Calculate antenna axial ratio from polarization ellipse axes, AR in dB, or cross-polar discrimination, with polarization class and same-hand CP mismatch loss.
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Antenna Axial Ratio Formula
The following formula is used to calculate the antenna axial ratio for given major and minor axes.
Variables:
- AR is the axial ratio (always ≥ 1 in linear form, always ≥ 0 dB)
- Emax is the major axis of the polarization ellipse (the larger ellipse semiaxis)
- Emin is the minor axis of the polarization ellipse (the smaller ellipse semiaxis)
To convert to decibels: AR (dB) = 20 · log10(AR). AR = 1 is ideal circular polarization (0 dB); 3 dB corresponds to about 1.4125:1, a commonly used CP specification criterion.
What is Antenna Axial Ratio?
Antenna axial ratio (AR) quantifies the polarization purity of a radiating electromagnetic field. A propagating wave traces an ellipse in the plane perpendicular to its direction of travel, formed by two orthogonal E-field components. The axial ratio is the ratio of the ellipse's major axis to its minor axis. When both components are equal in magnitude and 90 degrees out of phase, the ellipse collapses into a circle and the antenna achieves perfect circular polarization (AR = 1, or 0 dB). As one component grows larger, the ellipse flattens and AR increases toward infinity, corresponding to pure linear polarization where only one component exists.
For circularly polarized (CP) antennas, AR is the single most important performance figure. It captures how faithfully an antenna produces or receives a rotating E-field of constant amplitude, and it directly governs polarization mismatch loss in system link budgets. Because AR is defined as major over minor, it is always greater than or equal to 1 in linear form and always greater than or equal to 0 dB.
Polarization Type vs. Axial Ratio
| Polarization Type | AR (Linear) | AR (dB) | Typical Application Requirement |
|---|---|---|---|
| Perfect circular | 1.00 | 0.0 dB | Theoretical ideal; unachievable in practice |
| Excellent CP | 1.00 to 1.12 | 0 to 1 dB | Precision geodetic GNSS, phased array radar |
| Good CP | 1.12 to 1.41 | 1 to 3 dB | Consumer GPS, satellite uplinks, RFID |
| Marginal CP | 1.41 to 2.00 | 3 to 6 dB | Low-cost CP elements; functionally elliptical |
| Elliptical | 2.00 to 10 | 6 to 20 dB | Not classified as CP; significant mismatch loss |
| Pure linear | Infinity | Infinity dB | Dipoles, Yagis, standard patch in LP mode |
Polarization Mismatch Loss from Axial Ratio
Polarization mismatch depends on both terminals and their relative ellipse orientation. One ideal circular terminal paired with a same-hand terminal of 3 dB AR has about 0.125 dB mismatch loss. Two same-hand 3 dB AR terminals have 0 to about 0.508 dB loss, depending on relative ellipse tilt. The calculator assumes one ideal same-hand circular terminal.
Off-Boresight Axial Ratio Degradation
Axial ratio is not a single number for an antenna; it varies across the radiation pattern. A typical circularly polarized patch achieves its best AR at boresight (the beam center), and AR degrades as the observation angle moves toward the horizon. High-performance GNSS antennas can maintain AR below 3 dB out to plus or minus 60 degrees from boresight, while reaching 3 to 6 dB at 10 degrees elevation. Because GNSS satellites can be at low elevation angles during a measurement session, the AR beamwidth specification is often as important as the boresight AR value. Datasheets commonly express this as "AR < 3 dB for ±30° from boresight," and link budget models should use the off-boresight AR for satellites near the horizon rather than the peak boresight figure.
Axial Ratio and Multipath Rejection
Low axial ratio can improve rejection of opposite-hand circular components, including some reflected signals. Actual multipath rejection depends on reflection geometry, materials, antenna pattern and receiver processing; axial ratio alone does not establish a positioning-accuracy improvement.
Applications and Industry Axial Ratio Requirements
GNSS and GPS: The GPS L1 signal uses RHCP. Polarization requirements vary with the antenna and application. Opposite ideal circular hands are orthogonal and have zero ideal coupling; the familiar 3.0103 dB mismatch applies to ideal circular versus linear polarization. Real antennas have finite cross-polar response.
Satellite communications: Earth terminals communicating with CP transponders in geostationary orbit specify AR to control polarization mismatch loss in the rain-fade margin. At C-band and Ku-band, Faraday rotation in the ionosphere is small enough that linear polarization is often used instead, but at L-band and S-band, CP is preferred and AR specifications of 3 dB or better are standard.
Weather radar: Dual-polarization radars use horizontal and vertical channels. Their isolation and differential-reflectivity calibration require the full antenna/system polarization response; the circular-basis XPD conversion here does not establish a ZDR error floor.
Amateur radio and EME (Earth-Moon-Earth): CP is used for moonbounce communications because the long propagation path through the ionosphere and the reflection geometry both produce unpredictable linear polarization rotations. An AR of 3 dB or better keeps polarization losses manageable on a path with already extreme free-space loss.
Axial Ratio Measurement Methods
Spinning linear source: The most common technique. A linearly polarized source antenna illuminates the antenna under test (AUT) while either the source or the AUT is rotated about the boresight axis. The peak-to-peak variation in received signal level equals the axial ratio in dB. A perfect CP antenna shows 0 dB variation; any variation directly equals AR. This method is fast and requires only a scalar power meter or spectrum analyzer, making it suitable for production testing.
RHCP and LHCP gain comparison: Circular-component gain magnitudes determine AR and the dominant hand at each direction. Ellipse tilt additionally requires relative phase information and is undefined for ideal circular polarization.
From cross-polarization discrimination (XPD): For dominant and opposite circular components, AR (dB) = 20 log10[(10XPD/20 + 1) / (10XPD/20 − 1)]. Use the Circular co/cross XPD input method. XPD of 20 and 30 dB gives AR of about 1.7430 and 0.5495 dB, an improvement of 1.1935 dB. From 6 to 20 dB XPD, AR improves from about 9.5699 to 1.7430 dB, a 7.8269 dB change. This conversion does not apply to arbitrary linear-basis co/cross measurements.
