Active Filters for Intergrated-Circuit Applications 9781580538961, 1580538967

This authoritative resource offers you comprehensive knowledge and detailed design guidance on active filters for integr

227 27 5MB

English Pages 422 Year 2005

Report DMCA / Copyright

DOWNLOAD PDF FILE

Recommend Papers

Active Filters for Intergrated-Circuit Applications
 9781580538961, 1580538967

  • Commentary
  • 61132
  • 0 0 0
  • Like this paper and download? You can publish your own PDF file online for free in a few minutes! Sign Up
File loading please wait...
Citation preview

Active Filters for Integrated-Circuit Applications

DISCLAIMER OF WARRANTY The technical descriptions, procedures, and computer programs in this book have been developed with the greatest of care and they have been useful to the author in a broad range of applications; however, they are provided as is, without warranty of any kind. Artech House, Inc., and the author of the book titled Active Filters for Integrated-Circuit Applications make no warranties, expressed or implied, that the equations, programs, and procedures in this book or its associated software are free of error, or are consistent with any particular standard of merchantability, or will meet your requirements for any particular application. They should not be relied upon for solving a problem whose incorrect solution could result in injury to a person or loss of property. Any use of the programs or procedures in such a manner is at the user’s own risk. The editors, author, and publisher disclaim all liability for direct, incidental, or consequent damages resulting from use of the programs or procedures in this book or the associated software.

For a listing of recent titles in the Artech House Microwave Library, turn to the back of this book.

Active Filters for Integrated-Circuit Applications Fred H. Irons

artechhouse.com

Library of Congress Cataloging-in-Publication Data Irons, Fred H. Active filters for integrated-circuit applications / Fred H. Irons p. cm.—(Artech House microwave library) Includes bibliographical references and index. ISBN 1-58053-896-7 (alk. paper) 1. Electric filters, Active. 2. Integrated circuits—Design and construction. I. Title. II. Series. TK 7872.F5I76 2005 621.3815’324—dc22 2005041997

British Library Cataloguing in Publication Data Irons, Fred H. Active filters for integrated-circuit applications.—(Artech House microwave library) 1. Electric filters, Active 2. Integrated circuits—Design and construction I. Title 621.3’815324 ISBN 1-58053-896-7

Cover design by Igor Valdman

© 2005 ARTECH HOUSE, INC. 685 Canton Street Norwood, MA 02062

All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark.

International Standard Book Number: 1-58053-896-7

10 9 8 7 6 5 4 3 2 1

          





  

    

                           



      



       



 

  

                                      



                           



                                



        









!   " 





! $    



%   &    &     

'

 

(  (

                     

#

                         



            

'

                            

'



(  )

                            

#



(  *

                            

+

'

(  * 

#

*   ,   

!   

                 



                   

'

-

(  *$

                            



. /   &    &    

            

'0

'

1 .   (  $   /              

'

'

1    / 

       

'+

#

$



                                

!  / . 

'

-

  

                                

#

 

 !   "   



#

1 2                            

#



-'

$     /                  



$ 3  2 3(  4

                 

--



 3  2 3(  4                  

-+

'

 3  2 3(  4

                 

+0

                    

+

 2     







  '

           

+'

$



.    %  5  ,6 

                                

+#

  

                                

+-

5&                                  

0

$ %  & '   

(

'

1   "  

'

1  8      .  $ 

'

'

                          



1 7 / "                          

'

 $        

                

+

                 

0

'

$ 3$  %  5                 



'

$  5 

+

''

                     

$ /32/ ,8     " /            



'

1 $ / $                              

0

''

1 1 / $ 

0

'' '#

                            

    ,   

 1 

 2 $         



9 13$  2                



'#

     & 2 28

'#

 $/9     / 2 

        

'

                               

-

                                

+

5&                                  

'

'-

 

'+

  

 / 6 ' "  /     " / ' " / *: $ 5  ' " /   5  ' $



              

#

                    

#

                     

'

                                

'

 &  '      #



         



1 2    $                        

#'

#

1 *8     

                   

#'

#

1   "  *8              

##

#

1   $

"               

##

#'

1 .  $

"  

#-

##

              

1 .  .                        

#+

#

  2      ,6                   

#

                  

-'

#

$                               

--

#'

 / "1 /                             

-

#'

                     

+0 

#

##

//    ; 

1  /  

#'

 $ 3    1        / & 1    

%  3 1     1 1

/ /  /       / 1

/ /        

/  / 

½¾¿

 /

½¾¿ ?

  ?

1     1  

    

 R(½ C R(¾ C

½  0½ 0

L

#

½ L

'

 L

½  ¾ 0

¾  ¿







K

½

K

0

K



½  ¾ 0





       

+

I

s1

Is1

10

R1

V s1

v

i

x

1

20

v

R2

0.2

2

2

v

R3

25 ix

3

100

Ω H,F)

(

,

   ,6     &     6   

'@½

 ¾

0

A

¿

R(¿ C

00

L

L

 ¿ ¿  ¾ ¾

K



0

½

K



1 1 %      / @'AC



 ℄ L P℄ L

P



P



 ½  ℄

1

½ ¾ ¿ P

 

℄

P4℄

P(

½



½

K

 

0 



0

0

K

 

0

0

0

0

0

0

K

 

K

 

0

 

0 #

 '



@ #



71



0 0#A½

 / & 





@ #





0 0#

0

 

0

0

0

0 #







M

½



0

0

 

0 0



0 #

0



0 #



 

½

)

¾ ?



@'A

0 #

   1    1

 R(¾ ? 



 1 /  / 1  @½



 3

 ¾  A

0 0#A¾ ?  1 1 03M     /     3

1     /?  /  /    1    ?

 / 8 ? 

½ ?

  /

 

 

0

0 ,% @'A  

 



L 0 0½

½

@A

 1 /

         ?  / 1 E      ?

 

 1     /

    /    / 1

   

/     &  1 /   ?

   

 R(½ C 0

½ L

#



@

 ¾

A K

0½

½¾¿ 

 1

            



v1

V s1/10

Is1

v2

20

10

2

0.2 1.25(v 1-v2)

v3

100

Is1

(Ω,H,F)   '     /  / & /   

R(¾ @ 3 AC #

@



 ½

A L 0@

¾ L ½ A L  @¿ L ½ A L 00¿

K 0

 /  $     C

 ¿

¾ L ½ A K ¾

# K #@ '

¾ L ¿





#½

K

@#A

1 1 %      / @-AC



P

℄ L P℄ L



P



 ½  ℄

 

½ ¾ ¿

1

P

℄

P5℄

½

P



K

K

K

K

  @    

  /

L 0A½



#½

0

0

0

0

0



0

0

0

 

)

0

0

0

0

0

00

0

'



 # #  # # 0

,% @-A  

 

0½

0

0 0

   

M



½

@-A

0

   1    / 1

  #   ? 1     /



 / 8  & 1    ?  1

1       &  /        1    &   #   /      ?

½¾¿ ?

1  1    1  &  1     

1  6    1 1   / /

1       %?  /      6 

/        /     

 / /

1 1  



  &      

1 / Æ   &

      



(20+2s)I

10

+ -

R1

24

+ -

R2

(100+2s)

0.2

R3

R2 (

1

+ -

R3

20

V s1

s1

+ -

25 I

s1

Ω H,F) ,

  #     /  / &     



      

S  1   /  / 1  M3 /J          &     1   1 1 

/   & /    

> &  ? 1  M3 /J    /        &  

      /   

.   ? 1

? 1 1

1       

         



/   

  

1 

  

  

  





/   / &%   & 

    1 /     1  / "   !   

     /  1   /   &  M3

 /J       1 /  1

 & !

1/ &  

1 /   /  / &%   % / &       1 / /   &/        1  / 1    /  



/     %    (    / 1   1    1

/  &         &  ?  / 1



  / &% 3    1       1

/  &     / 

1 1    /3

       /      

!

1  &

        /       1 1   /     

!  /

 1        /   / 1 

  -

1      

  -@A

 ?  1  1  1 1  /    1 & 1      ?

  &  ?

/ 

 1 / >      ?

P



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

 /

  





   P

℄L

 /

¼ 

 P℄ L

 1 



 P



@AC

 ½ ℄

            

0

I1

I’ 1 N (RLC) [ ZL ]

V1

+ V2 -

N’ (R’L’C’) [ Z’ L]

V1

(a)

(b)

  -      

+ V2 -

!? @A?

  /   /     /   /

!? @A



 P

¼ ℄ L P ¼ ℄ L



P



1 /  % / @A   1    1 / /  /   1 

¼ ½ ℄

@A

 1   1    1   3

/  1   ? 1  

   ?  / 1   /

 / 1

 1 /?   ?   

 

¼ ¼  ¼ 





  1      $

  /



K

 

K

 

K

 

     

  1

@A

/ ?  /  ?  3

/    &  

/    1 5(   

  1& 

/?  1

  7

1 /    /  &   1  /   1   1       &  

  / 

!

    /

1 1    6 

 /  / 

! 1  

  1

 1

/ 

 1/   &   1 1   

    !  1

 & 1  

/  &   C P℄

K

P ℄

K

¼

 P¼ ℄    

1  / 

 ½ P0℄ ¼  ½ P0℄ K P  ℄ ½ P0℄ P ℄ P ℄







P℄

@0A

!  / /  1

/    /  000? 1   

 

/  &  ?

1     /   /  /     8 /  1    1   &     & 

 

.&

 7 1 / 

/   

/   /    

 &  / /       /? 1  8 



//

1  

   ?  / 1    / /  1   & 1    & 3     3 3    /  3 3   / /       8 / 

      



ω)

H(j

0

1

2

ω (rad/sec)

3

ω ')

H(j

0

k

ω

2k

ω

3k

ω ' (rad/sec)

ω

H(jf ')

ω

0

π

π

ω

ω

2k /2

k /2

3k /2

π

f ' (Hz)

  +  / /  &    &%       &%   

/    

    /      ? 1

     &  ?  /  

? 1    

  /      1 &  ?

 /      1  /       ?   1



&  

S   





 

   

  /

 1 ! 1      

1 



/    1 8  &     / /     %     1



 B   & 1   

 3

  / 8   

  + 1    &%    /  1 &  

1     & &%  1

 1   

¼ ?



 ¼?

1 



D

 ?



  / 

     

   &%    1 

% /    1   &  &

  1

36

! &  

 1 &%  1   



7

!     1      6 &   & 

    C

@ A℄P℄

P 



 



P

 ,% @A B 1



¼  A℄P℄

 1 

1    1     &% ?

@

¼ 



K

P0 ℄

K

 

K

P0℄

  &











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



K



     

 ¼

K



K





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



/ /  & &% ? 





 5  

/       C

A



K

K

 



@A

  0

1 & 



  C

 5  

@

¼

K

@

¼

A K

K

 ¼



K





¼

@A

            

-

s

1/s'

R

R'=R

(Ω) Ω

L/s'= 1/(C's') (

Ls

Cs

C/s'= 1/(L's') (



)

-1

)

   ,     &  1 (  )  &   

2

Z(s)

2

1

Ω ,H,F)

(

   (    &  ,6  '

 5       

@ A

K



K

/  C



K

@

¼

A K

 ¼

K





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



@

?   



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  





/ /  & &% ? 

K



 . /        (  1C

@

A

K





K

!

K

@

¼

A K

 /

!

¼



!

L

K

¼

K



¼

L





¼





@0A

!

        (  1C

@ A

K





K

!

K

@

¼

A K

 /

!

¼



L

K

1     &     1           &   



¼

K



¼

L









@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



&  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



 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



'

 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



K L

& 



K

1? 1 *  /









  !



 !

L  

'

L

'

@+A



%$  





K



!





K

!



L



L



 ¼

?

1 & 

1



 1

  /C

L   /

!

'

 '



K

¼  1 L 3 &   K 

 

 @A? 1 & 

 !

L

!

@A

/      /C



%$K



K

/1



 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





'

 & 

 & @-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 ¿

 1   0

1 *   1 3/*  /

  ¼

¼¿ 

0

1 ! 1   /

/1 &  1 (   

  /J 

/1 & 

              60

∆ω=0.5 Null BW

50

α(ω) (dBv)



40 30 20 ∆ω=0.2

10

3 dB BW

Flat Loss=6 dB

0 −0.3

−0.2

−0.1

0

0.1

0.2

0.3

Log10(ω)    %    &  1 * &  & @''A

" % !?  @ ¼ AC

%  3 1  

@

@

¼

A  

A



P#@

¼

P#@

¼



0 0

L A℄P#@

L A L

¼

¼

¼A ¼ L  A

¼

¼

¼

℄P#@



L

¼

P#@

¼

0 0 ¼

@#

L #A@#

¼

¼

@#



¼



#@







K



L 0 -0





0 0'#







 0'D

& 

K

1     &  @''A

A

  @



 1

 33/*3 /

¼

L

¼

A    /

¼

L

A L ℄



¼



¼



℄ L A

¼



L  #



L 0 +''0





L ' 0

¼



¼

@''A

L #A

L A





L  0+-



L 0 -0

L A



 K 0000  0#0D  /  K 0D & K  0+0D  / & K 00



 1



  ?  /   

1    

 & 1   /1   #C?

¼

L #A

L # 0

 

¼



¼

L  0+-





L #- #



L ' 0

¼

L - #

L ' 0@



0 # 1 =  



¼

L ' 0@



L A

L 

L - #℄



L A

¼

K #@



L

 0 @

K





1   



L

¼

0 0

K

A

 % 

0 0P#@

K

K

 @



1 3 /

/13

1 1  1    &  1 (    &  

1 - /* E    1 *   &%   /  1 %   ?   /     &   & 0#  1 / &%  & 1 (   

1 1

            

'

0.4762

2.1

1 8.4 V1

5

0.119

0.2

0.2

+ V2 -

1

5

(Ω,H,F)   0 *     / & 1 ( &    &   



"

& #

  !   

71

  1 (  *  &   ?

   @   A?

  1    1





 



!¾ 

 &   %/?

L 

¼

A?  1   

  0



/    &  1  *   ?  ' 0  K ' 0?

    ? # 0 0 K ' 0

¼

K #@

7  1 1

 1    1 &  1

1         1  & 3

"

1?  1 

"¾ 

% /   = 1 *     



/? 1     

1        / Æ 

 1 (  *  &    *  1   & 1      / /  1  &   & 3  ?

!¾ ?

  / / 1  1   / 1   %      & 

1  //  (  1 (  1?  1 1





  @A? 1 & 

  1

  / 1  &    // 

  



K

!  !

K

!¾ 

/  &  1  //  1

 &   1 (

/  &  

1  (  1 1



  ?

  1

& 

 1 / 

/ ?

&

K

& ?

K

  /C

 

!¾  ¾¼

  /   1 &% 

(

& 

 1

K

!@ ¼

/  &  & 

&

@'-A

 @ ¾ L  ¾¼ A

 

K

!@

¼

L

&  1  //  1 1

 P!¾ @

@'#A



  @A

&  *

*      &  1 * ?

   

¼

L

¼

A

¾ L  A ¼

¾ L ¼ ℄



¼

¾

¼

¾

K



&  @!@

¼

A?  / 1

 

  @AC

¼

L

¼

AA

              LP

#

BP s=A(s’+1/s’) ω 02=1/(LC)

1/(LA)

LA

L CA C 1/(CA) (b)

(a)   

5 &  /   (  1C

@A   D  / @A

 / %  

¼

!@

K

 P! !

@

&

,% @'+A 1

 1



1  

 /   1

L A

L



¼



?  /

¼ @ ¼ L A ¼ L @ L  ! A ¼



K

¼

@

¼

L A

 = 

K

@'+A

L A

 ? 1 *      &% ?

1 1 *  1 61       

%      &  1 &   @A    /    &   

& 

&  6  1   &  (  1

&

K



!

@

¼

¼@ ¼ L



 ?

¼

L

 /





K

L



K

L

 !

 /

  K & 

 &  /  &  

 



K

K

A

 !

&   1 /   &





& C



L A

  A@

1

  1

,% @'A

   



! 

!



¼

¼ ¼

L L



L L

¼

¼ L



 !

L

 !

 A



L



L

 '!

L

 '!

1   

@

¼



¼ L



A

@'A

 /

@'A

@'A   / 

*    &  6   /?

C

¼

@

 1  &  & 



 ¾½

¼¾ 



 ¾¾

¼¾ 

K

K



    

     !     ! 





 /

@#0A

            

-

1/(LA)

LA

ω 12

L1

L2

C1

C2

CA 1/(CA) zBP

z BP

ω2 2

Lmax /Lmin = A 2LC = Cmax /Cmin and L 1/L 2=ω 22 Where ω1 2 = 1+ ω0 2/(2A2 )-ω 0[1+ ω 02/(4A 2)]0.5/A ω 22 = 1+ ω02/(2A 2)+ω 0[1+ ω 02/(4A 2)]0.5/A > ω 12 ω 22ω 12 = 1

C1 = AC(ω22 -ω 12 )/(1-ω 12) C2 = AC(ω22 -ω 12 )/(ω 22−1) L1 = 1/(C 1ω1 2) = 1/(AC(1+ω 12)) L2 = 1/(C 2ω2 2) = 1/(AC(1+ω 22)) < L1 L1/L 2 = (ω22 -1)/(1-ω 12 ) = C1/C 2       

 &   %   &  & 1  //  (  1



.  @'A 

0  / 1

/  



 /



&  1 %  

   1C



K



½ ¾½

 /



K



@#A

¾  ¾¾

   

 = 1 %   &  1  &  / (  (  1 &   @A 1  %        / 1 6  1 1    



 1  & 

½ ¾ C

½ ¾

K

K

/ /  &

¾  ¾¾ ½  ¾½ @

K

! A

A

1 

  ¾  ¾  ¾  ¾¾

 ¾½ ¾¾  ¾ ¾  ¾½

¾ ¾ @ ¾  ½

!¾ T



½





!

 

 &  /  

  ¾  ¾ ½ ¾ 

¾¾

 ¾½

 ¾½

½¾ ¾¾

K   /

 /

@#A

              0.1243

0.0757

13.202

8.0481

+

1

V1

5

0.2

0.2

5

+ V2 -

1

(Ω,H,F)   

*     / &    &    " & #  1

%   1



  

$     1 ½ ¾ K ½ ¾  $ ?   & 1  %  

¾

  1 !

