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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Output Voltage, Vout (V)
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15
Hi Temp
10 5 Input Offset
0
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−5 Lo Temp −10 −15 −20 −200
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−100
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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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A &
!
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1
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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
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L
L
A
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&
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1
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1
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-
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71 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
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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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5
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100 Ω
i=0
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I
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B-
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Q2
Q1
+ I
Q2
+ I
V
E1
E
-
B2
I
E2
B-
I
V
E
B-
-
-
(-V)
(-V)
(a)
E
(b)
' * 3 C @A ? / @ A ,
/ & / & 1 B
A 7 1 1 ' @A / 1 3 3 ?
* ?
/ 1 & / 1
/ ? 1 &
?
" C
/
K
/ /#
K
/
K
/ $ / /#
R( 1 /
/"
K
/
K
"
K
0% & 00? /
1
/ 6 & 1
/
K
0% /
K
K
/
$ $
0% L A/
K @
@'A
" C K
0% /
0% / L / K @0% L A/ /" 0% K / 0% L 0%
@'A
1 1 / & N
1 E &
1 ?
& / 1 1
1 1 & ' @A 1 1 1 / 1 1 ? / 1 1
' @ A
1 &% / . &/ & @,A 1 & / 1
/"
1 / &
/
/ / & / 1 C K
/
K
0% /
'
K
/
K
/ L /
"
K
/" /
? &
0 0N
/
/
1
0% L
0%
0% /
K
L
/ 0% L
0% @0% L A 0% @0% L A L
K
K
0% @0% L A L / 0% L
@' A
0%
& 00? 1 , /
1
% / & 1 & ?
/ ?
/
B 1 & 1 // 6 ? &
/"
K & 1 ,
' @ A
" / 1 / / /
7 1
/
/" ?
K
*
K
1
1 ?
1
/ 6 'C
/ /
0 *@0
A K 0- 0
1 / 1 / & 1 3 &
/ 1 C
/ / Q K 0 *@0- 0 A K P+-
P
/# ?
& R( 6
" C /# P
*
/ / Q
/
K
K
1
K
/" /
/# A K 0'-
1 1 /
/ C K
/ L /
K 0 - /
K 000
*#
K
* L *
1 1 , / 6 & D
"
K # #
0 *@* A K P0 ++ #Q /
$ ? ?
1 &
0 *@
K
& R( /
1 1
Q
K 1 1
? 1
1 % / 8 / / 1
/ /
0%
K
0%
K
0%
K
/ /
K 0 0
K ++
"
&
1
$% 1( 2
1
'
1 1
1
1 / & 1
& & &
1 3 / & 1 &
/
#
IR I M=mIR IB1 I B2 Q2 ++ 2N3903B VB1 VB2 - IE2 R
Q1 I E1
(-V) '' 1 7 /
1
?
& ?
&/ 7 / ? 1 / & & 1
& 1 &
. /
? /
& &
2 1 & 1 / /
*
P
/ /
Q
/#
*
,1 6
*
!
.& 1 & ?
R( / @'#AC
/"
K
''? 1 &
/ AD
0 *@
K
0 *@
K
/
*
K
@
/ ?
/
L L
* C
*
/"
/#
1
@''A
/ /
/#
K
/ L /"
*
/# ?
/#
1
@'#A
/# A
@'-A
/ /
/ 1 1 & 1 / / 3
? / & & / / % # "M
/" ?
1 / % / 3
K 0 *@
1 /
K 0
/ 1
6 1 1 ?
A
1
/ R( %
7 1 % / 1 / /? &
1
* * A /#
1 % / & ? ?
/" C
K
K
1
/ &
/ 1 & % / @ /A ?
/
1
1 & 1 %
K ? @''A /
K # -# !M
1 # 1 0
' /
-
&
! 1 % 1 &
1 1 / & &
/&
3 1
/ &
K '0
%
'? / 1 1 &
*
K # C
3 1
1/
/
7 / /
*#
/
/
*#
L
/
K
*#
/ / Q /#
/
L
/
"#
1
&
/
*
/ / Q /
P
/
* /
*
/ / Q
P
/#
1 &
A K P# #00Q
/& A K 0#''+
0-*@
K
0-*@
K
/ L /
K
@
K
/ L / L /
L
K
@#
K !M
*#
*# A K P0+
K 0 +
*# A /#
*# A /
0 0Q
/"
/
/
K #0
/
K #00
0 *@
K
/
K
1 / 1
C
/ A K 0-0
0 *@
K
K
/ 1 & 1
K
K
K ' ' - !M
/ ? /
K
/
/C
K
/
/
*# A /
L
*#
1 / & 1 ! &
"'
D
/
L
/" A K 0- '+
*#
P
K 0
1 1 ?
@#
0-*@
*#
"
/
K
K
K
D /&
K #00
/ L / L /
Q
/
/"
K
0-*@
/ /
"
K
P
K
/ / & 1 !? 1 /3
/ D
1
/"
1 ? 1 1&?
/ 7 1 / 1 R( /
/ 1 %
1 /
* A K P+ +
#00 0Q
/
* /&
K '0
/ A K 0#0+
K
0 *@
K
0 *@
K
/ L /
* A K P'+
K ' '+
'0 00Q
"-
/
1 6 1
*
* A /#
K
@
K
/ L / L / L /
K
@#
* A /
+
K -'# !M
K ##
K + 0 !M
1 /
? // 1 & & 1 / 8
1 3
/ 1 3
/ 1
/ 8 8 1 & % /
/ 1 / /
$ (+ & '
7 1 1 1/? 1 / 1 @ A? 1 1
3
. 1 / /?
? & ? & //
/ 3 @ ? 0 A
1
/
/ 1 1 1 ? 1 1 1 1 1
1 1 & 1 71 / / 13
/ /
1
% / 1 &
,6 & / / 1 / / 8? / / ? / 63 1 / 8 1 / /
/
/ / 1
1 B & 1
/ 8 / &
/
1
1 &
1 / ? 1 /
/ 1
& & / ? 1
1 & /
'# 1
, ? "
1 1 ?
1 / 8 & 1 & / 1 / 8 ?
+
"
+
/
?
1
1
. 8?
1 / $ 1 1 & / ? ?
,
+
/
/
7
+
/
? /
1
1 1 / /
1 / /
1 & 1 / &
1 ?
/ & / 1 1
/ 1 1
1 R( 1 1
C
/ +
* 1
+
?
1 1
/ / 1 1
K
, L ,
, L ,
@'+A
1 & 1 13 ? 1 / 8
=
1 &
1& ? &
?
/
? 1 % / / / /
,
K
1 &
' '
C
(+V) 2N3906B Q3
Q4
α Mic1 -ic2)
i0=( ic2
ic1 ib1
ib2 Q1 ie1
v
2N3903B
Q2
ie2
v
g1
g2
I
(-V)
'# 1 / 8 @$A
, , ,
$ 1 &
+
K
*
L
1 &
+
' ' '
' ' '
@'A
/ 1 / / % ?
/
,
K
/ ,
+
&
K
*
+ ?
/
,
, ,
L
K
/ L ,
1?
1 & 1 / & 1 C
/
+ L +
+ + , ,
#
#
K
' ' ' ' ' '
K
K
K
K
K
K
$ $
* L 0 +
+
K @
+
& 1
A
$ ' ' $
+%
# '
K
@'A
& 1 / 8
* $ & , C
& /
,
,
&
& @'A
K
" , ,
@
K
&
/
/
# '
@'0A
" # '
@
#
@
1 /
L A
? 1 1 1 /? 1 ?
,
.
@'+A &
'
, ?
A
L A
/
/
K
, @+ A
@'AC
@'A
Output Current, i0 (mA)
Polynomial Model µCAP
1
0.5
0
−0.5
−1 −0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Differential Input, vd (V) '- 1 / 8 & C / 3 /
1 / &
,
@'A @&
1 1 &
1, 1+
K
, ?
@
A @
"
L A
# '
&
K
"
@
A
/
/
L @
#
A
?
"
@
@'A
L A
+ ? +
& 6 & @'A /
,
/ &
C
/# ' @#
1 1 & 1 ? 1
+ ?
1 1 / ?
!A
L A
'
1 / &
K 0C
+ L
@' A
2 * L 2 A / " K 0 @0 L A 1 0 *? 1 , K / K #00 ? * K 0 *@, A K 0-0 ? @# A K #0#+? / 1, 1+ @0A K ' J 1 & 1! 1 & 1 / 8 1 3
#
1 @
'-
A K @
$ & 1 & 1 &
? 1
1 ?
& & ?
3!
/
1
/ / &
/ $ /? 1
0 0 # # 1 ) * 2 3 #
0
& ?
" /
L
,
/ 1 / 8
&
& / 8
+% ?
?
! !
1 & & &
/
/
,
3 1/
& / 8
,% @' A
+% ?
?
& & & 1 &
)
1 1 / 8
1 1 & ?
&/ 8? / 1 / 8
+
A
1 % ? 1
1
+
?
/
+ #0
1
11 1
, /
+%
+
K
"
@
K
K @
+
/
1?
1& /
,% @''A 1
K 0C
" #' #' L
K
+%
1 / 8
1
6 & @'A /
6
?
1 / 1
1 1
1I
A
@
"
"
@
L
"
" L A #' L A
@ @
L A
' L A
# A+% L @0A
@
@
#
A
+% T
L
+% T
@''A
5% 1 3 / 1 1 1 1 /3 / /
+% @# A? +% '- #0#+ K 0 ? 1 & + & 1 & 1 13 / // ? / ? @' A
/ 6 1 3
1 & 1 2 B 1
/ & 1
1 1 / 8 // / /
1 1 1 / / ?
1& / &
# ' $
/ 1 1
'+ .
$ / / &
/ 1 / & 1 / 8
1
/ & ? / 1 / / /B 1 8 = 1
+ ,
K K
,
L
@'#AC
*
' ' $ $ $ ' ' ' / # ' + * / , / / # '
&
/
@'#A
# K $ / / 1 & + K * # 1 & ? # ? / / & 1 / 8
1 1
K
+
/ /
(+V ) I i0=I-ic ic
i
b + v
2N3903B
1
-
Vg
V0
'+
1
1 6 //
,
/
K @
C
# # ' +
/ A /
@
#
A
L @
6 & & ? & @'-A?
