Active Filters for Integrated-Circuit Applications
DISCLAIMER OF WARRANTY The technical descriptions, procedures, and...
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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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2.5
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ω (rad/sec)
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15
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10 5 Input Offset
0
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−150
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0
50
100
150
200
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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 /
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! ?
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3
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$
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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
?
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& & 1 1 /3
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&
& 1 3 &
1 1
& 1 1 3
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A ! ? 1 /
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1
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? 1 /
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1 & 1 3
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1
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-
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3 1/
3&%
/3
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71 1
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" 6 / A $ 1 3
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6 1 1 !
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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
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K
1
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.
(
#
K
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+ +
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K
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1
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&
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3 6
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1
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# # A@ L A@ L A@ L A ! #! @ L # A"@ A ! @ L A@ L A@ L A L L# L @ L
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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 ?
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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 =/ /
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1
3
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/
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1
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1
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5
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100 Ω
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& 1 & & / / // 1 &
/
' @A 1 ! 1
1
& 1 1 & 1
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1 / 1
/#
@$ / 6 ' &
,-.
Higher P otential S ource
I
R
I
R
R
I I
F
I =I C
Q3
M
+
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2(1-
V’ I
I
B1
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Q1
Q2
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+ I
Q2
+ I
V
E1
E
-
B2
I
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V
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B-
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(a)
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IR I M=mIR IB1 I B2 Q2 ++ 2N3903B VB1 VB2 - IE2 R
Q1 I E1
(-V) '' 1 7 /
1
?
& ?
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? / & & / / % # "M
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1 / % / 3
K 0 *@
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1
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L
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/ A K 0-0
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K
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D
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K
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K
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"
K
P
K
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1
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/ 1 %
1 /
* A K P+ +
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/
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K '0
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K
0 *@
K
/ L /
* A K P'+
K ' '+
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"-
/
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 &
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/
/ / 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
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Normalized Magnitude (dB)
50 45
|I0*103|
40 35 µCAP
30 25
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20 15 10 5 0
6
8
10
10
10
10
Frequency (rad/sec) '# 5 / &%
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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
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6 / / Æ / ? / 1
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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
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' & 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
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$ % ?
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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 /
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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 / &
+++
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&
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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
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1
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Ω
600 k
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2N3903B +
ib V1
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ce
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+ + Q
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-
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 *
,
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2N3906B ib V1
+
-
V2
ec
v v
eb +
+ ie
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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
+ + + + + + + +
," $" $($ "" ) *-( , " ) * "" "$ ," % $$# ( .%$ - -( /# % ,# 0 0 1 $& $ 0. "# %# 202 0 34 5 6 " $( $ "$$(
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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) '# & ?
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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)
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−25
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V =−0.1sV(s) 2
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1
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10
10
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--
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)
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kR
V+
V-
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-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 /
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/
1 & 1 / ? 1
1 / & 1 / / / & /
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1
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"
*! $ !
< & / / = * / 1 = & &% & 1 @/3 % =? /
/
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/
+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) #-
&
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6
&
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=/ / & / = / 3 / / 1 ! & 1 * / & 71 1 ! / = / & & ? 1
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V
n
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n
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V ol tage source output
#+ 1 /
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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
/
)
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+
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R2
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&
1 //
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A
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&
K
1& ?
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K
8 ?
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A
A
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? & 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?
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/ 1
@
! .&
! 1 & ?
1 @
#
A / 1 ?
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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 /
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/
&/
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(
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