Lect. 14 Frequency response of CS amplifier

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers (4.9)

Roll-offs at low and high frequencies! Why?How to determine fL and fH analytically?

CS amplifier (Example 4.14)

10K 10µF

0.79M

10µF

10µF4.2K

50K

3.3V

0V

0.45mA

PSPICE Simulation Results


Lect. 14: Frequency Response of CS Amplifiers

High-frequency small-signal response



( )

Since is very small,

can be assumed small

Then,

( )

( )

= (1 )

(1

o d L

d m gs gd

gd gs o gd

gd

gd

o m gs L m L gs

gd gd gs o

gd gs m L gs

gd m L gs

eq gd m

V I RI g V I

I V V j C

C

I

V g V R g R V

I j C V V

j C V g R V

j C g R V

C C g R

ω

ω

ω

ω

′= − ⋅= −

= −

′ ′− ⋅ = − ⋅

= −

′= + ⋅

′+ ⋅

∴ = + )L′

Id



0

0

0

(1 )

1

1

1 =1

1 1 = ( )1

Since

1

1

in gs eq gs gd m L

G ings sig

G sig sigin

Gsig

G sig sig in

Gsig

G sig sig in

o m L gs

o Gm L

sig G sig

C C C C C g R

R j CV VR R Rj C

R VR R j R C

R VR R R Cj

V g R V

V Rg RV R R j

ω

ω

ω

ωωω

ωω

′= + = + +

=+ ′+

⋅ ⋅+ ′+

⋅ ⋅ =+ ′+

′= − ⋅

′= − ⋅ ⋅+ +

Cin

High-frequency roll-off due to ω0

fH=f3-dB=ω0/2π

Below fH, capacitors don’t matter



CS amplifier (Example 4.14)

10K 10µF

0.79M

10µF

10µF4.2K

50K

3.3V

0V

0.45mA

0

3-

13

0H

1

1

For , 9.4 19.5

( 3.3 , 0.986,

2 2.9 from PSPICE simultion)

With 1.3 10 , || 9.875 ,

1f2 2

o Gm L

sig G sig

o GdB m L

sig G sig

GL

G sig

Dm

GS T

in sig sig G

V Rg RV R R j

V Rf f g R dBV R R

RR KR R

IgV V

C F R R R K

ωω

ωπ π

−

′= − ⋅ ⋅+ +

′< − ⋅ =>+

′ = =+

=−

′= × = =

= = 120

(From PSPICE parameters for 0.5- m NMOS given in Table 4.8,

= 41 , =9 , =41 +9(1+2.9 3.3)=137 )

sig in

gs gd in

MHzR C

C fF C fF C fF

µ

′⋅

×


Lect. 14: Frequency Response of CS Amplifiers (4.9)

(For parameter descriptions, see Table 4.7, p. 353)

(Table 4.8, p. 355)

Key parameter values for NMOS

Kn’= 170 mA/V2Cox = 3.7 x 10-3 F/m2

Cov/W = 0.4x10-9 F/mLov = 0.08x10-6 m

CGS= 2/3 WLCox + WLovCovCGD=WLovCov



Low-frequency small-signal response




sig

sig1

sigsig

1 sig

11 sig

V V 1

V 1( )

1High-pass characteristics with =( )

Gg

GC

G

G

C G

PC G

R

R Rj C

R jR R j

C R R

C R R

ωω

ω

ω

=+ +

=+ +

+

+




2

2

2

32

VV1 1

High-pass characteristics with

1

V 1( )

1High-pass characteristics with ( )

gd m g

m

m S S

mp

S

Do d

D LC

D Lo o L d

D L

C D L

pC D L

jI g gjg j C C

gC

RI I

R Rj C

R R jI R IR R j

C R R

C R R

ω

ωω

ω

ωω

ω

ω

= =+ +

=

= −+ +

= = −+ +

+

=+

∴



sigsig

1 sig

2

sig sig 1 2 3

1 2 31 sig 2

V V 1( )

V

V 1( )

V[ ( )

V

1 1Since = , , ( ) (

Gg

G

C G

d g mm

S

D Lo d

D L

C D L

o Gm D L

G P P P

mP p p

C G S C

R jR R j

C R R

jI g gjC

R R jIR R j

C R R

R s s sg R RR R j j j

gC R R C C R

ω

ω

ω

ω

ω

ω

ω ω ω ω ω ω

ω ω ω

=+ +

+

=+

= −+ +

+

⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞= − ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟+ + + +⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠

= =+

1 2

sigm

2 3 1

)

If =10 F and 1790 10 800 , 0.345 , and

g4.2 50 54.2

D L

C S C

G

D L

p p P

R

C C C

R R K K K K

R R K K K

µ

ω ω ω

+

= =

+ = + = =

+ = + =

∴ > >




2 1 46.22 2 0.345 10

pLf Hz

Kωπ π µ

∴ = = =⋅ ⋅



10K 10µF

0.79M

10µF4.2K

50K

3.3V

0V

0.45mA

Ex 4.14



Ex 4.14



HW: PSPICE simulation of CS amplifiers. Due before Tutorial on 10/17.

1. Set up the CS circuit schematic given in Fig. 4.63 (Ex 4.14).Use the PSPICE parameters for 0.5µm NMOS given in Table 4.8.A text file will be provided in the course web page so that you can cut andpaste the model parameters into MbreakN3 model in PSPICE.

2. Determine bias conditions for Cs=10µF and Cs=0. Hand in simulation results.

3. Determine frequency responses of CS amplifiers with Cs=10mF and Cs=0.Hand in simulation results showing fL and fH values.

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Lect. 14 Frequency response of CS amplifier

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