## Transcribed Text

Computer programs (such as Matlab, Mathematica, SPICE, etc) are not allowed.
Problem #1
Calculate the frequency response of the folded cascode topology shown below. Don't confuse
this topology with differential pair, as one of the transistors is an NMOS and the other is a
PMOS. (Cox=1.0fF/um², VTN=0.7V, Vrp=0.7V, UnCax=50e-6 A/V², upCox=25e-6 A/V², An=Ap=0, =
v=0. L.==.1um).
VDD=5V
t
/ bigs=500A
Rs
Vin
40/2.2
V bias =3.5V
in
o
80/2.2 (drawn)
1kQ
(drawn)
V out
10kQ
RD
Figure 1
a) Find KN, , Kp and Keal for the NMOS, PMOS, and tail NMOS transistors. (L=Ldrawn-2Ld)
KN unCoxWN 2
=
2
L
b) For an input dc voltage of 1.5V, calculate the transcondunctance and gate-to-source and
gate-to-drain capacitances of each transistor. Ignore the fringing effects (Cov=CoxLd. For
calculating the capacitors you can use the equations on pages 30-34 of Razavi. Ignore
Cdb and Csb.
gmn=
Cgsn³
Cgdn²
gmp=
Cgsp
Cgdp=
c) Draw the small-signal model for the amplifier. Ignore gate-to-bulk and drain-to-bulk
capacitors of the MOS transistors
d) What is the low frequency voltage gain of the circuit?
Av=
e) Use the method of zero-value (open circuit) time constant to estimate the bandwidth of
the above amplifier. Show all the time constants separately and identify the dominant
source (sources) of bandwidth limitation).
Tgsn
Tgdn
Tgsp
=
Tgdp
f-3dB²
Problem #2
The frequency response of the cascade topology can be modified by adding a shunt capacitor in
parallel with the common-gate stage. Ignore all the transistor's parasitic capacitors and only
consider Cx. You can ignore channel length modulation, but take body effect into account. The
bulks are connected to ground.
V
DD
R
D
V
out
V
bias
C,
X
M
2(gm2,gmb2)
Vin
in
M1(gm1,gmb1)
Figure 2
a) Draw the small signal equivalent of the above circuit.
b) Use the above small signal model to calculate the small signal transfer function of the
above circuit (Don't use any approximations beyond those mentioned above).
c) Now use the method of zero-value time constants to find the bandwidth of the circuit in
terms of circuit parameters.
d) Do you see any discrepancy between the result directly obtained by calculating the
transfer function in part b) and the result in part c)? In a few lines explain the reason for
this discrepancy. Which one is the correct result?

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