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

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

High-frequency small-signal response

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

( )

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

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

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

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

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

′⋅

×

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

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

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

Low-frequency small-signal response

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

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

=+ +

=+ +

+

+

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

Low-frequency small-signal response

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

= =+ +

=

= −+ +

= = −+ +

+

=+

∴

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

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

+

= =

+ = + = =

+ = + =

∴ > >

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

Low-frequency small-signal response

2 1 46.22 2 0.345 10

pLf Hz

Kωπ π µ

∴ = = =⋅ ⋅

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

10K 10µF

0.79M

10µF4.2K

50K

3.3V

0V

0.45mA

Ex 4.14

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

Ex 4.14

High-Speed Circuits and Systems LaboratoryElectronic Circuits 1

Lect. 14: Frequency Response of CS Amplifiers

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.