Active Filters for Intergrated-Circuit Applications 9781580538961, 1580538967
This authoritative resource offers you comprehensive knowledge and detailed design guidance on active filters for integr
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English Pages 422 Year 2005
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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
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? 1 1 1 1 / 1 & 1 ?
& ?
/
1 / > ?
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℄
K
P℄
L P℄ L P
℄P℄
¼ ¼ P ℄P ℄
½ ℄ @A
¼
℄
K
P ℄
1 %
K
P0 ℄
K
P0 ℄
C
@+A
1 6 & 1
1 / 1
P
1
/ /
1 1 &
1 1 &
P
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P
℄L
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¼
P℄ L
1
P
@AC
½ ℄
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I1
I’ 1 N (RLC) [ ZL ]
V1
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V1
(a)
(b)
-
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!? @A?
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P
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¼ ½ ℄
@A
1 1 1 3
/ 1 ? 1
? / 1 /
/ 1
1 /? ?
¼ ¼ ¼
1 $
/
K
K
K
1
@A
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/ &
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1&
/? 1
7
1 / / & 1 / 1 1 &
/
!
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1 1 6
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1
1
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1/ & 1 1
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K
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K
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ω)
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ω ')
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ω
2k
ω
3k
ω ' (rad/sec)
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H(jf ')
ω
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ω
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D
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&% 1
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1
36
! &
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7
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C
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¼ A℄P℄
1
1 1 &% ?
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¼
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P0 ℄
K
K
P0℄
&
¼
K
¼
@A
/ 1 / /
! & / & & 1
$ &
¼
1
/ 1 % / &% &
¼ @¼ A
K K
@ ¼ A ¼
P℄ L P℄ L
C
½ ℄ P ¼
/ 6
¼ ¼
K
* 6 @A? 1
¼
P ℄ L P ℄ L
¼ P
¼ ½ ℄
@A
// 1 / & &%
!C
¼ ¼ ¼
K
K
K
@ A
? 8 / 1 &% 3 & 1 @ A? 1 (
/ &
? 1
/
5( B & 1 1
K
K
K
@ A
¼ ¼ ¼
3 1 1
K
K
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
¼ K
?
0 !)=
/ / & M !M )
1
@'A
1
1 1
%
@'AC
1 /
/
& & 1
/
K
-
K #0
¼
& / 1 / / & ¼
¼
¼
K
K
0 '0
0
¿
¿ 0
#0
@-A
00#' 1 / C
K ¼ K #0 K - 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
1 / 1 6 1 7 1
!
?
0
M M K
!
1
- 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
1 & 1
K
-
0
K -#
1 6
0
/
-
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
¼ K L ¼ 1
&
K
L
1
? ? &% 1 / 1
/ 1 &%
& &% @ /J A? / 1 1 /
,6
/ 1
3 3
@'A / @#A
@( ( A & /
. 1
1 / &
1 & / 1 ( (
1 =/ 1
¼ K
K
¼
,% @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
. /
/ / & &% ?
¼
C
K
¼
K
¼
K
¼
K
¼
¼
K
K
¼
@0A
C ¼
K
¼
@A
1 % 1 1
@ A
1 &
1 ( / / / 1 1 1 & 1 3
&% 1 ¼
@AC
K
1 &% 8 & 1 &
& 1 / 1
/
K
1
/ / & &% ?
¼
5
/ C
A
¼
K
K
@A
0
1 &
C
5
@
¼
K
@
¼
A K
K
¼
K
¼
¼
@ 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
¼
K
/ C
K
@
¼
A K
¼
K
¼
¼
@'A
1 &
/
$ 3 & ( ) & 1 ( 1 %
@
/ & 1
1
@
¼
A
A
% 3 1 /
@A 1 1 @'A / 1
& ? / 1 1 1
!? / 1
1
/ &
! / / 3 @/ & 3
A &
C
+
1/2
Z(s)
1/2
1
Ω H,F)
(
,
) / & 1 ( &
C
@
A K
L
@#A
@-A
C
@
A K L
¼
@
?
K
A K
A
1 & 1 =
@
@
¼
K
1 / & &%
3 1 ( ) & 1 &
A? / 1 &% & 1
@
% 3 $
K
A K
'
L
L
=
! & ?
! & C
K
L
=
@+A
@+A 1 & /
! &
& @AC
@
A K
'
L
1 &% &
C C
= ? = ?
0 #?
L
L
K
C
D ? 0 #
? 0D ? 0
@
L A
'L
L
K
@A
Æ
0 Æ
0
? 1 &% 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 &
/
¼
&
@ %/ A / / &
!D 1
¼
&
& &
/ 1
/1 1 1 & / &% &
K
1 &
!
¼
L
!
¼
@AC @A
/ & 5( C
5
¼
/ / & &% ?
K
. / ( 1C
@
A
K
¼
K
!
K
@
¼
A K
/
!
¼
¼
!
L
K
¼
K
¼
¼
L
¼
¼
@ 0A
!
( 1C
@ A
K
¼
K
!
K
@
¼
A K
/
!
¼
¼
L
K
1 & 1 &
¼
¼
K
¼
¼
L
¼
@ A
!
¼
'
1 1 (
1
K /J
)
!
3 & 1 * & ?
#D /
* AD / 1
0¾ 0½
1 1
/ ? / 1
¾ " #
& 1
K 0@
¼
L
¼
A? 1 (
! @1 ( / 1 / /
! & 1 % / &% & . /3
"¾
& 1 /
!
$%&
1 + V1 -
+ V2 -
1
(Ω, H) # ( & ,6 -
1/10
10 + V1 -
+ V2 -
1
(Ω, H,F) - * / / & 1 & #
% 3 > 1 / ? 1 / &
! & 3
C
C
@
A K
0¾ 0½
K
L
K
@ A
C
@
¼
A
K
0
¼
L 0 ¼
K
¼
¾
L
¼
L
0 ¼
0 L
K
K
1 ( & & 1 3!
# ¼¾ L
@0
¼
L 0
¼
A
@ A
¼ ¼
L
#
* %/ & ? @ 'A? & 1
@ 'A
¾¼ & /
-
1
. //
¾¼ K 1 &% @!A & 1 /3 ? K 0 1 3/* / /1 & 1 1 " % 1 6 "? ¼ ? & 1 %/ ! & ? / 1
& ?
1
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
1.5
2
ω’ (rad/sec) ¼
+ 1 ( * &% & &
&
& / % 0
& & ? 7 /
K
¼
K
&
! 1 ( * &
/1 1
(
"
1 1
!
¼
1
% 1 /
/
/ /
@A / 1 / &
6 C
! 1 & @ #A
¼
1 ( / 1 / / *
1
& /3
K
K
!@ ¼
¼ A
+?
@ #A
¼
1
/ /
3 / &% & 1 ( ? ¼ / 1 36 2 1 1
@ A 1 ! & / 1 /
3 1
¼ 3
& 1 & /
& @A / 1 / / 1 1
/ ( 6 &% ?
7 1
K 0
¼
,% @ -A 1
K
K
!@ ¼
¾
¼
L
!
!
¼
¾
!¾
'
1 & 1 &
1 %/ 1
/
¼
¼
A ¼
1
% L
@ -A
? 1
?
K
?
&
¼
/
/ / 1 (
/ /3 $ / @ +AC
¼ ¼ 1 /
K
K
¼ K !
K
/1 & 1 *
¼ ¼ L 3 & K ? /
¼
¼
K L
&
K
1? 1 * /
!
!
L
'
L
'
@ +A
%$
K
!
K
!
L
L
¼
?
1 &
1
¼
1
/C
L /
!
'
'
¼
K
¼ 1 L 3 & K
@ A? 1 &
!
L
!
@ A
/ /C
%$K
K
/1
¼
¼
¼ ¼
K
!
/
K
@ A
1 & 1 ?
!?
1 &%
& ? / 1 / / &% 1 1 1 1 1 ( /
/1
?
1 ( * & / / ( 1 / * % ? (
K
!@
¼ L ¼A
! $ &
1 &
! & C
@ 1
&
/
A K
(
! & & /
& @
A
@
A
K
@ @
A
@'0A
A
1 ( = / ?
¼A
K
K
1 1
? 1 (
¼ ¼
! ¼ & ! ¼ ! ! !
¼ & ¼ !
¼ ¼ ¼ ! @
L
A
@
L
A
@
L A
@
L A
! & C
@'A
1 1 = & 1 ( & /
& 6 =
¼ 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 &
¼
¾ ¼
½ ¼
¼
¾ ½
K
K
L
!
!
/ = 1
1 1 &
*
3C
1 1 (
!
¾
!¾
'
¾
!¾
'
&
& @ -A?
/
1
@'A
,% @'A 1 1 / * &% 1 1
# 3 1 @
! & & 1 ( & &
A K
0¾ 0½
K
¾
0 0@ @
L A@
¾
L - #A
L 0 '
L A
K
@
& 1 & * &
"
A
C
@' A
& # 1
/ = & 1 * & ? / 1 & ?