  (

    / /  &  1   &  /  1

3   1 %       &  &  1   

 3

 0?  / /        &  1 /  / 

% 

¾

3 1   

  0  / &  (    & 

1 1

 ¼ K -# &  1  (  1?  K ?  / 1  &  &   ! K # $  1  / 1 & 

¾ ½

K

L

 &  1 %    &  /  1C

-#

#

@#A

#

-#

#

¾ ¾

K

L



K

#@A@ ¾



K



K



K

@#A

¾

L

L

#

L

¾

¾ #@A@ ¾ ¾  @½  ½ A ¾  @¾  ¾ A

 ½ A @

¾ ¾  ½ A @ ¾

-# '@#A -# '@#A

K 0-0-

K -'0'

¾

 ½ A K 0 A K 0'

K 0' K 00+#+

1  %   *         1      &  1      







K 0 00+#+ K -'0'?  / 







K 0 # K

-'0'?    1 &       1 1 'C  &  / &  1  1 *    1 1  



  0

   !   /  

&    / ?  ? 1



 

    

       %     ?

 / 1 61   / 8     1  &  1 /  &     

1   

    1 &   0 @ 1  1 1  %  

1 A  



   

    /   

            



1  1 %   / / 1 / 6  ?  / 1  

 36 



=  1  & 

  



   

 

 !

  /   /

1  1

1  

 1  

/   

! &  

! / 

1 * /  1 

 1  /   

  & 

   

/    

/   /

1  1 /   1 %   1     

61   1      

"



         

/ &%   

  #

1   &  ?  ! 1 *  &  ?

   3 3

     1 *  &  ?  /  ?



1   / 1    / %  

 &   1 

   /  1   1

/ 

/     1 

 / &  1 *  /?  /  ?          6  &  1   1  (  *$ &%   & 

  & 



  1 1  

 %     !  (  )     / 1  1 *  &   1 )   C

K

1 & 

¼



!@

¼

L

¼

A

K

@#A

!@ ¼¾ L A

   / &  5(   

 5  



/ /  & &% ? 



K



 . /       (  1C

@

A

K

K



K



K

@

¼



A K

!@ ¼¾ L A



¼ ! 

¼

@

L

¼ ¼

 /

¼

¼



A

K

 !

@#'A

         (  1C

@ A

K

K



K



K

@

¼



A K

!@ ¼¾ L A



¼ ! 

¼

@

L

 ¼

 /

1     & 1 *$      &  ?  / 1  &  &  

!



¼

¼



A

K

 !

 1 1

@##A



 /



&   /  1   /   &%   1    / 1 

     1 ? 

 &  1 *

     1 *  )?

!

 

/1?   

 1  &  1 *  &  

1 & 

              s



1/(As'+A/s')

R

R'=R A/L

L

L/A C/A A/C

C

  ' ,     &  1 (  *$  &   

1 

/       (  1



 )  &  1 





  

1



 / 1  *  &  1 

  / 1



  

(  1 1     &     1  &   & 

/    /

 

¼

K

'¼ ?

/

,% @#-A

  /

3  /   /





K



K



K

?  & 

 36  @#-A

A

 1  &   & 1 (

 ½

 ¼¾

/1?



¼

?    /   

C

K



K

 ¼¾ L

¼ !

 ! 











K



!

¾ /1?

L

K

¼¾





1 1  /



L

'



L



 ¼





!¾  ¾



K L

1? 1   /  /

¼

  #  / 1

0



¾

!@

1   /

¼

 / & 

 / /  1

1 *$ &%   &  ? @#A?  / 1 & 



1 ? & 

  ' &  1 (  *$

  #

&%   1 C

@#-A & 



1  / (  *$ &%   

L

! '½¼ ?





'





'

@#+A

L

@#A

L

@#A

!?

1     &  

 B 

&  C

¼¾

 ½ ¼

¾ ½ ¼

¼

K K



!

 /

 K

 ¾¼

@-0A

            

'0

4 3

ω=ω’/(1−ω’2)/A

ω (rad/sec)

2 1

P

P’1

Pass

0

−P’2

−P −1 −2 −3 −4 −2

−1.5

−1

−0.5

0

0.5

1

1.5

2

ω’ (rad/sec) ¼

  # 1 (  *$ &%   &     & 

,% @-0A 1

/1 & 



K



@    1

1  /    7  1 & 



K

½¼

K

¼

¾¼

 ½ ¼

¾¼ ½¼ 1 

 ¼ 

 1 1    & 1  //  &% 

1  1    &%  &   1 (        &  /  /

K

K K

L

!







!



36 A 1  K C

& @#+A & 

L

L



! ¾¼ K 



L

L

 '

!¾  ¾ 

'

!¾  ¾

 B

  / &  1 (  

 /



 / @-A

@-A &   1          % /  3

  





!

        

.   ?   /    

1  

! &     1 =  

  1  &/   3   $ 1   &   1 /3 / * 1 1

1 &  

 / Æ    =

  

 1



  -

1    %    71  1  1

/  ?

  

               1

'

2

V1

1

+ V2 -

1

1

(Ω,H,F)   -  1 /3 / *

1

1/(2A)

2A

V1

A

1 (    

1/A

1/A

R3

+ V2 -

1

A

(Ω ,H,F)   + *  / & 1 (    &   -

  ? 1  /

    ?  /   &  &   

   ? 1   / &  )

3      =  &  1 ( 

? 1  *  =  1          ?

 



 1 %?

1 6  

 1

/ & 

!

1 1

 

   

1 1     /          &   1

  



$% &    #  '  (

  +

  *  = &  1 (    

 /  B /  1 * &%   &  ?



 &  1    

/  1 1

 

&   1

" %   



 /

?

K

!@

¼

L

¼

  -

A 1    

 / 1    1/ 

   & 

>  ! 1  6 ? 1   1& 3

/ %    1 /  1 % /  &     . 1 1     !

 / &     &  &    



       1     1  1 

/  &   / /

3  

/     

     /  1 

! 1  1  /   8  1

 / 

/ 

/  

            

'

I

I

1

2

+

V1

+

V2

[Z]

-

1



-

(a) I

I

1

2

+ V

[Z]

1

I’

2

1:n

+

+

V

V'

2

-

-

2

n

2



ideal

(b) I1

I'2

+ V

+

[ Z' ]

1

n2

V'

2



-

-

(c)

   



3  

 

 3? 

¾



 /    1  /

1  1 1

3     /? @A

 &  / 

 (

/  &  

!

1



  &C

@A

/  &   ///   3?  / @ A

3     /

 /  %  1

M    1

/  & 

 3  &   M  

/  &   /      

   1  &  /  / &  1   

&  1     &3  1

 

/   & 

/   / 



?  1  

  @ A 

 / 

  @A , 1 8  & 1  1  1

 1  &   8  1  &     / 1 &   /

1 &3  

0½ ¼





¾ C

½  ¾ K K

0¾¼

K

(0¾  /



K

(¾



¼

@-A

0½  0¾ C ¼

&½½ ½ L &½¾ ¾ K &½½ ½ L &½¾ (¾  /

¾

¼

(0¾ K (&¾½ ½ L ( &¾¾ ¾

@-A

               1/3

1

V1

+

R1

x1

R2

1

V2

9

x1/3

 ¼℄

 1 

P

  & P

K

K

&½½ (&¾½ 

0

0

(

 ℄?

i deal (b) ,H,F)

  ?



(&½¾ (¾ &¾¾





℄

P

/  &  ?  /

 /  & 1

'

-

  /   C @A     ?

1   &  /  /



1

V2

1

-

(Ω



 ¼℄

+

V2

1

   >  /  &    

P

3:1 +

V1

-

(a)

 / @A    @A

1/3

1

'



@-'AC







0

0

(



0

0

(





&½½ &¾½

&½¾ &¾¾





0

0

(



@-'A

1   ? 1   / 1  / 

) 3 

 6 1  

     6  & 1 ?

  &     &       &  

%  *&        1 3  *        ?  1&   1     /   &  

& 

&   @A?



1  &  ?



@ A K

@

A K

0¾¼



K

K

! &  &  1   C

 

L  L 

 &     @A

?  31 / &

0¾ 0¾¾

   &    @A   1 1  &   1   D



@-#A

  @A?  1 3M      M  1

 1   &     @A  1  /   ?

   > //    1   

    / 1 & 

0¾ 0½





/

   

  / 1    1

0¼ ¾¾ 

! %     



   @A?

 ¾@

¾ A*½ @

¾ A  

)

?  /  1  M  /   

 / /  1  /   

K

 K

 ¾@

A

0¾ 0½

? 1  &   

0½¾

@ A ?  /

   1  1  

   @A?

$ ?  1    /  1   

  1

/ 8   /    

 %      &    @A   / /    

  ? @-'A?  1   

  @A  & 

   ? &  1   

P

 ℄ K P ℄ L



P

 *

  ? 1  

  @A?   & 

  ½ ℄ K





0

0



L











'



C

            

''

1

3/2

9

+

V1

3

V2 '

1

-

(Ω

,H,F)

  0     / / & 1    &   @A      



?      ?

 / 

!?

1

1 (  



 ¼℄

P

K

K

K

(

K  ?  P



0

0

 



0

0

 



0

0



.  & @--A &  

℄

P



L



0¼ ¾ 0½ ,% @-+A 1

 &  





0

0

 



0

0





L







 

' 

 

&   %    



 



' 

 



@--A

   / 1      0 $  //

   &   0  / 1 & 

  @A



 ¼℄

  P

( K  C

  / 



℄

K

 & 

 

L  L 

 1 1   



@

  0

1 1  1    

     1 

 

 

! &  C

A

@-+A

 %    1   

 %   

   = ?  ? 1

     /       &    T 1  

!  1 /   &   1 1&3 

 



/

/  &    1  1&3

  /    



U       1 3  *        

  -

3 >

     

¿

&  1   

  +?  /

 /  %      &  1      1    & 

(?

1     &  ?

% 

 1 

/    %

1  &  /   

3 1    ?   +? 1    @    /  3

 A  /  / 1 & 

℄

P

   C

K

P

℄ L P℄ L



P

  ½ ℄

              

℄

P

P

P

℄

  ½ ℄

1 P

5

K

K

       



0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0



!  !

   

!  !





0

0

0

0

0



0

0

0

0

0

0

0

0



0 

0



0

0

0

0

 ¼ ℄ K P(℄P ℄P(℄ K

0

0

!  !



 ! ! L  !  !

0

¼ ℄ L P ¼ ℄ L

0

0

0

0 0



0

0

0

0

(

0

0

0

0

0



0

0

0

0

0



0 0

!  !

0

0

0



P

0



0

0



!  !



0

!

!

0

     

0

0

   P(℄ K   

1

1

K

   

'#



0

           

@-A

 ¼ ½ ℄

P

     

@-A

 B      (  ?  1    

  /    @ & 1    A  1 &  ?

(?

  1

 &  /      C

P

¼ ℄

P

P

¼ ℄

 ¼ ½ ℄

K

K

K

   P(℄P℄P(℄ K      P(℄P℄P(℄ K  



0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0



     

!  !

!  !

0

0

0

0

0





0

0

0







     ½ P(℄P ℄P(℄ K   

0



0

0

0



!¾ (¾

0

0

0

0

0

!

!

!

!

     

0

0

0

0

 ! ( !

0

0

( ! (¾ @! L  !A ( !

( !  !

0

0

0

0

0

0

0

0

0 0 0

     

@+0A

            

'-

1  &   /   8  1  /    &   &    1

/  

1    /   

(   1       @  A

 6   /    1 1  & (?  P

¼  ℄



 /    =

1         1  %  = 

(  

 (  ?

 % /?  / 1 1        / (   1   

1 1  &    1/



 / 

1 1   @

1  A? 

@+AC



( !

( @! L

 !

A

1? &   1 /  ?



 (

,% @+A

 % /

 !

K

@! L  !A

K

(

 !





K

@+A

L

@+A

!



L A &    ! 0   ? !

¼

  8 /  1 1  & (?  / &  ( K 

  

¼  ℄ P

  & 

  ¼  ℄ K   P 

!



¼

!? P ℄

C

0

0

0

0

0

0

 !

0+0+ !

0

0

0

0+0+ !

@ ! L  ! A

0+0+ !

0

0

0

0+0+ !

 !

0

0

0

0

0

0



     = &  1  &  /      1 1 

! &  

  +  /    &  1   

 



0

0

 /

  / 8 

  ?



   

     

@+A

  

/   &   1    

 1 1

1

 

   /  1  &  1 

 / P ℄

P ℄C

0+0+

K

       1  / /  & (   

1  @!

¼

/   



!

 

!

/  % = 

(

.





 !

&  1    

  + 1        /   1?   1 1 & 





/       

 / /  1 * &  ? !   !

?



     1

  1 1  /     /C    / 8  

   



K





   !

! @

  / &  !  @+'A

1 1  /    (    'D  /  ? 1 & 

!

K A

?  1 



!



  



  1& 







@+'A

  1

      ! 1 1 ! ? 

     1  

(  



 &  1

/   1  &    ?  /  ?

               C

1 V1

R

1/A

1

R

C

1

C3

2

C

1/A

2

1

C3

R'

3

'+

R

1/A

4

R

+ V2 -

1

5

C =[2] A /([2] A-1); C =A /(A -[2] A+1); C =[2] A 1/2

2

1/2

1

3

2

1/2

2

1/2

2

3

   ( 3 / %   &  1    &   +

1  1



  

1 *     

 1 (  

      /   

  + .



/     1 / /

1     /  /  / & 1 

    1

 1 1      

/    1

!

*&  / 1  1       ?



 &  /3

   1 %       &  1   &     & (      



$%  ) $  (    ( & 

1  /   1  /  /  & 

 1        

1 3M     / 1   

&   /  1  

1    



0

!  /

!  /

 /  /

0

  & 

1



!  /   1   

! &  & 

 /  1

& 3 ?

 &  1   



 / 

!

  

 /  1 

! & 3

  @AC

  C 0

K



K



 ½ &½½ ½  &½¾ ¾ L

0

L

L

&½¾ ¾

 @+#A

&½½

  C 0¾

K K

0¾ 0

K

   0¾  0¾

&¾½ ½ L &¾¾ ¾  / ¾ &¾½ 0 &½¾ &¾½ L &¾¾  L &½½  L &½½ &¾½ @ A K @ L &½½ A@ L &¾¾ A





@

A

 &½¾ &¾½

 /

@+-A

            

'

I 1

+

V

V1

g

I

1

2

+

+

V2

[z]

-

V

1

-

L

-

(a)

I'

I'

1

+

I

g

1

V'

1

[y']

2

1

+

V'2

I

L

-

-

(b)

   @A   /   /   ?  / @A

 / 

!

      1 / 

'

!

  @A?

 1 1 & 

   %  

1  1 1   & / C  K

 

¼

 K

¼

 K

0½ 0¾ ¼

P) ℄

0

 K

0

½ ¾



K

¼

¼

)½½

)½¾

)¾½

)¾¾

¼



¼

 K





&¾½

   & 1 /    1  / 1 &   /



&½½



&½¾

&¾¾



! &  



 C



  C 

K

0¼ ½

 0 ½ ½½ 0 ½   ½¾ 0 ¾ ¼



L)

)

K

¼

¼

¼

¼

L )½¾ 0

¼

¾



¼

@++A

¼

 L )½½

  C ¼ ¾

¼

)¾½ 0

K

¼

L

 L )½½

¼

¼

)¾¾

 /



)½¾ )¾½

¼

 ¾   ¾

0¼ ¾

¾

¼



)¾½ ¼

¼

@ L )½½ A@ L )¾¾ A !  1



¼

¼

@

¼

 L )½½

 K

¼

)½¾ )¾½

/   

¼



A

 /

 00 ¾ ¼

@+A



!  / &   1

!

 L3/*    

   1  /  

  1 8  &      ?   #N    &  1         

1   ? @A  / @A?

  '?  /  1

/   @  A       &   /      1  /    /    &%    1

            

#

ω

j

s

j

ω

'

s’

2j

j

-2

σ

0

-1

0

σ

'

-j s=8(s’+1/s’)

-2j

  #  3= /    &    '

   1  &   1 ?  /      1 8  &           / 1 

! &%   

  1 8  & /  /   

     ? // # 

&  1 /    / 1  /   ? @A  / @A?   '?  /  1     /   &    &  1    / /

  

. /   /     ?



 

 //   

 1     1      /   1 / 8   &  1 

  

/   &% 

 1  

$ &   1 

E

   /  /   &   1 

'  

    

&  1 & 



! 1 1  3=  1

   & 1  &       D



"

& 



      &  1 &  

   / =   8 /  1  &  ?  / 1 @ /

/1A 



  #

! &   $! 1   3=  &  1  / 1  :

6 / / 8 

 1  /    / =   C

@

A K



 @

@

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

-



  -     &    -

#  

     1 1 & 

@

A K



! &  C







# 0-





L - -



L 0 

@A  / 1 *  &  &  ?

!?





L + #



L' 

L

% /   &  1  (

 &       /   /  1  3!)=  /      &%  &  !)= $ & 1   / &%   ? @A 71



 /





 1   /

/1 1   /    

& -0 /*    1   &%  & 1 I



% ?

 /

 ?

$ & 1 &3

1 /  1  -03/*  / &  1  

&   @ A   1  &   

1



! &  &  1     / 

K   /    &   

!  / 

?

 -   &% ?   3

 + $1

K

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



 / 1 

¼ ?

  +



/  

 % /  1 1   &% 

? /  1     



1 1 

 1  &

        1 1   &  1

 '## !)=

1   3

 1  / & 1    &  %/?

?  1 &% I

&  1  &   ?

 / 

 3

1   /? 1  / 



   '## !)=?

K ? 1 /  /

71  /  &   &  ?

!?

