If a finite (short) transmission line is terminated in its characteristic impedance Z0, it behaves as if it were infinitely long (no reflections are observed). Choose the correct truth value.
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ATrue
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BFalse
Answer
Correct Answer: True
Explanation
Introduction:A key matching condition in transmission-line theory is Z_L = Z0. When this condition holds, reflections vanish and the line appears to the source as if it continued indefinitely. This item tests understanding of that principle.
Given Data / Assumptions:
- Uniform line with characteristic impedance Z0
- Load Z_L = Z0 (perfect match)
- Finite physical length
Concept / Approach:The load reflection coefficient Γ_L = (Z_L − Z0) / (Z_L + Z0). For Z_L = Z0, Γ_L = 0, so no reflected wave exists. Without reflections, standing waves do not form and the input impedance equals Z0 regardless of line length, mimicking an infinite line extension.
Step-by-Step Reasoning:
1) Set Z_L = Z0 → Γ_L = 0.2) With no reflected wave, voltage/current are purely traveling waves.3) The input impedance Z_in = Z0 for any length.4) The source cannot distinguish between a matched finite section and an infinitely long matched line.Verification / Alternative check:On the Smith chart, the match point is the chart center; rotation (changing length) keeps you at center (Z0).
Why Other Options Are Wrong:
- False: Contradicts the definition of perfect matching (Γ = 0).
Common Pitfalls:Assuming physical length must be infinite; confusing loss-induced damping with reflection-free matching.
Final Answer:True