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.

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:

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