 / &%   

            

#'

70 60

Loss (dB)

50 AS=45 dB

40 30 20 10 0 0

0.5

1

1.5

2

2.5

3

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

 1  /

@   



  1

K   /



A K

 1 3/*  /

/ 3

/1 & 1 

/1  1 I



0 -@

¿



L  '

¾ ¾

 L '

L - #A L

  /  8   /J  /    =  

K ' /J  1 

  &  /    /   /

  

##

1  /  1

   &%   0 !)= 1  &   &  

 1   1 1  /

/1 

 1

/   & 

  

0 !)= @A 71  &   &   @A 

 % /I

1     &% 

 1  /  /  1 =

   I   &  1 

 

! &  &   0    1 1

    1 (  ) &%   &     1 

@

¼

A &  ?  / ! 1

  3= 

 / /   1    &  

1



¼

¼

3 

 ! 1



   ?     ? 1 1  / %     ?  1



  ? 1 1     @   A  1  

  ?   0

#-

            



        1   & 1  1     

½

   / 1 % 

 /

1   ? &% 3/ /   &  

    /  /   1  8  & 1   /  

    /

?

1 1 

   @



3&%   / A  3

  / &% 3/ /  

&  ? 1   / &%        

   1 /3

1 &%    1 ?    /

/%  

 1   &   )

1  3 .  /  

! &  

  

 

 &  /   / /

"       /  /    /  & 1 &    &       @ ?

/ B  ? /    / 1 1   / 

 

1

    /  &  1     = &  1 /  1

 &/  1  ! @  A & 

 / 1

&   1  

5&  PO℄   /  1  / & 1 1

P-℄ /    /

      //

1

5& 

/   &   &   ?  / 

  / 6 :  R 5   /   1   /

/       1 % &  5 

 8  A

 1 / 8   ?  1  1

& 1 & 

    

   /    1

1  & P'℄      

//  /   /  &  1  1  !  1 8  &   &% 3/ /   &   13 



/    / $  6    =/  1

/3 /

/1     / 1 6  1

/ @  / & A 

/

   

1

1 1 1 13 

1 &    

  

1 1 1

1  /   &     /     /      &

  /3    &   1  & 1  1 1

 

  

  /    / / &  1 

1    

 /

    1   / /

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





1  1



+

1 ("'# 1 

 / &  1   

  

 

  ?

  1 ! 



  13 .

  !  !  &

  /  1 #3

     1  /   1    1       &  1 !3 3!       . //  ? 1 1  &

  



           1      

 % /  / 

 1 / & 00



&   03

     @  A &  

         

#

Output Voltage, Vout (V)

20 Room Temp

15

Hi Temp

10 5

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 ?



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



  

@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?





 /

!

 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

  - 

      

 &     /     /



  -     /  &   R(  1  



 1 A  1

¾ ¾ ,¾

1  1



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



        ? 1     ?

!      @    /   A?     

  1/

   = &  =   1   /

1



1 1

?

+ ?

  ? 

  =  1? 1    &   1

   1 1    &/ !

  1    1 1

  



 !

 

 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







  6



   ?

/ ? 1

1  /3      &  & &%  / /  1  / ? 

½ ¾ 



@

)   ? 1   

K  ?

  @ 1

¾

½  ¾

K



  + 1  /   /

A? / 8    @

½

K





  

K  A?    3

K  A &      & / 8   % 

 %  & 1   

 1 1    &/ !  

/  1 / %    &  1 1  

!  1 #0 000 2 

   3   ?  1 / &

?



   ?

  ?    

1 1 ! 1

 1    

         B       /  1 / & 00   &     / 

.

 ?

 /  

1      /

     

/ %  1  / & 



¿         +    

                      +  

           

--



        &  1 / & 0  .

  !

1 

/  /      /  &%    1  8 &  1 1 &%  $ ?

  ?

 !

1  /      

  /   3   3   1 1



  1    

1 &%  / /   

1  !

@AC

!

!

@ A K

@ L

 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



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



K

3   3   





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



 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  

31/   

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*@0-0A 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 @&  



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          ) * 23                #  

    

          

0

   &  ? 

" /

L





,

 / 1 / 8  

     &  

&        / 8  

+% ?

?

 !  ! 

1  & &  & 

/

  /  

,

31/  

&       / 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     / /         



 1 8   &  1         

 ? @

*¼ ?/¼ A? /    

1   &



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







iC

gmv 2

gmv 1





+ 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



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?  /



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         



v g1

+ v1 -





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 -



iC

vR





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 -



,

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



(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   ?



 1   /      1   1 1 13 

1       1  /   1  ?



?  /  /?

1   / 1 !3 3!     &  1   



/  & 

?  /  

1   / 

  / 1  1       &  1    

1     /



  ?    / / 

  / ?  / 1 ?   3     /   =/  /   /

/1  1  1

71 1    

       

      ?

    &  1  /  ?

, ½ *¼ 

K

 / / 

* * K



L K L

?

1 1  /

 1      & 

"

- 1

       

0

(+V)

Q5

2N3906B

+ v

EB

-

β

+ i

R

V

S

0

Q6

ic/

-

ic

S

iL

I

2 RL

2N3903B

(-V)

  '-   /3       

,  K / L ,  ?  R( 1   % / & 1 / 8   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



+



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 & 









(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 # !)= '# 4J +# ")= 

"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% @

+

 /



@'''A

  @''#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

)



* ¼

?

L

/¿ 

1 1 

    

   8

 &/  1

& 1  

?



 / /  1  3   &  

   



   

 ? &  1   ? 1     &  , 1 1      8 @,

  







 8   /  



 @

L





 1

1  

A?  /  





  %     & 1 1 @+

K 0A

  *

A K

 /

      &  1     ?

@''#A 1 1   



     /  

?  1

  &

 1 

3&% 

    &  1    ,% @''-A  1  C



 1 



/ 



K

%

0 

1   1

L





@''-A

     1   

   1    & 1  /  





1







3

   ?  / 

?  / 1& ? 1  U  3     ,% @''-A 1  1 1 1    





   1   &

% /  3    1   1





  1  

 1 1  /    1  8 

1  3     & 1   1  / 8 

  /  1 8  B /  /?  1  / Æ 

   $    /   /  

    1 .  /

  1     1  / /      // 6    

1       1 1 13

   8 1   /  1  

  &  1 . /  1  1   

 & 1 /     & 

     / &   B  2  /           1    &    ?  1



      1  /  

&        *&   /  / 8     ?    !  1  3  3 &    &  1   

  '

  ' . / 

 &  1    1   





K #0 M? 





  0% 5( +

,

4



0*@,

K

/ 

P00# ℄ 

K

, ,





,





/ 

0 ?

/

K 0 

K 0 ?

K 

 0% 5(

K

 /

1

 @ , A K '- M

K

(  ) 

+



A K 0+-- 

K



    ? 



 1

 &     

K 0 "1  7 1

  &   1 ? &  1  0*

P,



 !  =    ?  /  ?

1     % 1    ? (

  3     /

 1 ?

K +' "1 @ 1 

0  @

 1 TA

  & 



+

A

+ 



+

 1

/ /       &  1   

         0    #            -4

              -     &        (       5  

          6   7      

          



b-

+ v

B

E

r

π

+ i

S

v

+

c

π

S

-

c

R

L

L

v

-

µ

m vb

g

C   ' $ 3     / &  1         

1 ?  R(  1   /  ?     ?  / @''+AC

)( ,

K

0

K

+

+ + , 7 1 

  4 ?    1? 1

L

(

) +

L

)( @+



+ A

 /

 +  @)( L 4 A@+  + A )( L 4 )( L 4 L 

)( L 4 L 

) @)( L 4 L  A L )( 

K

K

    & 

/ &%   / 1

 1

K



K



) P

4(

L@

@

) @ ) )

@''+A

   

 / /  1

4( L 4  A (

L@ L

4

L









         

 L

 1







+

& 

  

/ 

@''AC

 A (  ) L 4(  @( ) A℄





L  0 0 A



L

L L



+

L  0## 0 A

L  0#- 0 A@



 1

    6 

   1        / & 

+ ,

 /

  &  1   ? 1   1

K



4(

K

  -  .

 /  



@''A

1  @4( L 4 L  A ( K

) @ @0% L A L 5( A K '- 0 ?   

/    1      0 0 J  . 1   ?     1 0 3    & )   1  / /1 ,% @''A





 0## 0 

  1/ &  1 

1  

&      

@''A? 

7 1 1 1    ? 1  /

/1

  

    

  



+V0

Q7 iL>0

VS

iL     1     /    &    +¼  / + &  1   & /½ 

@A  

& 



K 0



 /

@A

@ A   1  /   1  



 /



1 /  &

1 %  / /

  3

  / 1       1 /

   / / & 1

   

 



+ 15 V



600 k

v

0



600 k

R

vg

R

1

-15 V

  '     &    ''

# ?   '  / /  1 # &  * K *  K *  )  1 !3 3!  8 /    / # I

'# 5  

/

1   ?



  &

'- $      

  

 /

*        

 & 

   ?  1

'+   

  ' ,6 1

#

13     / 1 !

 &   

1

$., 1   3   1 /    0 /*   &    / /   



 /        3

!  /  /     & 

/3

6 

1

  &% 

  / 61    0 /*J/   8       3

  1 / 1   /    1 /     !M

' >     @  '+A

 /3     / 8   &



7 1

1 &/ !  1 ! 1



  1



K  !M  /



1 1      6 

  / 

 1     /

' 5   '     & 



K  !M? 1 ! 1 &%    & 



1    ?

 

K 0  /





  1

 /  & 1  /

/1 

  

'0 2   1  /   &  1 ("+'  / 6

 / 

@A 1             /  

  

  1   1  & U      1       

1 1 / I

          

0

V+ I3

i IN R1 R2

iL

+ KV + E VE -

I3 V  '     &    '-

@A 5 @A &   ()00' @ A 5 @A &   (''' ' 1   / 1 1 ()00'

  ''0  /    1 / 8     

/ /    = 1     / 

 &    / 6    .

1

  

 /  1   8 

&    1 1 7 /   &   '@AI ' ( 1        ?

@

A K

 @ L  A?

 / 1   8

 &% ? 1

?

   3  &  & &% ?

 1 1  8 &%    &



 /

 /

0 

0@

A

'  1  &   '  1   ? @'-A? &  1  

 /  

)

 /  1  &  &% 3/ / 

/  1    &  & 

+ +  



0@

A 

1 1  

 &   '-I ''  

 1 & 

%  &  1       '' .  !

1 1    & 1      00 )=?  / @A 71   % / & 

/

0



K 00 &   1    

/      / / 

& 00 /* &  1 3!M  /I @A  / 1

 / 8    &  1    

@ A   1     /   71

&



 /   8     ?

 1  6   &

)

& 

K 00

 ? "I



 / 1

 



M

I

R

R

I

V-

  ''0     &    '

@/A 

)

'# $

)

K # ?

1  &    ///



/½ K 00 

1      &   ''  / 

   

 /   1  3        &%  &  

1

  1    00 )=I

&% 

0 /*  1  3  &% 

'-   1 1    /   &   '# 1 / 8?  /        /      &  1 8

 1  

/ /   1  /3     /I '+ >



   /   1  3   /   &  1

      

  ''

  1      

0 @A 71 /  1       

/  &    

    I @A   / J6

1 1 3/*  /

/1

  / /  

1 &    @1  1 1 ''3!M   A

' . 1    &   ''? 1 3         /



K



 @ ?

,

& 

, 



0A

K

, L ,

     1 1  1  3

 /



>  8  

K

0



/ &   1        1 8    

 C

S   

 1 / 

0

,

0? 



K



,  / , &  1 ,¼ ? /¾ ? 0½ ?  / 0¾ 



  &

'  %    1        1

& 

 /      

  '''

K 00 &   1      / 1 1   & 



    !M

1           / /  1     

          



+15 V Q2

i0 RL2

vg

I1

1 kΩ

80 µA -15 V

  ''     &     ''  / '#

14.4 k

I

V

15 V

2N3903   ''     &    '+

V+ i IN

Q1 i1

+ 1. 3 V

iL

i2

-

I2

Q2 V-

  ''     &    '

 



65 µA

15 V

+ vL -

5 mA

g v

0 g

vg



R L= 2 k

15 V

  '''     &    '

@A 71

)



 1    @ A &  1   I $ & 1

 & 

+ ?  / /  1

/3 3 6   /3

 /

 

&  1    & 1    @1      / 1 #3    A @A  /  6 &  1  ? ?

3&% 

    

 1

+ ?  / 1 ? +  1    1 /    &  3 0 ? 4¼ ?  ?  /   1  3    1    

 

*   /      1   

 ?  / /    & 



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?



K



   / / &  1  /   & 

    /        // 3    & 1   

K -##

S   B  

(



K 0

?

   1 3

&    & 1     1 /    1  /

1 6 

/    3     @A > 1   /  /  

*

 / 1  3 



3&%  1  & 

* 

/  & 1    &  1 

    71 8  /  1     1 1 / &  / / 8    & 1   I @A >



@    $.,  &

   &%  1

A   

     3

/ /       ?  /  

 &  1    &/     &  1 /  ) 1 /  1

/ /     & 0



?  

          

'

(+V)

I0

T1 +

v in

RL

T2

v

L

-

  ''#     &    '0

    /  / /  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?  ,?  ? F1  ,    /     " / &     @"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 33  

 1 C

1

,

K

½ ' ¼

K

/

K



 

7 7  1 & 

K



K

 *1

K

¼  ½ '



/ ' 0$

K ''#+   / 

@-#A00-

K -+

@'-A

 &  1 0-*     C

/ 7

K K



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 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



K

 @

A

 @, A



K

 @

A

 @, A

$"- ) *'%



 /





$"- )!*'%?

@'0A

&   1      

 !           + 9"-  "$  %#  ,   4 : ) * + -($"- ) *$ +34      4 ( " 4 ,"  $ % ;4$ 4 +$ $ #$#  $"# 4 ( .%$  - ' +<  , $"  ,# 4 5 6  +  "##  "  0 = 0  -  +   (  ," +   %$  ," +     ," ," $" -($"- ) *$ ()')!  (. '

)

. '7)

' )

. '! ! (( (℄    ℄ $ 2 -($.(( $ = -    $℄ ,'82- > -2' -(,& -  -   .$℄ ,'82- > -2' -,& - $, $-℄"" ) *- #$,$-.$ - -.' $, $-℄"" ) *-  # $,$-.$ -(- #.- # #.#  "# + 9"-  "$  %#  ,   4 : )!* + -$"- )!*$ +34      4 ( " 4 ,"  $ % ;4$ 4 +$ $ #$#  $"# 4 ( .%$  - ' +<  , $"  ,# 4 5 6  + 4  "##  "  0 = 0   +   (  ," +   %$  ," +     ,"

'

          

'

i

i

b

c

ideal

+

v

+ g(v

be )

be

v

ce

i -

e

  '+ 1   / 1

-

+ 

/ /  & 

*    

," $" -$"- )!*$ ( '))) (. '8!

. 8'7!8

!8')7

. '7 ! (( (℄    ℄ $ 2 -$.(( $ = -   .$℄ ,'82- > -2' -,& -  -   .$℄ ,'82- > -2' -,& - $, $-℄" )!*- #$,$-.$ - -.' $, $-℄" )!*-  # $,$-.$ -- #.# -#.#  "# $ &? 1 / /  

/   / /   1   3 

   1  / /   &

/?  /

       /?  1

  '+? &  1      1    / /?  / 1      / /      '

 //  



/

  /    /   &  & 1

  /    / &  1     

 1





 !           i -

i

b

c -

ideal v

'

g(v

eb )

eb i

e

+

v

ec

+

  ' 1   / 1

+

/ /  & 

+   

1    @  A   /  /  1 8  &



      1       &  1      1 1 1

 1 &  

/  1



  '

 *    ? 1

  

8   1     /      8   1   

  /  ? 1  8   1              

1   

 /  //  1 , 8    ?



 1



  '0 1

  &  1      1 1 ///    / 1 1    / .

/ 1 8  & 

 & 

*  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

00

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 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



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



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



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

#+

-0

0

#0

00

+0

+#

#0

'--

0

+

#00

0

0'

0#

0-

0+

0

0

#'

+

''

0

0'0

+#

'''

00

'0

-0

##0

+#0

''



10 µCAP Model R0



Log10[ ]

5

βac 0

−5 0.4

gm

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

veb (V)   '- " /   / 

   &  1 0-*

          

#

  //  1     &

 B   /     

Æ   &   @  /A /  / 1 1 6           / 8  / 1  / 

  1& 

/  /

           /         

1  /       1   /   /  /      /   /  / 1  

  

1 1  &  

" /         &   / / ?  / 1   & 

   

&  "   ! 1 /     "

   B    / /    / T

    

  

1   & 1   1

    /  !   / 1 /

 /  &   &     &/ !   

  

  6   

7  / 1 1 1 13

1 / 1  1 !

/  / &    1 1  /      &  

  &

 

"       

/  &  

 &   

 //    ?    /

1

/1?  / 

 & 1 ?   ?

1  /     /   &    &     /  ) 

?

/    &  &  1

 #@A

1  /   /

 ? 

 

 1 

 1 1  

     1  / &/ !   1     1  

1  /    /    1 &/ !    % 

  & 1 =

 %    & 1  

&% 3? 1 3?  /  3 3/ /  1 / &   #@A

/

1    / 1

&   

 /    /3 / /     

&% 3/ /  8  &      /  /

/ 

 3

 @= A91  /       ?

      &   0     1      /



&       & 1   

         / 1  9   @ 3

 A     1   



  &     &  / ?

     1        3  / 1

 &/ ! 8 

/1

1  / 1 

1  / /   /    / 

  8     1 ?        / &  /   &% 3/ /  8  71 1 /  1  1/    / /  /

1  1 !  

   /   8 ? 1 1 &      1   /    1 

   1 // / 1



 /

     ? &   /     1  / = 

1 /   /

.&  1   1 0 /? 1 1  

/      /  1    

       &  @  / A  &

#

  ! 

/ 

            

#'

+

0A

-

0V -

I

0

+ V0 -

+

(a)

I0

(+) +

Vx

+

Ri

-

-

+ V0 -

A(s)Vx

(-)

(b)

  #

$  /   / &    /      C

@A 3

     /?  / @A  /3 / /  /



 1 1    .&   &   !  

   ? 1  

            &  1 /  /  B 

1 % / &         /  1    &   &

  ! ? 

1 

 

     

& 1   1   &  /

    ? 1      

1



    

 1   &      ! 

"

$ %        

1   / 

   & F     G  1   

/          .   /

1 1  / //     /            

/ / 8   %   & /  /

  $1

1 & 

& 1   3   !   E

/   

$% 3 '   

  #? 1       /

      ? 1   / / E

  3

  & /    /  !



