ? & ?
0?
1
0?
/ & 1 / 8 & 1
1 / 1
H "; $" ..8";&
1 1
! 13
1 &
1 &
6 " /C
" !
-
; "$ ? ; + $ ,"$%6 $" $" %" "$ - $ ( ",%6- H #"6- H 4 . (",%' #" * "",% * "#" ' ' "; (* (* $ (2*. $ "# $ (2*. $ "# *( *( "# *F*.* 1 1 & 1 1 & 1 &
(
& %/ %/ ?
(
0
(13 /
=/
/ 1 /
/ & 1 &%
1 & 1 6 %/ 1? 1 1 )
/ /
1 1 1
/ /
= &% & 1
1 ?
1 / 1 1 1 ,6 +?
&1 1 1 /
& / 1 % / / / /
9 .
% %
1 1 13 & / &
& &
1 1 ) 1 /
!
1 1
& @#'A 5 & 1 6 / 1! 1 &
> & & 1 1
+
13 / 6 1 6 & D 1 ? 1 1 / 1 & ? @#'A? / 3 1 1 3/ / 1 @1
0A
/// / @ 1 / & 0A % / ! 1
?
1 1 1
C
'8'' ; "$ #(. (6- H? ; ' 6 H? ; #( '!) + $" : "" 4; + 4,# ( % " 4
1
"
-
Loss (dBv)
50
α
αapprox
H(s)
40 30 20 10 0
Phase Lag (rad)
0.0
0.1
0.2
0.3
0.4
4
0.5
0.6
β
0.8
0.9
1.0
0.8
0.9
1.0
βapprox
H(s)
3
0.7
2 1
10xDiff.
0 −1 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x=φ/π 1 & 1 6
%
+ , $4 .$" $% $" - ,"6 ;2; " ;=;" ". ;; ; ; . ;.; ; .;' ;=;.;=; "# #( '!) + $% $" 4 @ ". ( . ' ;.; + B$ #$- $- (.@ + C"# #$- $- @( "# (" ".(". ( E$E; " ,; ( ( ;.,' (;.,'''
" !
-'
;,' (;, "# *4$(.( $ + F$( 4 $ # ;$ 4 $% $" 2 1 1? 1 1 @ & A? / 1 /1/ 6 1
/ & 1
! &
3A
2 1 1 1? 1 ) 1?
@#'A / / & 1 6 1 ?
0 .
/
/ /1/ 1 1 / 8 1
! &
/ 03 13 @
1
/
1 1
1 !
1 1
1
/ T
7
/ 1 1 13 & / & & 1 1 / /
& / 1 ) 1 /
1 / & &
1 & &
1
& / ?
1 / 1 &
?
/ & ?
& @ ? A & & ?
0?
@#'A? 1
1 1 1
1 1 / 1 &
/
1 1
C
/ / 13
1 / 13
! !
/ & 1 1 & /
& 1 % / I
9
+) ' . 4 % /
71
! &
/
@#AQ? 1 1
1 1 )
)
=
1
%
/ ?
@
A /
* U
0 ?
0A /
1& /
= % /
1
1
A? / 1 1 ?
0?
0
@ ?
0
0
K
0?
1 / 8
/ 1 1?
@&
1?
1 1/? F 1
1 1 1 ?
1
1 1
! & & % / 1
0 & 1 6 7 !
/
6/
1 1
/ & 1 )
"@
/ /
! &
= & ?
1 6
1 / &
1?
1 1
&
/ 1 1
7 / !
/ 1
1 1
/ / 1
& 1 / 1
/G
B ?
1 )
& 1 % /
& 1 ?
?
1 & / 1&
1 Æ ?
&
1 // & P ?
/ & ?
/
U
1
1 / 3
0 A?
1
1 1 &
1
&%
1 / @& 1 ? ? 1 1 1 A & 1 & & ?
/ 1
0
/ / & 1 1? 1 ?
0?
/
1 1
/ 13
& 1 / 1?
1 / ?
?
0
2
0 ?
1 / 1
1 / 3
Phases/(π/2) (quadrants)
"
-#
5 4
βp βq
3 2
BQ
β
BP
1 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x=φ/π & 13 ? *< / *
?
0
? / 1 1 / / &
C / / &
1
/ 3 1 & 1 % & 1 & 1 % / 1 & / &
0
" / 1
1
& 1
@
1
/
1
A 6 ? @#-A 1
/ 1 / *
0 / 0 1 1 / 0 0 ? / 0 /
/ 1 / * 1 1 ?
0?
1 / 8 ?
+ $" ( (6 $ - $ $" *GE";& + $"$ $ $E$" *G *HE";& + "# *H "; #( ( .( . $ #( = + $"%" *H *H*H.#( *G*G. *G*G..#( + $"%" *G *H*H. "# "#
" !
--
& ?
1 1 / ? *< / * ? /
& %/
0
?
1
0 ?
/
:
K
A
. // ? 1
& %/ @#
/A? /
? 1 1 1 1 / & 1 & 1 / 8 % ? 1
& ? \? 1
/// 1 *< /
* / & ? /? 1 &13 / & ?
0
0
0
1
K
$" L \
K
$ 0
K
0
/
0 C
L\
K
0
$" $
@-'A
? *< / * 1 & 1 & / / 1 % / 1 ? \3& 1 & / 1
& & & $ *< / * # %/
(
1
(
/ @
%/ A
:
? /
1 ?
1 6 &
(
(13 /
1 1
/ 1 /
K 1 1 / & 1 6
/ &13 /
? 1 / =
/ Æ 1 / 1 &
1
& 1 1 & & 1 /
1
/ 1 6 ?
(
& 1 / 1
/ &
1
1
/ 1 \3& 1 1
& 1 1 1 1
1 8 1 13 &
? 8 1 /? 1 ?
