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Material Type: Exam; Professor: Smith; Class: Signals and Systems; Subject: Electrical & Computer Engineer; University: Boise State University; Term: Spring 2000;
Typology: Exams
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x(t)=V (^) in (t) R=1/5Ω y(t)=V (^) out (t)
L=1/20 H
C=1/5F
(a) (10 points) What is the transfer function
in
1
1 1
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.
20 5
R
Frequency (rad/sec)
Phase (deg); Magnitude (dB)
Bode Diagram H 1 (jω)
0
100 101 102
(c) (5 points) Draw a pole/zero diagram for this system. Label the diagram fully. Im
x Re
x
(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 H 1 (jω).
x(t)=V (^) in (t) R=1/5Ω y2(t)=Vout 2(t)
L=1/20 H
C=1/5F
H 2 (s)
H 1 (s)
Frequency (rad/sec)
Phase (deg); Magnitude (dB)
Bode Diagram H(jω)
0
100 101 102
Specify the equation and Bode diagram for H (^) 2(s).
Frequency (rad/sec)
Phase (deg); Magnitude (dB)
Bode Diagram H 2 (jω)
0
100 101 102
20
5 2
s
s
50
10 sin( 100 ) ( ) 2 cos( 50 ) +
t
t xt t
X j = − + + + <
X(jω)
ω -100 -50 50 100
2π 2π
100π (^10) π
used to sample x(t) so that full reconstruction is possible? Explain how you arrived at your answer.
Frequency ω (rad/sec)
Magnitude (dB)
Bode Diagram H(jω)
0
20
40
10 0 10 1 10 2 10 3 10 4