0¼ 0½ K

  @=  /  A  1 1

?            &  /

?  8  ? 1     ?

/  1 E

1 1



 1   

 1  1 & 1   

          

0A

-

+

0V - +

+

V1

##

1

V1

+

V0 =V 1

V0

-

-

  #     & 

   

R2

R1

0A

-

+

0V - +

+

V1

K

V1

+

V 0=KV 1

V0

-

-

  #     8

 

$%    ' 2 . ' 3

  # 1

          1    

 /  R(?

    1

    &  

 

0

K @ L   A

0

&  1     1

$%    ' #

 ' 2 

1  3     1

0

1

 # K  L   

? 1       

  R(  1

0 (

0 0

  #'   /  8/   ?

/

K #





 1/  & ?

K #



0

L

0

 L 

0

 ,% @#A   /

L    L /

0/

L    L /

@#A

/

Y K

 1



0

K

 L 

K

# @4

0

L    L /

L4

0

 / 4 K  Y

L    L 4/

0/

A

@#A

            

#-

R

(K-1)R

0A R

V1

-

+

0V -

1

V1

V0

+

R2

V2

R

VN

g

1

V2

g

VN

g

2

K

Σ

V0

N



N

  #'   

  

* 1 #  /  4 

/ /  &   % 

/    &   1

1   /  1      1  / / &

/    .&  1    &    21  /J      ? 1 1  # K Y  / 1 & 

   C

0

K

 0 L 

#

 K

Y

& 

1   

1

0

0 ?

 0

 1/  & 1  /?  1

     / ?  /  ? 1

 



/  /

    / &  1 1 1   

 /   / 

 

  

 / 8  

 1

0



 /

     

$% &  ' #

 ' 2 

1    1



  ##   /         1   

 1/  & 1  /

L    L / 0/ K

@#A

  1 

     ?

0



0



 / 1 ?

0

K

 R(  1    @



  K

 @ 0 L 

/

K

     1 1

A  /

0  0

L    L / 0 / A

  0

 1 &  ?

@#'A

  ?



/ /  &   % 

/    &    /  1    .  1      ?





   1  1

0

   / & 

     D 1

? 1    /?  ?

/ /   1

     /  /     1   

  /  / 1  1

0

?

  ##

           R1

V1

I

+

  

1   E



  1 & 

   /

 

 1

)

? 1



  ?

 ?

 & 



(



%

  ##?

 0

@##A

 1

   



K

 @0

 

K

0

K

0

  #'

  1  1

0 A



1 

 /

 %  / 8  &

@#-AC



0  0

L  0 L    L / 0/  L  L    L /

@#-A

 

  #'



/ /   1  / 

1   1

 1

0

 & 

 /

 



  

  ? 1

!

K

&  1   

    )?

 

  

/      

0

1 ? &  1   

K  

1   

0

 

 1   / /   1

,% @#-A   1  1

1

&  1

 /  1     / @0 A  1   



1 &  1

1

V0

GN

  1  C

 ? 1

-R0

Σ

 

  

1 

  ?



G2

V2 VN

  ## 

  /

G1

V1

V0

0V - +

RN

VN

R0

Σ

0A

R2

V2

#+

/

   ?

 &/

/   /

   ?  1   

1 1 

 % ? 1  

  

1  1

0

3



    /?

   / & /      

 1 1 ?  

  ?  3    C 1

  

 

$% &  ' & ' 

1 53      1

0

 /

0



  #-   / 

1 6 &%  /   

0

K







K





0

   



@#+AC

@#+A

            

#

C

IC R

-

+

+ V1 -

0V - +

0A

V1

+ V0 -

  #- 



-1/RCs

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 

1

?  /  ?



?  

  & /    

    /    /3 

    ? 1

  

   &/ !        ?  1 & 

" .

&  %

1 1   

    





   =/    & 6  

  *  2/



 / /            = &  1 & 



   /   &  C



1      

1¾ + 1 ¾

L'

1+ 1

L 0'+ K #+ @ A

   / 1  ?

+ @ A?

@#A

   &  &  ?

+ @ A     &  /      @#A   /    AC  (

+Z

  #+

K

1+ 1

1¾ + 1 ¾

 / + [ K

1    1

 /3 /  

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

'

L '@

-A

Y

'

K 

#

0  0  '



0'

@#A

  # 1   /

&   / /   &   . 1 1 

@ @

A 1   

 1 / /

½¾

@

K

0

0'



? 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

@ A @ A

0

/

K

1

! &    @#AC

#

¾

L'

@#A

L 0'

 

 / 

         I 1 

@#A

  ? /   &1

  &        11 1   

  / %  

  #

/  /

1 % /         / / /  7 1      ? 1  

!      &   / / C % /

       / !  /    &%  &   1    

1 / 

. 1  6 ? 1   

 1 &    ?   

. /       ?



   1  &

    1 1 

@ A    1 1 @  A !  & 1       .& 1 

 

            

-0

1/4 1

Vg

1/5 + -

1/4

2

V1

s

-s

V

1

1

V

1 -

-

V2

+

+

V3

V (s)

12 1

26 1

V

-

-26

(

V4

Ω F)

+

,

  # 53    = &  1     

? 1 

     /        &  1    

   8 71  

  #+

      &  1  / ?

      1     1 1       ! ? 



 61   

  &%     1    1 

/ ? 1 &      ?

0

0 0 0 0 0 0 0 0

  

K

0

0



K

-

1 

 1  &% 



@

@

K 

K

K

 @A

0 0 0 0 0 0  0 0 0 K

K

  / 1 / / ?

@ /*   1 A

  &

A?   & 

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

 1 ! &

0

@ A

K

# 00

0

0

'

@ A

00

0'

@ 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

 1 1

! &   1   1



! &  ?

0

@#A

   //  1 

 /     /



  / Y

  & 1 

 /

  #   1 1



K #?  1 ? RJY



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 / / 

0¼ 0

K

#@

¾

¾

! & 

L '00A

L'

L 0'



#00@ @

¾

½

 

1?

/  % =

  

@#AC

¾ 00 L ' A L'

½    0   #         #         

@#A

L 0'A

Ü

&   '" 

Ü

&  

           !  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 !/

"

!

#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   /

  /

'

  / -

#'

&%  &

    /

 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 >





A

1 0  /



- /* & 1 

   //    

   

 1 !   /   (#    /   /

 & 1 /  /

  1     &%  &  

 1    

   !)=?  / 1 3M  /  # !M

      0 ")=  1 ! 1   / 

/ 

1 ! 1 !    &   1  



5 

3 3   & 

   1/4

A1

+ -

0+

1

1

3

1/2

1

A2

-

-

+

+

1

1

1 -

A3

2

A4

+

1 -

A5

+

1 1

1

1

V

1

A6-

1

+

Vg

(

Ω,F)

  ##0     &    #

@ A % 3  1 / / &   1



"?  /  1 

      /

/1 &   #0 !)=

@/A      # . 1   

  ##0? 1 !      ? ? '?  / -  1

/   / /  - /*? # $1

1

 

1  8  1         /

/ / & 1      1  %   

#      & 

0 0

   & 

@ A K

@

¾

C

# @ ¾ L A L

L A@

¾

L

L #A

@A > 1    1 /  /  %    /       = 1  &  

   

1 0  /

 /* & 1     !  

@A 71    1  & & 1  % 

#

/  1

5/     1 1 !



#

     &   

1 1     

 I 1 

  1  1

    / 1   /  /      /B 1  &    > 1 / 

1   1  1 0 /* &   &%  @ A $  1 1        1 1   /          1  !M  / 1  /J    &%   1 &/   !)= >



   1  /     / 

1     &%     1     

"

#  1 13



! & 

   & 

0¼ 0

K

C



¾



L 0 0

L

            

0

@A         = 1 &   $  1  /    / !    00 )=    &   &  1    >   ? 



1  03!M / 

 1 ! &     & 

C

N    @( A   5   ?  / 3

 

 &%    &  /  / 1  0



&    & 0  

Æ

0 )=

K L#  > "    1 % & 

1   1  0    1

1   1

Æ

    Æ   & L#0  J    1     /



00

Æ  J 

  1    2 &%    &  3

/  / 1 &  1 



  &  0





Æ

+# 

! &   1  &% 

Æ

 & #  &  1    &

     >  03/*   &  1  /  

 C

S 

 /  / &       /  1

 1  1 (      /   Æ   &   1 1 

3&%   ?

!?

 / 1  3   /

/1?

$% ?

 3

 @A 5    1 $3R      = 1   #' >  / 1 /  /   5

/  

! &  

!?  /  /

1

6?  / 1 & 

% /        

&   1  &  ?

#?

1 /    

  /  >

!



 / "  1 !   /   /     1 1 1  /J    &%     !)=?    

#

K 0

  1 

/  

 /?  /

  1 /  Æ  ?  / 1  / /

1 /  1   1 !    

  1 

@

A K

0 0

K

#@



L #A@

L A@

L  A

L ' #A@

L A@

L  A

L # 'A@

##          &  1 & 





   &   , 1  @L 

  

  / /

.

    / 



L  #A@

@

A

! &   

 

/?  

3

     /   !  &  1  /  1  1   &   % /



1 / 

@

A

K

@

@

L

@

K



L

L -A

L A@



! &   



   ?  

@

A K

 L

L #A

L -A

L

L+

#- >   %/       = 1 &  

L

L#

/   @A

@

A?

L L

  / 

  

0

#+ 5 =  1 & 1 & 

 / 1 /

   * /      

>  &

       /   1 / &

1  3= &       = 1 /    &    & 1    @ ?   1 1     !3 3!

    A >



   1

 1 !  1 / & 

  

1  /     ?  /  1   /    

: K ;





1 ! 1 / &     &% 

@

¾ A K

@

L 0

L #A@

¾

L

L A

# > 1    1 /  / /         &  1 & 

 & &  C

@

A K

0 0

¾ K

@

¾

L

L #

L A@

¾

L

@A 1 ! 1 !  &  1   

  1 

?

L 0A

 / /   1  

    1   1 1   

1 !  / 1 /    1 - /* @A > " @  "1/A       ?  /  1   



     1       &

 /J   !)=  /  M   !M 1  /   1 /  /   00 ")=  1 ! 1 8  &     / 1 / &    #0 " / & 1   

  ##  /   1   1 1  &

   ? ?  / '

 

   &   & ' @ /*A

1     /  &  &

   

$1

1  !  1 

% /  / & 1       # 1    1 / 



  

  ##



     // 

 & 

!½ 

    &      / 

/   & 

 /  1 1 13&%  1 

  / 5/ 1  /    1 1    3

  /

1    / & 1    1    

$ &     

            

0

0.5

V0

1 +

Vg

-

1

A1

1

12

-

1 -

A2

A3

+

0.1

1

+

1 1

(

A4

Ω ,F)

1 +

  ##     &    #0

1

1

1/8 -

1/4 -

A1

A2

+

+

(

Ω F) ,

  ##     &    #

  



R0

1

1

1

1 +

Vg

1/2

R

2

VT

0

-

(

Ω,F)

  ##     &    #

# 1 & 



! &     1

01 0

 ##C

K

@ @

LL

¾

3    1

' /J 



$ & 1  &  / 

!?  / /

 

 3

L A

¼ A@@ L ¼ A

@A % 3  1      1 1





L A

 36 

= 

 

¼

K

! &  &  1  /

   /   &  1   

$ & 

    @A > 1  &         $3R  / / &  1 &   & 

/ / 

¼ ?

! &  

 C

.

    1  

  1 1     /  

@

A K

0 0

¾ K

@

L A@

L -

¾

L

L A

# > 1    1 /  /      &  1  /

! & 

,6  #

#' > 1    1 /  /      &  1 &  & &  C

0 0

K

@

¾

# @ ¾ L 0A L

L A@

L A

@A 2  / ?  /  & 1 6   &    1 6     

 3

#

&  1 &  

1 &    & 1

  1 % /  & &   /

/  

&% ?  /  1   /  /  1 / /   $    !M  /  !)=?  / 



@A 5/     / 1 /

 1 ! 1 / 

1 B 

 

/ & 1      1 1    

$  1

 1    

            



1 A1

+

V0 1

-

Vi

1/2

1

+s3

4

2

A2

-

-s

+

1

1

V0

-

1

A3

+s

+

V0

1 +

1

V0

-

A4

1 2

1 -2s

V0

1

Ω ,F)

A5-

(

+

  ##'     &    ##

## 1     &  ?

@

A K

  ##'  =   / (    

0¼ 0



     1

#- 1  1 







¾

L

1

 / & 1   

        & 0  

  ###

@

A

1

 

/  1 & 



#+ > 1    1 /  /      &  1 & 

0 0

& &  C

@ A K



@A >  &

!

1  //

        &    /

0 0

 @ A K ¾ ½  $1 L 0A @ A & 1 

! &  ?

K @

$1

 3

# @ ¾ L 0A @

L A@

¾



L

L ' #A

     ?  /  & 1 6   &

&  1 &      1 6        & 1 

#

1 &

  1 1    /  

@ / A  &%   /  1   /  /  1 / /   >



1 1 

 1 ! 1 / &    > 

!  /   !M  /  !)= / /   &  1 /

   &% 3  &    &  1    @A 5/     / 1 /   /  1 1    



  

1 B 

 

$  1

  1     &  63

> 1    /  1 ! 1 /

1

 # 2      / &   1 & 1 * /       &3 %    ? @A  / @A? 1

  ##- >  &

 

   ?  /   1 %  &  3=       = 1 /    &    &   1 / 

  



1

1

1/ 2

1

+

1

1

1

2

1

1

3

-

-

-

-

+

+

+

+

1

1

1

1

1

+

V1

(

Ω,F)

  ###     &    #-

|H| 10

dB -20 dB /dec

0 1

-10

10

100

f (kHz )

(a)

|H|

dB

10 -20 dB /dec

0 1

10

100 f (kHz )

+ 20 dB /dec

-10

(b)

  ##- 5  ? @A  / @A? &    #

V2

            

'

1

1/ 2

1/ 4

1/ 3

1

1

1

1

V1

V2 -

-

+

+

(

Ω,F )

  ##+     &    #

# 1       1

 &  ?

0¾ 0½



  ##+

0¾ 0½ K

@A ,6

1 1 

 / /    / 1  3

C

A@ L 'A

A@ L A

@ L @ L

    / 

@A 5/ 1       / 1    & &  @  L 



A        /  

   @    &

TA #'0         &  1 &   



 /



@

% =  & &  ?

A

  /B    &       &   1

 ?  / 1 /B     1

@

A K

¾

¾   L

@

 8 

A

L L

#' >   %/  /  /  /     &  1 & 



!

  ##



&   $ &     

@

A K



 -@

@

L A@

¾

¾

L #A

L'

#'    63      

L 0A

 1



/  1 $3R   ?  /          &/ !  /   = 1       ?

 ¾¼ ?

½¾¿

&    

 /

½¾ 

 

! &  ?

0¾ 0½

?

  &   



  1 %/ &    ? 

?  / /      / &   



 /

 /



 /   #'           1     $  1   

1  

 

! &  ? @#A? & ,63  / 

1 6 ?  /

  

#

R2

R1

R3 +

+

V1

C2

-

C1

0A 0V -

+

+

V2 -

(

Ω,F)

  ##     &    #'



    1  / &  

?

1      

      /  &   1 /  #'' 2       &  1  & 

A

>

?

! &  & ,6  # @

 /  1 &%     1  /

&  1  /     1

3   

1

 36 

=     1

   /  &  1 / 



K

@

@

¾

L

¾

L 0A

L A@

L A

)

 P℄ : 1  ?  ,?  / )  ? : (? 

  &  1     = 1 

  

%  3 1 *   

    -+ & 

 / / /

1  1 & / %    & 

04½

K



K

5 @0½ 6 @04½

 0¾ 



C



A K @0

L

 L 0



@ A



0A K @0

L

 L 0

A

0½  0¾ A 0 4½

@-+A

1    &      -    / /   & 1      -+  1  ..     

    1   1  &



 /



!  /

1 

    &  1

   /   

1   5(  / 1  4(?    71 1    &    

!

  -

 1 !/ &   /   ? 1 ! 

1 1 6     6 / 1    ?

!-?

        

  kC/20

'

kC/10

kR

V-

VA4

kR kR

V+ A1

2*kR

V+





-  /* 1   

1 1  

!?

6 ?

 !  1

 0¾

A5

   /

1    ? &  1 * 





*



 /   1 1  

!#

*

 / L

 

  ?

!?



!-

   / @

      &

 & 0  #? &   1 

1   

V+ + 15 V- + 15 -

V+

 

  -+

 1  /   &   &  @L- /*A    / 

   1 1 

  /  1    Y

V-

.define kL 1/pi .define kR 2e3 .define kC 250e-9/pi

+ V2 1.414*kR -

kL/10

10*kC

kR

2V 2

A6

-2*V2

  - (&  = ?



kR

V-

V+

1.414*kR kC/20 20*kL

10*kC

VI1

A3

A2

V+ 1.414*kR

kR/2 V-

V-

kR/2 (V 1-V2) kR

V1

kR

20*kC

V-

A7

kR

V+ 0.707*kR kR

kR

kR

   /



71 1    

0  0



* 

 0¾

  1  /  &/

A? 1 &   & 

1  ! 1



1 &/ !      /

!

1   

  



% /     3 / /    1 &%    &  1 & /  /  /      %  / /





+# /*?



  -?

711   1  /

   1   &   

  /   / /  1    

  % /    

  -

& 



.& 1

1 003  03!)=  ? 1 1   

  /   

 / /   & 1 & /  / 1  1



      '03/*      / -# ")=

 / 1 / &       /       

1

1 1 &       /  & /

1  1   /   &  1     &%  

 1

/ / & &%    1  

     1   

 / Æ    = 1  /      /3&   " 1 &   

!

  6 1 /   1

 1       1?  /     // &       /  /



    / 1 /

           

''

0

dB Magnitude

−10 2xIdeal

−20 −30 −40 −50 −60

2V2

−70 −80 −90 2

3

10

4

10

10

Frequency (Hz)   - %    &  1   

"

$  '. 4    %   $   6 

1  1 / 

  -

! &  

*  =

1  6  &  1 *  = &  33 

1 (    1

 /  /



  -

  1  

.

