Difficulty: Easy
Correct Answer: infinity
Explanation:
Introduction / Context:This question tests standing-wave behavior on a lossless transmission line when the load is purely reactive. Understanding how the reflection coefficient magnitude relates to VSWR is core to RF and microwave engineering.
Given Data / Assumptions:
Concept / Approach:The reflection coefficient at the load is Γ = (ZL − Z0) / (ZL + Z0). For a purely reactive load, |Γ| = 1 because the load cannot absorb average power; it only stores and returns energy. VSWR = (1 + |Γ|) / (1 − |Γ|).
Step-by-Step Solution:
Let ZL = −j·Z0.Γ = (−j·Z0 − Z0) / (−j·Z0 + Z0) = (−1 − j) / (1 − j).|−1 − j| = √(1 + 1) = √2 and |1 − j| = √2 ⇒ |Γ| = 1.VSWR = (1 + 1) / (1 − 1) = 2 / 0 → infinity.Verification / Alternative check:If a load is purely reactive, average real power at the load is zero; thus, all incident power is reflected (|Γ| = 1), which forces VSWR to be unbounded (infinite).
Why Other Options Are Wrong:
2 or 10 or 5: These correspond to |Γ| strictly less than 1; not possible with a pure reactance on a lossless line.1: VSWR = 1 only for a perfect match (ZL = Z0), not for a reactive load.Common Pitfalls:
Confusing the sign or value of the reactance with resistive matching; any purely reactive termination on a lossless line yields |Γ| = 1.Final Answer:
infinity
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