+
#
L @
T
A
+ T
'
L
1
/
1 @'-A
? 1
& &
1 &
#
A
& /
@'-A
K 00
? 1 / 8
/ 1 & 1 &
& @'-A
/ & / 1 13 / ? @
&
/ @' A
1 / Æ ? / /? 1 7
+
1 8
= ? / 1 3 @ Æ & 1 A
& & )
A
1
? 1 / 1 1
/ /
% /
1
1 / & 1 / 8
+% '- @#
.
+
A 1& ? 1 / & 1 / &3
& 6/ 1 & 1 0 @ '- A K
' ++ /*? 1 1
1
1 / / & / 8 / / / & 1
& 1 3
(
/
1 8
& 1 / 8
/01 C
/
K
3/ 3
K
"
@
A
"
@
A
/
1
3/ 3
K
0
@
L A
3/ 3
@'+A
200 I=I0=100 µA
Output Current (µA)
150 100 50 0 −50 −100 −150 −200 −0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Input (Vg) ' $ & & & 1
1 / / & 1 ?
" ?
/
@'+A
3/ 3
1 1 & 1 & 1 / /
/Æ
1 8 & 1
* ?/ A?
? @
/ 1 &
/
1 1
1
1 1 / / ? 1 1
@'A
3 C
/Æ 3/Æ 3 1 1
K K
/ / 3/ 3
1 @'A
1 1 / 8
1 1 / / * 1 / 8 / 8
& / 1
1 1 & 1 1 / ? 1?
/
& ?
0
. /
1 ? 1 8 1 / & & 1 / 8 3
1 / &
/ 1
& 1
? 1 / 8
& 1 3
.& 1 1 1 / &?
1 8
// ? 1 / 8 1 1
3/ 3 ?
1 / 8
1 ? / / 3&
1 1 / 8
0
.
1 & 1
αMi R
i0= αmi R-i C
cµ + v1 -
iR
cπ
rπ
cµ
iC
gmv 2
gmv 1
rπ
cπ
+ v2 -
+ vx -
v g1
v g2
' $ 3 / & 1 / 8
# *#' - . /
*& / 1 / / 1 / & ? ! 1 3 &% & 1 1 & 1 / 8 1
/
&
1 1 &
1 1 / 8 1 1 & 1 &
/
1& ? &% 1
/ 8 &
/ 1
/
/ /
3 / & 1 / 8 & '# ' $ / 1 /3 $
/ / &
/ & 1 ?
/ 1 /3 1 /
/
"
/
"'
$ PO#Q 1
"
/
"?
/
&
1 @ A /
1
1 % / 5 1 /
" / " 1 4 ? 5( ? / ) 1 & 1 " / " $ 1 & " / " 1 @ ? 1 * 1 A? 1 1 ) 1 / 8 & 1 ? 1 1 ) %? 1 / ! / & 1
1 ? / ? 1
% 31& & 1 ?
/ 1 1 1 / 8 1 &
/
1?
! ?
& 1 3 @ / 6
'A > & & 1 ?
/?
1 &
/
/ & 1 1 / /C
# C
,
K
#00
/
+
K
0 *@
, A K 0-0'
'
P
, , Q 5(
4
(
)
+ A K P+-
K
0 *@
K
@
K
@
K
+
K
#
, A K -+# 2 + L 2 A,
' ++Q
!M
K + "1
# C
+
P
, , Q 5(
4
)
1
K
0-*@
K
@
+ A K P# +
, A K #- !M @2 + L 2 A, K --
+
K
'' 0Q
"1
K
- +'
K
0-
1&
/ /
R( / 0
0-*@
K
( 1
, A K 0- ''
K
/ 1 / ? 1 (
)(
K
4(
+ ? 1 ( D 1 ?
L
/ @'AC
)( @+ + A 4
+
+
K @
,
1 &
+ + A 4
+
@
L
@
+ A
/
, @
+ A L )( @+ +
A @'A
@'0A 1 1 1 & R(
1 /C
1 ? / 1 & ? @
,
,
K
4
K
@
,
K
4
K
@
, ?
1
6" AC
" , ,
K
@
4 ) A+ +
@
4 +
+ A ) +
4 ) A+
4 +
@'0A
1 / R( 1
K
4
+ + A ) +
@'A?
1 1
6 / 1
, , A 6" ,
@
)
+
A@
+
A
6" P@4 ) A+
1 8 & 1 / 1
4 + Q
1
@'A
6"
0?
1 3 1 / / 1 / 8 & 1
1
1 /
/ /
@'A
/ & 1
1 / 8
& ' C
1 /?
,
+
+ ?
K L
6" ) +
K L
/
@'AC @'A
) 1 =
#
/ 1 3 ?
6" ?
/
0
*2 & /3 1 ' C
1 /?
+
+ ?
K
/
@' AC
,
K
@
@
6" A@4
4
) A+
) A+
)? 1 1 / ?
@' A
0
1
/ 1
& 1 / $ / / ?
5 ?
1 1 13&% & 1
4 & ' C 1 1 /? + K 0? / @''AC
,
K
P@
@
4
6" A@4
. 1 ? 1 / 8 /
)
1 / 8
&
@
) A+
6" A)
AQ
+ @''A
6 31& 1 / & 1
? &% 3/ / 8
1 1 & 1
&% 1 /
,% @'A 1 1 @''A / / / =/ & '0 1 1 /
0
/ 1 / ?
=/ 1 3= / 1 /
1 1
/* & 1 & &
4
1 6 &% ?
/1?
4 )
/1?
$% 1?
4 ) ?
K
4 )
?
/ 1 / / / 8
1 & 1 / #00 = /
K
1 1
?
1 3
& / C
K + 0
# 0 @ A K 0
1 1 / 8 /
4)=
/ / & 1
& & .
& 1 / 8 1 & 1 3
1 3 /
& '+
/ 1 &
4 5( ?
R( / 1 ?
, .
/ & 1?
6 !
/
1
' & 1
1 1 1 / %
, ?
@'#AC
4
K @
/
K #0
) A+
@'#A
1 1 %
& 1 1 / ? /
1 & '? /
1 1 & & % 1 & 1 1 / 8
/ & 1 / 83
1 /
1 1 / 8 / &%
&
1 / 1
Normalized Magnitude (dB)
-
60 |I0/(gmVg1)| 40 20
+20 dB/dec. Balanced Input
0
Unbalanced Input
−20
Common Mode Input
−40 log10|ωCµ/gm| −60
−2
0
10
2
10
10
Normalized Frequency (rad/sec) '0 8
cµ
v g1
+ v1 -
rπ
cπ
g mv1
i0
' $ 3 / & 1
Q6
2N3906B
+
Q5 + 10 V V
Q1
-
+
1
8. 7 V
Q2 -
v g1 + -
Vg1
Q3
-
3093. 7
+ 10 V
Q4 47. 04
-
2N3903B
'
& 1 / 8
1 / 1
/ 1
/ / 8 ? /
& 1 +3 / / 1 1
1 1 &
/ /
' K ' +'
3&% & 1 / 1 1
&%
@' A
1 / 8
/ /
4
1
1
/ ) 1
L0 /*J/ &% 1 1 / 1 1 / / / 1 /
?
/ /
1 / &
0
/ 1 &
1
/1 1
4 )
/J
.
/1 & / 1
/1 & 1
#' /
1 1
& /? &/ ? ?
/
/ 1 1 1
1
/ /
&%
" / / /
1 8
/ 1 &
/ 1 & /
+ + /* & 1
.
' / 8 / ? /
+% ?
/ 1
@ '#A 1 @'-A
?
+
/ 8
& 1 (
+
/
+
2
/ C
+%
K
+
K
+ + + L +
@'-A
Normalized Magnitude (dB)
50 |I *103| 0
45 40 35
Text Model
30 25
µCAP
20 15 10 5 0
6
8
10
10
10
10
Frequency (rad/sec)
'
1
& @'-A
&%
@'+AC
1 1 / ?
+
K
+%
+
K
+ ?
L
+%
+
L
+
@'A & /
@'+A
1 & 1 &
' % 1
/ & 1 1 / 8
1?
1
/
/
? / 1 & 1 1
//
& 1 & '0
+
+ C
K L
$
@'-A / 1 &
+% +
2
/
+
+ C
K
$
K
0
K
+
C
1 & 1
@'-A / 1 &
+%
+
K
K
0
+
C
2 / 8 /
+
K 0C $
1 & 1
@'-A / 1 &
+% +
* 1 /
K
+
K
0 #
+
( ! '0? -- /*
$ 1 /
1 ? / / %
1 1
/ = ?
?
C
1 & 1
/ /
/
1 / 1 / 8
1 1
/ ? & 1
1 / 8 / & &%
1 3 1 & 1 3= / &
/ 1 / 8 / ? 1
/1 & 1 &
& / 1 0 /*
& 1 & &%
/ ? 1 / / 1 / 6 1
1
+
# (*+( !3 2 (
1
& 1 /
1 !
1 . ! /
1
1 & 1 / / . 1 3 &% B /? 1
& '
/ 8 & 1
/ / & 1 & ' 1 1 1 / / & 1
$
& & B & & / 8 & /
?
1 1 / 1 ?
&
/ / / / ?
6 / 1 / / ! 1 / & & /
1 /
/ 6 /
/ /
1 / & /
$ ., 1 1 & /
/ / & E 1
1
1 3
1 / 6 1
&% & 1 3 / 8 1 & '
" ?
/ ?
& 1 / 1 & 1 / 8
71 1
/
+
+
/
+
/ / 1
+
"
+ ?
8 & /
/ / /
/ &
1 / / / 1
1 ? R(
@
"?
0 1
1 1 /
R(
'' //
///? 1 &
/ ?