& 1
/ . / ?
/ 8 1
1 / & 1 /
/ / 1 &
$ 6 1
& / 8 / / & / 1 \3& 1 1 &13 / & 1 6 1 /3 ? \? 1 / 8
* A
1 /1/ ? \ ?
&
0
.
/ \ /
/13/ ? \ ?
0
/ *< @
\
1
:
:
4 ? 1
\
&
1 & ?
:
/ & & 1 . / % !
& * 1
& & 1
/
: 1 0 4 ?
1 \3& 1 \
\
&?
1 1 &
? 1 1 1 & \ /
1 1 & 1
&
0
:
/
/
& 1 /? ? /
1 / \
1 = /? 1 /
1 1 \ /
0
0
& 1 1 ?
1 1 \3& 1 / / ? \ ?
1 ? *
1? \ ? 1
<% 0
"
-+
3.5
Ψ/(π/2) (quadrants)
3.0 Ψ2
2.5 Ψ
2.0
Ψ3
1.5
Ψ1
1.0 0.5 0.0 −0.5 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x=φ/π & / 8 / / \3&
&
0?
1 1 1 & 1 \3&
/
& & *< / * 7 ?
@
/ & 3
A /
"@
A? / % / 13 & ?
1 / & ? $
1
& ?
'
@ A
0 @ A?
/
? 13 / & /
1 % 1 & 1
/J 1 &
1 1 ?
0?
/
/ & 1 / / &
( C
&
@/*J-#A
1 1 / 1
' D
& &% ?
K ? /
1
?
/3
2 ?
/ 1
& @#'A 1 1 ? *< / * ? & 1 & 1 & *< @ / * A / 1 /? 1 6
(
0
?
J / & 1 & *< / 1 / .%. % ( L 0 L L ? / / 1 / Æ & 1 ( L ! & ( & ?
1 / 1
(
L
! & * &
/ %
@ / //31/ /A %
(
L '
' \3& *
.%.
0
/? 1 & \ L
/ 0 1 & $" K .%. /
" !
-
#
0
/
1 /
0 1 /? / 1 ) = & 1 3 ( ) = / 1 1 1 & J / @1 0A 1
//3 X
/ & 1 & 1 1
0 1 1 1 & @-A
1 )
P
#
= /
B 1
/
"
B
@-AQ
1
- 1 % / ?
@
?
A
1
/ 1
/ @ A
?
K 0 / &
K
@0A
& 1 / /
! & 3
K 0 / @- A 1
?
@-#AC
A
@
& $ - /
@-#A
A
@
6
! & 3
% / &
(
3 > 13 6 1 & ?
! &
?
& 1
,6 +? / 6 ? &
$ - ? 6 1 13 & &
"%$"
K L0
1 ? & 1 1 /?
1 / 13 6
%
3 1 03 6 ? / 1 /
1 & ?
Æ 6 & 1 &
1 & ? *< / * ? 1
1 / 1
1 1
1 1 1 & 1 / # %/ ? 3
/
"%$"
K 1? 1 \3& ? / / & 1 & *< /
* ? / ! 1 1 /? & 1? / &1 /? / / & 1 1 @$ A 1 @$ -A
$ '? & 1 \3& ?
/ / E 1 /
&
1 1
J
/
1
/// *< / * ! 1 1 / /
1 1 1 &
/ 1
/ ?
",
",?
1
1 & / 1
/ / /?
", "%$"% $ % *G % *H $ :#"%$"", + #$# # 6& G > H C5G*H*G %$ :# .% % *G % *H C5G"; G$% C5G (*GG$
:#
K
"%$"
L
"
-
(*HG$ 1 /
&36 ?
*< *
"%$"
// & 1 ! & 1
,A
%/ 1 & \ @
1 & / & 1
& *
/
(
:#
?
1 $ '
= & 1 & 1
1 1 %
(
&
J
/
1 /
/ 1 & 1 1 &% /
1
/
1 &
/ ? 1 / &% 1 / 1 1
/
1 & 1 )
= ?
<
$ /? 1
/ 3 / 1 &% 1 / 1 1
/ 1 /
&
C
:#. % $( %$" ( ( $. ""; % $( %$" ( ( $. ""; "# ;4;$( + # 5 ' F,;$ E H ;4;$( + # 5 ' F,;$ E G 1
6 / 1 1 1
1 / &% &
'
1 1 1 1 6/
/? /
1 / &% @ 1 & &% A & 1
1
)
/ /
1 1 1 1
/ 1 / / & 1
= C
K
1 /
L
@
@
A A
@--A
( & ;4@ A / ( & ;4@ A
1 & 1 )
1
= & & &
/ 1 % / 13 & . / $ #? 1 //3 / /
1 &
/ 1 1
/ 1 //3 C
+ 34 F,;$ E "# ( O$" ,"#O $'' + (6 $" $" $" " 4 ,"$ + ?, # $ 4 $" $ - , :#. $$ 9$( 9$( $ (9.$2 ; ;9 ;;9 (9 (9
" !
+0
p or
b
p
2
k
b
q p2
π/2
k
p
1
π/2
p
1
ω1
ω hk
ω2
ω1
. & )
/ &%
1 1 1
1 1
ω2
ω
(b)
(a)
'
ω hk
= &% & C
@A 3
/? / @ A / &%
/
; ;9 ;;9. (9 (9. "# ;4;; .; $. . $ (9.$2 ; ;9 ;;9 (9 (9 ; ;9 ;;9. (9 (9. "# ;4;; .; $. . "#
( .( ; .; + "# $"$ $ 6
( .( ; .; + % 4 4 $$" :#.
1
"
+
;4D
;4D "# :#.
;4D
;4D "# #
1 ?
/
#B ?
