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EE 541
USC Viterbi School of Engineering
J. Choma
Homework #07
99
Fall Semester, 2011
U
niversity of
S
outhern
C
alifornia
USC Viterbi School of Engineering
Ming Hsieh Department of Electrical Engineering
EE 541:
Homework Assignment #07
Fall, 2011
Due: 11/01/2011
Choma
Problem #37:
When terminated at its output port in a resistance,
R
, the passive network ab-
stracted in Figure (P37a) is to produce the voltage transfer function,
2
o
2
s
ss
1
V
1
aQ
a
H(s)
,
V2
a1s
s
11
a
a
1
aQ
a
where parameters
“a”
and
“Q”
are positive constants and the transfer function is written in
terms of a normalized impedance of
1 ohm
and a normalized frequency of
1 radian per second
.
In general, a normalized
one-ohm
impedance corresponds to an actual
R-ohm
impedance, while
1 radian per second
reflects an actual frequency of
o
radians -per-second
.
V
o
V
s
V
s
Passive
RLC
Network
R
R
R
Z(s
)
a
Z(s)
b
RR
R
V
o
(a).
(b).
Figure (P37)
(a).
If the network is realized as the constant resistance tee structure offered in Figure (P37b),
give normalized mathematical expressions for the requisite impedances,
Z
a
(s)
and
Z
b
(s)
.
(b).
Determine the relationship between parameters
“Q”
and
“a,”
such that
Z
a
(s)
is realizable
as an interconnection of a minimal number of branch elements.

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