VSWR Pattern with Resistive Load after Short-Termination Check A 75 Ω line is first short-circuited and minima locations are noted. The short is then replaced by an unknown purely resistive load, and the minima locations do not change. If the measured VSWR is 3, what is the value of the resistive load?

Introduction / Context:
Standing-wave patterns on transmission lines depend on the magnitude and phase of the reflection coefficient Γ. Comparing patterns for different terminations helps diagnose the load impedance.

Given Data / Assumptions:

• Characteristic impedance Z0 = 75 Ω.
• Initial termination is a short (Γ = −1, phase = π), minima at the load.
• Second termination is a purely resistive load with VSWR = 3 and identical minima locations.

Concept / Approach:

For a real load R, Γ = (R − Z0) / (R + Z0) is real (phase 0 for R > Z0, phase π for R < Z0). The position of minima near the load is set by the phase of Γ. If minima locations are unchanged from the short, Γ must retain phase π, implying R < Z0. The VSWR relation gives |Γ| = (S − 1) / (S + 1).

Step-by-Step Solution:

Verification / Alternative check:

Substitute R = 25 Ω: Γ = (25 − 75) / (25 + 75) = −50 / 100 = −0.5, S = (1 + 0.5) / (1 − 0.5) = 3, consistent with observations.

Why Other Options Are Wrong:

50 Ω gives Γ = −0.2 → S = 1.5; 225 Ω and 250 Ω yield positive Γ (phase 0), shifting minima; 75 Ω gives Γ = 0, no standing waves.

Common Pitfalls:

Ignoring the phase of Γ when comparing patterns; forgetting the VSWR–Γ magnitude relation.

Final Answer:

25 Ω