@ A?
¼
¼ ¿
1 0
1 * 1 3/* /
¼
¼¿
0
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0 −0.3
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L1
L2
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CA 1/(CA) zBP
z BP
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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
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//
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/ &%
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
@
@
¾
¾
L
L 'A
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 * & & ?
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L + #
L'
L
% / & 1 (
& / / 1 3!)= / &% & !)= $ & 1 / &% ? @ A 71
/
1 /
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& -0 /* 1 &% & 1 I
% ?
/
?
$ & 1 &3
1 / 1 -03/* / & 1
& @ A 1 &
1
! & & 1 /
K / &
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?
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+ $1
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¼
!
1 !
1 /
- (
&
%
0 0
1
L 0
M 71
M?
% 1
1 1
!
/
1 ( 3 @ K
$ ¼ @
1 & ? / 1
A / 3 @ A / / LA ,6 1 1 $ 8
¼
1 1 1 (
B / 1 & ? / / 1 / /
/1
1
¼
/ 1
¼ ?
+
/
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? / 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
3.5
4
ω (rad/sec) + ( &
& ?
?
% / 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
¼
@ ¼¾
L A?
! & ?
@
A? 1 3/* /3
K # > 1 / & 3
@
A / &
1 / = & 1 ? / 1 &
71
/? /
1
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1
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A K
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0 -@
¿
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¾ ¾
L '
L - #A L
/ 8 /J / =
K ' /J 1
& / / /
##
1 / 1
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1 1 1 /
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1
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0 !)= @A 71 & & @ A
% /I
1 &%
1 / / 1 =
I & 1
! & & 0 1 1
1 ( ) &% & 1
@
¼
A & ? / ! 1
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1
¼
¼
3
! 1
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? 1 1 @ A 1
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#-
1 & 1 1
½
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/
1 ? &% 3/ / &
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/
?
1 1
@
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/ &% 3/ /
& ? 1 / &%
1 /3
1 &% 1 ? /
/%
1 & )
1 3 . /
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/ B ? / / 1 1 /
1
/ & 1 = & 1 / 1
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/ 1
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5& PO℄ / 1 / & 1 1
P-℄ / /
//
1
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/ 6 : R 5 / 1 /
/ 1 % & 5
8 A
1 / 8 ? 1 1
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/ 1
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/1 / 1 6 1
/ @ / & A
/
1
1 1 1 13
1 &
1 1 1
1 / & / / &
/3 & 1 & 1 1 1
/ / / & 1
1
/
1 / /
½ ' ( ) # #+
#
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
+¼
1 1
+
1 ("'# 1
/ & 1
?
1 !
13 .
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/ 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
Slope=150,000
Input Offset
0
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
/
8 /
/
/B
1 1 ? , ? / ? 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
-K .& 1 / /
0
& 0 +
#0
@-00A
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 ?
+¼
,¼ ?
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
//
¾
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
1
)
?
/
A /
/
/ 1
? 1 #
1 #@ A
0 K
1 1 6 1
+¼
@ A
& 1 /
1
/
@1& ?
1 1 /
1 & #@A 1 1
1
? / 3 / 1 / /
#@A
1 / & 1 /
# / / ' 1 &
1 & 1
&/ ! ? 1
1 &
/
I
1 / / /
@
/ / 1 1
/ 1
1
1
! ( 1
/ =
= ?
/ C
+¼ !+ K
1 ! &
/ = A & ?
1 ! & 1 & /
/ &1 )
% ?
1 1 .
@ 1 /
1 1
$ & @ & A?
+¼
/
!
A / 3 @
+
6 /
-? /
? / 1 & 1 1
3
A 1 & 1 / / @=
¾ ! * % ! 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
-
& / /
+¼
- / & R( 1
+¼
1 A 1
¾ ¾ ,¾
1 1
+¼
1
K
1 1 1
/ @ 'AC
L0
@ 'A
L0
@ #A
R( / 1 / @ #AC
+ ½ ,½ K
R( 1
/ @ -AC
,½ ,¾ L
$ / @ +AC
+¼ +
K
K 0
¾ ½
@ -A
@ +A
-
R2 R1
(-) vi R i +
+ vg -
+ v0 -
+ Av - i
(+) + / ! 6 3
1
1
"
/ / &
3 / /
& 1
3&% ? 3 /
/ 1 / & 1 / & 1
1 1
+
/ = 1 & -
1 6 / 1 / &
+¼ 0
K K
!+ +
@
'
R(? / A L
R( 1 / @
* 1
/
!
1
C
¾ + !+ + @
A L
½ + + @
A
A & / /
@ AC
+¼ +¼ + . & @ A 1
K
K
P
!½ + ½ ¾ ½ ¾ ¾ ½ ! ½ !
!¾
L@
L P L
1
1
L
@
L
L
@ A
A℄
/
A℄
L
½ ¾
? 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 / 1 ?
?
/ &
8 @ A = & =
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
1 // /
/ ( 13 /
& 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
+¼
? 1 ?
! @ / A?
1/
= & = 1 /
1
+¼
1 1
?
+ ?
?
= 1? 1 & 1
1 1 &/ !
1 1 1
+¼
!
1/
1
+
1 & / @ A? &/ 1 /3 ? 1
½ / ¾ 1 ? / ¿ ! ! 1 = / 0# $ "1 1 ? 1 ? !? 1 1 1 & L ½ ¾ ? 1 /3 1 1 / ? ½ ¾ ? 1 ! 2 1 / & ? 1 /
1 1 1
/ ?
? /
1
& 1
½
¾
6
?
/ ? 1
1 /3 & & &% / / 1 / ?
½ ¾
½
@
) ? 1
K ?
@ 1
¾
½ ¾
K
+ 1 / /
A? / 8 @
½
K
¾
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
½ A@
! L
@ A
¾ A@ L ¿ A
. @ A? 1 & 1 1 &% / / & 1 & ? 1
1 3 ? / ? ?
!? ?
1 1 1 /3
/ &% / / ?
/ 1 =
/ @
1 / 1 &
1
1
!
L
@ A? / 1
1 A?
1
/ 1 &
# '* + * ,
/ 1
1 1 3
6 /
3 & @ 0AC
! )?
!@
A
!
!
@ A K
! L
@ 0A
½
1 & 1 & & ? /
!
/ &
+ +
@ A?
K
½ ¾
L
¼
L
1
½ ¾ ¼ ½
K 0? @ A
L
A
1
1 /3 ?
¼ ½
K
1
!
? 1 / 1 1 3 ?
1 1 1
!
,%3
& * / &
1 3 & ?
1 1
3
1 /3
1 /
/ &
1 & 1 3 / /3 & & 1 3
1
6 ? 1
@ 0A / @ A /
@ A
½ ¾
. @ A? 1 6 & 1 1 1 @ L
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
(A0)dB
-+
Open Loop
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
&
3 / /3
? & 1
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
½ A@
L
1 & 1 & & ? /
$
+ +
!@
A &
!
@ A?
K L
½ ¾ ¼
@ L
½ A@
@ A
¾ A
1
L
¾ 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 G1R2=30
20
G1R2=3
0 2
ω0 4
10
ω1
ω0
6
10
ω1 8
10
10
Frequency (rad/sec) 0 ,6 &
K L
1
K L
/
1 6
½ ¾ L ¾¼
¼
K
3 3
¾
L
¾¼
! @ L
L
¾¼
L
A
/ 1 1 1 @ L
/ 1 1 1 /3 & ? 1 1 ? 1
K
& @ A
?
! ?
K
A !
/ &
? 1 /
0 &
/ 8 & 3 / &
&
& 1 3 &
1 1
& 1 1 3
? 1 / 8
A !
/ / & 1 /
& & 1 1 /3
/ & 1 /
1 @ L
,% @ A / @ A /
* / &
@ A
¾
¾¼
1 ? / 1 /3
1 3 /
/1
? 1 /
/ / 1 3
1 & 1 3
/ /3 & . 1 ? 1 3 3 / 1
/1
! A
K @
? 3 /
3 &% @
& 1
1
/ ? /
/1 & & &
C
. 1 6 ?
K 0
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
" 6 / A $ 1 3
/ 1 13
"
K
?
'0 /*J/
! & 0
0 /*J/ / 1
1 1 / ! &%
"?
6 1 1
1/
1/
1 1 ? 1 !/ 1
1 ?
1 3 3 /
. 1 1
/ 1 /3 1
1 1
& &
'0 /*J/ ?
1 /
6 ? 1 / 8
1 /3 @
/1 @
/
1 /
K
! A
71
1 1 3 ! ! 3
& &% 1
/3
1
3 /
1/ &
/1
1 /
/ & /3
% 4 ? / 1 3 1 & 3 1 @ 3
0 /*J/ A
/ / 71 1 1 1
1 / & / & & ?
