EE 541
University of Southern California Viterbi School of Engineering
Choma
Solutions, Homework #03
35
Fall Semester, 2011
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:
Solutions, Homework #03
Fall, 2011
Due: 09/20/2011
Choma
Solutions
−
Problem #12:
In the filter of Figure (P12), the inductance,
L
, is chosen in accordance with the constraint,
2
o
L
R C ,
L
C
R
o
R
o
R
o
V
s
V
o
Z
in
Figure (P12)
where
R
o
is the resistance terminating the output port of the filter, as well as representing the
Thévenin resistance of the signal source applied to the filter input port.
In addition, note that a
resistance of value
R
o
shunts inductance
L
in the filter.
(a).
Determine the input port scattering parameter,
S
11
, referred to a characteristic impedance of
R
o
.
The input impedance,
Z
in
, of the filter is
3
o
a
o
o
o
in
2
o
a
o
o
o
o
2
o
o
o
o
R
sL
R
sR C
R
Z
R
sL
1
sR C
1
sR C
R
sR C
R
sR C
R
.
1
sR C
(P12-1)
Thus, because the filter is terminated in the reference resistance,
R
o
, scattering parameter
S
11
is null;
that is,
in
o
11
in
o
Z
R
S
0 .
Z
R
(P12-2)
(b).
How must inductance
L
or capacitance
C
be chosen to ensure that the voltage transfer
function,
V
o
/V
s
, of the filter establishes a radial
3-dB
bandwidth of
B
?
An inspection of the schematic diagram of the filter reveals that its voltage transfer function is

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