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GATE 2021 EC – Question 45

Electromagnetics · Transmission Lines · 2 marks · Multiple choice

The impedance matching network shown in 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 (S.C.) stub of length $0.25\lambda$ connected across PQ and the other one is an open-circuited (O.C.) stub of length $0.5\lambda$ connected across RS.

The impedance matching is achieved when the real part of $Z_L$ is

Diagram for GATE 2021 EC question 45
  1. $112.5\ \Omega$
  2. $75.0\ \Omega$
  3. $50.0\ \Omega$
  4. $33.3\ \Omega$

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Show answer and explanation

Correct answer: (A) $112.5\ \Omega$

Explanation

A short-circuited stub of length $\lambda/4$ looks like an open circuit at its input, and an open-circuited stub of length $\lambda/2$ also looks like an open circuit. So neither stub affects the match and only the quarter-wave transformer acts: $Z_{in}=\frac{Z_1^2}{R_L}=50\ \Omega$, giving $R_L=\frac{75^2}{50}=112.5\ \Omega$.