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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Correct Answer: 200
Solution and Explanation
The formula for the maximum input impedance is: \[ Z_{{max}} = Z_0 \frac{1 + |\Gamma|}{1 - |\Gamma|}, \] where \(Z_0\) is the characteristic impedance and \(|\Gamma|\) is the magnitude of the reflection coefficient. Substituting the given values, \(Z_0 = 50 \, \Omega\) and \(|\Gamma| = 0.6\): \[ Z_{{max}} = 50 \cdot \frac{1 + 0.6}{1 - 0.6}. \] Simplify: \[ Z_{{max}} = 50 \cdot \frac{1.6}{0.4} = 50 \cdot 4 = 200 \, \Omega. \] Final Answer: \[ \boxed{200 \, \Omega} \]
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