/ /
@'A
+
/
/ @'AC
L
,
K
0
K
) A+
K K
" + " + 4 , ) +
L
@
+ L ) @+ + A
4 ) A+
4 +
/
@'A
00
αMi R
ZM cµ + v1 -
cµ
iC
vR
cπ
rπ
i0= αmi R-i C
iR
gmv 1
g mv 2 c π
+ vx -
v g1
v g2
'' $ 3
1 1 131 / / & @'A @'0A 1
1
/ /
1 1 % &
/ 1 & 1
& 1 / 1 R( & 1 ? 1 / 1& & @'0A 1 ? @'A
+ v2 -
rπ
1
,
1
, ?
+
0 /
"
,
1 / /
& / R( 1 /?
/C
,
K
" , ,
K
"
"
@
4 ) A+ 4 + " L ) 4 ) A+
P@
4 + Q
1 / 1 & ?
@'A
, @
/ / / 1 1 /
A? & & 1
/
1 1 / 8
1 1
/
+
& ' ?
+
1
K
/ /
$ 1
@'A / @' 0AC
, *"
, '
K
K
L
,% @' 0A / 1 A /
"
1
'
"
" " )
@
L
4
/
&
1 &% 3/ / 1
! 6 @ ' A?
&
) A+
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,
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-
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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
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+ + + + + + + +
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100 80 60 40 2N3903B at V =2 V
20
ce
0 0.4
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Loge(ic)
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−10 −12 −14 −16 0.4
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0.5
0.55
0.6
0.65
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0.75
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i
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(a)
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ic(v ec-2) VA
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(b)
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5
Log10[ ]
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0
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−10 Cµ −15 0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
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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
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vbe (V) '' " / /
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Rπ
5
Log10[ ]
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gm
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0.45
0.5
0.55
0.6
0.65
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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
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0.85
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/ ! / &% & 1
1 /
. 1 6 ? 1
1 & ?
. / ?
1 &
1 1
@ A 1 1 @ A ! & 1 .& 1
-0
1/4 1
Vg
1/5 + -
1/4
2
V1
s
-s
V
1
1
V
1 -
-
V2
+
+
V3
V (s)
12 1
26 1
V
-
-26
(
V4
Ω F)
+
,
# 53 = & 1
#+
? 1 / & 1 8 71
& 1 / ?
1 1 1 ! ?
61
&% 1 1
/ ? 1 & ?
0 0 0 0 0 0 0 0 0
K
0
0
K
-
1
1 &%
@
@
K
K
K
@A
0 0 0 0 0 0 0 0 0 K
K
/ 1 / / ?
@ /* 1 A
&
A? &
A
@
A
@ A
@
K -
/
1
C
A
@#'A
-
!
K
0?
0
/ 1
K 00 @'0 /*A 1 1
? 1 / / / /
! 1
7 1 / ? 1 1 & 0 /
1
/ //
/ &
K L 0 @0 L 00A? 1 K 0 1 ? & K 0 ? 1 @ A K #0 1 #0 1 / 6 &
71 1
K
@
?
/ 1 &
! 10/4 1/10
Vg
100/5
-s
-
V/10
1 +
s
1
1
V
2 /100
V1
-
1/10
-
-
V2
+
V3
+
V (s)
0.45 1
104/100 1
V
-
-1. 04
(
Ω F)
V4
+
,
# 3/ & 1
#
1 A 1 //
1 %
& 1 ? 1
0 0
0
/ $
1
& & 00
1
/ 1 /
0
/
0
1 ! &
0
@ A
K
# 00
0
@ A
0
' 00
@ A
/ / / / & @##A ? # / #? /
@
A? /
00 1 % = 1
,% @#A 1 &
00
1 / / / /
0' 00
C
0
1
@ A
/
@##A
#
* 1
/ ?
1 ! / / ! / 8 & & 1
0 0 0 0 0 0 0 0
K
K
K
K
# &
0 0 0 0 0 0 0 0
K
00
K
0
K
0' 00
00
0
@
@
1
C
A
A
@ A
K 0'
@
A
@#-A
7 " 1! 1 / & 1 .&
/
1 ? 1
// 1 1
/ / &% / / &
/
1 " & 1 / / &
C
-
30 V1=s2V(s)
Magnitude (dB)
20 10
V4=−26V(s)
0 −10
V2=−sV(s)
−20 V3=V(s)
−30 −40 −50 0 10
1
2
10
10
ω (rad/sec)
#0 3 / & 1
#
; ?;? ; 4 4 . 4 48 . ! 4" 4 4 4 48 4# 8 8 6- 4#?; 8 4 (6- 4"?;' "# %"$ % 4& ;% ;$ 1 / @ / A 1 1 / / / & 1 ?
#0 &
1 / / 1 1
1 1 1
!
&
6 ? 1 1 / & 0 1
0
K 0
0
?
0
& 1 1 & 1
6 @L /*A? &
K 0 0
1 ?
K #
/ / 1 1
1
1
$ 1 1
0
K 0 0
K #
!
-
−10
Magnitude (dB)
−15 −20
V1=0.01s2V(s)
V4=−1.04V(s)
−25
V3=V(s)
−30
V =−0.1sV(s) 2
−35 −40 −45 −50 0 10
1
2
10
10
ω (rad/sec)
# 3 / & 1
1 6
0
K 0
? 1 6
# K 0 0
? J001 & 1 !
1 / / ? 1 1 &
#
! & 1 /
C
4 ' 4 .' 4 48 .'8 4" 4 4 4 48 4# 8 8 1 / /
# / 1
1 !
1 1 1 ! @ /*A 1 & ' 1
0
0
0' @L0 ' /*A 1 & ? / 1
/ 1 /
K 0 0
1 & 0
K #
1
0
1
K 0
?
1 1 /
/ / /
/ 1 1 / / 0 1 1 / 1 0C? 1 !
1 1 -#3& / / ? 1 / /
)9
1 & 1 2
& 1
-'
1
499 0A
1
s 2V /100
-
+
V0
0V - +
V5
1/4
V
# . 1 & & =
(( ' $ 6
3 ? 1 1
1 6 ? / /
! & 1 1 =
/
1
1/
1 1 6 & 1 / /
6 ? 1 &
0 0
K
#@
@#+A
% /C
L '00A
L'
@#+A
L 0'
1 & 1 1 1 6 // =
& @
K 0
,% @#+A
A? & 1 6 &
0 0 1
#?
?
0 0
K @
L '00A
0
@
00 /
C
A K 00
0
#
0
L'
00
1 1
! & 1 1
! & ?
0
@#A
// 1
/ /
/ Y
& 1
/
# 1 1
K #? 1 ? RJY
0
0
?
/ 1 / /
K 00 %
#
1/
K #00 &
$ ? 1 6 = & ? 1 /
/ / / / % ! " 1 1 6/ 1 '# /* @ & & 00A? / ? 1 & 1 / ? 6
71 1 1 1 /
? 3 3 @$ 5A
& 1 1 ! 1 1
1 / & 1 E & 1 1 ? 1 / /
0 0
K
#@
! &
L '00A
L'
L 0'
#00@ @
1?
00 L ' A L'
/ % =
L 0'A
@#AC
@#A
0 # & '" & #
! 10/4 1/10
Vg
1/15
-s
-#
V/10
1 +
s
1
1
V
2 /100
V1
-
1/10
-
-
V2
+
+
V3
V (s)
15.4 1
3
104/100 1
V
-
-1. 04
V4
+
+
V0
V5
3/4
-
2/3 1
(
Ω F) ,
# = /
& 3
1 ? 3 & /
0 00 1 1!/
"
!
0
#00
K
00
@#0AC
' 00
0
0' 00
0
@#0A
# 1 & 1
1 1 &
/ & 1 C
4 ' 4 .' 4 48 .'8 4 ' 8 4" 4 4 4 48 4 4# 8 8 1 &% 1
#'
1
1 ! @ /*A 1 / / &% & 1 . 1 / / 1
! 1 & 1 /?
1 1 8 % = 1 1 1 %
8 ? 6 = / / / / $ 5 & 1
--
Magnitude (dB)
40 30
V5
20
V3
V1 V2
V5
10 V2 0 V4 V3
V1
−10 −20 0 10
1
2
10
10
ω (rad/sec)
#' ,% =/ & 1
&
7 1 / 1
/ /?
/ 7
@
/ U !
"
3
. 1 6 ? 1
1 1 1 $ ., A / /
& & 6
0
1 /
!
/
#
/
@ A & &/
1
0
@ A?
0
@ A?
%
@ A & 1 @ 1 / & 1
! 1
% A?
/ 31 = 3 / 3 &
//
/ 3
1 =
! & 1 3
= 1 = % / & / ?
1
/ 1 1 1
= / & 1
3
! ?
1 / 1 1 1
1 1 =/
%
Æ
1 % / 3 &
1
(13 /
1
3 1 &
-+
6 & 1 / / / 1
6 & 13 / / & / @#AC
0 0
@ A
-
K
@
L 0A@
L
L +A
-
K
%
L
L'
L
L #'
@#A
L +0
3 ? 1 3 & ? / @#A? / 1 =
1 & 1 / & C
0 0 0 0
K
K
0
K
-
L'
@'
0
L
L
L #'
L +0
L #'
L +0A
0
1
@ A
@#A
3 / ? 1 1 =/
1
/ 1 Æ & 1 3 & / 3 ? 6 & 1
?
1 1
/ / -
0
@ A " 1
/ ! & 1 &
C
; . ?;? ; 4 4 .8 4 ! 48 .8 4 7 4!. 7 4" 4 4 4 48 4 4! 4# 8 8 7 6- 4#?; ! 4 (6- 4"?;' "# %"$ % 4& ;% ;$ 1 6
/ #'
0
D
0 0
4 / +0
@
L +0A
0
0
D
! 1
&% & / -
1 /? 4 1 & 4 / ' 0 D 4 / - 0 D 48 D / 4! / & 1
1 / / / C
Æ 1 /
#
1 ! /
/ 1 / /
@ A? / 1 1 / & 0 /*
1 / /
% ? /
1 # 1
/
/3 & 1
& ! ? 1 ? 1
-
# 3 4 & 1 & 5% /
#
! 4
@/JA
@/*A
'
0'
'00
00
+
+
'
'
-#
#
0
-
'00
'
$ /3 4 2 $ & 5 & 1
5% /
3 4
/3 4
@/*A
@/*A
0'
0+0
00
0'
'
+
+
-
'
-#
0
#'
#
0
30''
+0
-
'
'
00
@
L +0A
/ / & 1 & & % L0' /* # 1 /*
2
0 0 0 0 0
% L#' /* / & '
1 1 / / ? 1 /3 1 !
