GATE EC 2008 Electromagnetics Solution Q 3

GATE EC 2008 Electromagnetics Solution Q 3

One end of a loss-less transmission line having the characteristic impedance of 75Ω and length of 1 cm is short-circuited. At 3 GHz, the input impedance at the other end of the transmission line is_____.

(a) 0

(b) Resistive

(c) Capacitive

(d) Inductive

Ans :- (d)

Explanation

The short circuited line has input impedance given by

Z_{sc}=jZ_0\tan\beta l

It may be capacitive or inductive depending on the length of line.

Given length of line l = 1 cm.

\lambda=\frac{3\times10^8}{3\times10^9}=0.3=30\;cm l<\frac\lambda4

So it is inductive in nature.

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