1 ?  / &  &   & 1  

 1  %   &  ? 1 *          &   3   (  1

 &  =

/ 1 

/   = 

&  .@A &  1    1  /  ..@A &  1 1   1 &  /

 / /  1  

  &  1 

/  1 & 

   & 

 1 * &  &  1   

 / /

  /

6 

3 > & /  /   = 1 *  1

  -0 1 

1

   1? 





  -?  / 1  %  

1  @   A &   

"

& # 1   

  -0  /  /   &  1  1    /

  

%  3 1 & /  /  /           3        1    /    %      -0 1 

 1

%   1  & 

04½

K

C



  &  1  ?

¿ 

1    1



1 % / &

        

 

'#

ω 22=1.6404

ω1 2=0.6906 1. 308

I

0

1. 254

+

V

V2

1YI 1

0. 797

3

1

5

0. 765

+ V

3

0.2

(

1

V

4

0

K

,H,F)

04¿

K

0

K

0

K



0 ?

0 

 @#

@0





A@



L  0 ++ A 

@#

LL#

A

@0

4¿

"!

K #

A

 @0 +-#

  -?

 0 4¿ 0  0  0



A L  0

LL#

@ #'

-



  -0 *    &  1   

1 / / 

5

0.2

-

//   / ?

+

-

A

04¿



0A

@-A

  1 1    1  ?

 ?

/ /  

&  1 ///    1  /    6 

& 1   / . 1 /   & 1  6  1

1  /  

  / &  1 13 /    1 1   1 1 % 

@-A 

  /

 1 &    1

 - 1     % /   = @-A 

&  1 (    & 1    * ?      %  0    / -    @-

/   = 1  -3  

  ?   1 ?  /  

   A )

   !

1 

! &  &  1  .



 3

1  1    / 

! & 

?



/ 

   1& 

/

 /   

! &  &     ?   1 //3   

  - 1

 1   & 1 &  /  1 /  

   

/ / &  &% 

1    

  & 

 1  1     1     1 ! &   / &      0 ")=  1 1      !   1   /   & 1   



3/* 6 

/ &   1  /   /  /   & 1

/  

 1 ! & 1 !   ? 1   &



- /*  

!

 /

?  /   / 

!

0

@



1 !

? 1 / / A

  

¾       1  

          

      /)   0              

           

'-

kC/5

kR

-VI3

kR

V-

A2 kR

+V2

5*kC V+

kR

kR

Vin

kR

V+ kC/5

kR

kR

kR

5*kC V+ kR kR kR V-

V+

A11 V+

V+

VA7

-VI3 V+

kR 0.797*kC kR

V-

VA9

-V3 kR

A13

kR VV+

-(V2-V3 -V4)

-V4

V-

A5

V+

V-

kR

V- 1.254*kC kR

V+

kR

V+

A4

A3

A12

A6

kR kR

V-

VA1

-VI3

kR 1.308*kC kR

V-

kR .define kL 1/pi .define kR 2e3 .define kC 250e-9/pi

kR VA10 V+

V+ kR 0.765*kC kR VA8

  - (&     = &  1 *    1

V+



  -0

   

'+

0

dB Magnitude

−10 −20 Passive −30 Leapfrog

−40 −50 −60

2

3

10

4

10

10

Frequency (Hz)   -    & &  /      &  ,6  #

1 

 ! &    T

/ ? 1  @ 

1   

"

  1 13

!

A

 / L' /*

&   

 /   1 

1 1    1 1 1 !     1 

   (  1 1 

&  /   L' /*

&

1& ?

/ 1       /   1  

!

!

? L' /*

!

 $  1 1 1 

$    !  

-? L- /*

!

? L# /*

   A

&  /  

!  0

1     /  1  &

 & 

  1

?

!

  &

0







0?

 L' /  1 ! 

- /*? 1     1 /   /  L /*?

  &   & +' @K 0

!

 

1 1

 %  

  1 /  1   

 

? 1  /  

1  !  1    

1   7 1 1   /   ? 1 &      /  /     = &  1 

#

! &  & 1  *    @L /*A

 

1   6  / 

 /   & /  / 1

1 /   /  /   &    1 &    & /     /    1 1 

! & 

  % /

 /    /  1   &  1 /  /

  

1 

     &  D 1

/  

 / /    /

? 1 1  /   

  &   3

    1? 1 / /     &   1  1       

           

'

1/ 2

V0

3 s

+

1

1

1 1

1

1

1

R

4

0

-

-s

+

-

V0

2

s

+

-

V0

-

+

V0

1

-2s

1

2

V0

1

1

(

Ω,F)

+

Vi

  -     &    -

 /   & 1 & /

/ 1 %    &    

1 1        / 1 &  1 1 /  & ! 







!

/

1 /  1    

%  & 1   &     1 

1? 1 &

  /  1 

   ? 1  1 /     1  /  /

         

1 

 1/

 1  /     / 1   &

1  1   ? 1     &    

 1/   

1 6 1   / 

 /   

 /   

    1/   

    /  /

#

  

- . 1    &   /

  -? 1    &   

   1      & 1 - A ¼

@

A K

- 1   & 1   

0¼ 0 

K

¿



  

Æ    1   ?



@ ?

#

¾ L

L



L

     ?  1  ! &

? 



1 $3R     /         1     ! 1   &  @ /  A  1 $3R    @A        &  1 &  $ &

#?



!    &  

 /     1 1   Æ   & L#00

  

'

Z(s)

1

2.5/ π

1/π

(kΩ ,mH, µF)   -'     &     -'  / -#

Æ

Æ

 J   /    00 )=  /



%   1

1 L00  J  $ 

K  M  # !M



03/*  /

Æ



>



K  /J 

 1 !   &3

/1 @   !  A &   3

Æ

  0   +#  > /      1  1     &  / 8    

@

@A  = 1    / /     &   1  

# L 0  L

A K

L

       /

1    1    @ ?

 /   / 1   



-½

 /

/1  3

-¾ A

 

  &  &    

   

-     ? 63 ? %/  / / /     3     & 

Æ

 J ?



.&     1    Æ   & L#00

1   Æ  

1   Æ   & 



K



 % / &       1

  = I





L

   

 



-' . 1  /    &   -'? 1  /      & 

Æ

    & #  1      

  

 /  

1     &   /  /       %  1

 

#N  /  /    

1

3  &  1   & 1

 /3%/  6   &  1 /  &  & 1  /      1 1    /   1  "     

" 

   & 1 % & 1 6 /       &  &     6  $ &  /   1  

1    1   



-# 5   -' &  1  =   

Æ



1 1      1

Æ

K # ?  1      &

 L00  1      Æ     & 

Æ

L#00  J D

 

K



Æ

00  J D  /

 

Æ

C

K L'00  J 



Æ

#0 

 

K

#0

            1

1. 529

V1

1. 838

1. 159

1. 159

1. 838

1

1. 529

Ω ,H,F)

(

  -#     &    -+

-- " / & 1

/  ?

/       ")=

1      

1 1

  -  1   

/    1 1  1 3

5 1   &  1     1  

&%       /  

 /

,6    /  / /  1

     

  1  & 1  

   % &     I -+ 1   & 1   

  1 !

11 

 &    

       1       1  / 1    &  

1 

!

   /            

(   & #N  1    @A   &  &  1 (   @A  / 1 

! &  &  1 (  1

  -#

  -#?  / 

1  &   /        @ A 5/   1   1     &  /  @A  / @A    1 E   & - /* /  1 %   D  / 1 ?    1 

!  ' !M  / 0 !)=    0 "  

  &      8   /   &   1 /   ?   /        1   00 )= 0 !)=?     /  

1  &

.

 

/* !3 3!

   

-         &    &  1   (   --



 3

$   1    /        0 !)=  / 0 !M

5

  1   &  1     N (     & 

     /    5 0 ?  / 1

&%     

&   1   / 1 "        1 &   U            / 

     

-    / &    &  1    $  1     1   &   

  -+

  -  / 



 1  &%    &    /   "   

 

   &  1     ( !  &%      0 ")= 

  

#

1

1. 618

1. 618

0. 618

2. 0

(

1

0. 618

Ω,H,F)

  --     &    -

Ω2=2.76

0. 905

1

0. 145 1. 910

1

1. 910

Ω ,H,F)

(

  -+     &    -

/  1

 1       / 1 / /     

1   1 13&%  1  (A           % /

- 1 ?

& 

@

    &  

&   &   



- > 1   / / 1 % E

A

1     

71



&  1

 1 1  & 1     

I

@

  

   

/  / 1          1I

-0  / 1      &  ?

 

1   &  1    ! @ 1 1   I )

A K



0 -

¿

¾ L

¾

L



L  '

L

1   * 

1? 

  -  1

1

  -?     1 

  1 %    &     = &  1

   -  / 1 

! &  ?

 -'0?  / 1



1 

      

>

0¾ 0¾

 /





? &  1 5(    1 1 1 & 

K  K

¾ ? 

K 

"?

 /

 

 K @½ L ¾ A 



 /

 ¾¼



 3

/ /   1

 A

K  @



"A

K  @

& 

#

           

I

I

2

+

+ V

V2

10

1

20

3

1

0.05

0

+ V3 -

0.1

+

V4

1

-

-

-

(



,H,F)

  -     &    -

V 1Y VI1

+

Σ

-

1/(10s)

V I3

-

V I2 10/s

1/(20s)

20/s

-

V2

+

  - ,% E

Σ

1

V3

-

1 &    -

Out

V4

  

#

R1 C

Vg

L

R2

  -'0     &    -



@A , 1   /   &   1 

 /

¾¼

  & 1 3

       / 1     &   @ ?  /

1 A  C

1 ? 1  ?

           1 /3

1@A  / 1@ ¾¼ A .     

1    Æ   &  ? ?  /   1  1 / 8    / 1  % & 

  = I ,6    





@A   1      &  

  & 1 &       

 / 1     

- 1   

    1 $3R      

   &   -  1 $3R     ?

¾ 

1  



 /      



1 1  

½ ? ¾ ? ½ ?  /

 1  & 



   & 1    @A  /  1

1@A  / 1@ ¾¼ A

1 &  1 &  @A @A .

 

K K



  & 1 &   ?  / 

 &      C

 ½ K  K ¾  ½ K "  ½ K  K ¾  ½ K  " 

¾ K 0# "  / ¾ K "

 /

     1    Æ    1  1 / 8  

  = I ,6    





@A   1      &  

  & 1 &       

 / 1      &   1  .    1 1 1I ,6    



-' >  1   ? /  /     &    &  1       -' .   @  1 1 

1  // 6  A

 1   /  & 0 /*

-#   &     &  1     --   &  &  1 5(     71  & 

  -'

! 

  -'

   //  1    I ,6    

-+   &    &  1    1      /   &





  -'' $ & 

        1  1 / 

#'

            1

1

1 +

+

V

2

V

1

i

o

-

(

Ω,H,F)

  -'     &    -'

1

1

1

+

V

+

0.1

V

1

in

1.6

-

(

out

-

Ω,H,F)

  -'     &    -#

2

1

1/9

1/8

V1

1 1

(

Ω,H,F)

  -'     &    --

1

V1

5

1/5

+

10

1/10

1

V4 -

(

Ω,H,F)

  -''     &    -+

  

##

I

1

1

1

+

I

3

I =0

5

3

+

V1

V2

2

-

-

(

+

4

V4

10

-

Ω,H,F)

  -'#     &    -

0.929

1

V1

Ω 0=3.279 +

0.101 1.965

1.965

(

1

V4 -

Ω,H,F)

  -'-     &    -

-      &         = 1 

    

  -'# -   &  &    / %   & 1     

" & 0

  -'-

 / /

@A  / 1 % /   *   

1   &%    /J ?

 /  1  *    1 (  !    1 3     & 

(  !  / /

1 

$ & 

    &  1     @A    / &    &  1      

   !M  /  !)=?  / 

   

$ 

  1 ! 1   

& / &   1 1     /   *  -0   &  &  1 3/* 1 /3 /   (     -'+



$  1    / &  M  # !M  /  /J 

 !)=?  / 1 ! 1 /  

   

S    1

 /    1    1    @    /A & 1     8 & 1        /   

 1   1?      @/ 8 A   1

           

#-

0.865

1

0.214 1.852

1

1.852

Ω ,H,F)

(

  -'+     &     -0  / -

- > 1 

  -0  /   /  1 

 /   & / &  1  /  > 1    / &%    &   

"

& 0?

/ 

  -0?  /  1   &

1 &   1 1   6 /   - >    1 ! 1     /   &     

Æ

  #    1    &  1    ?  / 1

/ /?

 

  530   

1 &  1       

1  ?      /   &  1 3

   1 !          

/   -

1

/  8 /  

1 &   I

@A > 1 (        

  -'+  /  &

1&3   /  1  1 / 1  !)= >  03!M

"

& ''  / 

/  &  ?  /   /  !  & L /*

1  / & 1 

1 !   /   1

   /

1    

Æ

@A > L#0  J    Æ   &  B 1   

1

/ &  1 1&3  * ?  / 1 ! 1      & 1 

Æ

    L#0    1  -'   &       &  1 /     1  -' ,6

1



 /  &  1 %/ 

   1 1  /  &  /

1 1 & 

&

 

K

 

0

K

 

K



K

 

 /

        0 L      0 L   

 3



?

  1 1 /   

 & %  @ /AC

0







/  ?

 /

   I

1

#+

1

I

-

0

3

M

+

+

V1

I

2

C

1

V2 -

+

L

L

2

1

C

4

1

V4 -

Ω,H,F)

(

  -'     &    -'

)

 P℄ 2 1/? ) :? F. /    ?G

(    ?

  ? $ --

#

           



  #     1 "2$ .3&   1   1  /      1  &  1    & 

3

?   &?  3  / 

 Æ  ?  ?  / 

    /

?

3

1  

1    /  1 1 /   &    3 !

 !  1    1 1 &  &      

   & ?  /  ? 1 

 1/    

 / /   

  1 %    &     1 &  &        1   & 1  1      /  1

  1

 /  1 

6  /   1  1  1 /     & "2$ / 

1 / 

 6 !     

.

 &/  1     

& "2$ / 

  /

/    1   

1

 //

?

(

 

    E

1     1   1

0 0 

0

K

0 

&  1 & 

?

/     

 1   

/    .   +?

 /    E

( !

 1D

?

7

0



/ 

1     

 /  ?  2?  1    ?  1 /    % /  1  /J  

   1   3 3/    &  1  2  !  1  @ ?

  1

1  

  /  1    & 1 "2$ / 

  1 "2$ /   

1 

  +

/  1     /   & 1 

 / /    1    & 1 "2$ / ?





 1

 1

  &   +    /      1    /

 & 1    ?

&

P℄

  +  1  / &   "2$ 

 & &/       ?  /

1    1  B

&

   3

 1 1  & 1 /

$ *%  $     5

1    1 .

 1/    %   &

1   1     / 

 1 / & 

K 0 !M &  1 2 A

1 1       1 1 3 3   11 /   ?

 1 "2$ /    8  /    &  1 2 

1 2  1   3 3/  3

 1 / &   &  1  @ ?

#

7

K 00 "M & 

       

-0

+Vdd PMOS D

S G +Vdd

A

-Vss

I nv

B

Vgate

Source

Load

G S

i + v -

D NMOS -V ss

  + "2$  

 1  1 

A

B

Source + Vgate   + $  /

      E



i Load

 @  $.,A / &  1 "2$ 

+ v  1

  +

            1 2 A

1  & 23 32   

-

 1 0



0

0 /*  03/* /     ! &   /     1  !

/ 1 1 2   

   

 ? 1 



  

 1U 2   

 



K 0



 1D 1

?  ?

 &   1 

   /  /3

  (   1   & 1      / / 1  1 1 & 

 /  . / & 

0

  1 "2$ / ? 1





  +? @+A 

 C

0 0

01

0 0 01 0 0  01

K K



&  2



&  2

@+A

 1 11 /    &  1 / 

      ?

 1 1

0







     @+AC

0 0 0 0  L 

@+A

$  &  1   & 1        @+A  /   /   &  1      & 

C

0 01 0 0  01 0   ? 1     / 1 ?  /  1

0

 /

0

 /

0

  

&  1  1 1 

L

&  2



&  2

@+A

   /  "2$ 

0

 1   &

&  1  

. //  ? 1 11 /   

1 "2$ /  7 1  1 & 



    & 

/    1 /  &   

 C

+

C

0 01 0 0  01 0 0 01 0 L





+

&  "2$



&  "2$? 

L

C

0  01 0 0 01 0 0 01 0 



?

0

 / 1

 / 

0



L



L

&  "2$? 

&  "2$

@+'A

01 0 0 0

1 1       1  ?

  1?



    

0

0

K L

 /

L

K 

?  3 ?

1 1

  /  

      &  &  1 "2$     ?

       

-

50

R v



10 k

S

R



50

on

R

+

S

C

C= 5 p

v

v



ΜΩ

100

S

R

off

S

+ C= 5 p

v

-

(a)

  +

 

C

-

(b)

 1/       /     C

@A 2?  /

@A 2

&  

01



K  #   /

0



K  0 ?





 # 

 % /      1

 1    1 1   /       1 3 3/   

   &      E

&  1 

 1 )

/

?   1 /   

   1  %  1       1    ?   

0

  / &  1  

 /

0

&  1      7

 

1  1    /   &  1 3 3/      "2$      

  / 

8  1 

$% # %   /  ( #  '  1/         1  / /  1  8 

1   & 1 

   =/  1  1  & 1   1  

   /  1   

1? 1 %  

 /   &  

1     1          /?   ! /          !  

1 1  

 1 1   

1    +  1   "2$       



8/ ?



1 1  / 1    ?

?8/

71 1 

 1

?8!! 8!! 8/ ?

K



?8!!

1 1 

 2?  /  ? 1  K #0  ? &  1 

  +@A? 1    

?8!!

K

 1

?8/

  K @ L 8/ A  #0 

 2? 

 / 1    ?

1  

 &      /      1  1 .   +@A? 1 

K #00

 ? &  1  

  K @ L 8!! A

 /

?8/

 1 

K #00

    1 



@+#A 

8!! ?

1 1

@+-A

 1 /    &  ?