1 = 1 ?
/ /
&
1 & / 1
0
K
& ?
/
/
K
'?
0 ?
0
0
1
# 1 // &
@'
L
L #'
1
L +0A
0
@# A
## &
? 1 / 1 6 ?
/
1 1
/ 1 !M $ 1
K 0 1 &% &
1 1 1 & 1
& 1 1 &
K
A
K @
1 1 1 /
@# AC
1 / & 1 / & 1 /
'
1 !
/ /
0
0? /
J
K @ A
1
K #
1 % 1
1/ &
kR
3*kR Vg
kR
V+
V-
V8*kR/3 kR
-18s Va
+6s 2V a
-4s 3Va/3
kR/4 kC
H1
3*kR/4
-
VBP
4*kR/18 kC V+
H2
V-
kR/3 H3
V+
15
15
V-
kC 54*kR/170 kC V-
H4
V-
V+
24*kR/31
kR
H5
V+
+170Va/3
4*kR/3
V-
-(31s 2+170)Va /4
V+
H6
.define kR 8e3 .define kC 62.5e-9/pi
V+
*** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) ##
1 & 1
& 1 * 6
& 1 & 1 /
#- / / 1 / / &
"
1
6 & 1 / / 1 &%
& 1
.& 1 &% & 1 /
/ & /?
/ /
/ / 1
/
1 & 1 / ? 1
1 / & 1 / / / & /
! & . 1 1 ?
/
& &
/? /
/? 1 1 / &% & 1
1
.& 1 / % = !
& / %
!
& 1
&
1 ? 1 1
!
& 1
& &
1 1
) ? 1 1 1
1 / ? /
// 8 / 3
! &
1 1 /?
& 1
/
& / /
/
/ / 8
"
*! $ !
1
L
@ L M A @ L A@ L A@ @ L AM M
! & 1
?
L M A @M @
@
P@
L
K
L
K
36
A K
@
3
@
L A
@##-A
L A ! & ? @###A? 1
= ? 1
1
!
/ ? / 1 M
// 3
1 % /
@
A 1
0
Ra
Z
R +
T-T +
-
-
-
V2
# # /
& 1
3
K
/
)
-
.
?
1
# #?
1 1 / 1 &
K
/
1 1
K
K
@
L
/
@ A@
L M A L
A@
L
K
A
&
/ ?
@
L
A
@##+A
L A
A L @ L A A
@
L
1 1
! & & 1 /
! & C
@ L A@
@
1
#@
@
1 @
A
L A A
K
M
K
/
K
K
-
L
L @
M @ L A
1
1 / 1 &
3
A
%/ 1 / /
@ L
K
& & C
1
1 &
%
1
& & / /
1 = 1 / /
1
& 1
V0
3 @3 A / & ,6 #
1 M K
K
+
+
/ 1 /
Rb
R
Vg
C
K
K
L AM
/ / % & 1 1 !
K
@ @
L A L A
/
1 &/3
! 1 / 1 / C
A
@
K
L A A
@@
@ L
A@ L A
1 / /
K
-
K
K
K + MD
K - MD /
K # -
kR
kC/3
kC/3
kR
kR
Vg
kR
V- 36*kR A1
2*kC/3
kR/2
5*kC/216
7.2*kR
+ 15
15
V-
V0
-
.define kR 2e3 .define kC 0.25e-6/pi *** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=1M IOFF=5P SRP=13MEG SRN=13MEG IBIAS=10P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) # - / /
36
3
1 1 1 % & 1 $ 1 1 ? /
/ / 1 1
/
0
1
1
# # /
1 &%
# + & 1 /
1 1 /
# - ,1
/ &
1 / 1 1
/ ? / 00 !)=?
3 /
/ /
1 &/ ! ? 1
1 1
=
1
K !M /
& 1 / / 1
1
/ 1 & 1 1 3
8 > &
/ /
/1
1 / /
1&
K
")=?
/ 6 / 1 & 1
/ ? % ? /
/ 1 1 / $ # / # '
$% -(
& ? / %/ @1 & %/ A? / /
@
A K
// 3
! & & 1 & 1
0 0
K
2
@ @
L L
1
A A
L L
@##AC
@##A
20
|H(jω)| (dBv)
10 Theory
0 −10
µCAP −20 −30 2
4
10
6
10
10
Frequency (Hz)
# +
/ & 1
1 1 1 % & 1 /
?
1
1? 1 =
!
0
@
A 1 3
1 8 1
1 3 & ? & 1 3
K
@
0
#
L
L
C
@##A
A
// / 6 & 1
1 @A 1 1 1 / / &
1/ / / 1 / & 1 / &
& @##A 1 & ? @ @
AC
L L
@ L
. =/ 1
1/ & / 8
1 3 &
! &
1 / & 1 %/ /
/
?
% / /B
,6 #
L
L
A
A
@
L
A
0
K
0
K
0
K
1 1 & ?
#
@
#
@
0 0
A
L
#
@
0
@
&
A
L
K @
L
0
A
L
L
A
@#-0A
A? 5 # / /
! / &/ ! /
? 1
1/ b
1/ a 1/ K
1
1
1
1
+
1
-
Vg
s
+
Va
-
-
+
(
Va
-
Va
+
-
Ω F) ,
# / 1 %/ 3 & ? @##A
1
& 1 ?
& 1 3 & 1 ?
? ?
#?
/
& 3 ? 1
1
0 0 0 0 0 0 0 0 0
$ &
/
/
# ?
2
K
@
K
@
2
?
3
1
/ /
1
C
0
L
2
A
L
0
/
& %/ &
0
# 1
2
0 0
0 L
L
2
0
A
2
@#-A
/ @#-AC
K
K
P
2
L
@
L
@
2 L 2
L@
& @#-A 1 / / & ?
1 / ?
2? 1 ?
2
/
?
2 A@# A L A
/
2 2 # A L @2 2 # AQ @ L L A
@ A & @##A / 1 @ A =/ 1
1
2
K
2
1
K
2 2 #
K
2 2 #
&
@#-A
/ 3
@A
@#- A
? / 8 &
!
&
3 C
K
L @
L
L
A
@#-'A
'
1/ b
1/ a
Vg
1/ K
1
1
1
1
1
-
s
+
Va
-
-
+
Va
-
Va
+
1 1/ c
1/ c
0
V0
1/ c
1
2
+
(
Ω,F)
# 3 %/
1
/ @ / % / &
1 &
2
C
2 K 0 C =
A
/ 1
1 1 & @#-A? 3 3 ? K 0D
2 L 2 #
K L ?
2
K
# D / 2 L 2 #
K 0?
/
?
/
C
K
@
L
3 3 / 1 &
2 L 2 #
K 0?
2
K 0D /
L
@#-#A
A
/ &
2 L 2 #
K L ?
2
K
#
C
2
K 0D
; # C
K
@
L
3 3 / 1 &
2 L 2 #
K 0?
2
K
# D
L
@#--A
A
/ &
2 L 2 #
/
K 0?
C L2 2 K #
K LD
1 1 /
8 3 C
K
@ @
2
L
L
A A
L
@#-+A
#
3 3 / 1 &
2 L 2 #
K 0?
2
2 # D
K
/ &
2 L 2 #
/
8
C
K
@
L
3 3 / 1 &
2 L 2 #
K L ?
1 & ?
2
@
K
?
A A
L L
@#-A
/ &
# D / 2 L 2 # K ? 1 1 1 1 ? / / K
1 / / & 1 1 & ?
C L2 K L2D 2 K @ L 2A #
1 1 /
C / 1
L
2
2
K LD
K 0
1
! & / @#-A
1 / / 1 1 /
3
/ / & 1 / 8 & . // ? 1 / /
0
0
1 %/ . ?
"
? & 1 13
)
3 > 1 %/ / 1
@ $ &
1
1 & # ? 1 / 1 1 ! 1
#
A K
L
L 0A
L A@
@#-A
L A
& 6 1 1 ! 1 3
1 1 /
%
#@
@
! & @#-AC
3 7 1
K K
#'0? / 1
0 0
K
! & 1 1 / & ,6 #
#?
K
1 %/ ! 1 & 1
! & ? @#-A? = @#+0AC
# P2
L@
2 2 A
@
"1 @#+0A @#-A % 1
L
2
L@
2 2
AQ
@#+0A
L A
K ?
2
K ?
2
K ? /
#
K
# @
LA
$ / ? 1 1 1/ ! 1 @&
2
0
A &
1 1 /1/ 1
/ & L
#'0
0
1 1 / /
1 % &
5
!
1
# / 1 # / K # ?
K
#'
. / 1! 1 % ? 1 /
K 000 /
0
K
#'? / 1 / #'
1
/
1
#
/ 1 ? &
K ?
1 / 1 1 /
& 1 6
. 1
?
/ 1 ? #'
#
K
'?
&
/ 1 1 !
#
1 1
/ 1
! & / & 1
6 1 / / & 1
36
3 /
=
1 / /1
/
,6 # 1 &% 1
-
1
1
Vg
1
1
1
1
1
1
+
s
Va
+
-
Va
-
Va
+
K
0
1/ c
0
1/ c
1/ c
1
2
+
(
Ω,F)
#'0 & ,6 -
K
1/K
#' 5 = &
#
&% 3/ / &
V0
+
kR kC kR
kR
Va
kR
kC
VVg
kR
kR
V-
H1
V-
H2 V+
kR
H3 V+
kR
V+ kR/9 kC/K
V+
+ 15 -
+ 15 -
K*kR V-
V-
.define K 1.0 .define kR 2e3 .define kC 0.25e-6/pi
V0
H4 V+
*** Wide bandwidth JFET i/p opamp .MODEL LF351 OPA (LEVEL=2 TYPE=3 C=10P A=100K ROUTAC=50 ROUTDC=75 VOFF=5M IOFF=25P SRP=13MEG SRN=13MEG IBIAS=50P VEE=-15 VCC=15 VPS=14 VNS=-14 GBW=4MEG) #' / & ,6 -?
