For a lossy transmission line terminated with a resistive load R_L < Z0, the sign of the load reflection coefficient Γ_L = (R_L − Z0) / (R_L + Z0) is:

Difficulty: Easy

Correct Answer: Negative

Explanation:


Introduction:
The reflection coefficient at a transmission-line load indicates both magnitude and phase (or sign for purely resistive cases) of reflections due to mismatch. Recognizing the sign helps quickly infer whether the load is above or below Z0.


Given Data / Assumptions:

  • Load is purely resistive: R_L
  • Characteristic impedance: Z0 (real)
  • R_L < Z0


Concept / Approach:
The load reflection coefficient is Γ_L = (Z_L − Z0) / (Z_L + Z0). For a real Z_L = R_L, the sign is determined by the numerator's sign because the denominator is positive when R_L, Z0 > 0.


Step-by-Step Solution:

1) With R_L < Z0, the numerator (R_L − Z0) is negative.2) The denominator (R_L + Z0) is positive.3) Therefore Γ_L is negative.


Verification / Alternative check:
On the Smith chart, points left of the center (R < 1 normalized) map to negative real reflection coefficients at the load plane.


Why Other Options Are Wrong:

  • A: Zero occurs only for a perfect match (R_L = Z0).
  • B: Γ magnitude is ≤ 1 for passive terminations; infinity is impossible.
  • D: Positive corresponds to R_L > Z0, not R_L < Z0.


Common Pitfalls:
Confusing the sign at the load with the sign after rotation along the line; mixing magnitude with sign.


Final Answer:
Negative

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