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University of California
College of Engineering
Department of Electrical Engineering
and Computer Sciences
Problem Set 5
Due Monday August 7th
Octavian Florescu
EE40
Summer 2006
Reading:
Chap 12.1-12.6 Hambley.
Chap 3.3 of Rabaey
Problems:
Chap 12: 12.15, 12.24, 12.30, 12.37, 12.40, 12.47 (midband refers to the frequencies at
which the capacitors are short), 12.51
Additional Problems:
Problem 1
VDD
RD
R1
VO
VG
R2
M1
RS
The circuit above has the following parameters:
VDD = 5V, R1 = 20kΩ, R2 = 30kΩ, RS = 1kΩ, RD = 9kΩ, VTh(M1) = 0.5V
1.2
1
ID
(mA)
0.8
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
VGS (V)
ID
(mA)
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
VDS (V)
a) Find the value of VG.
3
3.5
4
4.5
5
b) From the ID vs. VGS curve below, find the values of IDQ, VGSQ.
c) From the values of IDQ, VGSQ and VT, draw the ID vs. VDS curve for M1. Assume
λ = 0. Annotate VGSQ, IDQ and the point where M1 enters saturation.
d) From the ID vs. VDS curve you drew, find the value of VDSQ.
e) Is M1 in saturation?
f) Find Vo.
Problem 2
V DD
RD
Rs
C1  
R1
VG
CL  
+
+
vin
R2
v out
C gs
_-
-
Consider the Common Source amplifier above. C gs is the capacitance between the gate
and the source of the NMOS.
V DD= 15 V
V Tn= 1 V
μn C ox = 100
μA
V
2
W
= 20
L
λ=0
R1= 4 M
R2= 1 M
R D= 2K
C gs= 5 fF ( 1fF = 10− 15 F)
a. What is I DSQ and V DSQ ?
R L = 20 K
R s= 10 K
Hint: All the capacitors, including C gs , are open circuit for DC analysis.
RL
b. Draw the small signal model for the circuit and find the vg/vin .
Hint: All the capacitors except for C gs are short circuit for the small signal analysis.
Do include C gs in your small signal analysis.
v out
c. Find the small signal transfer function, v . Draw the bode plot for the transfer
in
function.
Problem 3
The circuit
shown is biased
so that both transistors are in saturation. M1 is an N-MOS and M2 is a P-MOS. The
source terminals are indicated by the arrows.
a. Draw the small-signal model of the P-MOS transistor in saturation. (It should be
very similar to an N-MOS, differing only by signs). Give expressions for gm2 and rd2
in terms of the MOSFET parameters and large-signal current.
b. Draw the small-signal model of the whole circuit.
c. Find the voltage gain of this circuit in terms of gm1, gm2, rd1, and rd2.
Problem 4
Find the transfer function of the following amplifier.
Use R1 = 10k, C1 = 0.01uF, R2 = 1k, C2 = 0.001uF, and Gm = 0.01S.