Standing waves on transmission lines: Is the voltage standing-wave ratio (VSWR) defined as VSWR = E_max / E_min (or equivalently V_max / V_min)?

Introduction:
Voltage Standing-Wave Ratio (VSWR) is a fundamental measure of mismatch on a transmission line. It is obtained from the standing-wave envelope formed by the superposition of forward and reflected waves. This question checks the standard definition of VSWR in terms of maxima and minima of the electric (voltage) field magnitude along the line.

Given Data / Assumptions:

• E_max or V_max is the envelope maximum at antinodes.
• E_min or V_min is the envelope minimum at nodes.
• Sinusoidal steady-state on a uniform line.

Concept / Approach:

The definition is VSWR = E_max / E_min = V_max / V_min. It relates directly to the magnitude of the reflection coefficient |Γ| via VSWR = (1 + |Γ|) / (1 − |Γ|). For a perfect match, |Γ| = 0 and VSWR = 1. As mismatch grows and E_min approaches zero, VSWR grows without bound.

Step-by-Step Solution:

Verification / Alternative check:

Smith chart relationships and network analyzer measurements confirm that the ratio of maxima to minima equals the VSWR derived from |Γ|, independent of the physical length (loss increases only smear extrema).

Why Other Options Are Wrong:

• False or conditional claims restrict a general definition; VSWR uses voltage (or field) maxima/minima and is not limited to lossless or quarter-wave lines.

Common Pitfalls:

Confusing VSWR with return loss (in dB) or mismatch loss. VSWR is dimensionless and always ≥ 1, with 1 indicating perfect match.

Final Answer:

True