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A lossless transmission line with characteristic impedance Zo = 50 Ω is terminated with an unknown load. The magnitude of the reflection co-efficient is |T| = 0.6. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in Ω) is____.
A lossless transmission line with characteristic impedance Zo = 50 Ω is terminated with an unknown load. The magnitude of the reflection co-efficient is |T| = 0.6. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in Ω) is____.
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To compute the maximum input impedance for a transmission line, apply the formula \(Z_{{max}} = Z_0 \frac{1 + |\Gamma|}{1 - |\Gamma|}\). This formula is particularly useful in characterizing transmission line mismatches.
Updated On: Feb 12, 2026
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Correct Answer: 200
Solution and Explanation
To find the maximum value of the input impedance magnitude looking towards the load for a lossless transmission line, we use the relationship involving the normalized impedance and the reflection coefficient. The reflection coefficient |T|=0.6 means part of the wave is reflected. For a lossless line, the maximum normalized impedance, Zmax, occurs at a voltage maximum and can be given by:
Zmax = Zo (1+|T|)/(1-|T|)
Given that Zo = 50 Ω and |T| = 0.6:
Zmax = 50 Ω (1+0.6)/(1-0.6) = 50 Ω × 1.6/0.4 = 50 Ω × 4 = 200 Ω
This calculated value of 200 Ω fits perfectly within the given range of 200 to 200 Ω, confirming the accuracy of the solution.
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