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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.