VSWR (Voltage Standing Wave Ratio) is a measure of how efficiently radio-frequency power is transmitted from a power source, through a transmission line, into a load (for example, from a power amplifier through a transmission line, to an antenna).
In an ideal system, 100% of the energy is transmitted. This requires an exact match between the source impedance, the characteristic impedance of the transmission line and all its connectors, and the load's impedance. The signal's AC voltage will be the same from end to end since it runs through without interference.
In real systems, mismatched impedances cause some of the power to be reflected back toward the source (like an echo). Reflections cause destructive interference, leading to peaks and valleys in the voltage at various times and distances along the line.
VSWR measures these voltage variances. It is the ratio of the highest voltage anywhere along the transmission line to the lowest. Since the voltage doesn't vary in an ideal system, its VSWR is 1.0 (or, as commonly expressed, 1:1). When reflections occur, the voltages vary and VSWR is higher -- 1.2 (or 1.2:1), for instance.
VSWR is the voltage ratio of the signal on the transmission line:
VSWR = |V(max)| / |V(min)|
where V(max) is the maximum voltage of the signal along the line, and V(min) is the minimum voltage along the line.
It can also be derived from the impedances:
VSWR = (1+Γ)/(1-Γ)
where Γ (gamma) is the voltage reflection coefficient near the load, derived from the load impedance (ZL) and the source impedance (Zo):
Γ = (ZL-Zo)/(ZL+Zo)
If the load and transmission line are matched, Γ = 0, and VSWR = 1.0 (or 1:1).