1
? / 1 1 1 /
/1
/
/ 1 / 1 / / / & B & &/ ! .& / / / ?
1 1 / & //
? / 5
/ 1 & / / 6 ? 1
K
/ /
1
/
¼
!
3 3
1 1 5 & ? @
L
A @
L
1
¼ A?
" & /
1
/ / & 1 / 1 1 / *&
/ 1 /
/ 1 /3
1 13 6 ?
/ & 1 %/ & & @ A
$ & 1 = 3&% & 1 / & @ A / 1 /3 ?
?
@ 'AC
1 1
K
@
L
A
&
!
L
1 1 1 1 /3
1 ?
@ 'A
!/?
? / 1 &31& & 1 63&%
& & 1 13 6 //
! ?
/
1 &
1
/
/ &
+0
Magnitude (dB)
100
(A0)dB
Open Loop
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
/3 & 13
1 / 1
/ & 1 6 ?
1 1 /3 1 ! @ 6 A 1 13&% 1 3 /
/1
1
1 & 1
1 3 / 3 /
/3 . 1 ? 1 3 @. 1 / 1IA ? /1 1 K @ A
!
K 0 ? 1 1 / 1 3 /
1
3 6
/1? / ? 1 ! !
0 1 /3 & 1
/ 1 /
3 6 ? 6 1 1 &
1 /3 1 1 1&3 & 1 1
0 @# /*A
& /3 % 1
0 @& 1 A 1 1 * / / 1 &
.
/ 1 / & / &
(
#
K
1 /3 & ? @ A? / @ #A &
+ +
K
K
1
"@
A
K
11
/ 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 ?
! @ L # A?
131&3 1 ? ?
#
1
& 1 /3
1
1 1 / !
1 1 % " & @ #A & / ) /
? ? 1 B 1
1 = (
1 &
K
& 1 1 ?
36
/
% C 0
K
@
A L @ L L
L
A@ A
L@
P L ! @ L # A℄
L
L A@ A
/
@ -A
,% @ -A? 6 1 ? 1 @ ?
"@ A
1
% = A
1?
1
36 & 1 /3 &
/ @ +A & & @ #AC
& 1
K
! L#
L
K
K
0 #
K @
#
0
'
- A0
@ +A
K @
"@
1 1
!
+ - L
1
#
K
1
/
& /3 &
/
/
K 0
K
1 & 1&3 ?
71
/
#- A0
?
1 & P &
A? @ #A? / 1
#
K /*? @ #A
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
@
"@
1
! & A℄ & &
. 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 / / @$A
/ & / 1 =
/ 1 ? 1
@A? 1
' (
1 ?
/ 1
+ ,?
= 1
1 / @/
℄ . // ? 1 ?
/ / / 1
+¼ ?
A
1 1 / & / ?
1
& 1 @ A
1
1
?
1 8 1 & & ?
1 &
+ ?
! / P ?
+¼ +
1
/ / & 1 /
1 /
@$A / / & &
?
1 % =
/ / 1 1 1 $ 1
. 1 ? 1
/
1 1
+
R2
R2
R1 i=0 + vx -
+ vg -
R1
i=0
i=0 + Bix v0 -
+ v=0 -
+ vg -
+ Avx v 0 -
+
ix
(a)
(b)
/ ! / / /C @A $? / @ A $
?
, ?
/ 1
/
?
1 =
+, ?
= $ ? 1 /
1
& 1 & & & 1
1
$ 1&
)
?
! / ! / 83
/ / 1 &
& @ A / @ A & 1 & @? A? @AC
+¼ +
K
@ AC
+¼ +
/ / ? @ A
½ ¾ ½ ¾ A !
@ A
½ ¾
$
@ A
L @ L
K
L
1 @ A
& & @ A 1 &
!
/
$?
1
K 0? / @ A
&
!
/
& ? 1 1 @ A? 1 /
. 1
$
@ A / /
/? 1 1 &/ !
1 1 1 1I 71
% /
1 / / 3
/ 1 1 & 1 &% ? 71
½ ¾ ?
1 / 1 &/ ! ?
1 &/ ! *? 1
1
/ 8 1T 1
1
½ ¾ ?
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 / / / /
+¼ +
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
@ 0A
$
L
1 1
& 1 /3 & &
1 8 1 &%
)
? 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 A℄
C $
L
1 6
/3 ?
$
K 0
L
0 @ L 0 A@ L 0 A 0
0 L 0
/ 0
#
? P@ L 0 A@ L
# & / 8
K 00 !M? /
&
K
@ A
" / &
/ & / 8 &
1 % / 8 & 1 1
0 / & 1 / /3
. 1 6 1 1&3 3 / & 1
K
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
50
−40 dB/dec
G1R2=102
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'℄?
/ 1
1 ' & P℄
$! 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
@
L
1
/
&
0 0
1 /* /
K &
/
1 /* )
00A / 1 / / @ A K @ A .@ A? /
/ 1 / & ?
&
I
& 1 1 = ? 1 K 0
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
A℄
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
I
2
2
+
N
V1
V2
-
Vg
-
+
0 & '
1 & 1 >
! & ?
) 3 &
0 0 ?
K
) )
# 1
1 /? 1
/ ?
@
0 ?
&
@A 71 1 / = & @ A 1 &
@
A
@
3 ? / / 1
) 3 D
0 0
36
P
@
A℄
0I
= & 1
>
! K ! @ L A? / / 1 ! ? /
AI 0 /
!
1 1
@0AI
@ A 71 & ? ? 1 1
?
1
71 / / ?
&
1
/
+@A?
A K
1
I
!
/ 1
) )
71 1
1
?
/
% / &
/ /
?
K
0
R
1
I
-
+ V -
+
R
2
R
4
R3
& #
)
P℄ R ? * ?
! ?
-1 /? > $// 5 ? :C
)? P℄ "1
!? . ?
"# ! $ % & ?
> $// 5 ? :C
)? P ℄ " ? : ?
' ! ' ( # ! () *?
* ?
"C ) 1 " W ? P'℄ 5 ? : R?
+ ,-"# ?
S !C 7 3
? +# P#℄ 5 / ? " $?
$ ?
& ''. (
. !
5/ ? "C // 37?
P-℄ ? 4 ,? 4 ? : 4? / ) ? ( ?
* ?
S !C " 4
P+℄ = ? ? ( / ? :? / ) 1? 4?
& #?
+ ,-
3) ? +
'
.,,, $ ? ( / ? , /C
* "#
(/? 0 P℄ 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
! ! / '
½
& / !
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 ' &
½ ,-℄
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
Q2
+ I
+ I
V
E1
E
-
B2
I
E2
B-
I
V
E
B-
-
-
(-V)
(-V)
E
(b)
(a)
' * 3 C @A ? / @ A ,
/ & / & 1 B
A 7 1 1 ' @A / 1 3 3 ?
* ?
/ 1 & / 1
/ ? 1 &
?
" C
/
K
/ /
K
/#
K
/ ½ $ ¼ /
/#
R( 1 /
/"
K
/
K
"
K
0% & 00? /
1
/ 6 & 1
/
K
0% /
K
K
/
¾ $ ½ $ ¼ ¾
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% /
'
/¼
/
K
"
K
? &
0 0N
1
/ 0% L
K
0% @0% L A L / K / 0% / L 0% L 0% L 0% @0% L A 0¾ 0% @0% L A L %
/ ½ L /¼ /" /
0%
K
K
& 00? 1 , /
@' A
1
%
/ & 1 & ?
/ ?
/
B 1 & 1 // 6 ? &
/"
K & 1 ,
' @ A
" / 1 / / /
7 1
/ *
K
/" ? 1
K
1 ?
1
/ 6 'C
/ /
0 *@0
¿ A K 0- 0
1 / 1 / & 1 3 &
/ 1 C
P
/ / ℄ K 0 *@0- 0 A K P+- ℄ /# ¿ ?
& R( 6
" C
/# ¿ *¼ P/ ¿ / ¿ ℄
1 1
1 &
/ K ## /#¿ A K 0'- 1 1 / ¼ 0 *@* A K P0 ++ #℄
K
K
0 *@
K
& R( /
/ C / K / ¿ L /
$ ? ? 1
K
/" / K 0- / *# ½ K *¼ L *
1 1 , / 6 & D
"
K 000
K 1 1
? 1
1 % / 8 / / 1
0% ½
K
0% ¿
K
/ 0% ¾ K ½ K ++ /½ / ¿ K 00 / ¿
" &
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
¾
& 1 &
. /
? /
& &
2 1 & 1 / /
,1 6
* ½
''? 1 &
K K K
/ /
?
* ½ C
/#½ K / L /" ? /# ½ ? * ½ K
1 /
6 1 1 ?
/"
K 0
1
/# ¾
@''A
/" ? 1 @'#A
1 / % / 3
/# ½ A
0 *@
7 1 % / 1 / /? &
/ 1
R( / @'#AC
1 % / &
1
0 *@
K
/ ?
