For estimating and education only. Results come from the simplified models described below, are provided as is with no warranty, and are not a substitute for engineering analysis, simulation or measurement. Check them before relying on them in a design, purchase or safety decision. See the terms of use.
Equations
\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}
\mathrm{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|}, \qquad |\Gamma| = \frac{\mathrm{VSWR} - 1}{\mathrm{VSWR} + 1}
\text{Return loss} = -20\log_{10}|\Gamma|dB
\text{Mismatch loss} = -10\log_{10}\left(1 - |\Gamma|^2\right)dB
\frac{P_\mathrm{reflected}}{P_\mathrm{incident}} = |\Gamma|^2
Variables
| Symbol | Meaning | Unit |
|---|
Z_L | Load impedance, R + jX | Ω |
Z_0 | Line (reference) impedance | Ω |
\Gamma | Voltage reflection coefficient | — |
\mathrm{VSWR} | Voltage standing-wave ratio | — |
Worked example
| Input | Value |
|---|
| Load | 75 Ω resistive |
| Line impedance | 50 Ω |
| Result | Value |
|---|
| VSWR | 1.5 |
| Return loss | 13.98 dB |
| |Γ| | 0.2 |
| Mismatch loss | 0.177 dB |
| Reflected power | 4 % |
| Delivered power | 96 % |
| ∠Γ | 0 ° |
A 75 Ω load on a 50 Ω line gives |Γ| = 0.2: VSWR 1.5, return loss 14 dB, and 4 % of the power reflected.
Load this example in the calculator
Validity
- Single frequency, lossless reference line.
- Mismatch loss is the power not delivered to the load because of reflection. It does not include cable or antenna efficiency loss.
- Return loss measured through a lossy cable reads better than the load alone: a cable with loss L dB improves the reading by 2L dB.
Sources
- D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012. Chapter 2.