/
1 &% P
3
1 / B
) 1 ) $ -
K 0 1
/
@A
/
?
/
&%
Q 1
@-A & 1
= / //3
& 1 ) /
@A K 0?
1 /? 1
1 &
@
A? / 1
= & ! // & 1 1 &
/C
F " 4;4 FF ;4D ;4D "# +$"# #' 6"%$ % G "# H $ %:# + 9 :# ##P G-" H-" + 5-" 4 #$" E G## H## G-" + :# $ -" H-" G## H## + A## 4 #$" E "# :#. G##"-G## ;4D H##"-H## ;4D "# :#. G-""-G-" ;4D H-""-H-" ;4D "# G G-"G## H H-"H## . (F 6- G ' 6- H
1
" !
+
1 & ?
B &
& )
= // & ?
1
/ / = 1 // / / = /// @ A &
1 & @-#A
? & 1 ! & 1
(
1 /
1 3
1 1 /
D
//? 1
1 1 /
?
1 // /
1
/ 1
&
&
// / ? C
( C "
K
B L B L B L B
K
P
LP0
=+ P"Q
L
B L 0 L B L 0
B
B
L
L
B L 0 L B
L
B
K
C1P"Q L =+ P"Q
L 0Q L0
L
B Q
@-+A
1 / =
( 8 C "
K K
B L B L B P
B
L0
LP0
C1P"Q
L
L
B
L
B
L
L0
L
B L 0
B
K
=+ P"Q L C1P"Q
B Q L
B
L 0Q
@-A
1 / =
1? 1 & 1 / 1 / 3= % / // / & % 1 )
< Q?
1
= & ? P
L0L
& 1 & 1 @ 3 / 1 // /
//3 / 1 ? A 1 1 /?
1 1 / / P ?
@
A K
" Q
/
1 / 1 / & 1 1 &
",
" ?
! &
1
1
K 0 ? @ ?
1 & & 1
:#
K ' #A
5 1 1
! &
. &
1 1 /3 / 1
1 /
&
#
& &13 / 1 1
1 !
/
1 & 13 / /
1 1 1 1 3 / /?
1 1 &1 / 1
1 / 1 1 1 1 /3 & 13 / 1 1 1 1 / / / 1
/ 1
1/
/ = & 1 / ,6 7 1 1 & 1 1 / 6 / 1
& &
/ & & &% 1
.
13
=?
1 1 & & /
& / 1 / &
!?
"
40
+
αest0
Loss (dBv)
(a) 20 αapprox 0
α
est0
40 Loss (dBv)
(b) 20 αapprox 0
40
αest0
Loss (dBv)
(c) 20 αapprox 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x=φ/(π/2) # & & 1 / / &
", K 0? :# K D :# K #
@A
@ A
", K ? :# K 'D
/ @A
", K ?
" !
+'
9
+ : ' .
1 6 1 & 1
1
/
&
/ & &% 1 / & 1 6 1
1 1
& / 1 / & &
1 &%
1
/ !
1
& ? \? & 1 & 1 1 ) /
1 1 B & 1 6 1
/ & 1
=
1 ? ? = 1 "
1 & /
@ A
/ B & ? 1 ? 1
@ A
K
K
! & 1 1 &
& C
-
@
L
@
L
A@
L
A@
L
A@ A L # A@ A L #
@
L
@
L
A@ A@
@-A
A
A
(13 / 1 ( ) = / //3 1 1 K 0 @/A % ? 1 & / @ A & & & (13 / C
1
( . 1
@+0A
1
(
( A L K ( L
K @
(13 / (L Æ & 1
/ / & &
&
1
& 1 K P
? / 1 &% ?
1
1
% 1
=@
K
@
@
A K
1
@+A
1 / 1 %/
/ &3
& 1
@
A
/ " /
%$" 4
& & & ? !
=@
/*
C
@+ A
1 @/*A
1 ?
&% ? &
A
C
1 & & 1 ?
A K -#
/ /
@+A
@-A? & & 1 1 1? 1 /
/ ? 1? 1 / &
* 1
@+AC
# # Q
1 ?
?
@+0A
1 3
1 =
= &
A / / 1 1 /
= + 1
"
+#
/ 1 ? 1 & 1 B & ?
'%
1 B & & 1 /B 1 ?
?
1 B & ?
1 1 / /
1 1 /? 1 1 & *
3?
% /
%$" 4
!
/
=@
A 1 /
/ / ! 1 1 & /
1
&
/
& /& &
1
/ 1 /
1 1 1 & 3 & /
$% "
/ / 1 2 1
#000 / /
$%
/// 1 1 1
1 &
/
? / 1
! 1 & ,6
&
+ C $" "; + "' ' (?' ," $" 4,# ( %# #$ "; $" ..8"; + " 2;2!'8
; "$ + (? $- $%$E$" ,"6 + C $" H '8'' ; "$ #(. (6- H? ; ' 6- H? ; #( '!) + $" : "" 4; ", + C $" " - $%$E$" ,"$ ;2; " ;=;" + : ". ;; ; ; . ;.; ; .;' ;=;.;=; "# 4 '!) + #*- . 34$ $ 4 $$# ," $" + C $" 8 $"$ $ % %$" 4 $" F,;$ E % ?;? ; ;4;4 F:# 4,; ;; ", :#;4;4 +$"$ $ 6"%$ . (F 6- ?;' 6- ?; + #* ( . 4 + $"$ $ #*-
C
" !
+-
+ C $" "; $%$E , $" ; ;'D ;4'D ;4'D F + $"$ $ % - (? 4 ; + $"$ $ (? $- +6 $" +68 + %$"&(? &6 4 ; + / ( # ( 0$" 7 $" $% &/ $ &&/ ,"- & %$" 4&(? & $" 4 ; + / ( # 0$" 7 (? 4 ; + $" (? $- + C $" ! "" 4 "4". % "4 "4 "4
".
