EE 541
University of Southern California Viterbi School of Engineering
J. Choma.
Final Examination Solutions
1
Fall Semester, 2010
U
U
U
niversity of
S
S
S
outhern
C
C
C
alifornia
USC Viterbi School of Engineering
Ming Hsieh Department of Electrical Engineering
EE 541:
Final Examination
14 December 2010
(SOLUTIONS)
11:00 -to- 1:00
Problem #1:
Solution
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(25%)
The circuit shown in Figure (E1) is a simplified model of a MOSFET technology
amplifier that combines shunt peaking via the inductance
L
1
with series peaking through induc-
tance
L
2
to achieve a broadbanded network.
The two inductances utilized in the circuit are un-
coupled.
The input signal is the voltage,
V
s
, while the output response to this signal is voltage
V
o
.
It can be demonstrated that the input/output voltage transfer function,
H
n
(p)
, normalized to
the voltage gain realized at zero frequency is of the form,
2
n
2
2
1
kQ
p
H (p)
,
1
p
Q
p
+
=
+
+
where
“p”
is complex frequency
“s”
normalized to the uncompensated circuit bandwidth, say
B
u
.
Specifically,
B
u
represents the radial
3-dB
bandwidth that is realized when
L
1
= L
2
= 0
.
g V
m
s
L
1
L
2
R
L
C
L
V
o
Figure (E1)
(a).
Determine parameter
“k”
in terms of the two inductances,
L
1
and
L
2
.
The input/output (I/O) transfer function,
H(s) = V
o
/V
s
, is easily confirmed to be
(
)
(
)
(
)
1
L
1
L
o
L
m
m
L
2
s
L
L
1
2
L
L
1
2
L
1
sL
R
sL
1
sC
V
R
H(s)
g
g
R
,
1
V
1
sR C
s
L
L
C
R
sL
sL
sC
⎡
⎤
⎛
⎞
⎡
⎤
+
+
⎢
⎥
⎜
⎟
⎢
⎥
⎝
⎠
⎢
⎥
⎢
⎥
=
= −
= −
⎢
⎥
⎢
⎥
+
+
+
+
+
+
⎢
⎥
⎢
⎥
⎣
⎦
⎢
⎥
⎣
⎦
(E1-1)
where the zero frequency value, say
H(0)
, of the I/O voltage gain is clearly seen to be
–(g
m
R
L
)
.
Moreover, we note that when
L
1
= L
2
= 0
, the transfer relationship in (E1-1) reduces to
1
2
L
L
0
L
L
H(0)
H(s)
,
1
sR C
=
=
=
+
(E1-2)
which clearly projects an uncompensated
3-dB
bandwidth,
B
u
, (i.e. the bandwidth of the circuit
with the inductors replaced by short circuits) of

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