A 50/60 Hz transmission line has Z0 = 300 ∠0° Ω and is terminated in ZL = 150 ∠0° Ω. What is the reflection coefficient at the load?

Introduction / Context:
The reflection coefficient Γ quantifies the mismatch between a transmission line's characteristic impedance and its load. It determines standing wave patterns, return loss, and power transfer efficiency, making it a core parameter in RF and power transmission.

Given Data / Assumptions:

• Z0 = 300 Ω (real).
• ZL = 150 Ω (real).
• Steady-state sinusoidal regime; standard transmission-line theory applies.

Concept / Approach:

The load reflection coefficient is Γ = (ZL − Z0) / (ZL + Z0). For purely real impedances, the sign of Γ indicates whether the load is lower or higher than Z0 (negative for a lower load impedance than Z0).

Step-by-Step Solution:

Verification / Alternative check:

Magnitude check: |Γ| = 0.3333 < 1, as required for passive terminations. SWR would be (1 + |Γ|) / (1 − |Γ|) = 1.5, a plausible modest mismatch.

Why Other Options Are Wrong:

• 0.5 or −0.5: Would require ZL of 100 Ω or 900 Ω, not 150 Ω.
• 0.3333: Wrong sign; implies ZL > Z0 which is not the case.
• 0: Only for perfect match ZL = Z0.

Common Pitfalls:

Forgetting the sign when ZL < Z0; using magnitude only; mixing up series vs. parallel combinations before evaluating Γ directly at the load.

Final Answer:

-0.3333