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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

  1. $112.5\:\Omega$
  2. $75.0\:\Omega$
  3. $50.0\:\Omega$
  4. $33.3\:\Omega$
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