ECE 453: Homework Assignment 1 Solution
116 Solution
The bandwidth of a raisedcosine pulse is
W
=
1
2
T
(1 +
β
)
. With
T
= 1
μs
and
β
= 0
.
5
,
W
= 750
kHz
.
The
bandwidth occupied by a DSBSC signal is 2W, hence the bandwidth occupied by the transmitted signal is
1.5 MHz.
32 Solution
The 8 possible topologies for a 2terminal RLC circuit are shown below
(a)
R
L
C
(b)
L
C
R
(c)
L
R
C
(d)
C
R
L
(e)
C
L
R
(f)
C
L
R
(g)
C
R
L
(h)
L
R
C
Figure 1: Eight possible twoterminal RLC circuits.
Only (c), (e), (f), (g) have impedance with finite real part at 0 Hz. Of these, (e) and (f) can be ruled out,
because each of these has impedance with finite real part in the limit
ω
→ ∞
,
whereas the data show that
the real part goes to zero in the limit. Case (g) can be ruled out because that topology will have impedance
that will behave like
j
ω
L
in the limit
ω
→ ∞
whereas the data show an impedance that is capacitive at high
frequencies. Hence, the circuit must have topology (c). The impedance for (c) is:
Z
=
1
j
ω
C

(
R
+
j
ω
L
)
or
Z
=
(
R
+
j
ω
L
)
j
ω
C
(
R
+
j
ω
L
+ 1
/
(
j
ω
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 Spring '08
 Staff
 Impedance, 2W, Inductor, LC circuit

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