VSWR vs. return loss vs. reflection coefficient: converting and interpreting

These three numbers describe the same thing: how much of the incident wave is reflected at a port.

Definitions
- Reflection coefficient: Gamma = (ZL - Z0) / (ZL + Z0). Complex; magnitude |Gamma| from 0 (perfect match) to 1 (total reflection).
- Return loss: RL = -20*log10(|Gamma|), in dB. A larger positive value means a better match. (S11 in dB is the same magnitude with a negative sign; many plots show S11 = -RL.)
- VSWR = (1 + |Gamma|) / (1 - |Gamma|). Ranges from 1 to infinity.

Handy reference points (computed from the formulas)
- |Gamma| = 0.333, RL = 9.5 dB, VSWR = 2.0
- |Gamma| = 0.2, RL = 14 dB, VSWR = 1.5
- |Gamma| = 0.1, RL = 20 dB, VSWR = 1.22
- |Gamma| = 0.0316, RL = 30 dB, VSWR = 1.07

Reflected power fraction is |Gamma|^2. Mismatch loss (power not delivered because of reflection) is -10*log10(1 - |Gamma|^2). At VSWR 2:1, about 11 percent of the power is reflected and mismatch loss is roughly 0.5 dB. That is why "VSWR below 2" is a common antenna specification: the delivered-power penalty is small.

Interpretation pitfalls
1. Good return loss does not mean a good antenna. A 50 ohm resistor has perfect return loss and zero radiation. Efficiency and pattern must be measured separately.
2. Cable loss flatters the reading. Measuring through a lossy cable makes the reflection pass through the loss twice, so RL at the instrument looks better than at the antenna. Calibrate at the antenna reference plane, or de-embed the cable.
3. Environment matters. Small antennas detune near hands, enclosures and ground planes. Measure in the final mechanical configuration.
4. Bandwidth definitions vary. Always state the threshold used (for example RL > 10 dB).

Worth repeating the cable point: with a cable of loss L dB between the VNA and the antenna, the measured return loss improves by about 2L dB. A 3 dB cable can make a poor antenna look acceptable.