". F " GH :# %"4 %"4 "4 + 4 " ; ," $" $ F G H . (F 6- G?;' 6- H?; ( . 4 1 / &36 $ 1 = &%
: K A . $ 1 / ' ? A / & 1 % 13 (;9 1 / (>,(? / / & 1
/ / & 1 / / @ 1
/ 1 & $ 1 & &% & ? / / $ &? 1 1 1 / / 6 & /
?
4,;
/
,6 1
1 / & & &% D
;
1
/
1 / /
1 & 1
1
/
$ ' 1 1
4,;
& 1
;
& 1
& 1 & ! / 1
13 / & D / ", 4,; / 1 ? @ A? @( A )
/ ?
"@
( A
A? @
)
1 / //3 ? 1 /?
6-
#B D
1
:# ! 1 )
/
1
@
A /
= D 1
= D 1 //3 ?
"@
A
D
?
#D /
= & 1
// Æ & &
?
1 &
! & ?
1 / & 1
1 1
1 / &%
/ + # ) 8)
"
++
$ # & 1 1 " = 1 &% 1 ?
:0?
1
& / & 1
%$" 4
1 ? 1 )
:<
=/
1
D
1
(?
@1
'%
%$" 4
6
/&/AD 1
1 / D 1 / & 1
@ /*AD / 1 &% %/? $ - ! 1 =/ ?
// & ?
/
"?
; ? &
%$" 4 / !
/ 1 =/ 3
1 / & 1 / 1? 1 / /
= & & @-A? /
1 1 3
/ & 1
& 1 B & ? ?
! 1 1 &
3
/
1
! & / &
1 / =/ 1 & 1
-@OA 1
=/
/ & 1 & &
",
/ @
K 0A
",
1 & & / 3
K 0 ? 1 3
1 &
1 / ! & /*
! & - /*
1 / 1
/ 3 &3 / ? 1 / 1? / & /*
/ & 1 3
& ? 1
1 /3 / / ? 1 / 1 1 E6 /B 1 /
1 / & #@ A? &
", K ?
1 / &
1
6 & 1 & 13 /
1 !
0-- /* 1
1
&% / ? 1 & 13 / / 1 / & 5 1 1 /
", K ?
. -@A? &
/ & & &13 /
1 6 & 1 &13 / /
8 1 / 1 & 13 / 1
1 /
D 1
0- /*?
. !
1 1 & 13 /
? 1 / / & 1 1
/ / / 8 1
1 1
1 1
1 /
1 &13 / 1 & 13 /
1 1
/ 1 & " U
%$" 4
= 3
/
! & 1 / / &
7 1 1 1 1 /?
1 1
/ 1 / 13 & 3
& & ? / & 1 / // 1 % $ 1 / /
,6 1
/
1
& /
1 &1
. 1 / 3
8 // /
1? 1 / // 1 6 & 3 4 ? 1
8/ 1 & !
1 /
& ? 1 / 3 ! 1 &% / 1 / / Æ 6
1 & ?
1 1 / 1 8 // / / 1 / & 1 1 B & /
/
" !
+
4
|Error| (dB)
Initial
(a) 2 Optimum 0
4
|Error| (dB)
Initial
(b) 2 Optimum 0
4
|Error| (dB) Initial
(c) 2
Optimum 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
x=φ/π -
:# K D
@A ", ", K ? :# K #
2 =/ & ,6 & C @ A
", K ? :# K 'D
/ @A
K 0?
"
+
50
Loss (dBv)
40 30 20
Spec Est
10
opt
0
|Error| (dB)
0.0
0.5
1.0
1.5
2.0
1.0
1.5
2.0
0.3 0.2 0.1 0 −0.1 0.0
0.5
ω (rad/sec)
+ 5 & & / & ,6
-
3 > 1 / B / / /
/ 1 &
& ? 1 @ / / 1 ?
! &
( & &%
$ & 1
! & A / 1
/ ? &% ? / ! 3= & 1
", K
>
& 1 /
;$" '' #( .$ ;.'
%
3 1
", K & A
/ & 1
/
1 & /
1 / / @$ / 6 & &
1 & 1 1 / =/ 1
+ 1 =/
! &
/ 6
1 1
/ & 1 & ? 1 / 8 @ A 3
1
/ 6 & 0 /*
? 1
1 =/
1
1 /
/ 1
1 & &% / / %/ & 1 1 3= /
1
& 1 &
@ / A & 1 =/
! & C
" !
0
jω
1.0
jω (rad/sec)
0.5
0.0
σ
−0.5
−1.0
−1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2
σ (Nep/sec)
0.0
0.2
3= & ( % & ,6
"
A
K
@ "@
K
0 K # 0
@
A
K
"@
A
K
;
K
5<< P @
K
0 #
K
5<< P"@
K
0 +
@ 1
A A
L -#'+
L 0 #0
L 0+#
L 0 0-
L ' 0 L 0 0--
1 3= /
0-D 0#-'D
/ 1
1 6
1 1 1 6
L + -#+ 0
0'0
0
'#
0 #++
& 1
3 ? ! *
/?
L
AQ
@ /
AQ
6 @ /
1 1 /
36 A
& 1 ( & ?
1 / 1 1? /
36 A
/
1
1 = /B 1 1 1 1 1 / 1
36 ?
1 1 & 1 /
/ & 1 1 & 1 6
1
& / /
& & &% / / / / / / @
1 / A / /
1 /
1 / 1
1 & &% / / /
1 & / &
1 & 3 1/ &
1 / 1 / % /
/
3 >
/ & 1 &
& 2 & 1 & &
1 / &
6 &
",
K ? / 1
*
1 /
/ $ & 1 & ? / 1
3=
", K
;$" '' #( . $;.'
