Name: __SOLUTIONS__
EE 222 Signals & Transforms
Exam #3
Fall 2000
1) (40 points) You are given a system that relates the input and output voltages of following circuit
y(t)=Vout(t)x(t)=Vin(t) R=1/5
Ω
L=1/20 H
C=1/5F
+
-
+
-
(a) (10 points) What is the transfer function )(
)(
)(
1sV
sV
sH
in
out
= as a ratio of polynomials?
1
1
1)(
1
)(
1
)(
1
)( 2
1
1
1
1++
=
++
=
+
+
+
=
sLCs
CsLs
Cs
Ls
Cs
sH
R
L
R
R
R
(b) (10 points) Draw the Bode Plot for this system Use the attached semilog paper and label the
plot fully.
)1)(1(
1
125.001.0
1
1
1
)(
520
22
1++
=
++
=
++
=ss
R
LsssLCs
sH
Frequency (rad/sec)
Phase (deg); Magnitude (dB)
Bode Diagram H1(j
ω
)
-50
-40
-30
-20
-10
0
100101102
(c) (5 points) Draw a pole/zero diagram for this system. Label the diagram fully.
Im
Re
x
-5
x
-20
(d) (5 points) Is this a low pass filter, a high pass filter or a band pass filter? State why you chose
your answer.
Low Pass Filter. It has a maximum value of 0dB which occurs for ω<5.
(e) (10 points) A continuous-time LTI system with frequency response H(jω) is constructed by
cascading another continuous-time LTI systems with frequency response H2(jω), after H1(jω).
