GATE EC 1989 Electromagnetics Solution Q 3

GATE EC 1989 Electromagnetics Solution Q 3

A 50 ohm lossless transmission line has a pure reactance of (j 100) ohms as its load. The VSWR in the line is

(a) 1/2(Half)

(b) 2(Two)

(c) 4(Four)

(d) \infty (Infinity)

Ans :- d)

Explanation

\Gamma=\frac{Z_L-Z_0}{Z_L+Z_0}

= \frac{j100-50}{j100+50}

\left|\Gamma\right|=\frac{\sqrt{\left(100\right)^2+\left(50\right)^2}}{\sqrt{\left(100\right)^2+\left(50\right)^2}}=1 VSWR=\frac{1+\left|\Gamma\right|}{1-\left|\Gamma\right|}=\frac{1+1}{1-1}=\frac20=\infty

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