%
3 1
/ / / & 1 #3
/ 1 & 1 / 8 &
"%$"? &
1 / 13 ?
",
% / & 1 1 & ? '0? / ' / 0 /*? ? &
", K
@
A
K
@ "@
A A
&
",
1 3= & ! &
",
1 6 & 1
1 / / & 1 &
=/
.
C
/ 1
& / % # & 1 & 1
+? '0?
? 1 / / & 1 K
1
'
1
" !
Loss (dBv)
50 40 30 20
Spec Est
10
opt
0 0.0
0.5
1.0
0.5
1.0
1.5
2.0
2.5
3.0
1.5
2.0
2.5
3.0
|Error| (dB)
2.5 2.0 1.5 1.0 0.5 0.0 0.0
ω (rad/sec)
,6 0 / &
", K ? :# K -
Loss (dBv)
50 40 30 20
Spec Est
10
opt
0 0.0
0.5
1.0
0.5
1.0
1.5
2.0
2.5
3.0
1.5
2.0
2.5
3.0
|Error| (dB)
1.5 1.0 0.5 0.0 0.0
ω (rad/sec)
'0 ,6 0 / &
", K ? :# K +
"
Loss (dBv)
50 40 30 20
Spec Est
10
opt
0 0.0
0.5
1.0
0.5
1.0
1.5
2.0
2.5
3.0
1.5
2.0
2.5
3.0
|Error| (dB)
0.2 0.1 0.0 −0.1 0.0
ω (rad/sec)
' ,6 0 / &
1
", K ? :# K
K
-- 0
K
P 0 '- - + 0# 0 0#0# - 0+ + - # +- 0 00Q
"
K
P 0 0 - ' ' + +' - #+ -0 ' 0 0 -## 0-0Q
1 1
1
1
3 @ ? 1 Æ
& / /
/ 1 & 1 A . // ? 1 3= & 1 *
/ & 1 ( & /
1 / & 1 ( 3= 1? 1 * & / 1 &% & 1 ( & / / / 1
,6
1 &
1
",
& 1
% /
/
/ * & &1 & 1 6
1 1 / & /
* 1 1 1
K 1
& 0
1
' ?
1 1 1
1 1 &%
1 1
% /
3
/ &%
@& 1 ?
K A &
1 & 0 #0 /* 1 // ( 3 3* & 3 / @/ /
1 A / 1
1 /
/
@ A
6 / / / /
1 1
1 & &
1? 1
/
1 1 & / 1
" !
'
1.5
jω
jω (rad/sec)
1.0 0.5 0.0
σ
−0.5 −1.0 −1.5 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1
σ (Nep/sec)
' 3= & ,6 0?
0.0
0.1
0.2
", K ? :# K
"
#
50 45
Loss (dBv)
40 35 30 25 20 15 10 5 0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
ω (rad/sec)
' ,6 //
1.6
1.8
2.0
& 1 * & & ,6 0
1 1 1 & 1 @
/ @
6
A
0A &%
. 1 &
?
1
&
/ 1& /
/
1 / & * %
1 /
1 1 1 &
3
& &% & 1 %
1 %
1 1 / 1 / 1 1 3/* & &% 1 !)=? / 1 / 1 / 1 1 03/* & &%
1 !)= / &
6 / ( 1 1 1
/ 1 /* &
1 / / 1 +0 /* & & &%
1 # 1 / 8 &%
1 1 ( / &
1 /* & &% 1 !)= / 1 -- /* & &% 1 !)= /
,6
/ /*
1 1 1
" !
-
' ( 1 1 &
% C 1 / 1 /
1 /* & &% 1 !)=? / 1 / 1 /
1 -0 /* & &% 1 # !)= @A 71 3 / *
1 &
% / 1 3
% I / 1 ? / & & 1 /
> 1 / ? / 1
!
& &% @ A 5 1 1 & $ & 1 6
6
3
/ 1 / 1 / % @A .
@
A
& 1 % $ & 1 3
! & ? / 1! 1
/ ) & & 1
& =
#
@ /*A
1 "
1 1
! &
3 1 1 '0 /* & 3
K +#?
1 1 1
1 / 1
1 3 % 71 & / /
/ & 1 I ,6
* @:A K @(AA? * @:A K 00I ; C (
1
- / 1 / & 1 1 ?
AA
@
K
:?
: 9 K (A?
&
:
71 & 1& ?
A
K
/
9 (?
1
/ 1 ?
1 + 1 &
( & 1 / /
& &
@A 1
@A / 1
/
K
@ A
L #
A
@
@0 #
K
@ 0 #
A A
A@0
A@ 0
@ A @ A % / & 1 / !1 ) / = 1 !
/*
& 1I S % / & 1 @ A 71 1 / / 6 / 3 & 1 & I 1 &
& / / % C
@A
K K
L
A
@
K
@
A
1
" @A 1
+
& 1 & ?
/
1 / !
/
A
@
A?
@
! 1
! & 1
1 & &
1 &
L /J
>
/ 1 Æ 71
I 1 %
@ A > 1 & ? 1 1 ? / / 1 & ?
@
A $ &
@
/ = > " 1! 1 & & .
!
A & ? / 1
@ A 1 /
1 / / /*
? / 1
1
1 1 & &% 1 L /J
1 3 6 /% 1
@
A
% I (
% / 1 6 / & 0# /* /
/ & #0 /* 1 / 8 &% !)=?
1 1 /
@A $ & 1 /? 1 *
(?
% /
% / - !)=
% / / 1 (
1 / 1
1! 1 71 &
! & ? / "
/ % /
/
1 &% I @ A $ & 1 1
6
/
(
1 (
/ 1
1
! & ? / " 1!
