A transmission line terminates in two branches, each of length λ/4 as shown. The branches are terminated by 50Ω loads. The lines are lossless and have the characteristic impedances shown.
Determine the impedance Zi as seen by the source.
(a) 200
(b) 100 \Omega
(c) 50 \Omega
(d) 25 \Omega
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} Z_1=\frac{Z_0^2}{Z_{L_1}}=\frac{\left(100\right)^2}{50}=200\Omega Z_2=\frac{Z_0^2}{Z_2}=\frac{\left(100\right)^2}{50}=200\Omega Z_L=Z_1\parallel Z_2=100\Omega Z_i=\frac{Z_0^2}{Z_L}=\frac{\left(50\right)^2}{100}=25\Omega