/" C
/ ¾ AD 1 0 *@* ¾ A / ¾ L / ¾ / R( % *¾ L /#¾ @* ½ *¾ A /#¾
K
!
.& 1 & ?
/"
K
1
/ &
/ 1 & % / @ /A ?
/ ¾ * ¾ P/ ¾ / ¾ ℄ /#¾ * ½
1
1 & 1 %
@'-A
/ /
/ 1 1 & 1 / / 3
? / & & / K ? @''A / K #-# !M / % # "M 1 # 1 0
¾ ' /
-
&
! 1 % 1 &
1 1 / & &
3 1
/&
/ &
K '0
%
'? / 1 1 &
*
K # C
3 1
1/
/ D
1
7 / /
*#
K K K K K K K K K K
/ L
K K
/
"#
1
&
" / " 1 1 ?
/ L / L / @# *# A /
L
1 &
K K K K K K K K K
/C
/ 1 & 1
/ ? /
K
/
/" A K 0- '+ 0-*@*# A K P# #00℄ *# / 0-*@/& A K 0#''+ 0-*@*# A K P0+ 00℄ / L / K 0+ @*# *# A /# K '' - !M / L / L / L / K #0 @# *# A / K !M
/
/ * P/ / ℄ / / * / * P/ / ℄ /#
D /& K 0 D /
0-*@
1 / & 1 ! &
"'
K #00
/ / & 1 !? 1 /3
/ / L
/
*# P/ / ℄ *# / *# P/ / ℄ /# / L
/" K /"
1 ? 1 1&?
/ 7 1 / 1 R( /
/ 1 %
1 /
/"
/
/
C
1 / 1
0 *@/ A K 0-0 0 *@* A K P+ + #000℄ / / * /& K '0 0 *@/ A K 0#0+ 0 *@* A K P'+ '000℄ / L / K ''+ K #00
"-
1 6 1
* * A /# K -'# !M / L / L / L / K ## @# * A / K +0 !M
K
/
+
@
K K
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 / 8 & 1 & / 1 / 8 ?
/
/ 1
+ +
?
1
1
. 8 ?
1 / $ 1 1 & / ? ?
,
+
/
/
7
+
? /
/
1
1 1 / /
1 / /
1 & 1 / &
1 ?
/ & / 1 1
/ 1 1
1 R( 1 1
C
/ K , L ,
* 1
+ +
?
1 1
/ / 1 1
,
L
,
@'+A
1 & 1 13 ? 1 / 8
=
1 &
1& ? &
?
/
? 1 % / / / /
,
K
1 &
¾
¾ '½ ½ '½ ¼
C
(+V) 2N3906B Q3
Q4
α Mic1 -ic2)
i0=( ic2
ic1
ib2
ib1 Q1 ie1
v
2N3903B
Q2
ie2
v
g1
g2
I
(-V)
'# 1 / 8 @$A
, , ,
$ 1 &
+
K
*
L
1 &
+
¾ '¾ ½ '¾ ¼
K
¾ ¾ ¾ '½ '¾ ½ '½ '¾
¾ '½ '¾ '½ '¾ ½ '½ '¾
@'A
/ 1 / / % ?
/
,
K
/
,
+
&
K
*
+
?
/
,
, ,
L
K
/ L ,
1?
1 & 1 / & 1 C
/
¾
K
¾ $ ½ $ ¼
+ L +
K
+
K
K
¾ $ ' ½ '
K
¾ $ ½
+
, ,
# #
¾
K
* L 0
+
& 1
+ +%
+
K @
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 @&
,¼
1 1 &
1,¼ 1+
C
¾' /#½¾ @#½¾ A
K
1 1 & 1 ? 1
+ ? / &
1 1 / ?
!A
,¼ ?
@
@" L A ¾' ¾ #½¾ L A
&
?
@'A
+ ? 1 + K 0C
/ &
& 6 & @'A /
,¼ K
"
@
A
/ L / @#½¾ A
"
@
L A
'
+ L
@' A
#½¾ A K @ ¾ * L ½ A / " K 0 @0 L A 1 0 *? 1 , K / K #00 ? * K 0 *@, A K 0-0 ? @#½¾ A K #0#+? / 1,¼ 1+ @0A K ' J 1 & 1 ! 1 & 1 / 8 1 3 ¼
1 @
'-
¿
¼
$ & 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
+
?
/
, /
+%
+
K @
1 / 8 /
+ #0 1
1
11 1
1?
6 & @'A /
6
?
1 / 1
1 1
1I
+% K + K 0C
1& /
,% @''A 1
" #' @" L A " ' #' L @# L A @" A @" L A +% L @# A+% L @0A
K
K
'
" L A
@
@
#
A
+% T
T
L
@''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
,
@'#AC
@'#A
# K
¾ $¼ ½ / / 1 & + K * # 1 & ? # ? / / & 1 / 8
1 1
K
+ L * ¾
¾'½ ½ '½ ¼ ¾ ¾
¾$¼ ½ $¼ ¼
¾ $¼ ' ' ½ ' / # ' & + * / / , / / # '
/ /
(+V ) I i0=I-ic ic
i
b + v
2N3903B
1
-
Vg
V0
'+
1
1 6 //
C
, K @/
+ L @# A
' / A / @# A#
6 & & ? & @'-A?
1
? 1 / 1 1
+
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
& & )
/ /
% /
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
/
K
@
" A
/
1
" A /
@
K
0
@
¼
L A
/
@'+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
/
1 1 & 1 & 1 / /
/Æ
1 8 & 1
? @
*¼ ?/¼ A? /
1 &
/¼
1 1
1
1 1 / / ? 1 1
@'A
3 C
/Æ /Æ 1 1
K K
/ /¼ /
1 @'A
1 1 / 8
1 1 / / * 1 / 8 / 8
& / 1
1 1 & 1 1 / ? 1?
/
& ?
0
. /
¼
1 ? 1 8 1 / & & 1 / 8 3
1 / &
/ 1
& 1
? 1 / 8
& 1 3
.& 1 1 1 / &?
1 8
// ? 1 / 8 1 1
/ ?
1 / 8
1 ? / / 3&
1 1 / 8
0 ¼
.
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#℄ 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
, A K 0-0'
0 *@
'
P
, , ℄
K K
@
4
K
@
K
+
K
#
5(
(
)
+ A K P+-
0 *@
, A K -+#
+ L A,
' ++℄
!M
K + "1
# C +
P
, , ℄ 5(
4
(
)
1 1
0-*@
K
0-*@
K
@
K
@
K
- +'
K
0-
, A
+
+
K
+ A K P# +
'' 0℄
K # - !M
L
A,
K - - "1
1&
/ 1 / ?
/ /
R( / 0
, A K 0- ''
K
)(
1 (
K
4(
+ ? 1 ( D 1 ?
L
/ @'AC
)( @+
+ 4
+
A
+
K @
+
,
1 &
@
+ 4 A
+
@
+ A
L
/
,
K
4
@
K
@
K
4
K
@
+
A L
)( @+
+
A @'A
@'0A 1 1 1 & R(
1 /C
, , 1 ? / 1 & ? @
6"
,
, ?
1
+
) + +
) +
4
A
@
4
) + + 4 + ) + + 4 +
A A
A
@'0A
1 / R( 1
@'A?
1 1
6 / 1
AC
6" , ) + + 6"
K
" , ,
K
@
4
, , A
@
A@
A
4
P@
1 8 & 1 / 1
) + 4 + A
℄
1
@'A
6"
0?
1 3 1 / / 1 / 8 & 1
1
1 /
/ /
@'A
/ & 1
1 / 8
& ' C
1 /?
,
K L
+
K L
+ ?
6" ) +
/
@'AC @'A
) 1 =
#
/ 1 3 ?
6" ?
/
0
*2 & /3 1 ' C
1 /?
+ ¾
+ ½ ?
K
/
@' AC
,¼
K
@
@
6" A@4
4
) A+ ½
) A+ ½
)? 1 1 / ?
@' A
0 1
/ 1
& 1 / $ / / ?
5 ?
1 1 13&% & 1
4 & ' C 1 /?
+ ¾
K 0? /
,¼
1
K
P@
@
4
)
1 / 8
&
6" A@4
. 1 ? 1 / 8 /
@''AC @
) A+ ½
6" A )
A℄
+ ½ @''A
6 31& 1 / & 1
? &% 3/ / 8
1 1 & 1
&% 1 /
,% @'A 1 1 @''A / / / =/ & '0 1 1 /
¼ 0 ½
/ 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 ½¾ @ A K 0
1 1 / 8 /
4)=
/ / & 1
& & .
& 1 / 8 1 & 1 3
1 3 /
& '+
/ 1 &
4 5( ?
,¼ .
/ & 1?
6 ! R( / 1 ?
/
1
' & 1
1 1 1 / %
,¼ ?