#
K
20 10
|H(jω)| (dBv)
0 −10 −20
µCAP
−30 −40 −50 Theory
−60 −70 2
4
10
6
10
10
Frequency (Hz) #' 1 & ,6 -
1 &% ? 1
1
1 ! 1
&
#
3
/ &%
3 7 / 1 1 / /
1 3 /
@##AC
0 0 .
1 /
/ 1 / 1? 1
1 1
K
# L A
@
L
1 1 & & 1 %/
/ 1 %/ &
,
1 1
+
1 /3
/ & 1 %/
%
3 $ &
1
0 0
0
& 1 3 & ? / 1 =
C
#
K
0
1 /?
& 1 = & 1 3
1
#''
@
L
A
0
/
0
/
! & 1
/ 1 / %/? 1
# ?
1 % // / 1 & %/ & 3
)
? 1 & / / Æ
1/ b
1
Va
+s
1/ a
-
VBP
+ 1
Vg
1/ K
1
Va
s2
1
-s
1
Va
Va
1
1
-
VHP
+
(
-
Ω
-
+
-
VBP
VLP
+
1
,F) 1/ c
1/ d
V BS, V AP
1/ e
+
2
-(cs -ds+e)
Va
#'' 1 / & %/ &
1 1 1 %/ & 1
# .&
/ / 1 &
1 ? 1
#''
# 1 & // &
/ 1
/
1 / A ,1 1 8 &
3 C
K
0 0
K
#
L
L
C
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dB -20 dB /dec
0 1
-10
10
100
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(a)
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0 1
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10
Magnitude (dBv)
0 2xTheory
−10 −20
Initial
−30 −40 −50 −60
Modified
−70 −80 −90
2
4
10
6
10
10
Frequency (Hz) - 5 & 1
1 1
I
3
R
L
+
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3
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0
dB Magnitude
−10 2xIdeal
−20 −30 −40 −50 −60
2V
−70
2
−80 −90 2
3
10
4
10
10
Frequency (Hz) - % & 1
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$ '. 4 % $ 6
1 1 /
-
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1
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kC/5
kR
-VI3
kR
V-
A2 kR
+V2
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kR
kR
Vin
kR
V+ kC/5
kR
kR
kR
5*kC V+ kR kR kR V-
V+
A11 V+
V+
VA7
-VI3 V+
kR 0.797*kC kR
V-
VA9
-V3 kR
A13
kR VV+
-(V2-V3 -V4)
-V4
V-
A5
V+
V-
kR
V- 1.254*kC kR
V+
kR
V+
A4
A3
A12
A6
kR kR
V-
VA1
-VI3
kR 1.308*kC kR
V-
kR .define kL 1/pi .define kR 2e3 .define kC 250e-9/pi
kR VA10 V+
V+ kR 0.765*kC kR VA8
- (& = & 1 * 1
V+
- 0
'+
0
dB Magnitude
−10 −20 Passive −30 Leapfrog
−40 −50 −60
2
3
10
4
10
10
Frequency (Hz) - & & / & ,6 #
1
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1. 838
1. 159
1. 159
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(
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0. 618
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Ω
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S
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50
on
R
+
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C
C= 5 p
v
v
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100
S
R
off
S
+ C= 5 p
v
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+
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2.5
Voltage
2.0 vS
1.5 1.0 0.5 Hold 0.0 −0.5
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Hold 1.5
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vg1=φ1
5 4 3 2 1 0 0.0 5 4 3 2 1 0 0.0
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VL 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1.4
1.6
1.8
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VL 0.2
0.4
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Load
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v
Load
C
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(b)
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1
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-
4.0 3.5
v1(kTC)
vC (V)
3.0 2.5 2.0
v2(kTC)
1.5 1.0 0.5 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(t/TC−k) + 6
1/ &
+ v1 -
CR
+
+
v2
v1
v2
-
-
-
R =1/(f C )
C
C R
+ 3 / % &
1 /
+
1/
+0
ix
swmod
swmod v1
1e-9 +
-
-
1ix
+
va
1e-9
vb
.IC v(6)=-6.25 .MODEL swmod VSWITCH (RON=1e3 ROFF=1e7 VON=1 VOFF=-1) .MODEL V1 SIN (F=1000 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL VA PUL (VZERO=-5 VONE=5 P1=0.1u P2=0.2u P3=24.8u P4=24.9u P5=50u) .MODEL VB PUL (VZERO=-5 VONE=5 P1=25.1u P2=25.2u P3=49.8u P4=49.9u P5=50u) +' / % 8
3 1 1
+'
% 8 & / /
1
&% & 1
1 !?
+
K 0 !)=
?
+ ?
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1/
+
/
+ ?
+ ?
1
/ 1
/ 1 /
+
& 6 1&3 /
1 / & 1 / 1&3 ?
A
1
6 /
1 1 1
/ 1 / & 1
1 & / 1 ?
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71 1
+
1 &
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//? 1
/ 3
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,+
1 1
1 1 // 1
& !M / 2 & 0 "M
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1
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+
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1 & 1 1 / 1? /
*
+
+#?
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& 1 / /
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1
+
/
1 / 1 1 6
+
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1 1 1
Æ
& 1 &/ 0 ?
1 A . & !3 3! /
/ 1 % ?
K
1 1 &
0
K '
C
2
+
V =4.0 V 1
1
pp
V2
0 −1
1
2
V and V (V)
−2 0.0
0.2
0.4
0.6
0.8
1.2
1.4
1.6
1.8
2.0
1.2
1.4
1.6
1.8
2.0
V =12.8
5
v(6) (V)
1.0
pp
0 −5 0.0
0.2
0.4
0.6
0.8
1.0
t (msec) +# 7& & 1
0
1/
K
K
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0
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0
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0
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0
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p
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Offset Waveforms
AB A+B 00 1 01 0 11 0 10 0 NOR
φ2
q
7
+
31 !
q=φA
6 5
p 4 3
φ
2
2 1
φ1
0 −0.4 −0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
t/T ++
31 !
&
1.6
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R
C
1
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2
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+
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1
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1
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1
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1 1 1?
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&
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1
C
+
R
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I
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+#
+
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2
C
V0
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2
V
2
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+ 0 V
0 V -
C
I
1
+
C
0
-
(b)
(a)
+ $
/
+
C @A ? / @ A
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! #
0 0
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K
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0
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1 / 1/ & 1 1
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0
K
C
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1 ///
1 &/ ! 1 1
@
0
1
0
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/
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0
0
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+
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R
1 C
I
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2
+ R
0
+
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+
C + +
V
2
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1
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2
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C
I
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0
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! ' & 1 % 1
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1/ / % 1
1 1
/ 1 / 8 ?
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C
0 0 ! #
K
K
0
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A
&
K
K
C
0
K
K
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0
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@
1 1
1 1 1 & & 1 &
@ A @ A
0
0
0
0
@+A
? 1 / 8 /
1 1 1
1 1
/ // / &
1/
C
C
1
++
2
V1 C
C
1
2
V2
V1 R
R
1
+
-
C
C
R1
2
V2
R2
-
+ 0 V
0 V
-
+
-
+
(b)
(a)
+ /3
!C @A ? / @ A
1/
1 & 1 .
+
/
C
0 0 C
0 0
K
K
@
@
@
@
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A L A L
A L A L
@+A
! & / 1 1
! & / / &
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0
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& 1 3 1 1 1
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& & 1
+
C
V2
V1 R
R
-
+ 0 V
+
-
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%
3 1
! & & 1
+
/
3
0 0
@
K
1
K
1/
1
K
K
?
@+0A
/ 1
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0
K
0
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1
1/ % / & 1 % & C
K
K
K
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31 !?
0
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K
'0 0
#00 0
+ / + ?
K
1 #3
0
0
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1 1 1 1/ 1
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L
& 1 3
1
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K
1 /
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A
1 / #00 !M 1? / ?
1
+
L
L
@
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1
1 & & 1
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3
1 ? 1 1 1
+
2e-9/pi vsw
vsw
50e-12
V1 a V2
vsw
va
vsw 50e-12
b
b
a
vb - 15 +
V3
+ 15 .IC v(5)=0 v(8)=0 v(9)=0 .MODEL VA PUL (VZERO=-5 VONE=5 P1=0.1u P2=0.2u P3=12.3u P4=12.4u P5=25u) .MODEL VB PUL (VZERO=-5 VONE=5 P1=12.6u P2=12.7u P3=24.8u P4=24.9u P5=25u) .MODEL V1 SIN (F=200 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL V2 SIN (F=2040 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL V3 SIN (F=10040 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) +
1/ 3 /
0
&
&%
& 1 / / &%
1? /
1 / & @ A & 1 / 1
71 & & @ A
& 1
?
/ 1
1 1 &%
6 1
@$ / 3
A . ? 1 / & &% ?
A ? / 1 % = ? 1 &% // ? 1? & 1 ? 1 000 / 1
K @0
1
1 &% // X
K
/ #?
K '0 0
000
1 &
& 1
K '0 )=? / ?
1
1 &%
3
& #? #?
1 &% C
K
# '0 K 00 )=
K
# '0 K 0'0 )=
K
# '0 K 00'0 )=
1 1 &%
1 /?
1 /? /
1 /
?
1 1
?
& 1
/ & 1 / 1 & ? 1 =
/ & 1
1 / ?
K @
$
A
1?
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1 / / &
/
&
& & & 1 3 1 1 1
& & '+#
'- 6 = &
1
1 / 1 /
. ? & 1
1
K '0 000 K ' +# ?
& 000 & 1 ? 1
000 & 1
& 1 / /?
