Formula
The reflection coefficient magnitude and the SWR are two names for one match. Return loss is −20 log10 of that magnitude. Mismatch loss is −10 log10 of one minus the magnitude squared. Reflected power is forward power times the magnitude squared. For a real load, the magnitude is the absolute value of (ZL − Z0) / (ZL + Z0).
|Γ| = (SWR − 1) / (SWR + 1)
RL = −20 log10|Γ|
mismatch = −10 log10(1 − |Γ|²)
A perfect match has an infinite return loss. The page shows a dash for that cell rather than a fake number. Mismatch loss is not the coax loss. The dipole length is a planning cut, not this measurement.
Worked examples
SWR 1.5, 100 W forward. |Γ| = 0.2. Return loss 13.979 dB. Mismatch loss 0.177 dB. Reflected power 4 W.
75 Ω on 50 Ω. The same 0.2.
4 W reflected from 100 W. |Γ| = 0.2, and the SWR is 1.5 again.
Reference
SWR 1 is a match. SWR 2 is |Γ| = 1/3, return loss 9.54 dB, and 11.1% of the forward power reflected.
Questions
What reflection coefficient is an SWR of 1.5?
0.200. Return loss is 13.979 dB. Mismatch loss is 0.177 dB. Of 100 W forward, 4 W is reflected.
Is 75 Ω on a 50 Ω line the same thing?
For a real load, yes. (75 − 50) / (75 + 50) = 0.2. A complex load needs the magnitude of that same ratio. This page takes a real load.
What is mismatch loss?
The fraction of forward power that is not delivered, −10 log10(1 − |Γ|²). It is not the cable loss.
Sources
- SWR = (1 + |Γ|) / (1 − |Γ|). Return loss −20 log10|Γ|. Mismatch loss −10 log10(1 − |Γ|²).
- Real-load reflection coefficient (ZL − Z0) / (ZL + Z0).