VSWR and reflection coefficient – Correct relationship Let r_v denote the magnitude of the voltage reflection coefficient at a reference plane and VSWR be the voltage standing-wave ratio on the line. Identify the correct formula relating VSWR and |r_v|.

Introduction:Standing-wave behavior on a transmission line is quantified by the VSWR, which is determined by the load mismatch. The mismatch itself is captured by the voltage reflection coefficient Γ (here written r_v). Knowing the exact relationship is essential for converting between return loss, VSWR, and Γ in measurements and design.

Given Data / Assumptions:

• Single-frequency sinusoidal steady state.
• Lossless or low-loss line so that VSWR definition is meaningful.
• |r_v| between 0 and 1 for passive terminations.

Concept / Approach:

Define VSWR as the ratio of maximum to minimum line voltage magnitudes. With forward wave V₊ and reflected wave V₋, the maxima/minima occur when the two are in phase/out of phase. The resulting ratio reduces to VSWR = (|V_+| + |V_-|) / (|V_+| − |V_-|) = (1 + |Γ|) / (1 − |Γ|) when normalized by |V_+| and using |Γ| = |V_-|/|V_+|.

Step-by-Step Solution:

Verification / Alternative check:

Invert to obtain an equally useful form: |Γ| = (VSWR − 1) / (VSWR + 1), which is widely used to convert between specs.

Why Other Options Are Wrong:

Option B inverts the ratio; option C is the algebraically inverted but dimensionally incorrect form; options D and E are not standard and can violate bounds for passive networks.

Common Pitfalls:

Plugging signed Γ instead of magnitude; attempting to use power reflection coefficient (|Γ|^2) directly with the VSWR formula.

Final Answer:

VSWR = (1 + |r_v|) / (1 − |r_v|).