U
niversity of
S
outhern
C
alifornia
USC Viterbi School of Engineering
Ming Hsieh Department of Electrical Engineering
EE 541:
Homework Assignment #03#04
Fall, 2010
Due: 09/28/2010
Choma
Problem #10:
A lossless, lowpass, filter boasting a
3dB
bandwidth of
2 GHz
is to be used
to couple a
50
Ω
load
(R
l
)
to a
50
source
(R
s
)
, as is abstracted in the diagram of Figure (P10).
It has been determined that the desired filter must be a
4
th
order Butterworth (maximally flat
magnitude) structure for which the desired transfer function of the entire system, (with load and
source terminations) is
+
−
Lossless
Lowpass
Filter
V
2
V
1
V
s
R
l
R
s
Z (s)
in
Figure (P10)
v
2
v
23
4
s
A(0
)
V(
s
)
A (s)
,
V(s
)
1a
sb
s a
s s
==
++
+
+
where normalizations with respect to a
50
impedance and the
3dB
bandwidth of
2 GHz
have
been exploited in this mathematically delineated transfer characteristic. Moreover (and as will
be investigated later in class),
a = 2.6131
and
b = 3.4142
.
It should be noted that for this
4
th
or
der Butterworth filter,
2
2
v
vv
v
8
)
A (s)
A (s)A (s)
.
1s
+
(a).
Determine the normalized driving point input impedance,
Z
in
(s)
, that necessarily supports
the indicated voltage transfer function.
(b).
Design the filter.
Submit a network topology that shows the normalized values of all
branch elements, as well as a topology for which denormalization has been executed.
(c).
Simulate the finalized network topology on HSPICE or equivalent circuit analysis soft
ware.
What
3dB
bandwidth and zero frequency voltage gain are projected by the simu
lated frequency response?
Problem #11:
Convert the finalized filter topology developed in Problem #10 to a notch
circuit architecture for which the notched frequency is
800 MHz
and the filter
Q
is
10
.
Simulate
the final design on HSPICE or on equivalent circuit analysis software.
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View Full DocumentEE 541
University of Southern California Viterbi School of Engineering
Choma
Homework #0304
26
Fall Semester, 2010
Problem #12:
With reference to the system diagram of Figure (P10), let the normalized
driving point input impedance,
Z
in
(s)
, be
2
in
23
s
1s
2
Z
(s)
,
7s
s
s
1
363
++
=
+
where the normalizing impedance is
50
Ω
, and the normalizing frequency is
2 GHz
.
Synthesize
the structure in both normalized and denormalized formats, and determine the normalized sys
tem transfer function,
V
2
(s)/V
s
(s)
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 Choma
 Electrical Engineering, Frequency, Input impedance, Butterworth Filter, Southern California Viterbi, California Viterbi School

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