@'#AC
4
K @
/
K #0
) A+ ½
@'#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 &
/ /
@' A
1 / 8
/ /
1
/ 1 1 1
1 / 1 1 /
1
?
/ /
1 / &
'
¿
0
K ' +'
&%
/ 1 &
1
/1 1
4 )
/J
.
/1 & / 1
/1 & 1
#' /
1 1
& /? &/ ? ?
4
/ )
L0 /*J/ &% 1
/
1
" / / /
/ / 1 /
1
/ /
&%
3&% & 1 / 1 1
1 8
/ 1 &
/ 1 & /
+ + /* & 1
.
' / 8 / ? /
+% ?
/ 1
@ '#A 1 @'-A
?
+
/ 8
& 1 (
+ ½
/
+ ¾
2
/ C
+%
K
+
K
+ ½ + ¾ + ½ L + ¾
@'-A
Normalized Magnitude (dB)
50 |I0*103|
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 / ?
+ ½
K
+ ¾
K
+ ?
+%
L
+%
+ L
+
@'A & /
@'+A
1 & 1 &
' % 1
/ & 1 1 / 8
1?
1
/
/
? / 1 & 1 1
//
& 1 & '0
+ ¾
K L
+ ½ C
$
@'-A / 1 &
+% + 2
/
+ ¾
K
+ ½ C
$
K
0
K
+ ½
C
1 & 1
@'-A / 1 &
+% +
+ ½
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
/
R(
'' //
///? 1 &
/ ?
/ /
0 1
1 1 /
+
+
/
+
/ / 1
+
"
+ ?
8 & /
/ / /
/ &
1 / / / 1
1 ? R(
@
"?
@'A
+
/
/ @'AC
L
,
K
0
K
) A+
K K
" + " + 4 , ) + L
@
4
+ L ) @+ + A
) 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& & @'0A 1 ?
, "
1 1 % &
/ 1 & 1
& 1 / 1 R( & 1 ?
@'A
+ v2 -
rπ
,
1
1
, ?
+ 0 /
1 / /
& / R( 1 /?
/C
,
K
" , ,
K
"
"
@
4 ) A+ 4 + " L )
P@4 )
A
+ 4 + ℄
1 / 1 & ?
@'A
, @
/ / / 1 1 /
A? & & 1
/
1 1 / 8
1 1
/
+
1
& ' ? K
+
/ /
$ 1
@'A / @' 0AC
, *"
, '¾ '½
K
K
L
,% @' 0A / 1
A /
"
1
"
" " )
@
L
)
4
/
&
1 &% 3/ / 1
! 6 @ ' A?
&
A
+
@' 0A
"
@ 1
1 !
/ &
? 1 1 &
1 1
"
/
"
1 & / .
1 / / 1 1 / & C
"
K
4(¼ L 4 ¼
(¼
L @
L
)¼ A
0
"
4 ¼ )¼ A
K
@
. & 1 1 1
&
&% ? /
"
@' A
1 1
?
/
3
? 1 &%
3
$ ? 1 / / 1
" ? 1 0 ¼ @0 ¼ L A?
?
?
& &%
"
8 /
1
D
&%
1 1
/
K
L
K
4(¼ L 4 ¼ L
4¼
(¼
4(¼ L 4 ¼
L @
L
)¼ A
L
(¼ L 0#) A ¼ ¼ L @( L ) L ) A
1
'
L@
@' 0A / @' AC
@
)
@
)
4
)
4
A
+
A
+
@' A
@' A 1 &% 3/ / 8 & 1 ?
/ 1 & 1 % /
4 ¼ )¼
4(¼
1 !/
$ ?
1 1 & @' 0A 1
/ $ & @' A
, *"
.
)¼ @(¼ L )¼ A
& 1 1 &% .
1 1 / 1
1
& / & 1 ? /
1 1 / P @' A℄
' $ & & 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
+ +
L
& 1 ?
, ?
K
0
*
,
?
1 3
% /? / ? 1 @' 'A 1
& 0
%
+
K
0
/ @ * L A
C
@' A
/ / / ?
"
A
1 & 1 / 8 ? /
& 1 / 8
% /
P @''A℄ 1 /
6 @' A
/ , @ * +% /
/ 1 1 / 8 /
"M
1 /
@00 /*AC
@' '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
/ !?
/¾
1 / ?
/ / &
1 3 ? 1 , ?
/ 1 "M
"
#
" 5¼
- .
? /
/ /
/% 3 3 & 1 & 1 ?
,¼
1 / 1 1 1 13
1 1 / 1 ?
/¾
? / /?
1 / 1 !3 3! & 1
/ &
? /
1 /
/ 1 1 & 1
1 /
? / /
/ ? / 1 ? 3 / =/ / /
/1 1 1
71 1
?
& 1 / ?
, ½ *¼
K
/ /
* * K
*¼
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 ¼ , K * , 0% 71 1 ? * K * K * ? / 1 & 1 / ? ,
K * "- 1 , K / L , 1 / % / & 1 ¼ / 8 1 , K * , 0 . ? & "-? %
1 1 ?
1
X
+
K
,
K
X
1
/
*
, ,
1
?
*
¼ 0%
0% / ¼
K
+
% X
K
@
¼ 0%
* L AX+%
@
@' #A
1
* L A K !
0%
1 /
/
/
1 @' -AC
+
X+%
.
? /
X
K
¼
X
, ?
@' -A
1 1 1 1
? / 8 1 . 1 1 &
1
@' #A 7 1
1
1
¼ 0%
0 !M
K 00?
/
K ? / / / ?
/ % /
3
@' -A 1
!
"-
K 0 ? @' -A
, ? 1 / / ¼ 0% $ 0 ¼ ? 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 % /
71 1 = ?
= ? / ? 1
1 ? R( 1
/ 8
10
3
& / &
, ' 1 *
+ 10 -
Q5
% 1
"- / @' +AC
,+ + K * / 0% * * ¼
K K
@' +A
8 % / 8 &
1 1 1 8? @
" A/ ? / 1 / 8
/ 1
@' +A 1 % /
8
1 @' AC
,+ +
@+% A+ + 1 8 1 &
K
/
" A
@
' @
#
L
A
/
@
" L A '
#
@
* / 0% / @" L A ¼
/
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#
/ 1 ?
, + P, , ℄ 0, "#
* 1 ?
K K
K #00
"-?
1
, A+ +
0
K
$ & 1 8 &
3 K
+
?
@' A / & 1
/ 83
C
@
?
+ K 0C
+ K + 0- ? / 1 * , K ''
K
@
+
/ ? 1 3
/ 1 / 1 / 1 8
*
1
71 1 /
0-*@
% / 1 = ?
/
/
, A K 0- '+ 0-*@+ A K P# #000℄ , , K '#0
K
/
/
K
1
/
= ? 1 ?
+% A+ + K 0--#
1 / 8 / ?
1
1 1 ?
'+ &
1 / 8 /?
+ A+ + K 0#@+% A+ + K 0#
@
1 / 8 1 / / / ? & 1
/ / 0 # ? 1 1 1 1 1 6 & =
1
/ 1 & 1 &
% ? 1 / = . & / 8 / & Æ
& '+?
1 1
JR
Æ
/
/ 1 / 8
/ % @
/
3&% / 8 3 &
& / ? / 1 1 1&3
/
, ?
/1 & 1
3
' & 1 .& 1 /
1 A )
1 1
/1 0 !)= & 1 ? 5 1 1
0 /
1 1 8 1 & 1 ?
1 / 1 / 7
/ & 1 / 1 / /
1 1 8
1 8 / 1
/ / / ")= 00 ")=
/
0' /* + /* / 8
& 1 / & @' -A & 1
1
//? 1
6 0
+
1 1
/? 1
'
? 1 ' 1
1 6 % ! 1 3 / 1
1
& 1 8 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
/¾ ?
/ & // 1 1
/ / ? 1 / & &
"#?
1
R( %
R( 1 / @' AC
0
+ L 4 ¼ + L )¼ @+
K
4 ) +
) @
+
K
@
& R( 1
)(¼
,¼
+
,¼
K
4(¼
K
@
L
L
¼
) ( ¼
¼
/
@' A
/ @''0AC
)(¼ A+
L
+
) 4
)¼ @+
4 )
¾
L@
¼
¼
A
¼
(
L@
¼
L
71 / 1 /
A
A
@ K
+
A
¼
(¼
L
¼
/ ¼
A
) A A ¼
L
@''0A?
@4(¼
/ / / 1 1
4¼ (¼
4 ¾ ¼
( ¼
1 1 1 &
¾
½
(¼
@
L
)¼ A
( )¼ ¼
L
A
@''0A
& / 1 1
@''AC
/
@4(¼ L A (¼ )¼
'
@''A
6 & C
4¼ ½ (¼ @4(¼ L A )¼ 4 ¼
K
5(¼ )¼ 0 ¼
L
@''A
0
1 /3 / / 1 &
/
& 1 C
5( ( ½ ¾
K
¼
K
¼
1
K
K 0 "1 #- !M 4 K -- "1 / 0 -+' / ) K 0- + ! J # !)= '# 4 J +# ")=
"1
/
¼
¼
¼
K
1 1
1
3
' 1 / @''A & / 1 @ /
) ? ¼
1 1 ?
