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Frequency Response

S-Domain Analysis Poles and Zeros

M

 jj 1−:= N 40:= z1 ! jj⋅+:= z" 0:=

i 0 N..:=  p1 ! ! jj⋅−:=  p! :=

 j 0 N..:=  p" !−:=  p4 0 " jj⋅+:=

ei

10#1− i 0#4⋅+:= ω j 10#1−  j 0#4⋅+:=

$ e %,& 'e z1+ % jj⋅+& ' e z"+ % jj⋅+& '⋅( )

e % jj⋅+  p1+& ' e % jj⋅+  p"+& '⋅  p! % jj⋅+ e+& '⋅ e % jj⋅+  p4+& '⋅:=

Mi j, $ ei  ω j,( ):=

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,ample #"

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Frequency Response

,ercise #1

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3o%-Frequency Response

ω 1

1

ω  "

1

ω  "

+ +"−

ω  "

+"−

ω  "

+ −−

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5sin6 S/or+-7ircui+ and 8pen 7ircui+ .imes 7ons+an+s

For +/e Approima+e De+ermina+ion o$ ω3 and ω

Open Circuit time Constants

ω1

i

7i R io⋅∑

Short Circuit time Constants

ω3i

1

7i R is⋅( )∑

Dominan+ Pole ,is+s

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,ample #9 - S+udy

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Low-Frequency Response of the Common-Source Amplifier

" Second :uiz;

 

/a+ is +/e

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Low-Frequency Response of the Common-Source Amplifier

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Low-Frequency Response of the Common-Source Amplifier

Using the voltage divider rule cwe can find Vg

>6

s& ' >i

s& ' Rin

Rin R  +1

s 771

⋅+

⋅

>6

s& '

>i

s& '

Rin

Rin R  +s

1

771   Rin R +& '⋅

⋅

ωP11

771

Rin R  +& '⋅

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Low-Frequency Response of the Common-Source AmplifierNext

?d s& ' ? s& '>6 s& '

1

6m

Zs+

?d s& ' 6m >6 s& '⋅@S

6m @S+⋅

@S

1

ZS

1

R Ss 7S⋅+

?d s& ' 6m >6 s& '⋅

s1

7S R S⋅+

s

6m1

R S

+  

  

7S

+

⋅

ωZ1

7S R S⋅  ωP"

6m1

R S

+

7S

1

7S

Rs1

6m

⋅

R S

1

6m+

 

 

 

  

 

⋅7S introduces a zero at ZS

at infinite, which means Vo zero

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Low-Frequency Response of the Common-Source Amplifier

r o R D> approximation is valid

after hevenin!s theorem and some manipulation

>o s& ' ?d s& '− Parallel R D r o, R 3,( )( )⋅s

s1

7

7"

R 3

R D r o⋅

R 

D

r 

o

+

 

 

 

 

+

⋅+

⋅

ωP!1

77" R 3

R D r o⋅

R D r o+

  

 

 +

⋅

77"introduces a zero at zero fre"#

and a real pole a

P!

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A3 s& '>o s& '

>i s& 'AM

s

s   ωP1+( )⋅

s   ωZ+

s   ωP"+( )⋅

  s

s   ωP!+( )⋅

AMR in−

R in   R +  6m⋅   Parallel R D r o,   R 3,( )⋅

Low-Frequency Response of the Common-Source Amplifier

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3o%-Frequency Response o$ +/e 7ommon-Source Ampli$ier 

Desi6n o$ +/e 7ouplin6 7c1 and 7c"

 and *ypass 7apaci+ors 7s

.o place +/e lo%er !-d $requency %l a+ +/e speci$ied

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,ample #B

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,ercise #C

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,ercise #

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Analysis of the Common-Emitter Amplifier

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Analysis of the Common-Emitter Amplifier

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,ercise #

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,ercise #10

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A M8SF,. common-source ampli$ier &a' and a *E. common-emi++er ampli$ier &'# /ere V  s and  R

 s represen+ +/e

./

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Miller’s Theorem

An admi++ance @ &@H1IZ' is connec+ed e+%een +/e +%o nodes and +/ese nodes are also connec+ed +o

o+/er nodes in +/e ne+%orG# MillerJs +/eorem pro" and >1 is 6i"I>1

.o $ind @1 and @" 

'

V(

V)

'(

V(

V)

')

*(

*)

*(

*)

( )( )

( ) ( )( )

( ) K Y Y 

V Y  I 

 K YV  I 

V V YV V V Y  I 

−=

=−=

−=−=

1

1

1

1

111

11

1"1"11   ( ) ( )( )

( ) K Y Y 

V Y  I 

 K YV  I 

V V YV V V Y  I 

11

11

1

"

"""

""

"1"1""

−==

−=−=−=

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+s

Cgd

(-gm+

.!/

Cgs

gm

vgs

vgs

+.! v

ov

i

Cgd

0(-(1gm+

.!/2

34 Cgd

C

( )[ ]   sT  s Lm gd  gs H 

 RC  R R g C C 

1

N1

1 =++

≅ω 

CS Amplifier – i!h Frequency Response

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CE Amplifier – i!h Frequency Response

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"ifferential #air

5e have seen that a symmetric differential amplifier can beanalyzed with a differential half circuit# his still holds true for

high6fre"uency small6signal analysis#

+7   +7

*

vout

-vd1)

6vd

1)

+s

+s

+s

Cgs

gm

vgs

Cdb

Cgd

vout

vd1) +

7

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$ariation of the CMRR with i!h-Frequency

./e 7MRR o$ a di$$eren+ial pair

de6rades a+ /i6/ $requency

due +o a numer o$ $ac+ors#

./e mos+ impor+an+ is +/e

increase in 7M 6ain %i+/

$requency due +ocapaci+ances#

ω ,log scale/ω8

ω

ω9

ω

ω ,log scale/

,l l /

C:++ ,d;/

d;1dec