EE 541
USC Viterbi School of Engineering
J. Choma
Homework #03
30
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 #03
Fall, 2011
Due: 09/20/2011
Choma
Problem #12:
In the filter of Figure (P12), the inductance,
L
, is chosen in accordance with the
constraint,
2
o
L
RC,
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
.
(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
3dB
bandwidth of
B
?
(c).
Determine the transducer power gain,
G
T
, as a function of signal frequency
.
(d).
The socalled “insertion loss,”
IL
, of a filter is expressed in decibels and has been defined
(albeit controversially) as
T
10
2
11
G
IL (dB)
10
.
1S
log
(i).
What is the engineering significance of an insertion loss of
0 dB
?
(ii).
What is the engineering significance of an insertion loss that equals the decibel value
of the transducer power gain?
Problem #13:
If a second order, passive notch filter, such as the abstraction in Figure (P13),
displays a symmetrical frequency response (identical very low and very high frequency gains),
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USC Viterbi School of Engineering
J. Choma
Homework #03
31
Fall Semester, 2011
its transfer function is the form,
2
o
n
o
2
s
nn
s
H1
ω
V
H(s)
.
V
ss
1
Q
ωω
In this transfer relationship,
H
o
, is the gain at both very low and very high frequencies.
In a pas
sive filter, the magnitude of
H
o
is less than unity.
Moreover,
Q
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 '06
 Choma
 Electrical Engineering, Frequency, Input impedance, Circuit diagram, Lowpass filter, Electrical impedance

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