 1/      %   1  @ A  /

1 1 / 1 1  &        @ /  1  %    A?  1



  +'

. /   %  1  

1 / 

  /

1& & 1  !  /? 1 1&3 / 1 /   1  1  

 

           

-

3.0 vC

2.5

Voltage

2.0 vS

1.5 1.0 0.5 Hold 0.0 −0.5

Acq. 0.0

Hold 0.5

Acq. 1.0

Hold 1.5

Acq. 2.0

2.5

t/TC   +' 1&3   @ 2A

1 

 1/   

&   %  1      



 1 2A  / 1 / 1  % /  &   1&3   @

 1

       

-'

  #?8/

0 #

8/  ? 1 & 

 

K #@

/ 

 L 8/ A

 % / &  1 

 1  ! C

 08/   #00  ?     ")=?

  1    ?  %  1       2  1  

 

 % /  



 1&3 /

  % /?



  /   1 /

 &  1  / 1&3

1   1  1 1/  1 1        

   3&    &    1  1  6  1 

 ?* 

*

8!!

  / / &   1  

1 

  

1    1 @+A  

1&   !  / &  

X

@

@++A

*



C

@

*



   &

@+A

/ &  1 /  1  / 1 2   &

 1

71 @++A  / @+A   /?

 !  /C 0

  1 

8/     @8!! 

. 1  ? 1      

8!! 

  1 & 

   /

@+A

    1

1      1 1    &  1 

/  1    ?

@?

  /  1  X

* @        /

8/

 1 /    &  ? #



 /

 &  

8!! 8/ 

 @ 8/

*

 1

@+0A

8!!

1   / & 1 

 1   

8  # %  '   (      1 "2$     / 8   / 31 @$$ A 

 /    /  !?    ?  

 1 &  ?  1   3 3/ 31 @ A *  1

&? 1    

1 / 8  

@$ A  / / 3 3    3 3 31

 1  1   %  1  &  3

 1/  !? / /  1   &  @1  31



 1 %  

  &   ?   

31  !?  1

+ ½

K



 /

+ ¾

A¾ 

1    

A   !  

  +# &   3

1  & 1

? & 23 32  23 32?

F!3& 3 !G @ A



     1

 1   F"!3& 3!G

@ A %       &  1   

K





&   .



   1

 1  /         / 1   & &

 /   1  $  

&  

 1     /   /  1   1 1  1  1

1  ! 6 ?   



  +-@A 1

1 1  1 



 1 

  +   /

  +-@A /     

. 1   ? 1    $ 

 1

 1



1

vg2=φ2

vg1=φ1

            5 4 3 2 1 0 0.0 5 4 3 2 1 0 0.0

-#

VH

VL 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

1.4

1.6

1.8

2.0

VH

VL 0.2

0.4

0.6

0.8

1.0

1.2

t/T   +#   

  1/ 

 1

31  !

1 /   &   &  1  1&  !   1

   

 &  1  / 1&3   1         1   1 1  1

 1 

1 / / 6  

 1/   

$ 

1 

 1 

 1    !     / 1    

    &  /   1   1 %    &

1 

   

 1  /      

 1?  1



  ++

/  1    /   &  1  1&3 / & 1

 !   1    /  

  /

      &   

1  / 1&3  

 1



/

  + 

+½ @ A?  / +¾ @ A K +½ @ A

1  1&3   1     %  1 1    1  / 1&3  ? 1     /



/  1

5  1 1 &  1   %  

  @A?  /  ?

     1 1

 /

 1/   

1   

 

 1   /  /

 &/   

  

 1       / -'O--℄   +

 

      3

  /

1  1 1    /    P? 

 ? 



  

 1  

1 1    @A & 1   ?  /

 1 / & 0N &



  

  1

1 1    @A & 1   ?  /

 1 / & N & 1    ?

    /

1

"2$  1 3

    "2$ / &   E    ?

        /

 3

 &   1  1

1        

 1     

1 ?

1    &

1

/   &  

   1  /

 

/ /  1 / / 

       

--

G

vS

φ1

G

1

2

φ2

C

Load

(a)

v

Load

C

S

(b)

  +-  $    6 C @A  1  &  $    /  1  &  $ 

 1 ?  / @A

 1 

1

3 C

2

4

  ++      

+ v1 -

C

$ 

 1

v2 +

  +   /   

  

           

-+

C CT

CB

  +     / &   "2$   

+ v

φ1

v1

C

CT

φ2

  +0 $

  

C-

φ2

CB

v2

φ1

 1/   

1     

1    / 1       &       & /    /   ! 1 1  / / 



1

 /



/ /  & 1 1  E



  

  



 1/   

 1



  +0?

 1  & 1    71

 /



 2?







 1

 / &

6  1       



 2? 1  

 2  /

1  1    1   ? A?  /



  

 1 

&     1 /



@ / 

 1    /?  /





A?  

 /



 

  1

  /     

 /

1

 /  1 /

  1 6  1    1   ?

 1 1     

1 

1 

  /    

  8 /  1   &





 /

?

 1? 1   

   71



 +½ 

 2?  /  ?

 @ 1 / / A    1   ?

 /    /?  /



1 &  $$

 1  / &  1   1  ! 1  //    /  







@ / 

1 !  1   

 1/       ?  1   

1 1 / /    

7   

  &    8     6 / 8    

    1  ?   1   

8 

1  6

$% !-  /    

7 1  & 1    !   /



1 %       &    1

   /  /

  +?

1    ?

      /    &  1/           



?     /  

/ 8 

       

-

1

2 q

+

v 1(t)

v

C

C

-

  +     

/





 1/ 

 

  

  / 1  1             &

 

 1  /?



2

1       /?    /   1   & 1 

/   ? 

v (t)

R

1 

  3 /  6   1 

   //   1

1   

+½ @ A

@ 1

   /   / 

 1



 1  A

 /   / ?

 1 1 ?

  1 

1

1

 1   1  &

1 ? 1  / 1& & 1  ?

 1   1  &

+¾ @ A





1   



 1   1  / 1

    /  /  ? 1 1&3 /?  ?    1  %     1 1     @8/  A  ? 1  1  E &  /    /   1  /    /  &  C

 /  1 1 

" X

X

 @+½ @ A  +¾ @ AA  / 

K K

> 1 /  &  ?      ?

 ? 

  + &  1

@+A

, K X" X ?  / %  1    /

  /   / ?

    1 

 1/   

%     C

,@ A

K

  

K

"  @+½ @ A  +¾ @ AA K   +½ @ A  +¾ @ A    K M   

X

X

@+A



  1 1  %      /    1   1          1  ,% @+A    &  1  & 

+¾  1      +½ D 1

  1   / 21 U 

&  1  ?  



 ?



&     

 1/   

1

  

? 

3

    

  !  

    1   /  &  /

    */ 1     ? 

1

1

 1

  + / 

 1 1 1  1 1

   1   

 %    1        

  +

 1  /

           

-

4.0 3.5

v1(kTC)

vC (V)

3.0 2.5 2.0

v2(kTC)

1.5 1.0 0.5 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

(t/TC−k)   +  6  

 1/         & 

+ v1 -

CR

+

+

v2

v1

v2

-

-

-

R =1/(f C )

C

C R

  + 3 /      %   &   

 1  /

+

 1/   

       

+0

swmod

swmod v1

ix

1e-9 +

-

-

1ix

+

va

1e-9

vb

.IC v(6)=-6.25 .MODEL swmod VSWITCH (RON=1e3 ROFF=1e7 VON=1 VOFF=-1) .MODEL V1 SIN (F=1000 A=2 DC=0 PH=0 RS=1M RP=0 TAU=0) .MODEL VA PUL (VZERO=-5 VONE=5 P1=0.1u P2=0.2u P3=24.8u P4=24.9u P5=50u) .MODEL VB PUL (VZERO=-5 VONE=5 P1=25.1u P2=25.2u P3=49.8u P4=49.9u P5=50u)   +'     /    %      8 

  

3 1    1



  +'

%      8  &     / /

1  

&%  & 1  



1  !?

+

K 0 !)=

   ?

+ ?

 /    @

 1/   

+

 /

+ ?

   / 1 

   /   1      /  

+

&   6   1&3 /

  1       / &  1  / 1&3     ?

A 1

1      

  6  /

  1  1 1

+ ?  / 1      /         &  1   

   1 &  /  1   ? 

 1  /

+

 1   &

71 1     /   /?

   //? 1

 /    3 

/  3  /       1     /   / - 1        1   / /     %  &   1

, + 1   

1 

 1   1 //  1

&  !M  / 2    & 0 "M

/   2   

1      

1  & 1    1

/  1?  / 

*  

+

  +#?

 

1

+

+



 /

 1  / 1 1   6  

-# A? 1 1   1   +  /   / @ 1 &   1 &/  0Æ?

 @&     /  &

& 1    / /  



*

  3!)= '3



 1 /  &  1



   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

Vpp=12.8

5

v(6) (V)

1.0

0 −5 0.0

0.2

0.4

0.6

0.8

1.0

t (msec)   +# 7&   &  1 



 1/      



0

K

  K



K

 0





 K    1    K  0  0    K 0'  > 1 ? @+A? &   ?  K 0   K '  0  0  0  K 0  1 / 8  & 0' 

* 1       ?   % / 1 /?

 

  1 

     0#N  

1 ?  /



 %  



&   / & 1 %      ?  / 1 %  & 1   8 /  1  !    / &    / 1  2  / 2  $  

 /  

    8  

 1   1  1  &  1  6    / /

&    &  1  

8 

 1  /  & 1  /  / /

$.   /   (   - 

1 %      &     * 1 /   ?

+

 1/   

 /

+

  &% ?

 ?

 

 ?

 / 1

1     

1 1     / 1 1 6 &% ?

 /         

 /  3 / / 3

?  & /  1    ?

/  1         !  /?

?

 1

 1 Æ  ?  /   2  3

!    > / 1 6 &% 

1     & 6 6   ? 

+ @ A

K

 1/ ? 1

0@ A





@+AC

       

+

+ @ A

+ @ A

1  

 ?

 1

0 1 0 1

K K

 / @+A

     !         ?

 1 1    / 1   &

&% ?

 1?  ?



  





 1 



K 0

        

  

   @ ?  





1 / & 0

 A

 



7 1



&     



K 0 ?

 1/   ?

K 0 "M      &   /  /

 &  

K

 /   /   &      

      /    /         ?



/ /  & 1   



1

K 0 !M

K 0 ?

/1   

 

 

1   

 1/    %        /      

 1 / &  /

   / 3 3  ?   1 /   1   3 %    1

&      &%     

   1  /  





/    !   1    /  





? 1

/ 

1  & ? / 1  /  ?

   &  1  ! &% 

   &   3   @#  



1    ? 1     1    3

?8/ A?



  /   ? / 

  /    

1  

    /  1 &     /    &   0 ")= 

  ,% @+'A   1   &  1 1  &  ! &% ?



  



1 1 1 1  / / 









8/ 

#

8# 1 1

@+'A

  ? #

?8/

  6 ? " / 1  6     / 00 !)=?  /

?8/

1  #



 ")=?

00 !)=

? 1   

 C

  1 & 



  

 1

    & 

 



K

 C

 ")=

 &    /   &    71

    1  ?  1   / ?

8# 

/1 1 / &



  !  / 8 

  / &1    1

1  & 1  ! &%  /    1   &     % /  &      /  *& 

     

 1/    6 ?

   1 / &       

    

& 1  ! 1 

  1



 

 / 1

   !?

   1  ! &%    //  /

 1& 

/  

      

 1



/ 

  1  //

  +-?

    / &    & 25  1 

 /  &   E 3E       ++

!   1



31  !

A ?

7&   &  1           

1

/  &



A 

B

  1 

 / 

1 /

31   

A ?

 / 1





  3   /

½  ,$  $3℄   !

     

    

  !



           

p

φA

φ1

  +-   

Offset Waveforms

AB A+B 00 1 01 0 11 0 10 0 NOR

φ2

q

7

+

31  !   

q=φA

6 5

p 4 3

φ2

2 1

φ1

0 −0.4 −0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

t/T   ++

31  !   

&  

1.6

       

+'

R

C

1

C

2

0A

+

+

V1

-

0V -

+

-

0A

+

+

V2

V1

-

-

C

1

+ 0V -

  1  



 /

B

+

-

V2

+

-

(b)

(a)

  + 

2



  C @A   ?  / @A 

/  &     &

. /  !   1 E 3E   1 ?

 1/   

&  ?    / 

 1&   1

A½ K @ L A¾ A?  / A¾ K @B L A½ A? 1    / A¾   1  ?  / A¾  1 1 1 

    / /  &   1 

B

1 1    /





 1 1

  1 



1  

&    1   

6 1

&    ++?    / 1  !  3   / &  

1   1

  1  1 25   . 1  ?   1

A½  ? A¾ 1  B   1 1?  /  ?  1   / A¾ 1   / & B  1 ? 1   / A¾  1  ? A½

 1 1?  / 1  1   //    / & 1 3A¾     1         B 1  & 1 1  !  1   71 B   1 A½ 1 1? 1  / 8 ?  1  1  A¾  1 6

1   1   1 1    / & B    7 1  1 1? A½

1    & 1 1     / & 1      1 1  A½     1 B   1 /  A¾ 1 1? 1   &  /   1 1 A½ 1 1    / 1 A¾      / 1

 1 1  / A¾

1 1?



 1 1 1  / 

 1  / & 1 

1   

 /?

1  1

   1    

1? 1

B

 /





&     

31  ?

A½ 1 1   /    1 ? A ?  /   A   

 / A¾ 1  / /   1  1 1 @2A   / /    /  1 1 /    C  K 0# ?   7 1 ?   ? 1 /   /  A¾         % /

.

 $! *

*& 



1  

! 6 ? 

    ! &  %

 

 &            

 1/    %   &  

 ' 8 '   1 

 1/     & 1

7 1 1 & 





  

! &   &  1 

 1

  C



  +

            R

V1

V1

1 C

I

V0

R0

+#

+

V2

2

C

V0

-

2

V

2

-

+ 0 V

0 V -

C

I

1

+

C

0

-

(b)

(a)

  + $

 /

+

    C @A   ?  / @A 

 1/

  

 

C



K



! #



 1 

K





¾ ¾ ½  ½ ¾

 1  ! &% ?  /

 1/      

&  1 



K

K





 ½ ¾

  C 0¾





 1  ?

  //

+½ @ A?

@+#A

6 &%  1

  & 1 %      /

 1/   

1         / /?    +?  1 /     



@  A

  

 !  '   1 

! &   &  1   

 B 

  +   & 

B     @ 1 A

 1 /   1/   & 1   1  

 



1 ///

 1 &/ !      1 1   1    

C



! #

K





@

¼ 0¼ L ½ 0½ A

  C 0¾

K



K



 /

¾  @¼ 0¼ L ½ 0½ A ¾

@+-A

       

+-

+

V1

-

V0

R

1 C

I

V2

2

+ R

0

+

-

+

C + +

V

2

-

0 V

1

-

+

V0

(a)

  +0

2

V1

0 V -

C

I

(b)

$   /

    C

@A   ?  / @A 

 1/

  

7 1



K



K

?

    1 

 & 

  &  1 

 1/

     C



K

0 0½

  @ ¼L ¾

A

@++A

 !   '       &  1   %    1 

  

 

  +0

/ @ 1 /A

 1/    /   %  1

  1 1     

/   1 / 8 ?



/  

 1 1

/ 8 

 

C

0¾ 0¾ ! #



K

0

K



K



  C



K

K

* 

0 0 0

@ ¼ ¼ L ½ ½ A ¾  @ ¼ ½ A &  ¼ ¾

K

 1 1    

1  1 1  &     &    1  &

0 0¼

 ½ @ ½ ¾   ½ @ ¼ ¾

 

0 0½

A

A



@+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

0¾ 0½   C

0¾ 0½

K

K

 ½

½ A @¾ L ¾ A @

 ½

L

 ½ A @¾ L  ¾ A @

.  & 1   6 ? 1  

6 &%  

L

@+A

! &    / 1 1 

!   &    /   /    &  

 $  ! ? 1 

 1/     / /     % 

& 3 &    

 / 1

!  /  % =   /

 



   

! #

&

 1  / &     / =3

   / &    = &/ ! 

   1  ! &%   1   3

?        & 1  /  ? 1  &     & &     /   . 

? 1 &     3/   

1 &

!

1  / 

+½ @ A

K

 0 ½ P

@ A

1 ℄

1 1  3 / / 



 /

 /

+¾ @ A

3/   ?

K

1  

 0¾

0½ @

P

1 ℄?

@ A

A  /

0¾ @

A

  /  / @ ? 1   3

 A

   3 1   & 1  6  &  1  3       1 1     1 



K 000





  /  

  +

J @#00 )=A?

 1/      

1   

 % / 

1 #003!M %       /

 1  '0 !)= . //  ? 1    1 /  / @    A

  & &     1 

       

+

C

V2

V1 R

R

-

+ 0 V

+

-

  +   3 

%  3 1 

     

! &  &  1   

  +

  / 

3

  

0

@

K

0



 1



 

K 

 & 





 1/   



K



K K

1 

31  !?

?







L

 @+0A



K



K

0 







 / 1

K





K











0

0





! & 

 1



 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 ; $  3B EE ;  ; E$%E 3.3 $% 3.3 GE'! 6E$%;

       





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



0¾



K



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 '



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



 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/        

     @ ?   1 1 



& 

 1

    

¾A



  +

 



1

1 1  



 1/               %

 1        / 

 1/     / 

/    /     

   @+'A

        & 1

C3

 1/    

/

/   

  / 

. //  ?   1  /   

1?



 /

 

&  1

 & 1        / / &  

   ? 1

¾  ¿ ?  /  & 1?   1      1  &   &  ? ! K "? 1       ¾  ¿ ?  /  & 1?        ! K "   ? "   ?   % 1 6  (         /   %

 & 

1   1 ? 1 *   ? 1 6     

" ?

1  1     

 

"  "  C

  1  & 





  "  " "  (  K "  /   K  " @1  A &     1/

    / ? 1   &   @+A  / /  @+''AC  "      " @+''A  : 

1       /  /  1  & " 1 &   1     % 1 

  C





"



 :   ¾ 

:   

@+'#A

       

0'

,% @+'#A   &     1 6 

1 3   /   1   &      6 ? 

