U
niversity of
S
outhern
C
alifornia
USC Viterbi School of Engineering
Ming Hsieh Department of Electrical Engineering
EE 541:
Solutions, Homework #05
Fall, 2010
Due: 10/07/2010
Choma
Solutions
−
Problem #20:
A linear feedback amplifier, whose equivalent circuit is the topology
embedded within the dashed box in Figure (P20), is terminated at its output port in a resistance,
R
L
, and is driven by a signal source whose Thévenin equivalent resistance is
R
S
.
When meas-
ured with respect to a characteristic impedance of
R
o
, the reflection coefficients of the load re-
sistance,
R
L
, the source resistance,
R
S
, and the feedback resistance,
R
F
, are
ρ
L
= 9/11
,
0
, and
ρ
F
=
19/21
, respectively.
If
g
m
R
L
=
10
, find the input port reflection coefficient and all scattering pa-
rameters, where it is understood that the scattering parameters are measured with respect to the
reference resistance,
R
o
.
+
−
R
F
R
S
g V
m1
R
L
V
1
I
1
V
2
V
S
Figure (P20)
The diagrams in Figure (P20.1) display the configurations pertinent to the evaluation of the driving
point input resistant,
R
in
(R
L
)
, and the driving point output resistance,
R
out
(R
S
)
.
A straightforward
analysis of each of these circuits reveals that
gV
R
L
R
F
V
2
I
1
V
1
(a).
R
S
R
F
V
1
(b).
I
x
V
x
Figure (P20.1)
()
1F
L
in
L
1m
VR
R
L
R
R
I1
g
R
+
==
+
,
(P20-1)
and
x
FS
out
S
x
mS
R
R
R.
(P20-2)
g
R
+
+
With
ρ
L
=9/11
,
S
= 0
, and
F
= 19/21
,