ECE 3025: Electromagnetics
Solutions to TEST 1 (Spring 2008)
(1)
Short Answer Section
(a) a) coplanar strip, b) microstrip, c) symmetrical stripline, d) coaxial cable, e) parallel
plate
(b)
Z
L
=
Z
0
/N
, Γ =
1

N
1+
N
(c)
Z
L
=
NZ
0
, Γ =
N

1
N
+1
(d) False
(e) open circuit
(2)
Discharge of a Long Capacitor:
This problem is identical to the homework problem,
only now the long, skinny capacitor is mismatched to the ﬁnger, with a reﬂection coeﬃcient
of Γ
L
= 0
.
9. As such, it will take a lot longer than 2
T
to discharge because a diminishing
voltage waveform will continue to circulate around the line, gradually stepping down the
total load voltage:
0
0
0
0
0
0
200 V
200 V
180 V
190 V
171 V
190 V
180 V
z
z
z
z
z
z
t
= 0
t
T
=
t
T
= 2
t
T
= /2
t
T
= 5 /2
t
T
= 3 /2
D/2
D/2
D/2
D/2
D/2
D/2
D
D
D
D
D
D
100 V

100 V

100 V

90 V

90 V

90 V

81 V

90 V

90 V

90 V

90 V

90 V

100 V
+
100 V
+
100 V
+
90 V
+
90 V
+
100 V
+
90 V
+
100 V
+
100 V
+
90 V
+
100 V
+
90 V
+
190 V
180 V
(a) Each stepdown in voltage occurs during even multiples of a transit time:
1
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0
T
2T
4T
3T
5T
6T
time
V t
L
( )
(b) A charged, lumpsum capacitor has simply an exponential discharge across the resistive
ﬁnger:
0
time
V t
L
( )
(c) The graphs in part (a) will resemble the graph in part (b) if either of the following
conditions are met: the capacitor is relatively short (small
T
) or the line is much more
capacitive than inductive (small
Z
0
). Either of these conditions will cause the steps in
part (a) to appear small and/or drawn out in time, so that it will simply look like a
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 Spring '08
 CITRIN
 Electromagnet, iL, LC circuit, Transmission line

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