1 @A 2 / & 1 1 1 & ? / 1 / 1 % / &%
1! 0 1 &
% / ( / C
@A
C
0 # /* & 0
@A
! C
-0 /* & 0 !)=
!)=
@A 1 1 1 3 % @ A $ & 1
! &
1 / &3
/ @%/ A & ? / / 1 & 3 % / & / & %/ @A $ & &% & & 1 1 % / 1 &
/ &
@A
K
0
L @
&
0C
0#A9@ 0#A @ A9@ A
A9@ A L @ A9@ A
@
> 1 / & ? &
K
@
A?
1 %/ /
1 & &
0
" !
1 1 / / 1 /
S
3/* 1 ! @ A & 1 & ?
1 //
@
1 1
$ &
A & ? / 1 / = &
> 1 1!
1 / &
1 / / / > 1 &13 / &
1
/ 1 1
! &
1
% C
@A @A $!1 1 1 & 1 1
@A
(
$ &
-
/
6
L
8 * @ A
?
/ & 1
@A
?
/ / 1 /
1 1 1 0# /*
1
8 K 00
& 1 1 /* / &
!)= / & 0 /* &
' 1 &
8
1 / & -0 /*
@ A $!1 1 1 & &%
K
'0
!)=
% & ( / 1 6
/ 1 / 1 0# /* & &% 1 !)=D 1 / 1 / 1 '# /* & &% 1 !)= @ ? '# /* 0# /* 1 & &
% / & 1 / A @A *
1 ( 1
% @ A $ 1 & /
1 1
1 !M / 1 & %
>
1
&%
1! 1 / & & &3
% 0 ")= # 5 ' 1 1 - > 1 / 1 1
! & / ( 3
& & 1 / 1 !)=? / /
1 /* & &%
1 % - /* &
&% 1 # !)= $ & 1
! & ?
? / 1 &% & % / 1 > " 1! + ( % 6 / & 0# /* & &% 1 00 )= / / & 0 /* & &% 1 #0 )= @A / 1 & / 1
1
1 = 1 %
3 & *3
"
R1
R0
R2
v1
-
v2
+
C
'' &
@ A 1 / " 1! 1 & & &% @A 1 / / 1! 1
* / 1
1 & 1 8
= 1 &
'' / / 1 & & ?
/
0 0
?
$ & & 1
1 3 & @
L A @
L A? 1 &
& 1 1 6
1 &
' 3
! / / / &% 3
/ & &% ? / /
?
/
1
1 6 1 / ? / & / /
1/ Æ / / 1 6 3
. 1 & Æ / 1
/ & 1 /* / & 1 1 & / &% ? / 1 / &
1
@A
@ A
@A
@/A
@A
:
K
A ?
3
/* ? / 1
/ @ / A
'
K
P0 0 # 0 # 0Q /J
K
P 0 0 # 0 0 0 0 - 0 # 0Q
'
K
@0 # # #A
K
#@ L @-
'
K
P0 +# #Q
K
P0 -Q
'
K
P0 +0 0 # # 0Q
K
P- 0 0 +Q
'
K
P0 +0 0 # # 0Q
K
P+ 0 0 -Q
@' 0#AAA
" !
0
0 5 1
1
/
/ 1 / / &
. 1 / 1 /
1 /* $ & 1 / 1 1 & 1
1
#? &
/ & 1
! 0
! 0?
1 1 3
/
1 6
. ,6 '? & 1 / & * ? 1 /
1 =
@ A
/
6
& @A 1 /
6 / / /
1 6
1
> " 1!
5 % 1
@ A
@A / /
1
6
) PQ 4 ? , ? PQ ( = ? ?
! # % 8 ?
?
'((( "
S !? SC 7 ? #+
> $// 5 ? :C )? #-
P Q . ? )? / 4 ? " :? F ?G
& 1 6
! ?
$3'?
#? "
++
&
!/ 6& &
/ (
1 / 6 / & 1 ) & / 1 1 / / & 1 6 ?
6&
& ?
?
L 0
1
@ A?
& &% 1 ?
/
1 &
1 / / 1 1 ?
0?
! & C
@ A
K
-
@ A
K
0 @ A
K
1
K
( $ 7
1 ) & ? @'0A?
7
K
;<4 @ A @A
/
@A
! ? / 6 &
1
/
0 0 @ A?
/? / 1 1 ?
4 ? !
/ ?
/
. / / & 1 / & ? & / & 1 13 &
/ /
&
! " !
10
Re[h(jω)]
8
a=0.1
6 4 2
a=1.0
0 −5
−4
−3
−2
−1
0
1
2
3
4
5
2
3
4
5
6
Im[h(jω)]
4
a=0.1
2 a=1.0
0 −2 −4
−1/ω
−6 −5
−4
−3
−2
5 /
−1
0
1
ω (rad/sec)
& 3
/ / & 1 / & ? ) & & 1& /
/
0
@ A
! &
1 % / 1 & 1
&
1 & / 1
1 1 &
1 / & 1 / /
/ @ /A & &
/ 1 /
8@ A
/ &
K
&
8@ A
1 /
@A / /
K 1
/ 0
. & @A 1 1
K
0
@ A K L A @ L A L L @
1 1
&
0
8@A
.
0? 1 & 1 1 /
@A
1 3 1
/ / 1 1 /
1
/ / & & 1
! &
K
/
1?
1 1 1 / &
8@ A
& 1
1 1
& 1
& / 8 &% ?
/ (
1
!
/ /
1?
@A 1
0? 1
" !
1 / 1
!
K
1
K
& / &
&
C
L
'
A
@
K
K
@ A
1 ? %
?
& /
0? 1 &
%
1?
/ / & 1 & 1 ?
