GATE EC 2024 Set 1 — Question 58
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Electromagnetics → Transmission Lines → Input Impedance & Reflection
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Question
A lossless transmission line with characteristic impedance is terminated with an unknown load. The magnitude of the reflection co-efficient is . As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in ) is __________.
Correct answer
200 to 200
Solution
The standing wave ratio (SWR), denoted by , is related to the magnitude of the reflection coefficient by the formula:Given , we can calculate the SWR:For a lossless transmission line, the input impedance varies along the line. The maximum value of the input impedance, , is purely resistive and occurs at the voltage maxima. It is related to the characteristic impedance and the SWR by:Given the characteristic impedance , the maximum input impedance is:Thus, the maximum value of the input impedance magnitude is 200 .
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