0? ¼
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 00 !M
/
0
¼
K 00?
C
K @ L 5( A 0 0 K '00 ¼
1 &
¼
1
. & ?
1 6 ? 1 1 1 /// @ 3 3
/// 1
) // 1 B ? 1 ¼
"-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
* / * / A
,
K
/
A %
"
7?
*
L
+ /
* /
1 1 / =
7
,
/ ,
K
?
*
/
A
?
"
+ /
1 1 /
/
/ 1 @% K
/
+ /
/ @
"
/
K
71 1
7D ? & 1 / / ? 1
%
?
6
? /
,
1 1
1 ? 1 1
/
1 Æ & 1 /?
*
? /
7 ?
1
*
K K
/
K
*
@ &
"
+
/A
/? / 1
* * K
? / ?
0
+V0 βDCi b
ib
Rp B
E
V b0
vS
i0
RL
+ vL -
-V0 ' / & 1
/3
6 /3
*¼ /¿ ¾ *¼
.&
/
K
& C
*¼ / ¿ *¼ / ¿
K
& 1 ?
1 0C 1 1
?
@'' A
/¿ ?
1 1 % / 6 / 1 8
/ 1
1
1 /
1 1
/3
/ 1
"+
1 ! 1
1
1 1
/ $ & 1 1
1 & ?
*¼ ?
&/
1 /
/1
& / & & 1
'
/ 3
1
/ 1
@1 1 A / / & &
/ 1
/¿
,+
1
1 ?
/ //
> & R( / 1 /
@'''AC
0% L A, ,
@
/¿ L + / @+ *¼ + A
K K
1 / 1 & 1
0% @
+
/
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@''#A
L A 1 / 1 & 1
+
K
,
K
,% @''#A 1 @ A? / ? 1
+ *¼ A /¿ L
@+ *¼ A L /¿ L
@
1
+
K 0? 1
@''#A
/ 8
)
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?
L
/¿
1 1
8
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& 1
?
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? & 1 ? 1 & , 1 1 8 @,
8 /
@
L
1
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1
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0
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1
3
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1 1 1 13
8 1 / 1
& 1 . / 1 1
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/ & B 2 / 1 & ? 1
1 /
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'
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1
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/ &
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1 1 3/* /
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1 & @1 1 1 ''3!M A
' . 1 & '' ? 1 3 /
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K
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&
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0A
K
, L ,
1 1 1 3
/
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> 8
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0
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0
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K 00 & 1 / 1 1 &
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vg
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'' & '' / '#
14.4 k
I
V
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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
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/
& 1 & 1 @1 / 1 #3 A @ A / 6 & 1 ? ?
3&%
1
+ ? / 1 ? + 1 1 / & 3 0 ? 4¼ ? ? / 1 3 1
* / 1
? / / &
4¼
1
> 1
/ &
00 /* & 1 @ A / 6 ? & 1 ? & 1
8
% / & = ? / & 1 % /
4¼ K 0
¿
1
"1
@/A & 1 & 1 % / $3 1 & 1 / / &
'0 1
''#
.
& 1
K #0 !M?
½
K
¾
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/ // 3 & 1
K -##
S B
(
/¼
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?
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1 6
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*
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3&% 1 &
*
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71 8 / 1 1 1 / & / / 8 & 1 I @ A >
@ $ ., &
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?
'
(+V)
I0
T1 +
v in
RL
T2
v
L
-
''# & '0
/ / / 1 /
@ A > 1 1 /3
1 1 ! & 1 & & / & 1 @/A / J/ J 1 1
// =/
1 1
3
1 / 1 3 / 8 3 1 6
)
P℄ = ? ? ( / ? :? / ) 1? 4?
& #?
'
.,,, $ ? ( / ? , /C
* "#
(/? 0
P℄ / !? 4 7?
"# 3 7 " ?
...? 5/ ? "C
// 37?
P ℄ 4? .?
& # 3 " ?
* ? 25C ! 6? . ?
+-
P'℄ 4? ,? ? F 1 , / " / & @ "A?G
!((
?
P#℄ $ ? * 4?
?
S !C 7 ? -'
! ! ( *8 ?
> $// 5 ? :C
)? 0
P-℄ *!? 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
'
* ? / / & @, A / @, A 0' + 0 1 / 1 '? 7 1
& 1 / ? 1 1 & 1
1
1 3 1 1 & 1
ic
2N3903B +
ib V1
V2
v
ce
+
-
v
be -
ie
' &
, A /? 1 &
> " / 3% 1 @
&3
& /C
" K P ℄ K @+ @, A A K P-#
℄
@'A
1
,
1
K K
' P+ + ℄
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 @, A /C
K P
℄ K @+ @, A A K P
+00 #0
0#--℄
@' A
1
,
1
1 & '
K
P+ + + ℄
K
@''A
/ 1
1 * 0' + 0 1
/
' '
K
@'#A & 1 0-* / 1
"
K
P
,
K
'
,
K
' '
" & ?
1 &
K
P
'-0#℄
'+-' -'+
''
/ +-℄ 1
/
"" ) *'% / " )!*'%?
@'#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 Loge(ib)
−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
+ + + + + + + +
," $" $($ ℄"" ) *-(
, " ) * "" "$ ," % $$# ( .%$ - -( /# % ,# 0 0 1 $ & $ 0 . "# %# 20 2 0 34 5 6 " $( $ "$$(
," $" $($ ℄"" ) *-( ()')! (. '
)
. '7)
' )
. '! ! ( ( (℄ ℄ $(6- (-( $ 6- -( + + + + + + +
," $" $($ ℄" )!*-(
, " )!* " "$ ," % $$# %$ .( - -( /# % ,# 0 0 1 $ &$ 0 . "# %# 20 2 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
,
K
½ ' ¼
K
/
K
¼
7 7 1 &
K
K
*1
K
¼ ½ '
/ ' 0$
K ''#+ /
@-#A00-
K -+
@'-A
& 1 0-* C
/ 7
K K
¼
K
*1
K
K + & /
@ A00-
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 / ! & 1 ? 0'
1&
1 &
/
/ / /
3 1 / / 1 &
+ 0
.
+
C
, # C @, A
K
½ +
+
K
@ @, A
L
¼
¼ ½ A
@'A
, #
C @, A
0
+
K K K
, # C
¾ + ¾
L
½ +
L
¾ +
L
½ +
L @ ¼
¾
½
¾½
. %
¼
@, AA
' ¾ @ ¼
@, AA
/
@ ¾ A
@'A
/3
, K , 1 / @'A +½ & , 1 ? ,½ K , K , L , 1 , 6? +¾ K +½ 00 ,¾ K , L , & +¾ 1 1 , D 1 ? ,¾ 1 ,½ ? 1 '- $ 1
& 1 /
?
1
'- / @'0AC
1
1 " & ? &
C
1¾ +½ 1¾ ,½ ,¾
1½ +¾
+
K
1½
K
@
A
@, A
1¾
K
@
A
@, A
$"- ) *'%
1½
/
$"- )!*'%?
@'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 &
&
* K * 2
/ 1 , 8
/
// //
1 B
* * 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
3
? ?
/
/ 1 & 1 / &
& 1 ? ?
/
'@A?
'
. 1 ? 1
1 '@ ? A 1
1 & 1
/ / ?
P '@ ? A℄ & & R 11 8 U
,+
?
* 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
+
g(vbe )
ideal
v
c
ic(v ce-2) VA
be
+
v
ce
i
e
-
i'
e
(a)
i
i
b
-
c
g(veb )
ideal
v
i'
c
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
R
)
b
+
+
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
*
X+ ½ ' ¼ X+
K
K
,
@'A
¾ ' ½ ' ¼ , @ + L AX+ K X+ X+ @ + L A, * , ¾
X
K
1
+ ,
X
&% AC
K
@'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
X
K
@
K
X
K
@
L AX+
A
/ ?
)
8 C
8
K
)
K
?
+ C 4
L
X
+
L
)
+
@X
+ X+
4
K
+
AX
)
?
K L
)
L
)
L A
@
L A
@
4
@''A
L
L @
)
@ A
K
8
@
8 8
/
4 @ L AA 8
4 @ L A
&
4
&
A
4
L
@'-A / / & 1 & 1
= / @ ?
A
1 ?
8
@'#A
@A // / & @'#A / 1 &
+ A
/ & &
X
X
4
4 @ L A 1 /
K
+
)
K
&% 6 ?
1 1 &
L AX+
0
+
@ 7 1 !
, X+
/ & 1
1 & ? ! R( X
@
/ ?