8@ A
&
&
/
1
=/
1
@'AC
8@A
K
L A Æ @ A
K
@
@'A
1 & 1 & 1 ) & / / 1 /
7
K
1 & &
L 0
& 1
,% @'A 1 /
A
? @
7 1 // 1 &
! ?
K 0 / /
1 1 1 &
& / &% C
; 5
@
Æ A
Æ @ A
Æ @ E A
( 1 ? & ?
@ A?
?
>4 5
@ E A
1 / 8 ?
1 &
@#A
@E A1E ?
/ / 8
K
E?
&
C
1
10
1
1 K @E A1E Æ @ E A
10
K
& @-A .
E
1
K
0 @ A
K
&
E
@-A
0
1E E Æ 1E E
1 / 1
@ A
@E A1E @ E A
/
@ A @
@ A
@ E A
EA
@+A
@A
! " !
α(ω)
2 1 α(ξ)dξ 0 −1
ξ 0
5
10
15
20
25
20
25
2
dβ
1 0
ξ
−1 −2
−α(ξ)dξ/(π(ω−ξ)) 0
5
10
ω (rad/sec)
1 / 8 &
1
1 &
?
6&
@ A?
0?
/ 8 &
0
0
&/
@A
/ / ?
?
1 @'0A . 1
1
& & &%
(
1
/ & ,6 / 0 1 1 1 / 6
/ & 1 /
@+A?
1 &
1 / 1?
15
1 1 /
6 /
! ?
1 &
&
1 ! / & 1 1 / 63 / 1
/ / E
1 1 &
%'% 3 1 /
/
1 / 6 C
& /
3 1 & / & /
& . ! & 1
"%$" & 1
/ / 6 /
/ . 1
Æ ? ? & 1 /
" !
'
4,;
3 1 & &
. ! 1
?
& B &% ? / 31 / 1 1 / &
/ /
1
1
@1 / / /
! & 1
& 1 )
!
=
1 ? /
& 1 )
3
= A 1
1 1
3 1 1 & )
// Æ // =
/ /
= &
1 % &
1 1 & 1 / 8
3 //3 / 1 /
(?
! & 3
3 1 1
& /
&36
! & ? )
= 3
? 1 & B &% / / 1 %/ & 1 &
1 1
/ & @ /*A 1 & / 1 " &
%$" 4? 1
3
1 1 = 1
/ &
1
1 / & ? 1 @ /*A? 1 &
/ 1
4,;
1
)
= & / 1 1 &
K P
& 1
! &
& C
# #B Q
1 / 1 %/ ) = & @ A / "@ A? # / #B 1 //3 & 1 ? / 1
& 1 & @ A 1 1 & & C
@ A K
@
@
1 & ) 1
A@
A@
= ?
A
A
(85
(? @ A
K
L #@ L #B@
( ?
1 1 C
= =
L A 2 L 1A
@ @
;<4
K
1 & /
A@
A@
A
A
& & 1 &
K 0
/
% 1 /
1 &
@ A K
@/*A
%$" 4
C
! " !
6&
#
* ! 4
1 / & 1 / 1 3 1 6 / /
/ /
%'%
1 1
3 1
/ 1
1 / 1
1 1
+ % ," '% + @%'% B(
+ %#$6 ,
" + $" KG 5 % ) $" <4 +", +;$" ''" +#( .$ ;.' + $" #*+ $" *G 5 % $" <4 ", ;$" ''" #( . $ ;.' + $" #* GHF ;#(", :#" 4G. ;$" % ; + " ,"$ ?;? ; + , ", $" - " ,"$ ";" 4; 4 #( ;2;#("; ;=;"; + #* ";. #( #( ;; ; ; 4 4 . ;.; ; .;' ;=;.;=; "# . (F 6- G?;' 6- H?; ( . 4 $, 4#
1
%$" 4 .
" / 1 "
" !
-
,( ; 4 &&; &..&$# ;, % ; $ ;, . "#&C&&5 @Q R& 6 (&K #*-&&B" $E&8 ,( ; $# %% $ ;, .' ' % 6 (&N5N #*&&B" $E&8 (&S% # &&B" $E&8 $, 4# E G H ,( E$% E&&''' $% &&$# % ( E ;,% ($% E $ .' ' ' .;, ;, $&, & 6 (&?S% # &&B" $E&8 (&S$% " &&B" $E&8 3 1 & 1
& 1 @6
%$" 4A
/ / / / 1 6 / /
1 1C
," $" GHF ;#(" + ," $" GHF ;#(" + T" , , $" $"# " ; ," $" $ + $ $.;$ $4 .$" "" # ," $" + 9", + ; ,"6 $" "% $E# ,"# ; # + #( - , ; ,"$ #*- + " #$# (- %$"$%,% # + G "# H $" 6"%$ $$" - + 34 " ; ," $" $ F G H + B( 8
#( '!) + $" $" : "," "" 4; $ " 4 L " &" 4 '"' " 4;& "#
! " ! "; + "' ,"$ (? + "; " ( $" # % $" ..8"; + " ; "$ + (? $- $%$E$"
+
$- ," $" ," $" 2;2!'8 4$$ ,"6
+ , ", $" - $%$E$" ,"$ ;2; " ;=;" + : ". ;; ; ; . ;.; ; .;' ;=;.;=; "# 4 '!) + #*+ $"$ $ % %$" 4 $" F,;$ E % ?;? ; ;4;4 F:# 4,; ;; ", + "; $%$E , $" ; ;'D ;4'D ;4'D F + $"$ $ % - +6 $" +68 + %$"&(? &6 4 ; + / ( # ( 0$" 7 $" $% &/ $ &&/ ,"- & %$" 4&(? & $" 4 ; + / ( # 0$" 7 "" 4 "4". % "4 "4 "4
".
