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
r = \pm 10^{\mathrm{AR}/20}same sign for the same sense\mathrm{PLF} = \frac{1}{2} + \frac{4\,r_1 r_2 + (1 - r_1^2)(1 - r_2^2)\cos 2(\tau_2 - \tau_1)}{2\,(1 + r_1^2)(1 + r_2^2)}L_\mathrm{pol} = -10\log_{10}\mathrm{PLF}dBLinear / linear
\mathrm{PLF} = \cos^2(\tau_2 - \tau_1)Cross-pol
\mathrm{XPD}_\mathrm{circ} = 20\log_{10}\frac{|r| + 1}{|r| - 1}, \qquad \mathrm{XPD}_\mathrm{lin} = \mathrm{AR}dBVariables
| Symbol | Meaning | Unit |
|---|---|---|
\mathrm{AR} | Axial ratio: 0 dB is circular, large is linear | dB |
r_1,\ r_2 | Signed linear axial ratios | — |
\tau_1,\ \tau_2 | Tilt of each polarization ellipse’s major axis | rad |
\mathrm{PLF} | Polarization loss factor, 0 to 1 | — |
\mathrm{XPD} | Cross-polarization discrimination of one antenna | dB |
Worked example
| Input | Value |
|---|---|
| Antenna 1 | RHCP, 3 dB axial ratio |
| Antenna 2 | Linear (40 dB), tilted 30° |
| Result | Value |
|---|---|
| Polarization mismatch loss | 2.273 dB |
| Polarization loss factor | 0.5925 |
| Best case (tilts aligned) | 1.704 dB |
| Worst case (tilts crossed) | 4.643 dB |
| Cross-pol discrimination, antenna 1 (circular) | 15.34 dB |
| Cross-pol discrimination, antenna 2 (linear) | 40 dB |
An ideal circular antenna loses 3.01 dB to a linear one at any tilt. With a 3 dB axial ratio the loss swings with tilt, from about 1.7 to 4.6 dB.
Load this example in the calculatorValidity
- Far-field coupling between two antennas in each other’s main beam.
- Axial ratio and tilt are those of each antenna toward the other. Both change across the pattern.
- Multipath changes the arriving polarization. One reflection reverses the sense of circular polarization.
Sources
- W. L. Stutzman, Polarization in Electromagnetic Systems, 2nd ed., Artech House, 2018.
- W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 3rd ed., Wiley, 2012 (polarization efficiency).
- IEEE Std 145-2013, IEEE Standard for Definitions of Terms for Antennas.