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testsol1f

# testsol1f - ECE 3025 Electromagnetics Solutions to TEST...

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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 step-down in voltage occurs during even multiples of a transit time: 1

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2 0 T 2T 4T 3T 5T 6T time V t L ( ) (b) A charged, lump-sum 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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testsol1f - ECE 3025 Electromagnetics Solutions to TEST...

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