GATE EC 2021 Set 1 — Question 45
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Electromagnetics → Transmission Lines → Impedance Matching (Stub, λ/4)
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Question
The impedance matching network shown in the figure is to match a lossless line having characteristic impedance with a load impedance . A quarter-wave line having a characteristic impedance is connected to . Two stubs having characteristic impedance of each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length connected across PQ and the other one is an open-circuited (O.C.) stub of length connected across RS.
The impedance matching is achieved when the real part of is
Correct answer
(A) 112.5 Ω
Solution
1.Analyze the stubs:
- Short-circuited (S.C.) stub at PQ with length : . This acts as an open circuit.
- Open-circuited (O.C.) stub at RS with length : . This also acts as an open circuit.
3.Apply quarter-wave transformer formula: For matching, .
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