GATE EC 2007 Electromagnetics Solution Q 8

GATE EC 2007 Electromagnetics Solution Q 8

The parallel branches of a 2-wire transmission line are terminated in 100Ω and 200Ω resistors as shown in the figure. The characteristic impedance of the line is Z0 = 50Ω and each section has a length of λ/4. The voltage reflection coefficient Γ at the input is______ .

GATE EC 2007 Electromagnetics Solution img5 - Grad Plus

(a) -j\frac75

(b) \frac{-5}7

(c) j\frac57

(d) \frac57

Ans :- (d)

Explanation

We know that the input impedance offered by λ/4 line is given by,

Z_{in}=\frac{Z_0^2}{Z_L}
GATE EC 2007 Electromagnetics Solution img6 - Grad Plus
R_1due\;to\;100\Omega=\frac{50^2}{100}=25 R_2due\;to\;200\Omega=\frac{50^2}{200}=\frac{25}2

Therefore final load offered is

R_1\parallel R_2=25\parallel\frac{25}2=\frac{25}3 \therefore Z_s=\frac{\left(50\right)^2}{25/3}=300\Omega \therefore \Gamma=\frac{Z_s-Z_0}{Z_s+Z_0}=\frac{300-50}{300+50}=\frac57

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