: 

¿

K 0

 /





" 1    /

 1/       

K D 1 ? & @+'#A

 1 6   /

"

 &   ?

  1  1 13

 

"





K # 

1    /  1 /  

"

 

      !  

 1 / 1     /  1 /    /    

& 1  1  &     /?  /  /

1

 36  = ?

1 ? 1

1      / 1        /        @+'#A

7  / 1 1  

@+'#A

  

1 ! & 

  /     / &    &     /  %   

.

  

+ 1   & 1   

 +'0?

1

/ 

  / 1 

 1/       &  3

 1  /  

 1 1   & 1  1

 1      /     /     

@A > 1  1 

 1/    / &  %     ? / 

! &  &

 





+

  &  &    &% ?



& 1       1 %      / 

1 1    &%   / 8  

*

 & 

&%    @A 1  1  !     ")= 5  1 

!   1  

  & &   &  1    ?  / /  1   

! &  @  /A     &%  1  1

/     1   

+ 1         ?  1 

 1/    

  1

.

  +

  S 



  +'? &    

 / /     & &   3

 1   ?  / 

&

  /  / /

 1   ?  / ?     / &  1 /

8      @, A

1  

    & 1        @ 

 A?

 1      1

 

/ &



/   /

 &     %   

  ?  / 

 1

1 1 

71  1  6 / 1 & 1    / 1  

1

1  1 /  / /  1   I   &  1   

 

6 1  

 1 1   /  /  /   &  

 1

, 

+   //  %/   

 1



  +'

      ?  / /  

> 

 1/   

 1/       & 

1  %/    ! /   & 1 &  1     % / & 



1 

&    / 

 1/     /

$ &     

 

0#

vsw

ix

vsw

-1ix

100p

v1

100p

.Ic v(6)=0

Vb

Va

+ vC -

.MODEL VA PUL (VZERO=0 VONE=5 P1=1u P2=2u P3=49u P4=50u P5=100u) .MODEL VB PUL (VZERO=5 VONE=0 P1=1u P2=2u P3=49u P4=50u P5=100u) .MODEL VSW VSWITCH (RON=1e-3 ROFF=100MEG VON=4 VOFF=1) .MODEL V1 SIN (F=1e3 A=1 DC=0 PH=0 RS=1M RP=0 TAU=0)   +'0     &    +

v+ b

a q3

v+ v-

v1 a

v+ vq1 1e-8 va

+ 15 -

q3

b

v15 +

ix q1 vb

-1ix

1e-8

.IC v(8)=0

.MODEL VA PUL (VZERO=-10 VONE=10 P1=10n P2=20n P3=490n P4=500n P5=1000n) .MODEL VB PUL (VZERO=10 VONE=-10 P1=10n P2=20n P3=490n P4=500n P5=1000n)   +'     &    +

       

0-

1/b

1/a

Vg

1/k

1

1 1

-

s

+

1

-

V

-

+

BP

LP

out

V

1

-

V

+

out

  +'     &    +

1

1. 108

2. 251

0. 8015

(

0. 5058

1

0. 1735

Ω,H,F)

  +'     &    +#

+' 1 & 

 & 

 % / &        3

  .  / /   = 1 &      

  / &  1  

  

 1/      /

! &  ?  /  1 /

 1/    &   1     

 /  &     ! &%   1

0 0

K

 



K 00 

00A

000A@ L 0 A

L00@ L @ L

+# 1 &13 / 4   1 1   !)=  /

/    &  ?





  +'

 % /  

 1/     =  2  

   / ?  /  &     ! &%   /

    00 

&  ?  1    1   1   0  1 1    4   3/*  /

+- .

 / /    

 

   =/   /J 

 1/         =  &% 3 /

 & 1       1 &  

/1

 1/

/   

 &  /J  # !)=



  +''@A 1 / /  

 

0+

1

V1

V2 1

1

+

-

0 V

+

-

15 V + -

+

(a)

V1

-15 V

-15 V

-15 V

φ2

C

φ1

C

-15 V

φ1

R

φ2

-

R

C =5 pF

V2

-15 V

+ +15 V

(b)

  +''

  

    &    +-C

@A  

  ?  / @A 

 1/

  

@A >  3")= 

 1   /  / 1 &/ !   ?

% / &  1     1 1 1 

  +''@A?



1 1 

 1  /       

  1 &    & 1 





 /





 1/     &    &3

%   ? #?  / 0 !)= >  3 !   / & 

  & 

3

K # 

@A >     "2$ 

   1  

?

 1   

 /  /     3



 1

 1 & 3

A¾ 

@ A >   / /3   ?  / 1 6 / !    & 



&   1  

 &% ?  /  1 

 / & 1    @/A 71 1 ? 

 &  ?

! ?

& #   #

1 /

 1  & ?

&

      1/   

I

++ .  / /   = 1 &   

 1 

 1     1 1  

!

1 1 

 



@

A      /   1

 1/     1   .    /   = 1 & 

 1      ?  1



  +'#?

1

1 1 / %  

       

0

=s3V 0

I

Vi

1

1

1

V

0

C

C1

+

1

C

0.543

C

+

+

1

-s 2V0

-sV 0 ISC C

0. 543

  +'#     &    ++

 /    / 1 / /    &   1   &  1 & 

1     =

 &1    1 &      

     1     1

1

1 % / 1      

   / & 1         1    1  

 1/         1

  ?

 ?

1    ? 1 

          & 

@



0 -@

A K

¿



L  '

¾ ¾

 

L - #A L  '

L

$1

1     % /  / 1

  

/  &  1 / / 1      

+ .

 / /   



1   /  1 

 1/      /   / 3   1

"    

"    "? 1 

  1    &%    !)=  /    

1              1 

  

 1/      /  M   

/ /?  /  ?



1 1   0 

 / 1 /  I 71  1 

 1 % /

 1  !  / 



 1 6 

"  1 

/    &  I 71

   &  1  ! &% I

+ . 1    &   +'-? 1 &  M

    /

 % / 1 1    &  1  /    1 /

    00  71

  

1 

 1/

:



    /  %     

1   

 / /  !    

1  

 % /    /  # !)=? 1   &   #0  1 

/    &   1   /  / 1    !

&%  1   /  / 1    @ /A    +0 71

 1  & &  ?

 +'+I   



 1 

0¼ 0

 ? &  1       

 3

 1/    % /   /   M %  

 1  !  /

 

0

V1

VI3

I

C1

C1

+ -

+ 2

C1

5

+ C1

3

V2

V4

  +'-     &    +

C

1

Vi

0. 5

C1

C1

+

0. 4

C

1

V0

+ (F)

  +'+     &    +0

       

0

V4 C2

C1

V3

+ -

CU

V1

CU

-

V2

  +'     &    +

+    5(          /

1  

 1/   

   1 6   /     (   %  #  / 00'?    .  &1 % /  &% 3  1   &

 /J  ' !)=   &  1   &

$ &   

/    &  ?

 1/     ! &% ?

    00

1   & 0 

+ $ & 1   &  &

    1



 ?

 ?

 / 1

 1    



1   /  1   &  

 1/

  +'

+            1       /     1   & 0#      /  M  ' M?    . 1            &



K  /J 



 1/      

K # !)=

1  1      

    ! &% ?  /  &    1     &

 / /  

1  &% 3 

 1   

   #0

 1/

/    &   

  1 %    

 / &    1  &  ! &% I

+' .

 / /    5(  /      



1 6 



 "

 0 









 1/   

1     

"

 

 / 1

1 6   /        

  M  / 0# M?    1  /      1   

  

1   0 

>:

  &  1

00  &  1 

/    &  ?

&%    &  ?

 ?





//  1 

+# .

 / / 

 1/      /

 ?

"

 / 1

1  

    03!)=  /    

/1?  /

  /

     

    1    &     1    3!)=  /

"?

  &  &

 / 1 /  1 6 

>,(

 

 1/ 3

1 *  % 

    1  (      &

 



0#  0      

! 



/       &

00 !M  



@A >

K 00 !M?  &             

 = 1    @A $ & 1 6  

 1 &%  1   /

1  

 /      +-  

/

1 /   &  ,6  '? 1  /1 1 /

1    

 / &  1    



 1 &%  1  1

 ! &%  &  1 / &  / &  ,6  ' & '0 !)=  00 !)=?  / /  1 1   /1?  

&   ,6     / 1 !?

3  /    ?    

1  / /  /1

++ 5   +- &    ! &%  & 00 !)= +   1 /   &  ?

 ?

   

,6  '

&  / &  1 6 ?  /     1  

 / 

+  /  / &  1 / 

1  /  1  1     

  & #0 !M



/ & #00 !M 5  1 /     

  1

1 6  / /     

  +-? 1    !  1 ! 1

 1 232    8   1  /1 @ 3  /   A 3

 / &  1    1  1  00 "M &  2 1   & 0



 1 232   0 M &  2  /

      /   

C ?  '0 /*?  / /  1 1 

/ 

 1

 /1?

&

       

)

 P℄ *!? 5 :? ( ? ) 7?  / *  ?  ,?

!  ?



&+!

  * .  . 

S !C .,,, ? . ? 

&+!  

P℄  ?  ,?  / )  ?  5?

  * ?



7 1?

HC ) ? 5 1  / 7  ? + P℄ )

? 5 7?

*   ?

 / /? > $// 5 ? :C   

)?  P'℄ 2 1 ?  ?  / $ 1&? 5 7? / 5 ? :C    )? +#

*  !   

? > $/3



       

  $# %   6

!  $ !

$ &

 1 / / 1

  /     /  / &%   

 1      &      /    / &  3 /   

! &   "   /  /  1 

 

D 1

? 1 

3

1     / U %    / 1 % /  

71 1 1 ?



 &        / /   ?  3

! &  ?    / 1 % / &    &  ?    &      1  6    

 /    

1 6 &%   ? 1  1   / 

  1 / 1  /   /   

?

!

 &/

 /   / 3

! &    / / 

     1 /   /           /   &  

9 

&(   %  

1   / &%     / &  &     

.    

L /J ?  /   /

    &   &% ?

1  / 1     /

½ -

1  1  1 &  ?

 &   / @A?

  1 & 



/ 

1    &  1 &%   /? 



1 1 

/ &  

   &  1

.



  

? 1    /

/1 &  /    / K @ L 0A  K 

 1

 = D 1?

 &  /  1

>

 @ A?

/  /

/ 1   &



     &  C

 @ A



;

K



K

0 & 

K





& 



 

 

;

P

9@ L A  9@  A℄

&  



@A

         !

    

          #  

          !

   

     #      - )        -  Æ    1     ½



 "   !    

'

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

1.5

2.0

ω (rad/sec)    %     / &  

8

@ A





K



 ½ 







  @

@

A

 

 ;

@A

A

  ?

    

 &  1 6  @

 

A

@

 ! 1 & 1     1

?





K

  / 1 /  ?

1  

1   

?  ? 

K



 ½

/ 

 



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 K

&  ?



 /

  @

A K

@

A

1   =     /

  1  1

    

 / 1?  

@

1  

  





   .

 / &   & 

  &   ?    1 &     / / 1    



?

1 1?

 

A   !  



1 

;

? 

?

   =  

K @M

A 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     &    

8

@ A

         8

8 8

   8

1   8

1    

@

@

A

 / & 

A

K

@ A

K

@

@

A L

@ A L

A

@

1  

A

@ A

@ A

@ A

1 &%  /   & 

  @

A   & 1 

 =  1 ?

8

 8

K

K

8

@ A

K

A

 1

    /

@ A & 

K

@



  '

1 1   &

@A

1 /   &















@M



@

@M





A

A



@M



 @ A

A

 @M A

L





A





    /

C

 1 1 1  ½       1   1                   



 





@AC

@







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

1.0

1.5

2.0

ω (rad/sec)     / / 

 &  

10 b=0.1

dH1 / dω

5

0

−5

−10 −2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

ω (rad/sec)   ' %  /   &  1



 &

  @

A

2.0

"        



8 @ A

 @M

 A

 @@M L A







@M L A

?

 1  /  1     /

8@ A

K

8 @ A L 8 @ A

8@ A

K

Æ @ A L

1   1

@ L





0

 1

A  @@ L A

A  @

A @ L A

 



?

 



& @'A  /

?

 // /

0? 1   

   / &/    & 1

K 0

8@ A

@#A   1   &  1

    & 1

& @A? &  1     /?

 / & 1   1 1 1

 /? &  /    /?  1 1    1 1

@#A

   1   /   & 1        1   1

0  /



/1

 0 1 ///     /? ? 8 @ A?  /  8    1?         @ A  1 1      1  

   @A   # 1



@'A

   & 

  ?

 /    &



A  @@M  A

A

 @M  A



  1 1  1  1  1 ///     1 1 

1 / 1

& 

A

 @ A K ? 1 1   ? 8 @ A K Æ @ A?  /  ?  @ A   1 @#A   1 1   /

7  1        ?

/

 A

   & 

&% ? M K  L



A  @@M

@M L A  @@M L A

K

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  .  ?

  1   6 

/ (

   61     /

9 

  -   ( #(.*# / 

1    &    &  1   

! &   /

  

@

A K

 &      

0

8: 1 @ A

!

@

A

 @A ¾ ) 

 1    / =  &  

   / /3 &%    &  

     

 

K

0

K

0 0

?

8: 1

  1 & 

@ A K

4/

K

@

7

4/ @ A  1    @    A & 3

A 



@ .@

 1 C

A A

  @ A   K  /  .@ A  

   % %    

 

 "   !    

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.@ @

 1 =  &

A

K

1 / K

?

K

  / K

     ? 1   

@

A?

 @

@

A

K

#

 @

A

K

#

1 6 &% ?   &

 @

.

?

.@

A

.

@+AC

 @ A  .@ A  / 1  @A 1  @ A K 1 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

@

A

K

@

 @ A @

A

K

@











L @

L A@   L

@

K

 

 L A@ 

L A@





L

L







L



L A K

L

L0

L

L



L

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 

 @A

K

 

 @ A

    @ A @ A     . @ A. @ A 





K

@A



 @ A @

A

K

  /

.@ A.@

A

K

 L @A

1 & 1&3  @1A  

1   (



@-A?

  1 & 

 & 

C

    &

.@

K

   





 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

2.5

3

3.5

4

4.5

5

ω (rad/sec)   - *

1  6    

 

(

1  

 



.@

A

1    /  & 



 

K

K

L & 

(

//

K

 & 

(



@

A

@

(13 /

A &  1

&  1 / / 

A

*

 (   (         (

K

1

3 

  + & 

A 

 1

K

 (

.@

A

K

@

.@

A



1    1

& 

& 

(

1    ? K #  / -

36 

&  / & 

A

(



! &  

(    (       (    



( K  ' -

@A

L

1 1      ? 



K

K

1    /  /    ?  1



.@ .@ A



/ (   & 

(

//



A

K

@A

 (?

  / 1

   1 ?   //?

1 *

1   ?

1 1

@AC

   L A

  /

,% @A

K







@

L   @@

 @

 L 0#AAA L A

 L 0#AAA L A

L   @@

 &  &  1 *

& 

(

& 



(

//

@A

1    &     &

(

"       



(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

−1.0

−1.0

−1.5

−1

0

−1.5

1

−1

0

Σ (Nep/sec)   + ,6  *

1 

   / 

1      &  @A

" 1  1 1  &

      /  @1  1





 @A ¾

7



"- &  ?

  1      & 

!   6    1

  1  

 0C   K  C   C

& 

& 

/* & 

     

 @A 

1 



!

( &   

 / D 1

7 1  1 & 

?

1 



!

C

 @A K 0  ½¼  @A ¾ ¾ L  /

K

0  ½¼

K

L0  ½¼



0  ½¼ @A K 0 /*

K

0  ½¼ @A K  0 /*



0



(  ½¼ 

@'A

1    @* /A    &  1 *  1

 / 

1    /  &   

 1&    / 1    1  & 1 * &   (

1 1

@0A?   /   6   1 ( 

  1  /   %   



( K #?  / @A ( K -

,6  A

  -? 1 *

 & &  ?

1

Σ (Nep/sec)

   &  / 8   &

(

1    & 

1 1   /  1

: K  ½¼ @ A   1 1  8 &% ?  K ?  1 (   / 1   / / & 1  /  8  ?  K 0? 1     0 /* &   1    1 (  / 1  3   1  1       & ( &     %   

  1  ?   &  

  

3       &

 1 & 

(

&   *

1    

(  &      &    &%   

&      1    /      6   /   &  /* 

½ K 00 )=  /     /   & #0 /*  ¾ 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    K   & 



0   @ L   A 0   @ L  ,% @#A

A

 

1

 1     1 C

 #0

@#A

 1  /      &  (

@  A



K @   A

@00 00A

 ?

0



0

 K '

 $  (   

              





0











0

(



 @'A



   

0 0







K 

 1  ( K 0   1    %   

1   & ( 6 / 1   %     1?  /  ?  1    &%    &         / 1 & 

1 1 /   

 &       1

 ?   @#A

1 %  &  ( K 0

C 



K



@0



 

A

K 0'+



 

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

f (Hz) 2.0

ω (rad/sec)     *

1    /    (  %   

:  : 







A

 

K

@0

K

0-    K 0

K ++

1    1 1  13 / *  /  #03/*  3/*  /

 

1   

/1  & 0?

1

0   1     2    1  



  &  3

  %    &

/      K 00  /

K   K 0 &  1     13 /  1   /  &%   

&   & 0 K 00   K  &  1 /  1    Æ    &  /   & 1 & 

" 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    

 /

1

 /  1 / U &   /

1   &   

9  $% %).%  .  . 1     ?

  // 1 *

(

  /    /  ?  6    1 & 1  



  1    1   

(13 /

K



! &  ?

@+A

6 * @ A℄

* @:A

K

@

A

K



  0?  1

 

/  C

(AA 

:A

@

:

@A L &  / 8   &

1      / %     1       & / &    / 6  & 

 1  &  1    7 1  1 1 &  & 

(

1   



:

:

& 

(

*  @:A * @:A L *  @:A  /

* @:A

(?

? 1

   /  

1      /

:

 

  /    &      1  1

* @:A



1 1

  1

:

/      1 1     // &   &

//  /   &   &

/ /   



A?



@+AC

 P L

1 1

3  &  

11    1 1 1 & 

1  1

1 

   1      1

  1 / 1  1 1  & 11    

 @A * @ A

.