! & / 1 1 / @ /A
)
/
L @'-A
1
'
' & & 1 0 *
+ @A ( @!MA ) @ "1 A ( @A ) @A 0 ¼ @!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
,
K
$ @''A & X
?
,
P@
K
@
K
K
½
+ ?
(
(
½ ?
( ½ ? 1 1 /3 1
+
' 1
+
L
)
L
L
4(
) L
)
+
@X
)
)
)
L
+½
½ A K 9½ L +½
@
X
)
+ A
L
4
4
/
5(
&
X
L ¼
+
+
L
@'+A
1 ?
L ¼ L 4 A) ½ @) ½ L L ¼ A
@
&
@'A
( C
L ¼ L 4 A@ L ¼ A ¾ ¾ ¾ P@ L ¼ A L ) ½ ℄
@'A
& & 1 ?
& / / 1 1 & 3
K 0 / *¾ K - 1 1 0 ) / 0 1 1 / / + ? 1 / / , / , ? $ / 3
/
/ & 1
X
L ¼
3 & 1 0 * '@A
4
L ¼ 4 A) @) L L ¼ A
@
) ½
/
@
@'A / 1 &
K
X
( ½ L 4(
K
(
4( ℄X+
L
K
, +
X
, C
) ? (
@ A
/ 1
4( AX+
X
K
L
L
9½ L +½ ,%
4( X+
) L ( A
K
/ ?
? R( X
X
X
0-0
/
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 ¼ @!MA ¼
¼ ¼ ¼
¼
¼
0#0
0##
0-0
0-#
0+0
0+#
00
''-0
+'0
-#0
0
0#+
0 '
00'
0
0
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0
# 0
00
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0
+
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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 /
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1&
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/
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B / / / T
1 & 1 1
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6
7 / 1 1 1 13
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&
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#
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+
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I
0
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+
(a)
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Vx
+
Ri
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A(s)Vx
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##
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+
V0 =V 1
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-
-
# &
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+
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+
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K
V1
+
V 0=KV 1
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-
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1
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0
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0
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K
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@#+A
#
C
IC R
-
+
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0V - +
0A
V1
+ V0 -
#-
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V0
. 1 / ? 1 / @#AC
+¼ @ A . / ? 1
K
+ @0A
1
¼
¼
+½ @ ¼ A
@#A
1 /
//
K 0
.& 1 1 1 / 8 1 ? / 8 1 1 &/ !
1
1
?
& 1
?
1 1 1 & .
1
/ 1 / 1
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& %
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1
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L'
1+ 1
L 0'+ K #+ @ A
/ 1 ?
+ @ A?
@#A
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+ @ A & / @#A / AC (
+Z
#+
K
1+ 1
1¾ + 1 ¾
/ + [ K
1 1
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K #+ @ A
1¾ 1 ¾ ? 1
'
1+ 1
@1 1 1
0'+
E
1¾ + 1 ¾
@#0A /
1
% / 1
!
v
2
5
g
d v / dt
Σ
2
#
dv / dt
- I dt
v
- I dt
4
4
-26v
-26
#+ 2 & /3 / / &
1 / ! / / ?
1 E
# 1 1 P1 ? @#A℄
¾
0
/ / 1
1 / & 1 1
@ A
0
'
@ A
¾
0
@ A?
#
K
#
#
0
0'
@ A
@#A
@#A / 1 1
0 0 0 0 0 0
K
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L '@
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Y
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K
#
0 0 '
0'
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A 1
1 / /
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K
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? 1 ? @#A? 1 1 % 1 1
/
# 1 !/ 1 1
K ' L ' L # K ¾
1&
3/ % & @#0A
0 0
@ A K #
& 1
? ? Y
/ & #+ 1 53 & 3
A K
A? 1
0 0
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0
/
K
1
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#
¾
L'
@# A
L 0'
/
I 1
@#A
? / &1
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/ %
#
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1 % / / / / 7 1 ? 1
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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? &
C
A
@
A
@ A
K -
@
A
@#'A
/ -
1
!
K
0?
0
/ 1
K 00 @'0 /*A 1 1
? 1 / / / /
! 1
7 1 / ? 1 1 & 0 /
¼
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
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0
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0
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@ A
00
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@ A
00
/ / / / & @##A
? # / #? /
@
A? /
00 1 % = 1
,% @#A 1 &
00
1 / / / /
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
V2=−0.1sV(s)
−35 −40 −45 −50 0 10
1
2
10
10
ω (rad/sec) # 3 / & 1
1 6
0
K 0
? 1 6
# K 00
? 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 &
0¼ 0
K
¾
#@
¾
@#+A
% /C
L '00A
L'
@#+A
L 0'
1 & 1 1 1 6 // =
&½¾ K 0 ,% @#+A @ A? & 1 6
0¼ 0 1
#?
?
0¼ 0
K @
¾
¾
&
@
L '00A
0
00 /
C
A K 00
0
#
0
¾ L'
00
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K #? 1 ? RJY
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K 00 %
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$ ? 1 6 = & ? 1 /
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71 1 1 1 /
? 3 3 @$ 5A
& 1 1 ! 1 1
1 / & 1 E & 1 1 ? 1 / /
0¼ 0
K
#@
¾
¾
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L '00A
L'
L 0'
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¾
½
1?
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¾ 00 L ' A L'
½ 0 # #
@#A
L 0'A
Ü
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Ü
&
! 10/4 1/10
Vg
1/15
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-#
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 & /
¾
0
00 1
1 !/
"
!
#00
K
0
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 / / 1 !
#'
1
/*A 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
¾
0
@ A?
0
@ A?
%
@ A & 1 @ 1 / & 1
! 1
% A?
/ 3 1 = 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 @A 0
-
K
@
L 0A@
L
L ' L
L +A
L
-
K
@#A
L +0
L #'
% 3 ? 1 3 & ? /
@#A? / 1 =
1 & 1 / & C
0 0 0 0
K
L ' L
K
0
K
-
@'
L #'
L
L +0
L +0A0
L #'
1
0 @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
1 / / / C
/
0 D 4
1 /?
0 D 4
4
1 &
0 D 48 0 D 4 / +00 D / 4! / & 1
@ L +0A0 ! 1
1 ! /
Æ 1 /
/
'
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#'
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/
0 @A?
-
#
/ 1 / /
/ 1 1 / & 0 /*
1 / /
% ? /
1 # 1
/
/3 & 1
& ! ? 1 ? 1
-
# 3 4 & 1 & 5% /
#
! 4
@/J A
@/*A
'
0'
'00
00
+
+
'
'
-#
#
0
-
'00
'
$ /3 4 2 $ & 5 & 1
5% /
3 4
@/*A
/3 4 @/*A
0'
0+0
00
0'
+
+
'
-#
0
#
0
30''
-
'
'
00
/ / & 1 & & % L0' /* # 1 /*
2
0 0 0 0
0 '
#'
+0
@
1
0
K
& ?
/
0 ?
0
1
0
@'
L
1 6 ?
K
# 1 // &
L #'
1
L +0A
0
@# A
## &
? 1 /
/ '?
@# AC
1 / & 1 / & 1 /
/
1 1
/ 1 !M $ 1
0 1 &% &
1 1 1 & 1
& 1 1 &
K
A
K @
1 1 1 /
'
% L#' /* / & '
/ /
&
K
0
1 !
1 & /
L +0A
1 1 / / ? 1 /3 1 !
1 = 1 ?
/ /
-
¼
K @
1
0? /
J
A
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 / ? /
/ / 8 / 3
! & .& 1 / % = !
1 1 /?
& 1
/
& / /
/
/ / 8
"
* ! $ !
/ / / / & 1 &
/?
! & 1 / & 1
1 / 8/
@
A K
¾
0@
@
¾
L A@
L A
L
L #A
#0 = 1 &
0¼ 0
! & C
K
¾
@
@
1
/ 1
¾
L A@
3
L A L
L A
@A 1 1 1 1 6
/ 1 ! &
1 & 1
! &
? 1 @L @ A >
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1/ % / & 1 % & C
#00 !M K
K
'0
0
#00
0
K
0
0
#0
+ / + ?
1 #3
/ % /
1 1 1 1/ 1
1 1 / 1 1
K
& 1 3
1
/ &
& 1 '03!)=
A
1 /
#00 !M
L
1 / #00 !M 1? / ?
1
+
@
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 / & &% ?
K @0 A ? / 1 % = ? 1 &% // ? 1? & 1 ? 1 000 / 1
1
1 &% // X
K
/ #?
K '0
0
¿ 000
1 &
& 1
K '0 )=? / ?
K
#
K
#
K
#
'0 K 00 )= '0 K 0'0 )= '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
000 & 1
K '0 000 K ' +# ?
& 000 & 1 ? 1
3 & #? #?
1 &% C
½ ¾ ¿
1
1 &%
& 1 / /?
