GATE EC 2021 Set 1 Q35 — Transmission Lines

The impedance matching network shown n the figure is to match a lossless line having characteristic impedance $Z_{0}= 50 \:\Omega$ with a load impedance $Z_{L}$. A quarter-wave line having a characteristic impedance  $Z_1=75\:\Omega$ is connected to $Z_{L}$. Two stubs having characteristic impedance of $75\:\Omega$ each are connected to this quarter-wave line. One is a short-circuited ($\text{S.C}$) stub of length $0.25\lambda$ connected across $\text{PQ}$ and the other one is an open-circuited ($\text{O.C}$) stub of length $0.5\lambda$ connected across $RS$.

The impedance matching in achieved when the real part of $Z_{L}$ is