1/? / 1 1 1 &
/
" 1
3 / 1
1
& / 1 / 1 1 & / / 1 8 & & 1 P'Q
# # 7@ 8'# . $$ + ' 3$% 0$" 0, % A" ; : B8 #B : # : . & 0A ' ? + 0 $", $" % $" ; - 0#(#( (0A :. & + C$" ,(# ;$"#;
;'7 $ $"$ :'D + ", ;$"#; + ;"$E -$"# 7@ 88))! -, # 7@ 88))! 09: -$"' ; : 0A13 -, ' ; : $, ,( . #(09:: ''' . !' "$E&..&$# $ B . ' . 6 (&9", #*-&&B" $E&8 ,( . #(0A13: ''' . 0#(&..&$# $ B . ' . 6 (&A, , #*-&&B" $E&8 (&B,"6 FE&&B" $E&8 B % $% $" % $, ,( -$"$# $ .7' 7' 6 (&9", 0&&B" $E&8 ,( -, $# $ . ' ' 6 (&A, , 0&&B" $E&8 (&3$% %&&B" $E&8
1
& &
/
- A?
1
1
& & 1 1 &%
+' 1 1 & 1
1
/ 1
% / @0 / & 1 003)=
1 1 0?0'03)=
! 1
1 & 1 1
1 003)=
1 0'03)=
? 1
/ 1
/
/ 1
1 3/ 1
/ 1 1 / & #
/ 1 13 ? 1 / 1
/ 1
1
.&
1 1
/ 1 &% @ / = A
& / / &%
Input (V)
5 0
Output (V)
−5 0
5
0
5
10
15
20
25
10
15
20
25
5 0 −5
Time (msec) +' . 3
& & 1 3
1/ 6
Input (dBv)
10 0 −10 −20 −30 −40
Output (dBv)
−50
0
2
4
6
0
2
4
6
8
10
12
14
16
18
20
8
10
12
14
16
18
20
0 −20 −40 −60 −80 −100
Frequency (kHz) +# $ & 1 3
1 / 1 1 ! & !
1 1 & 1 1
1
1/ 6
1 1 & +#
? / 1
/ / 1
/
& 1
3 / 1
?
1& ? / 1 /* & 1 1 C
0
0 1 /1/ 1 1
1
/*
Æ
K
0
K
L- 0
1 L- /* & & .
1 1 % / 1 & / 1
1
/ 6/ 1 / @
/*A & 1 / / 3 @ A 1 1 &
0
K
1 / / & 1
/
)
C
0
L
#00
K
@ L
/* 1 / 1
. /
#00A
1 1 6
/ 1 / / 3
.& 1 8 &%
/ 1
/ 1 /
1 &% ? 1 3
/1 @
& / & 1 2 6 6 1
A
1 / &
'
V
1YI 1
I =0
2
5
I
3
+
V2
1
1
-
(
+
V4
1
1
-
Ω,H,F)
+- 13 3
1 / 1 / / 1
1
&%
3 / 1 &
& 1 3 13
1
1/
+-
1 / &% 3/ & /J #00 )=
3
1
. // ? 1 =
1 / 1 & / / & 1 / / @ ? 1
%
*
3 1 & 1 % 1 / / &
0
K
04
K
0 0
1/ 1 / =
A
/
0
K
04 04
@
@
L A
0
@
@
L A
0
04
@
A
A
0A
@+A
% 1 3 + ? /
! 1
+
04
0
,% @+A / / / / /
/
/ & / 8
1
0
1 &/ ! &
0
K
04
K
0
6?
K
@
L A
@ A @
L A
04 04
0
04
@
/ & & 1
1 6 ?
1 &% ?
0
?
0 0
1/
1
1 / / @
C
@
@
04
%
/ &
1 /
% A 1 % 1 &
C
0
A
A
0A
@+A
1/ =
K '0 !)=?
/
1 1
Vi3
Vi1 a
Vg1
vsw
vsw
b
v-
15 +
a
vsw 100p vsw
Vg2 Vg3
#
v+
v+
b b vsw
50p vsw a
a
vsw
v- 4e-9/pi b
X2
b 2e-9/pi
X1 + v15 -
a
a
vsw
X3
vsw a
v- 2e-9/pi vsw
2V4
vsw 50p
a
++
1/
vb
vsw
v+
2V2
va
b
b vsw 25p vsw vsw
100p
vsw
b
& 1 3
3
+-
/ & ?
M
K #00 !M 1
K
#00 C
K
0
K
'0 0
0
K
K
0
1 ?
0
04
@ 1 1 1
1
M 1 & & =/
K #0
K
1 / A 1 1
04
/
0
/
1
6
K
? 1 / 1
? 1 / 1 & 1 1
/ /
1 &/ !
1 1 / ++A
04
04 04
=/
%
1 / 8 ?
0
0 04
/ 1 &? ? & 1
/ & 1 / 8 ?
1/
=/ 1 3
% 0# M / 5
1
/ /J #00 )= 1
& 1 ? / 1 ? 1
0
@+A 1 =/ @
++
?
1& ? 1 & & 1
1 %
1 &% &
1/ ?
1 #0 C
/ 1 &
0
0
/
0
?
1/
1 &/ ! @+A ?
0
% 1 &
& 2 1
3
++ & 1
1 = &
/ 6
& 1 &
(13 /
3 /
. & & / /
-
Input (dBv)
0 −20 −40 −60
Output (dBv)
−80 0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
0 −20 −40 −60 −80 −100
Frequency (kHz) +
"/ & 1
13
1/ / &
1 / / 6 1 1 / 1 6
1
1 /? 3
/? / / & 1 / & ! / +
1 &% /
1
+
+ / 1 &% / 1
1 6/ & 1 / 1 6/ ? / 1 &
0 0 0 0
K
K
@
L
L
L A
K
@
0?
?
L
L A
/
@
L A@
L
L A
1 " / / & 1 6 1 6 ?
L A@
0 0
C
1 / / 1
& 1 6/ & 1
1 1 / A
''' # : . ? 0 ' ' 'D 0#*#( (0 '''
0
@ /
+
Input (V)
5 0 −5 0
1
2
3
0
1
2
3
4
5
6
7
8
9
10
4
5
6
7
8
9
10
Output (V)
2 1 0 −1 −2
Time (msec) + "/ 3/ & 1 13 6
1 & 1 ? 1 1 +
/ 1 6/ 00 /* / 1
1 & 1 /
/
/ 1 1 0 !)=
! /
/ 1 / /
% ? 1
3 1
1 & 6/
1 / & 1 / . ? 1
/*
1 / /
& 1 @/ A &%
1/ 1 / 1
& / / &
3/ / 1
+ & 1 13&%
/ 1 /
1 / / & 1 0 1 #3 &
@5 1 1 '-
000 X /
K #
/
& 1 A
/
3 / 1 1 1
1
1 13 1 / B &
1 1 3!)= / 03!)= / 1 3 6 1 / 1 / & 1 13 /
/ 1
1 /
/1 /
/
8
# %( *
71 1 6 1 / /? 1 6 1
/
1/ /
/ / & 1 1 /
*
1 & / ? / 1
/ 1 % &
/ /
/
1
& ?
! &
/ 3
6 1 & / = ? 1
1
1 %
! &
$ 1
1/ 6 & 1
& / 1? ! /? 1
3
/ 3 1 1 3 8 1 & & 1 & 1 & & ?
?
1 &
1 1 / /
? &
/ 1 /
1/
A ( 1 1
0
1
K
0
+@?
@L
A
1 & 1 1 // ? @+ AC
0 0 0
@ A
K
@ A
K
@ A
. @+ A? 1 / &
0
@+ A
1/ % 1
1
1 /
& &
/
1
& 1 % & +@ A? 1
1
1 1
+ @
L
A
K
" 1
X X
1 + @ A + @
,% @+'A 1
1
L
1
1 1
1
L
+ @ A
A + @ A
?
1
1
1
/ 1 &
+ @ A 0Q
P
+ @ A /
C
L
+ @ A
/
+ @ A
1/
% & & 1 / !
1
?
@+'A
1 ?
/ 8
K 0
& / 3 3 1 %? 1 / 8 % & / 3
3 % 1 &
?
1
&
K
@
1 C
0 & 0 & 0 &
& A
@ A
@ A
@ A
& 1
& 3 & &
K
K
1? @+'A 1 /
@& A @& A
0
& & ? @+ A / @+#A? 1
/ / & 1
@+#A
1 &
C
& K 1
@+-A
1 1
& 1
/ @
1 / /
K
K
L
1 / / /
L
L
/
& &
A
L
T
1
L
T
@
L
T
L
T
A
@
A
/ & 1
/ / 1
1
1
@++A
0 @ ? &
13
&% A
$
3 /
& 1 (
= / / 1 &
0 0
1/ / 1 3
- 1 1
K
@0 -
@
L '
@+A
L A 1
/ & &
1 &% & '0 !)= 1 63
/ 3= / / 1 / 3 1 / &
3
L A
L '
$ 1 /J / &% 00 )=? 0# "M & 1 ? /
36
! &
/ /
/? = @ A? / /
& 1
%
3 1 3 / / / / / /
36 =
?
1 1/ 1 &
-? 1 ?
K - ) 1 1 1 &
@ L @
L
A
04 0 0 0
K K
A
K K
04 @ L @
1
@+A 1
L A
K K
K
0 0 0
K
A
?
K K
? E
1 %3
1 1 1
/ ?
C
0
04 04 0 0 04 04 0 04 04 0
@
L A
P
@ L @
L
0
@
@
04
L A L
L
A
0
AQ
A
P
L
Q
A
04 0
P
@
/
0
L A
@
0
0
AQ
/
@ L @
A
K 0 0#' @
A? /
04
P
L
0
Q
@+A
K - ) 1 %
1 1 / / / & 1 3 & /
0
C3
V2 V i3
C3+C4
1
1
-
+ 0 V
-V 4
+
-
+ 0 1 // & &
0
?
