What is the Voltage Standing Wave Ratio (VSWR) and how is it related to the reflection coefficient Γ?

• A. The ratio of the maximum to minimum voltage on the transmission line, with VSWR = (1+|Γ|)/(1-|Γ|).
• B. The ratio of forward to reflected power on the line.
• C. The magnitude of the reflection coefficient Γ.
• D. The ratio of average to peak power on the line.

Answer: (A)

VSWR measures how much of a signal is reflected on a transmission line due to impedance mismatch. When a forward traveling wave and a reflected wave superimpose along the line, the voltage at a point varies from a maximum to a minimum as the waves interfere. VSWR is defined as the ratio of those extremes: Vmax to Vmin.

The reflection coefficient Γ represents the ratio of the reflected wave to the forward wave, and its magnitude |Γ| tells how strong the reflections are. The combined waves produce Vmax = Vf(1 + |Γ|) and Vmin = Vf(1 − |Γ|), where Vf is the forward-wave amplitude. Plugging these into the ratio gives VSWR = Vmax / Vmin = (1 + |Γ|) / (1 − |Γ|).

So, VSWR is the ratio of the maximum to minimum voltage on the line, linked to the reflection coefficient by that formula. A perfect match has Γ = 0 and VSWR = 1; larger mismatches push |Γ| toward 1 and make VSWR grow dramatically.