Reflection coefficient Γ on a transmission line: match Γ values to load conditions and the general formula. List I (Statement) A. Γ = 0 B. Γ = −1 C. Γ = +1 D. −1 < Γ < +1 List II (Condition / Formula) Γ = (ZL − Z0) / (ZL + Z0) ZL = Z0 (matched load) ZL = 0 (short-circuit load) ZL = ∞ (open-circuit load)

Introduction / Context:The reflection coefficient Γ quantifies how much of a traveling wave reflects from a load on a transmission line. Knowing how Γ maps to typical loads is essential for impedance matching, VSWR computation, and power delivery.

Given Data / Assumptions:

• Z0 is real and positive (lossless or low-loss line assumption for intuition).
• ZL is the load impedance, possibly complex.
• Γ is defined at the load: Γ = (ZL − Z0) / (ZL + Z0).

Concept / Approach:

Special cases: a perfect match (ZL = Z0) gives Γ = 0; a short (ZL = 0) gives Γ = −1; an open (ZL → ∞) gives Γ = +1. For all other finite, non-matched loads, |Γ| is strictly less than 1, with angle determined by the complex ratio.

Step-by-Step Solution:

Verification / Alternative check:

Substitute ZL = Z0 into Γ formula to get 0; let ZL → 0 and ZL → ∞ to get −1 and +1 respectively. For any other finite ZL not equal to Z0, |Γ| < 1, consistent with energy conservation on passive terminations.

Why Other Options Are Wrong:

• Swapping open and short signs for Γ mixes boundary conditions: voltage reflection is in-phase for an open and out-of-phase for a short.
• Equating Γ = 0 with the general formula is incomplete—only ZL = Z0 yields zero.

Common Pitfalls:

Forgetting that Γ is complex. Students sometimes compare only magnitudes and miss the phase that determines standing-wave positions along the line.

Final Answer:

A-2, B-3, C-4, D-1