0
1 & & /
1 1 1
/
1 1 1
+ 0 1
1
1
1 / / & & + 0
&
0
@+A
7 1 1 / / 1 % 1 / /? 1
1/ 3
1 /C
0 # "M
K
K
K
K
K
1
K
00 K - 0 # K 0
'0 !)=? 1 M
0
0
1
1/
K #0 / & 1 ?
- -
K
K
0 0#' 0 0#'
L
K - #
K 0#' 0#'
1/
?
/
K ' #
K +
1
+ 1 1 /
0
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1 =/ & L
0
1 1 1
$ ?
?
1 & ? 1 / 1 ,6
1 % /? 1
& L
04
? / 1 1 &
0
& 1
? 1 1 =/ & 1 13 /
1
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6 ? 1
/
/ '-
3 000 1
1
1 X
K '0 !)=J0
1 / &
K '0 )=J
1 1 &% / //
@ +A?
&%
K 0'0 )= @ #A? / M
K -0'0 )= @ #A
K #@00A K 000 )= & 1
36
K 0 )=
1 6/
= & 1
!
Vi1 Vg1
a
Vg2 Vg3
b
v15 +
Vi3
vsw
50p
a vsw
va 50p
vsw vb b 37.9p - V4
vsw
v+ + 15 -
X1
v-
b 435.8p 50p a
v+
+
vX2
b vsw vsw a
V2
1 &
vsw
50p
vsw
668.5p
37.9p b vsw
vsw
vsw a
vsw vsw
50 p
vsw
b v+
vsw
X3
a
b
V2
435.8p v-
b
vsw vsw
50p a
- V4
1/ / &
"
a
vsw
36
=
/ / 1 3= 6/ &
1 / / 1 / / / / @+-AC
# # 7@ '# . $$ + ' 3$% 0$" 0, % A" ; : B8 #B : # : . & ? :. & + C$" ,(# ;$"#; ;'7 $ $"$ :'D -$"# 7@ 8))! -, # 7@ 8))! 0 -$"' ; : 0 -, ' ; : + .E ,"$ #, %$" #$ $" G'! !' H '8 '8 E G H ; $ 3 B EE ; ; E$%E 3. 3 $% 3. 3 GE'! 6E$% ;
jω
15
Zero−s Zero−z
10
krad/sec
5
Pole−s
Pole−z
0
σ
−5
−10
−15 −6
−5
−4
−3
−2
−1
0
1
2
kNep/sec + 3= 1 & / & 1 / 3 / &
1/
HE6$% ; F6- G' 6- H FE6- GE' 6- HE 1 3= 1 1
+ 1 /
1 / 1 = 1
/ = // 1 / 3
1 1
& 3 & 1
& / % & = 1 1 / 1 & & 1 6 1
36
!
1 1 3
= ? 1
? 1
1 1 & 1 / / 1 &/ ! J 1 & 1&3 $1 1 &
1 = 1 / /
36
/ 1
8 1 6/ / /3 & 1 $ / 1 / /*A & 1
+
1
+ & 1
1 1
? / 1
1
1/
1 / @
1 /3' 1
1 1 /? 1 1 / & 1 /? / 1 1
1 /
1 / / /
3 / B ? 1
36
Input (dBv)
0 −20 −40 −60 −80
Output (dBv)
0
1
2
3
4
5
6
7
8
0 −20
z−Distort
−40
s−Proto Measured
−60 −80 0
1
2
3
4
5
6
7
8
Frequency (kHz) + "/ 6/ & 1
= 1 1
+
1 / ? /
1 / 1 1 1 / / & ?
/ / &% ? 1 1 / 5 1
& 3 & /
// 1
1? 1 /1 & 1 6 &% @ ? 00 !)= &%
/ 1 / 1 1 &
1
13 1
1 . / 8 1
1 1 / 6
? / 1 /
% / /
1 &% & / 1
36
=
1 / 1 / 3
&% / ? @++A? & ( / 1 @++A / 1 &
1
@
&% 1 &
A
1 6 ?
1
/ &
1 / =
/ 1 1
/ & '0 !)=A
1 /
1 &?
$1
& 1 / 1/ 1
?
36
- L
K
&% ?
@+ 0A
? / K -00 ? 1 1 3 K 00 K +' J 1
K #
6
? 3 / 6 ? 1 1 1 & 1
& 1 /
K
C
+ 6/
5/ 1 ! / 1 8 /
1 1 & $1 &% 1 &/
1 & 1&3 /
/ 1
1 6 1 8 $ +- 1! 1
'
?
1 / / 1
1
8 1 / & 1 6
?
/
1
1
/ & ? (
& 6/ 2 1 % / / & 3M
. 1 6 1 2
// 0 "M? / 1 3M
/ 0# "M &
& 0C @- /*A 5/ 1 & #0 !M / & 00C? 1
1 / & 1 1
$ + 1! 1 &
3/ / & 1
)
? 1
+ 1 1 !
/ / & 1
! 3=
% & 1 / 3
& / 1
1
% % & 1 / /
8
(
1 6 1
/ 1 1
/ / & / / 1 &
1 / /
1/
/ 1 / 3 & 1 &
/ /?
/ & & 1 / 3 1
1
$ 1 /
K
1 ¼
K
1
! & ? @+#A?
0 0
0 0
K
K
&
K
@
& A
@& A / K .
1 ! /?
? @+-A 1 &
?
! & C
1/
C
.
1 1
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7 1 1 / ? 1
&
,% @+ A B 1 /
K
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&
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1
1
3= 1 &? /
8/ 1 & 1
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36 &% & /
K
.
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! & 6 1 /3
! &
/ / /
/ @ ?
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36
= / 1 A .&
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1&
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/ 1 = / 3=
1
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? 1 3= !
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! 1 / /
#
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+ ' &
1
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6
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! & & 1 !
C
3 C
0 0 0
0 '0 '0 '
K K K
K
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@+ A
# C
0 ' 0 0 0
0 0
K
K
K
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0
$ 1 & ?
L
0 0
A
L
@+ A
' L A
C
0
0
0 0
L @ ' L ' L A
K K
0 0 ! & ? @+ 'A?
0
L @ ' L ' L A
@
0
6
0
"#
1
@
L
' L ' L A @' L ' L ' L A
@
K
@+ 'A
1 / / & & %/ ?
1
'
?
?
/ 1
'?
@+ 'A? / / 1 &%
1 /?
?
1 / ?
?
/
1 / / & 1 > 1 / 1 K # K @'0 !)=A / K -00 K 5 $// 5 ? :C
)? P'Q 2 1 ? ? / $1&? 5 7? / 5 ? :C )? +#
* !
? > $/3
$# % 6
! $ !
$ &
1 / / 1
/ / / &%
1 & / / & 3 /
! & " / / 1
D 1
? 1 3
1 / U % / 1 % /
71 1 1 ?
& / / ? 3
! & ? / 1 % / & & ? &
/
1 6 &% ?
1 6 1 1 / 1 / 1 / /
?
!
&/
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! & / /
1 / / / &
9
&( %
1 / &% / & &
.
L /J? / /
& &% ?
1 / 1 / 1 1 1 & ?
-
& / @A?
1 &
/
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1 1
/ &
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.
? 1 /
/1 & / / K @ L 0A K
1
= D 1?
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>
@ A?
/ /
/ 1 &
& C
@ A
;
K
K
0 &
K
&
; 9 P
@
L A
9@ AQ
&
@A
!
#
!
# - ) - Æ 1
" !
'
1.5
|H(jω)|
1.0
0.5
0.0
−0.5 −2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
ω (rad/sec)
% / &
8@ A
K
K
K
1 ;
?
& 1 6 @
@
1
2.0
A
?A
?A
@
!1 & 1 1
/ 1 / ?
/
1.5
@A
@
?
1 6 /
1 1 /
K 0A? / ? 1 3/
/
/ ? 1 = ? 1 7 /? 1
? 1
& 1 &
& Æ / & ?
??
0
/ 1 = ?
1 1 = 1?
& & / 1 / 1 3 / / / 1
/ / /
& @= 1A?
1 / & ? ! & 1
1 1
? / @A
@ A & ?
K
/
@ A
K
1 = /
1 1
.
/ & &
& ? 1 & / / 1
?
1 1?
;
1 ?
@ A ! ? 1 =
K @M A 1 = 1?
/ / / .
1 8 1 1 / 1 1 & 1
"
#
0.40 0.35 0.30
τ=2π
0.25
h(t)
0.20 0.15 0.10 0.05 0.00 −0.05 −0.10 −3
−2
−1
0
1
2
3
4
5
6
t/π (sec) . &
1
@ A
!
/
1 = / & & / / 1 1
/
1
& &
/ 1 &
@A
K
@ A L @ A
@ A 8@ A
K
8 @ A L 8 @ A
8 @ A
@A 1 1
/ &
@ A
1 &% / &
@ A
& 1
= 1 ?
8 @ A
8
K
K
K
8 @ A
K
8@ A
8 @ A
1
/
&
1
'
1 1 &
@M
A
@M
1 1
@
1
A @
@ A @M A @M A L
A
@ A
1 / &
/
C
1
@ AC
1
A
" !
-
1.5
H(jω)
1.0
0.5 a 0.0
−0.5 −2.0
ΩS
−1.5
−1.0
ΩS
−0.5
0.0
0.5
ω (rad/sec)
/ /
1.0
1.5
2.0
&
10 b=0.1
dH1 / dω
5
0
−5
−10 −2.0
−1.5
−1.0
−0.5
0.0
0.5
ω (rad/sec)
' % / & 1
1.0
&
1.5
@ A
2.0
"
8 @ A
@M
@M
K
@@M
A
L A @@M
@M
K L
?
8@ A
K
8 @ A L 8 @ A
8@ A
K
Æ @ A L
1 1
@ L
0
& @'A /
1
A @@ L A
A @
A @ L A
?
?
// /
0? 1
@#A
/ &/ & 1
K 0
8@ A
@#A 1 & 1
& 1
& @A? & 1 /?
/ & 1 1 1 1
/? & / /? 1 1 1 1
/1
1 / & 1 1 1
0 /
@'A
0 1 /// /? ? 8 @ A? / 8 1? @ A 1 1 1
@A # 1
A @@M A
A
@M A
L A
L A
&
?
