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______ .
(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}
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