EE 350
PROBLEM SET 10
DUE: 10 December 2007
Reading assignment: Lathi Chapter 6, Sections 6.4 and 6.5
Laboratory sections meet the week of December 3.
Problem 50:
(20 points)
Consider the circuit shown in Figure 1.



1
6
F
+
f(t)
+
x(t)
+
y(t)
1
F
2
10Ω
15Ω
Figure 1: Secondorder RC network.
1. (2 points) In order to calculate the transfer function of the circuit, assume that all initial conditions are zero and sketch
the circuit in the frequency domain.
2. (6 points) Write the node equations (in the frequency domain) associated with the node voltages
X
(
s
) and
Y
(
s
).
3. (3 points) Using your results in part 2, ±nd the transfer function
H
(
s
) relating the output
y
(
t
) to the input
f
(
t
).
4. (6 points) Find the zerostate response
y
(
t
) if the input voltage
f
(
t
)=
e

t
u
(
t
).
5. (3 points) From the transfer function, write the diﬀerential equation relating
y
(
t
)to
f
(
t
).
Problem 51:
(20 points)
Consider the circuit shown in Figure P6.45 on page 465 of the text.
1. (7 points) Obtain an ordinary diﬀerential equation that governs the behavior of
y
1
(
t
) for
t
≥
0.
2. (3 points) Take the Laplace transform of the ordinary diﬀerential equation obtained in part 1, and ±nd an expression
for
Y
1
(
s
).
3. (4 points) Determine the value of the terms
y
1
(0

) and ˙
y
1
(0

) that appear in the expression obtained in part 2.
Note
that it is not necessary to determine the value of either
y
1
(0
+
)or ˙
y
1
(0
+
), as was the case when solving a diﬀerential
equation using the classical solution method described in section 2.5 of the text.
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 Fall '07
 SCHIANO,JEFFREYLDAS,ARNAB
 Laplace

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