1/? / 1 1 1 &
/
" 1
3 / 1
1
& / 1 / 1 1 & / / 1 8 & & 1 P'℄
# # 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
/*
0
Æ
K
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 #00A
/* 1 / 1
. /
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 / &% 3 / & /J #00 )=
1/ 3 +-
1
. // ? 1 =
1 / 1 & / / & 1 / / @ ? 1
% 3
0
1/ 1 / =
*
A
/
1 & 1 % 1 / / &
0
K
04¿
K
0
K
@
L A
L A
0 % 1 3
! 1
0 A
@
@
0 4¿ A
04½
@
0
04¿
@
0A
@+A
+ ? /
0
/
/ & / 8
6?
1
0
1 &/ ! &
0
K
04¿
K
0
K
@
L A
1/
@ A @
L A
0
0 4¿
@
1 &% ?
?
0 1 0
1 / / @
0 4¿ A
0 4½
@
04¿
0
C
@
/ & & 1
1 6 ?
%
/ &
1 /
% A 1 % 1 &
04¿
+
,% @+A / / / / /
C
0 A 0A
@+A
1/ =
K '0 !)=?
/
1 1
Vi3
Vi1 a
Vg1
vsw
vsw
b
15 +
a
vsw 100p vsw
Vg2 Vg3
#
v-
v+
v+
b
vsw
100p
vsw
X3
vsw a
vsw
2V4
1/
vb
v- 2e-9/pi vsw 50p
a
++
va
vsw
v+
2V2
vsw
b
b vsw 25p vsw
b vsw
50p vsw a
a
vsw
v- 4e-9/pi b
X2
b 2e-9/pi
X1 + v15 -
a
a
b
& 1 3
3
+-
/ & ?
M
K #00 !M 1
K
1 &% &
#00 C
K
0
K
'0
0
K
K
1 ?
1
0
M 1 & &
=/
K #0
04
K
1 / A 1 1
04
/
0
/
1
6
K
? 1 / 1
? 1 / 1 & 1 1
/ /
1 &/ !
1 1 / ++A
04
04 04
%
0 0
04 0
1 / 8 ?
/ 1 &
0 0
/
=/
/ 1 &? ? & 1
/ & 1 / 8 ?
1/
0
=/ 1 3
@ 1 1 1
0
% 0# M / 5
1
/ /J #00 )= 1
& 1 ? / 1 ? 1
0
@+A 1 =/ @
++
?
1& ? 1 & & 1
1 %
1/ ?
1 #0 C
?
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
0
& 1 6 / & 1
1 1 / A
''' # : .℄ ? 0 ' ' 'D 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
1
/*
1 / /
& 1 @/ A &%
1/ 1 / 1
& / / &
3/ / 1
+ & 1 13&%
1 / / & 1 0 1 #3 &
3
1 & 6 /
1 / & 1 / . ? 1
@5 1 1 '-
000 X /
K #
/ 1 /
/
& 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
1
0 0 K
+@?
@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
+ @
L
A
K
1 1
1 + @ A + @
,% @+'A 1
" 1
X
L
1
A
L
?
X
1 1
1
+ @ A
+
A
@
1 1
1
1
/ 1 &
+ @ A
P
0℄
+ @ A /
C
L
+ @ A
/
+ @
1/
% & & 1 / !
?
A
@+'A
1 ?
/ 8
K 0
& / 3 3 1 %? 1 / 8 % & / 3
3 % 1 &
?
1
&
K
@
&
1 C
0 A
&
@ A
0 & 0 &
@ A
@ A
& 1
& 3 & &
K
K
1? @+'A 1 /
0
@& A @& A
& & ? @+ A / @+#A? 1
/ / & 1
@+#A
1 &
C
&
K
1
@+-A
1 1
& 1
1
/ @
1 / /
/ / 1
K
K
L
1 / / /
L
L
T
A
@
A
/
/ & 1
& &
A
L
T
1
L
T
@
L
T
L
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 @
L
04½
K
0
K
A A0
K
0
K
04¿
K
0
K
L A A0
K
0 1
@+A 1
K K
?
K
E
1 %3
1 1 1
/ ?
C
0 @
0 4½
L A
P
0 4¿
04½ L
04¿
0
@ L @
0
@
L
0
@
04¿
L A L
A
P
A
0
0
L
0 ℄
@
A℄
/
04½
P
04¿
A
04¿
0
0
L A
@
0
0
A℄
/
@ L @
A
K 0 0#' @
A? /
?
04¿
P
L
0
℄
@+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
K
K
1
0 # "M
K
00 K - 0 # K 0
K K
K K K
'0 !)=? 1 M
0
0
/
1
1/
K #0 / & 1 ?
- - K -# L K 0#' 0#' K ' # 00#' 00#' K +
1/
?
1
+ 1 1 /
? / &
0
0
1 =/ & L
1 1 1
$ ?
?
1 & ? 1 / 1 ,6
1 % /? 1
04
& L
? / 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
K 0 )=
1 6 /
36 = & 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
b
V2
435.8p v-
b
vsw vsw
a
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 &
¼ 1
@
1 6 ? &% 1 & 1
/ &
1 / =
/ 1 1
/ & '0 !)=A
1 /
1 &?
$ 1
& 1 / 1/ 1
A
K
¼
¾¼
¼ ?
36
¾ ¿¼ - L
&% ?
@+ 0A
? / ¼ K -00 ? 1 1 3 ¾¼ K 00 ¾ 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 /
¼
K
1 ¼
K
1
! & ? @+#A?
0¾
0½
0¾
0½
K
½
K
&
@
& A
1 ! /?
? @+-A 1 &
?
! & C
1/
C
½ ½ ¾ @& A ¾ . / ¾ K K . .
1 1
. ,6 '?
7 1 1 / ? 1
&
,% @+ A B 1 /
K
1 / 1 &
@ A
@ A
K
&
@+-A . ?
1
1/
' 1
1
1
3= 1 &? /
8 / 1 & 1
/ 1 @ /A 6 &% ?
6 & & 1
36 &% & /
@+ 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
0½ 0¾ 0¿
0 0 ' 0¾
' ' ½
K K K
0 0
'¾ ¿ K '
K
@+ A
# C
0¿ ' 0 0 0
0 ¾ 0¾
0 ¾ '¾
K
¿
K
¿ @'
$ 1 & ?
¾ L ¾ '
0¼
L
@+ A
½ ' L ¼ A
C
0
0
0 0
¼ L ½ ½ L ¾ ¾ ¾ @¾ ' L ½ ' L ¼ A
K K
0¼ 0 ! & ? @+ 'A?
0 0
K
0¼
6
L
@
"#
1
0
½ ½ L ¼ A L ½ ' L ¼ A
@
¾ ' ¾
½ ' L ¼ A ¿ ¾ @' L ¾ ' L ½ ' L ¼ A @
K
L
@+ 'A
1 / / & & %/ ?
1
'
?
?
/ 1
'?
@+ 'A? / / 1 &%
1 /?
?
1 / ?
?
/
1 / / & 1 > 1 / 1 K # K @'0 ½¾¿ K 5 & 1 &%
C
1 1
/ %
&
:
C
>,(
$%
0
K # ?
&
1/
:
K # ? / 1
!M
"M
0 0
#0 0
0
1 &%
# 0
K 0? /
K
C
/ & 1 /
& 1 & 1
-00 # 0
>:
@+'A
1 ? ? / &
0 ,% @+ A / 1 &
K -00 ? $' K 0 !)=? $% K ' ")=?
K #0 !M
/1?
6 ? / 1 / & 1 & 1
/
/
:
1 1
1 &% 1 / & 1
@+ +AC
&
K
C
/ &
&
2
0
-00 # 0
+ -? / ? / & @+'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
>,(
1 1 & '0 !)=
'
0
#0
>,(
0 !)= .
'
0
0
'
#
0
' ")=
1 1
/ &
/ . // ? & 1 6 1 1 & 1 & / / 1 & @+ A℄
/
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
K K
0 4 04 0 0 0 4
K
K
K
K
K
/ &
0 @
L A
0 4 0 4 0 4
@
0 0 0 0 04 04 04 04 0 @
C
A
A
@
A
@+' 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/
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τ=2π
0.25
h(t)
0.20 0.15 0.10 0.05 0.00 −0.05 −0.10 −3
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0
1
2
3
4
5
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t/π (sec) . &
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ω (rad/sec) / /
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5
0
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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
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0.05
0
−0.05 −50
t (sec) # . & 1
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K
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|T(jω)|2
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0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
ω (rad/sec) - *
1 6
(
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(b)
jΩ (rad/sec)
(a) 1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
−0.5
−0.5
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−1.0
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0
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1
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0
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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 &
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3 / / % 1 K &
0 @ L A 0 @ L ,% @#A
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1
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Relative Loss (dB)
"
50 dB
50
Specification
40 30
nth−Order Butterworth
20 10 1 dB 0 0.0
f1=100
0.5
f2=200 1.0
1.5
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ω (rad/sec) *
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0.4
4
0.5
0.6
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0.7
0.8
0.9
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