/     /  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 11    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 ?

 @:



 ':

*

K @'

:

L 

* @:A :





K

K

 @  

@ L

:A K -:  L A  

(AA





 

*  @:AA

'

: L :

1      1 1 11 



* 

@

   &  &

 A

(AAA

@ L @

@0A

  %  @ L

! &  ? @+A?   & 

1& ? 1    / &    1

 / & 1&3       3  &  &   @+A? 

 /  &  1 *

* A  K

1   

@

A     /

 "   !    

-

  4   / &  11   

(

5 

*

0













 ' # +

:@:A   :@:  A  :  :@':  :A  @:  A   :@:  : L A  @':  :A    :@-:  0: L #:A  @:  : 

L A

 /  ? 1  3  11   ?

6  / (

: :    ':  :  :  : L    -:  0: L #:   :  ': L : 

. /   / / 1

! &  1 

1  1  ?





/ 3

   1&

  !  1    1  & 1     &  &  1 11 

! &  

 ?

 @A 

  ? 

. //  ? 

  

  1   /* &  1     & 3 : K  /   1     1 

 K 0    @A 

 

K L0   @ L

6 * @ AA

@A

A

@A

* @A K   /  0   @ L 6

1     1 6   /   &  1  (   6  &  

1? 1  ?

6?



/ /  &

1 1   /  

 & 1  / &    &  1 / /   

1 /?

(?



/ /   & 1   /    %     1  & 1   / @   1  / & 1     /A * /  ? &   &      





(?



   /  1  3

   1  1 C

:   K 



*   : K         0   @ L 6 * A 0   6   A L 0(    &    0   @6



1      &  1 11  1 1      /  1 *

6



 ? 0   @ 

1 ? 

A

//  ?



/ / 

 8 & =  1 3

/* 1 11 ? 1& ? 61    1  8

@      /A 1 1 *    1  11   



@A

  & 





1 &   1 1 

(

K -  /



6



K 0 #

 3

1 8 1

 0   @0 #   A K ' 0 /* 1  8  1 13

1    &    1 /  & 1  / & 1  1 * & 

   1 @ / =  A 

  /

     &

1

 3 

. 1  /? 1 11  &    /  %  

  / /  1  &

6?  



K 0   @ L

6

A

"       

+

80 Chebyshev

70

Loss (dB)

60 50 Butterworth

40 30 Asymptote

20 10

0 −1.0 −0.8 −0.6 −0.4 −0.2

0.0

0.2

0.4

0.6

0.8

1.0

Log10(ω) ( K - 6 K 0#A

   11      @

  

3  / 1 11  ?

(

 /

6?

  & 1 ( % 3

  & ,6    /  & 1 &%    &   &  1    /  . //  ?  / 1   &  1    3  &   /  & 1 3

@

! &  ?

% 

# .@

A K

A

3 7 %   6    &  /* &   &%   1



00 )=  /     &   &%   1  

7 1 11 ? 1  /  / 

 /  

 



 

K 







  /

6



 /







6

K 0 #0 



K





@0



K ?  1    

0   @ L



A



6

 /  / 

  A

* @A > 1    & 

* @A

 



 /*



1   /

6 * @AA

 

 

#0 @0





 /  1  & 





6

K 0 #0

  / 

K  1      1& ? 

0   @ L

K

K  1 6   /  

     &  1 %    

1   

 / 



K  &  1 11 &  ?  / 1  

1 

K 00



K 00 )= $  3

- '#' 

A



(C





K ?

6 K -'#'

1 3

K 00? 

 

1 1

 "   !    



80 70

Loss (dB)

60 50 dB

50

Specification 40 Chebyshev

30 20 10

ω1=1

1 dB

0 0

50

ω2=2

100

150

ω (rad/sec)

200

250

300

f (Hz)    

(13 / 11    1  1 (  % 3

 





 $ 

(

(

 % /   

 



-' 0'



  @A

 ?

5  1   13 / *





 @-' 0'A

 1 

(

1   



K # #'

K - &  1  / 6   % /   1  

   &  ,6   1  &   ? 1  

(

  /   1 11    & 

 1 /  1 !/    1

(

 1       1 /  ? @A?

  1 & 

* @A K @- 



& 

 ?  /

K -  1   

* @AC 

@AA K # 0

* @A   1 -'#?  % / 1      //  &   &  ( &  1  6  1           /     @       /A?    

1  &

( 1

  &  

 @A 1

* @ A

  1 ! 1      1  &  1

 / &     /  

6 K 0#  / ( K -?  & 

K

K K



K

    &  1   

C 

 * @ A  L 0#* @ A   @  ' L   A     0'  0+ L '#-  + L '0  - L0 #

L

"        

  





K

& 

@

A







K

  @

@

 

AC



A K

.@

A

.  @

A

1

.@

A

.  @

A

K



 L 0 #@0'



L+ K 1 1   & 

 0--

.@

#-

A  





0 0-

L 0+



L '0



L +-









0 '0?

L A

L ''





L '#-

L -



L -'







0 +

L 0#



1   1     / 1 / / 



L



L  #





0 +++?  /



0 '+

! &   1



@'AC

@ 1

.@

A

A

K

K



.@ -

A





L # 00





L# +' 1    

  /



L  0'



L ' 0





L  '#



L  0

1 1 1 & 1 & 

'%3C + ," $" G 4(6" :- !  + "  4 " 4 #  1 & 



! &  ?  1   &  ?

0  > &%   ? A K    @ A?  /     3   0  :   &  : K A  ?   /  1     

 / 1  &  ?

1

5 1 

!       1 1  

1

% 

 /

0

3 (

K



A

K

"@

A

K

@ "@ 

A A

K

L



"@ A "@ A L#



L#

L

L

@#-A

&  1   / /3   &  

 &  /  & 

@ 1   & 

@

1



C

 @A

K

@ A

K

 @ A - "@A -   @  @ A "@ A A 

0 @ A

K

@

/ 

-

K

 @ A 

"@A

 -#   1  

/

A  

@#+A K

?

 1

 "   !    

#-

50

α (dBv)

40 30 20 10 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.7

0.8

0.9

1.0

Angle (rad)

4 B

p

2 0

Bq

−2

B

−4 0.0

0.1

0.2

0.3

0.4

0.5

0.6

x=φ/π   + ,6  +    / 13 &   &

    B  6  ? 

0

 @ A

K

½

K 

  1 &  @

>  P

  &  1    / 1   /

@ A℄

61   /     1 

P

/   1

 3

0 ? 0 ?

 /

0

K



 

   &

1 1

 

"@ A





/?

 . 1



  &

1    / /

 1

 

/ @/ /    

 1  1 =  / 1   & L 

1 1   1

"@ A

  

? 1

  =   1

1  & L 



? 1   B 

/? 1    & 1 /3%/   

1 1  L    

  L  

 /  & 1

 0

 1 1 &   &   

1    1     1  / %/   &% 

& L 

0

1  & 1

   /  1  

  

A  ?

"@ A

"@A

    1

&

K





 1

1 1A 1   & 

:

?

2 1  1   & 







1  1  1  ?

   &  6  

@   A & 1      /

 @ AC

@ A℄A

1    /  /  = 

1 /       1

   1  &  /

½ @ A  

K  

&  1   &

1  / Æ 

    & 1   /

A 

1 1  6  &   1

7  //  1 1 1 /      /        /

K

 

  + 1   &  61   ( 1 ?

0?

:

1

 &% ? 1  

1 1     1 & 1 %/  

. 1   &   

?



 /?

1 &13 /     1   

(+−)Real−Imag. Parts

(+−)Real−Imag. Parts

"     

#+

2 1 0 −1

Re(Q)

0.0

Im(Q)

2B /π

−2

Q

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

2 1 0

2BP/π

−1

Re(P)

Im(P)

−2 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x=φ/π    1 /   &    ? 1     & 1      /

 @ A

  

 /

"@ A?

/ 

 "   !    

#

 

  1 L

/



1? 



 & = 

     1 F G

   & 

1 /  

   &     &     !



 3

/      



1        /  1

    =  1    

1 

0

K

"@A

K

0 A

 @

&

1   &  1



"@A 



0 -+

K

#



0







K 









 @ A "





 

 3

1 

1

 1 

L A L

#

L A

#

L A

P

@

P

@

 "  '

 @

 

A℄

L



L







#

L A 

 

@

L 0 -+A@

L ' 0A

L 0 'A@

L  ''A



?



1  

0







  





 ''?

 







 1      =

  & @#A !

 

@#A

  = ?  

? 1  



1 3

A℄

@

 1 



 1 

  > "  

L#

@

1 / %/   /    



 @ 

  / 1 6     



L#

            

1 1     



C

K 



L



@

K



 1 1 & 

   / /  

K





! 1  &   /  !  1   

  1 /     ?

 &



1  1   1  & 

   /   & 1    1 &  ?

&    1

0 '

 1  

 / /        1 1   & 

"@ A  /  /  3 6    @ A K "@ A

1   /

1

@' %/ A   1 

 1    & 

 1

/

 1      ?    ? &  .



*& 



  1        

  1  @   

A  //      & 

  1 

0  

? 1  

#             & =  #

0

1&

 @ %/ A

? 1     1

1 1       

' 0? 1      = ?  / 1     



 ?

? 1     1  1 1  %/    /  ?  / 

L

 

  / "@ A 

K #

/    ?





1     

1 1    / & 1

     / % 



 1   %/  &%   B /  /  1      & 

  ?

 /   &  1

C

  % :

















K

P0 ' 0 -+  '' ' 0℄

K

P0 ' 0 #0  +-  0+'℄

K

A 

K

P0 -0 0 '' 0 ##+ 0 +'0℄



K













  % A

@





1 1  /

 3



:

K

A 

"     

#

    & 1  

0

1

1 1  /      & 

      

 1 1   6  /  1    &  1

& 1   ?

"@A

    1 1 1     /    1 1 61   1   

1  &   

   

    &/   )

/ 1 )

= &  ?  & 

 &% 

=     /  

? &  1 

! &  ?

 

@



$ 1 1



A @ P℄?  -?

&   / AC

@ 1

@

A

@ "@

K

  A

K

A

K

K

1 

A

 

K @

 L 

 =+ P @ A℄ L C1P @   B  K @B L B  =+ P"@ A℄ L C1P"@

K

"@

A

A℄

(

711

L

  L   L   A

 /

L

B  L   A L @B

L

B  L B  L   A

A℄

@#A

! &   /  /

  /

  L   A L @

L

 

1  1    1 1

    //   / 

1 1   

?   //? 1 1 1 13 /   1     ?

 1 

 

  & 1 )

0 A

 @

K



 1 

(



 &% ?

  &

0

& 

1  1  1 %/ 



 !

"@A?

 A@

  ?

L

  ?



A@

L

L

 A   

  A   

 @-0A



(13 /    1  3   %  & 1       / 1  %  1 & 

&  1

@-0AC

  &  1  ?

 

=   &    

0 ? &  "@ A

@-A

1   ?

 @A

1 &  1    

@#A   // / & 1

 / 

$

1    

 /    

 0

@

 1 )

1  1     & 

L

              

   &    1

# @  A@

% 

0

& 



C1P"@ A℄  =+ P"@ A℄  



 &  1 &% ?

0

= &  &  1   C

1

&  / &   /    & 1 &  

( L   

L

 /  1 = &  6 B      &    /    

&   @ L A 1  L  L  A 1   /     "   & 1

() &    1 

&     1     6 ?  / @



1      Æ  

1   

 "   !    

-0

10 8 6 4

tan(Bq)

2 0 −2 −4 −6 −8 −10

0

1

2

3

4

5

6

Bq/(π/2) (quadrants)    $1

  

1  

  /          1    

 / 1  !  //  1 1 1 1 &  

 ? 

, 1  

&    &  @  1

1  1

(

/ & 



$ &?



@-A?   / 1  



  &  ? 1 &   

& 

 1  1

    1    /   1 )



/  /?



/  & 1 

    &

 

/



(

   &  ? @-0A   1 1 & 

0 A

 @

K



=

 &%  1

2  1     &

 1     /  1     

1 //  & 1         &  1



 1

= &  & 1   ?  /   

 3 /    / = 

 / 1 1 & 1 

(



  /  1

   ,% @-0A 1

  & 1    1     

&% 

1   

  %  & 1 1  /

0 A  1 )

0

    

 1 1   &  1   / //  

  & 1    &  1

1

 1    &   /

1? 1   X 



L

@

  A@

# @X A@ 





    

      A

@

A@

L

L

    & 1

  

0  1 1 X

  /C

# @  A@ L



 A   

  A   

A 

  

&  

"     

-

5.0

β/(π/2) (quadrants)

4.5 βq

4.0 3.5 3.0

βp

β

2.5 2.0 1.5 1.0 0.5 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x=φ/π (rad/rad)   0   / 1   &    

#



0 @X AA @       A A @        A

 @

1? 1 1   &         

1   !

&   1   ? 1 

@

A K

@ "@

A A

K



1     ? 



1  1    /   1

      > 1 )

! & 

 !  & 

@

L

  A@

L

  A@  A L #

@

L



A@

@

L

  A@

L

  A@  A L #

@

L



A@

 ?

= & 

C

  A

  A

@-A



  &  1          1  3

  / /   & ?   ? 1      /

&% ?  1   1

@-A

@X

K 0    1     

1    1

1  / 

1? @-A  

&     /  /   &   &

! &  

1       &  

1    1  ?  / &  1     /  1       ?  &  ?

0?

 1



  0? 

 / & 1 / 8  & 1 

1      /  1

H   ℄ "; $" ..8";&

1 1 

! 13

   1 &  

1 & 

6  " /C

 "   !    

-

; "$   ? ; +  $ ,"$%6 $"  $" %" "$  - $ ( ",%6- H  #"6- H 4 .   (",%'#" * "",% * "#" ' '   "; (* (* $ (2*. $ "# $ (2*. $ "# *( *( "# *F*.*   1 1   & 1 1 & 1 &

(

  & %/   %/ ? 

(  /

  0

(13 /

   =/ 

   

1  /  

/  & 1 &% 

1 &    1 6 %/  1? 1   1 )

 

/  /



 1      1  1

/  /  

= &%  &   1   

 1   ?    

 1 / 1 1  1 ,6  +? 

 &1 1 1    /





      

&   / 1    % /   /  / /  

9 .



    %      %

   1 1 13 &  / &  

&   &     

1 1 )  1  /

!

1 1  

&     @#'A 5 & 1   6    /  1 ! 1    & 



>   &   & 1    1



  +   

 13   /  6   1 6       &  D 1 ?  1    1  / 1 &  ? @#'A?  / 3  1   1   3/ / 1  @1



  0A

/// / @ 1 / &    0A % /  ! 1    

?

1 1  1



  C

'8''℄ ; "$   #(.   (6- H? ; '6 H? ; #('!) +  $" : "" 4; + 4,# (  %  " 4  

1

 

"     

-

Loss (dBv)

50

αH(s)

40

αapprox

30 20 10 0

Phase Lag (rad)

0.0

0.1

0.2

0.3

0.4

4

0.5

0.6

βH(s)

3

0.7

0.8

0.9

1.0

0.8

0.9

1.0

β

approx

2 10xDiff.

1 0 −1 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x=φ/π    1 &  1   6       

+  ,    $4 .$" $% $" - ," 6     ;2; " ;=;"  ".     ;; ; ;      .  ;.;; .;' ;=;.;=;  "# #(  '!) + $% $"  4 @  ". ( . ';.; + B$ #$- $-

(.@ + C "# #$- $- @( "# ("

".(". ( E$E;  " ,; ( (   ;.,'  (;.,'''

 %

 "   !    

-'

;,'  (;, "# *4$(.( $ + F$( 4   $ # ;$ 4 $% $" 2 1   1? 1  1  @ & A?  / 1 /1/   6   1 

 / & 1  

! &  

 3 A

2 1 1 1? 1 )  1?

@#'A / / & 1  6   1   ?

0 .

 /

 /   /1/      1 1 / 8    1

! & 

 /  03   13  @

 1 

 /





1 1

1  ! 

 1 1 

1    

/  T

7

 / 1 1 13 &   / &   &    1 1   / /  

   &   /  1 )  1   /

1   /   &   &     

 1   &   &

1

 

& / ?

 1  /  1 & 

?

     /   &  ?

  &  @ ?   A &  &  ?

0?

@#'A? 1

 1  1   1

1  1    /  1 &  

/



1 1

  C

 /    /  13

    1  / 13

!  !

/ & 1 1 &    / 

   &      1 % /  I

9

+)  '  .  4  % / 

71  

! & 

  /

@#A℄? 1  1    

   



   1 1   )

)

 

=       

1  

 % 

 / ?

@

1    /   &   *   U 

  1?

0 ?

 



"@



0A  /

 1&   /

=   % /

 1

    1

A?    / 1 1  ?

0?



0

@ ?

0

0

K

0?

 

 1 / 8  

 / 1    1?

     @& 



  1 1/? F 1  

1 1 1  ?

1

1 1   

1?

/  & 1 )

  0 &  1  6  7  ! 

/

 6/

 1  1

! &   &  % / 1

1 6  

A  /

/  / 

! & 

= &  ?

/  /  1  

 &   1     / 1

7 / !

 / 1   

     1 1  

1 1 

    &

  /  1 1  

/G

B ?

1  )

     &  1 % / 

 &   1   ?

?

  1  &  /  1& 

 1    Æ  ?

   &   

1  //    &  P ?

   /   &  ?

 /

U

1

 1 / 3

0 A?

 1





1    1 &   

  

1

 &% 

   1   /  @&   1   ? ? 1  1 1   A &  1  &    & ?

  / 1 





0



 /  /   & 1    1? 1  ?

0?

 /

1 1

 

/ 13

 & 1 /   1?

1   /  ?

?

0 

2 

0 ?

 1 / 1

1      / 3

Phases/(π/2) (quadrants)

"     

-#

5 4

βp βq

3

BQ

2

β

BP

1 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x=φ/π      & 13   ? *<  / *

    ?

  

0

 

      ?  / 1 1 / / &

C  / / &

      



1

/  3  1 &      1 %    &  1   &      1 % /     1 &   / &

0

" / 1

 1

   &  1

@

1 

 / 

1 



A 6 ? @#-A 1      

  /  1  / *