Engineering
RF VSWR, Reflection Coefficient (Gamma) & Return Loss (dB) formulas
Calculate RF transmission-line impedance mismatch using Gamma = ABS((Z_L - Z_0) / (Z_L + Z_0)), Voltage Standing Wave Ratio VSWR = (1 + Gamma) / (1 - Gamma), Return Loss -20*LOG10(Gamma), and reflected power.
Reflection at a resistive load
This example assumes a positive real characteristic impedance and a nonnegative, purely resistive load at one reference plane. It does not model reactive loads, complex characteristic impedance or propagation through a finite length of lossy cable. A cable marked 75 ohms is not automatically a 75-ohm input load regardless of its termination.
The magnitude of the voltage reflection coefficient determines VSWR and reflected power fraction. One minus the reflected fraction is accepted power at the load plane, not necessarily radiated power: antenna efficiency and other losses are separate.
An exact match has zero reflected power and infinite return loss. A zero-ohm short has total reflection, infinite VSWR and zero-dB return loss. The formulas return text for infinite limits; do not treat these labels as ordinary numbers in later calculations.
| RF Transmission-Line Metric | Formula | 75-Ohm Load on 50-Ohm Coax | Matched 50-Ohm Load |
|---|---|---|---|
| Reflection Coeff |Gamma| | ABS((B3 - B2) / (B3 + B2)) | 25 / 125 = 0.2000 | 0.0000 (Zero reflection) |
| Standing Wave Ratio (VSWR) | (1 + Gamma) / (1 - Gamma) | 1.2 / 0.8 = 1.50 (:1) | 1.00 (:1 Ideal) |
| Return Loss (dB) | -20 * LOG10(Gamma) | 13.98 dB | Infinite dB |
| Reflected Power Fraction | Gamma ^ 2 | 4% reflected; 96% accepted at load plane | 0.00% reflected |
Voltage Standing Wave Ratio VSWR = (1 + |Gamma|) / (1 - |Gamma|)
For positive purely resistive loads, VSWR simplifies to the larger of ZL/Z0 and Z0/ZL. This avoids subtracting two nearly equal numbers when reflection is close to unity. A short is handled explicitly.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<=0,B3<0),"Invalid inputs",IF(B3=0,"Infinite VSWR",ROUND(MAX(B3/B2,B2/B3),2))))RF Return Loss (dB) = -20 * LOG10(|Gamma|)
Larger return loss means smaller reflection in this model. A VSWR of 1.5 corresponds to about 13.98 dB; an exact match is the infinite limit. This alone does not establish transmitter suitability.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<=0,B3<0),"Invalid inputs",IF(B3=B2,"Perfect Match (Inf dB)",ROUND(-20*LOG10(ABS((B3-B2)/(B3+B2))),2))))Reflection coefficient magnitude
Use the same resistive-load assumptions and reference plane.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<=0,B3<0),"Invalid inputs",ABS((B3-B2)/(B3+B2))))Reflected power fraction
Use the same resistive-load assumptions and reference plane.
=IF(COUNT(B2:B3)<>2,"Invalid inputs",IF(OR(B2<=0,B3<0),"Invalid inputs",ROUND((ABS((B3-B2)/(B3+B2)))^2,4)))Try the example
Use the original values or change them to test your understanding.