". F " GH :# %"4 %"4 "4 ," ," $" ;4 ;4 F :# 4,; ;; ", + 34$ ,(, $" ," 4 F,;$ E 4 " " %, $$ + "# "# " " F "% $E 6"%$ $ 4 + #$# ' 9" $" $ ,# $" 4 $% + 4 F,;$ E ' U "
";" 4; @ "" 4;
" !
". . ' ;.; + B$ #$- $- .@ + C"# #$- $- @ "# " ".". ( E" 4; " ,; ( ( ;.,' (;.,''' ;,' (;, "# ( .( $ *GE"; + $"$ $ $E$" *G *HE"; + "# *H "; *53 ( .( . + 9 ( $" $" # $"P $ *53 = + 9 $ $ $" $" $"%" *H *H*53 *H. + (6 4 %," 4 $" *G*G. *G*G..*53 + 9 $ $ # $" $"%" *G *H*H. + (6 4 %," 4 # "# "# "%$"% $ % *G % *H $ +%$"$%,% # :#"%$"", + 4$ $ #$# # 6"%$ G > H C5G*H*G + "; $ + U "
+ C5G$" ( %$ :# .% % *G % *H C5G"; C5G% C5G (*GC5G (*HC5G ("; $ ("; $ $ 2 :#. N 2 :#. &A(? $- ,"6 " $ % & "# :#. %$( %$" ( ( $. ""; %$( %$" ( ( $. ""; "#
! " ! + ;4;$( + # $% # F,;$ E H + ;4;$( + # $% # F,;$ E G + 34 F,;$ E "# ( O$" ,"#'O + * $% ,"# (6 $" $" $" + " 4 #$ ,"6 - , :#. $$ 9$( 9$( $ (9.$2 ; ;9 ;;9 (9 (9 ; ;9 ;;9. (9 (9. "# ;4;; .; $. . $ (9.$2 ; ;9 ;;9 (9 (9 ; ;9 ;;9. (9 (9. "# ;4;; .; $. . "#
( .( ; .; + "# $"$ $ 6
( .( ; .; + % 4 4 $$" G H :#. GG ;4D HH ;4D "# :#. GG ;4D HH ;4D "#
'00
" !
G
H F. " 4;4 FF ;4D ;4D "# ," $" GH :#;4;4 + 34$ , $" "- 4 6"%$ # % + F,;$ E % "# # 6"%$ $$" $ %:# + 9 :# ##P G-" H-" G## H## G-" + :# $ -" H-" G## H## "# :#. G##"-G## ;4D H##"-H## ;4D "# :#. G-""-G-" ;4D H-""-H-" ;4D "# GG-"G## HH-"H## ," ," $" (? 4 ; + (? 4 ; + $ $-" ", $" ," $" 4 - ; ?; ? ; + ,$" 4 F,;$ E - $ ( $"# 4 " ; ," $" 6"%$ + % ;4 "4 ;4 "4 F + ;4 ;4 , # F,;$ E GC > HC $-6 + 4 ## %, $$ "# + F $ 4 " " %, $$ 4 " ; ," $" + $'' FCF GC HC " " 4 "4". "4 "4". + 34 F,;$ E %, ( # (
! " !
'0
+ %" "$ 6 $" $" - , "# "4 ; ; "; " 4; ""; ""; ( ; ". # ; ". "4 ' .; ' "4.; "# "4 ( (' .; # #' "4.; "# 4 " ? (' ? # . (4 + #* ,% . 4 'D + ,% ( . 4 + U " "
#
'0
" !
# # / ) . / 1 *$,, & 1 21 $ > #-? 1 "$,, & "1 . & 1 @". A (1 1 > & " ? 000
+ ? 1
#? / 1 1 &
& 1 >
1 1 3 /3 8 1 / 1 & -+
. 0 1
/ 1 & & , /
, ? 1 1 1/ 1 1 ? & 0 000?
/ 1 13&% @>)A /
000
)
1 & % = 1 %
) / 1
&
3 3/ @A & 1 .,,, $ //
? 30? 7& " / ? & 000 1
!/
1
++ 0?
1 / / 1 % 4 ". ( ( ?
/
1
1 / / & / / /
/ 1 / & 13 1 % & 1 1 = & 1 13/ - -+? 1 & 4
!? . ?
1 1
/
1 &
1 1 /
& & S 1 > & " 7 1CJJ
/J /
. U / 1 /
'0
'0'
" !
%
! " #$ "" % ! "
" %+,- " ( " . %%%- "" " ! " " * $ " %+,- $ " $ * " $
- " " * " & & ) & )
! ! $ & ! ! ! '! " # ! ! ( $ " ! !) !) ! !) # ! "" ! "" ! * !& !& $ !
/ #
! & ) " & &
! " '0#
!
'0-
& !
" " ! !
! $ ! ) " 3!!4
0 & " & !
) " ) #1 2%
'! " '$ '$ ! !
! * ) &
$ " ! !
$ " " ( (( "" ( $ ( $ . " . Æ + ! . . " ) #1 ) " ) ) "
$
" " ! " ! $
)
$ * "" "" "" ) ( 21 #1 " 21 #-
!
'0+
+ & " 0.5 "
$ * 21 #1
$ *
& $
&
" ! $ * " $ " #$ % ! " '$ % ! Æ $ "
" ) # ) $ * % ! " ) % ! " ) " ! 6 7 " 6 77 " % ! - 8
! "
$ * "
$ * " " $ * """ 9 ""
! "
$ !! "
!
'0
/1/6 " /1/6 " !! " -1/6 " $ " " " " ! " $ "
! % ! " "
" ! 21 #1 21 #- """ " ! " " 21 #1 " 21 #- 21 '1 " 21 21 " + ! ! " $ 6 ! ! $ * :%:- $ Æ $ $ 2 ; ; "