/ &
A
1 1 1 1 1 /// 1 1
1 / 1
&
A
1 / 1 /
7 1 ?
/
A @@M
L A
&
&% ? M
@ A K ? 1 1 ? 8 @ A K Æ @ A? / ? @ A 1 @#A 1 1 /
1 ? 1
+
1
1
?
K 0 # /J
1
/
8 @ A
1 //
#? 1
1? /?
??
/
/ 1 1
1
! 1 & 1 / &% 1 / = 1 & . 1 / /?
1 1 &%
& 1 1 / / & ? 1 & 1 1 &
1 &%
/ 1 1 1 . ?
1 6
/ (
61 /
9
- ( #(.*# /
1 & & 1
! & /
@
A K
&
08:1
!
@
A
@A
1 / = &
/ /3 &% & @ A
K
K
04/
K
?
08:1 04/ @
A
7
@ A 1 @ A & 3 1 &
@ A K
K
@ .@
.
A A @ A @ A
1 C
/
) % %
" !
Impulse Response
Impulse Response
0.4 Nonideal 0.3 b=0.25 rad/sec 0.2 0.1 Ideal 0 −0.1 −20
−15
−10
−5
−45
−40
−35
0
5
10
15
20
−30
−25
−20
−15
−10
0.05
0
−0.05 −50
t (sec) # . & 1
@A
K
K
1 &
/ / / &% &
@A @ A @ A @
.
@ A. @
@ A
A
@
A
@
1 = &
K
1 / K
?
K
/ K
? 1
@
A?
@
@
A
K
#
@
A
K
#
1 6 &% ? &
@
.
?
@ A 1 @A 1
.@
A
.
@+AC
.@ A / 1 @ A K 1 3
1 .@ A 1
@+A
1 1
36
C
@
.
@-A
A? / 1 1 &
A 1
/// &
// ? 1 1 / /
@A
A
@
.
.
A /
.
A @A
@= A &
#
.
@
@ A ,% @ A
A 1 & 1 &
L
.
A
@A 1
@A
1 1
"
7 // / 1 1 / & ?
36
?
@
A?
/
1 &
@
A?
1
6 C
A
K
@ A @
A
K
@
A
K
@ A @
A
K
@
L @
L A@
L @
@
A
K
@
@ A @
A
K
@
K
L
L A@
L
L
L
L A K
L
L0
L
L
L A@
A K
L
L A@
0
A K
L
L
L0
L
L
A
L
? 1 & ? 1 / 3
1 / 1
& &
1
@A
1 !
K
! 1
@-A / 6
/
(
9
$% % .
/ 1
! / & @AC
@A 1
@A !
K ?
@ L
@A
A
*
@ A
1
(
K 0 # &
U ! 1
/ ( 3
- 1 1 / 1 /
1 / /
3 / 6 1 / &
& ? 1
&
K
0?
/ / *
1
(?
1 / ?
! ?
@
&
(?
/
1
1 6
A /
.@
A? & / &
@A ,% @A 1 & / / K
K
C
@A
K
.
@ A. @
@ A
A
@
A
@ A
K
@A
@ A @
A
K
/
.@ A.@
A
K
L @A
1 & 1&3 @1A 1 (
&
.@
@-A?
K
1 &
L @
A
L
@0A
@0A / &
.@
A 1 1 &
L @A
&
K
0
A? / C
@
A K
" !
0
1.2 1 Ideal
|T(jω)|2
0.8 0.6 0.4 n=2,4,6 0.2 0 −0.2 0
0.5
- *
1
1.5
2
(
1 6
.@
K K
1 1 ?
K
@A
K
L &
(
//
K
&
(
3
1
&
K
(
.@
A
K
@
.@
A
K
(
1 ? K # / -
36
& / &
A
(
( K ' -
@A
(
1
5
.@ A & 1 (13 / * 1 .@ A & 1 / / ! &
+ &
4.5
K @A
&
A
4
/ ( &
( ( ( ( ( L
1 / / ? 1
3.5
A
1 / &
3
ω (rad/sec)
1
2.5
(
1
//
A
K
@A
(?
/ 1
1 ? //?
1 *
1 ?
1 1
@ AC
L A
/
,% @ A
@
@
L @@
L @@
L 0#AAA L A
L 0#AAA L A
& & 1 *
&
(
&
(
//
@ A
1 & &
(
"
jΩ (rad/sec)
(a)
(b)
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
−0.5
−0.5
−1.0
−1.0
−1.5
−1
0
−1.5
1
−1
Σ (Nep/sec) + ,6 *
1
/
1 & @A
" 1 1 1 &
/ @1 1
@A
7
( K #?
/ @ A
"- & ?
1 1
1 &
! 6 1
1
1
K
0
K
L0 L
0 C
0 @A K 0 /*
K C
K
0 @A K 0 /*
C
0
@A
K 0
!
& ?
1
!
C
@A
/
(
@'A
1 @* /A & 1 * 1
(
/ D 1
7 1 1 &
&
&
@A
/* &
/
1 / &
1& / 1 1 & 1 * & (
( K -
@0A? / 6 1 (
1 / %
1
,6 A
-? 1 *
& & ?
0
Σ (Nep/sec)
& / 8 &
(
1 &
1 1 / 1
: K @ A 1 1 8 &% ? K ? ( / 1 // & 1 / 8 ? 1 0 /* & 1 1 ( / 1 1 1 & ( & %
1 ?
1
&
K 0?
3 &
1 &
(
& *
3
1
( & & &%
& 1 / 6 / & /*
K 00 )= / / & #0 /*
K 00 )=
" !
90 n=4
80
Loss (dB)
70 n=3
60 50
n=2
40 30
n=1
20 10 0 −1.0 −0.8 −0.6 −0.4 −0.2
0.0
0.2
0.4
0.6
0.8
1.0
x=Log10(ω) & *
%
1 &
3 1 / / % !1/
&% &
3 / / % 1
,% @#A
A
0 @ L
A
K @
@00 00A
(
1 &
(
?
K '
$
/ 1 &
A
0
(
1
#0
0
0
0
K &
@'A
(
C
@#A
(
1
0
0
K
K 0 1 %
6/ 1 % 1? / ? 1
&% &
1 1
1 / &
A
@
0 @ L
(
1 1 /
& 1
? @#A
1 % &
C
K
@0
A
K 0 '+
( K 0
"
50 dB
Relative Loss (dB)
50
Specification
40 30
nth−Order Butterworth
20 10 f1=100
1 dB 0 0.0
0.5
*
f2=200 1.0
ω (rad/sec)
:
K
@0
A
K
0-
/ #03/* 3/* /
K ++
K 0
1 1 1 13 / *
1
/1 & 0 ?
1
0 1 2 1 K
& &
0
2.0
1 / ( %
:
1.5
f (Hz)
& 3
% &
/
K 0 0 /
K 0 & 1 13 / 1 / &% K 00
& / & 1 &
K
& 1 / 1 Æ
" C
," $" J( ; 4" 4$$ " $%" J + " $ ## ". J"-J $" 4$4$ "# J + " $ -" ". J"-J $" 4$4$ "# "#
" !
'
( K 0?
1 &
/ & 1 *
1
& 1 / @ AC
. @
A
K
@
L 0
@
L +0
K
L A@
L A
L +#'
L 0 ' +
L -' '
L ' 0
L ' 0
L ''
L A
L -' '
L 0 ' +
L- # 1 % /
L 0 00
L A@
L - #
L+' '
L A@
L 0
@-A
1
! & ?
@
. @
A K
A? /3
/ 1 1 1 & 1 / 1 0 / =/ # $3R @# AD # %/ @# AD 3 @0 A &
? 1 ? /
& &
& / 03 *
1 (
/ 1 1 & 1 & / &
1 1 1
/
9
1 &
$% %).% .
. 1 ?
// 1 *
(
/ / ? 6 1 & 1
(13 /
K
! & ?
0? 1
K
@
K
/ & / 6 &
1 & 1 7
/ C
(AA
:A
@
:
(
&
@A L & / 8 &
1
:
:
&
(
* @:A * @:A L * @:A /
* @:A
(?
? 1
/
1 /
:
/ & 1 1
* @:A
1 1
1
:
/ 1 1 // & &
// / & &
/ /
A?
@+A
1 / % 1 &
1 1 1 &
@+AC
6 * @ AQ
1 1 1 1 1 &
A
1 1
3 &
P L
* @:A
1
1 1
1 1
1 1
.
1 / 1 1 1 & 1 1
@A * @ A
1
/ 1 / U & /
/ / 1 / @A
( L AAA @(AA @AA @(AA @AA
K
@@
K
@@
K
@
K
( AAA @(AA @AA L @(AA @AA AA @(AA
:* @:A
:* @:A * @:A
@A
9 ) : ; :
0
"
#
2.5 2.0 1.5 n=3
Vn(x)
1.0
n=4 n=1
0.5 0.0 −0.5 −1.0
n=2
−1.5 −2.0 −2.5
−1.0
−0.5
0.0
0.5
1.0
x (
0 1 1 1 & / 8 &
7 1
* @:A
@A
K /
* @:A
K
: 1 & ( K 0 / ? ?
/ 1 /
2 1 // / & & 1 & // ? 1 % %
:
K 0?
: K ?
(
// /
1 1 // % =
:
K 0
1 1 1 1 / /
1 & ? 1 1
!
A
.
/ 1
1 &
:
. 1
1 1
& 1
/ ?
/
1
1 1 & 1 / 1 % / %
1 // & 1 1 1 &
/ & 1 %/C
*
* 6 ?
@ :
':
:A
@
K
K
(AA
@
@ L
*
:AA
@
: :A K -: ': L : L : L A *
K @'
1 1 1 1 1
*
@
& &
A
(AAA
@ L @
@0A
% @ L
! & ? @+A? &
1& ? 1 / & 1
/ & 1&3 3 & & @+A?
/ & 1 *
* A K
1
@
A /
" !
-
4 / & 1 1
(
5
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