Antenna Axial Ratio Calculator

Enter the major axis and minor axis of the antenna into the calculator to determine the axial ratio.

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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.

AR = E_{max} / E_{min}

Variables:

• AR is the axial ratio (always ≥ 1 in linear form, always ≥ 0 dB)
• E_max is the major axis of the polarization ellipse (the larger orthogonal E-field component)
• E_min is the minor axis of the polarization ellipse (the smaller orthogonal E-field component)

To convert to decibels: AR (dB) = 20 · log₁₀(AR). An AR of 1 gives 0 dB (perfect circular polarization) and an AR of 1.41 gives 3 dB (the accepted industry threshold).

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 Mismatch Loss from Axial Ratio

When two CP antennas communicate and both have finite axial ratios, polarization mismatch loss (PML) enters the link budget. For the common case of one perfect transmitter (AR = 0 dB) paired with a receiver having AR = 3 dB (linear 1.41:1), the worst-case polarization mismatch loss is approximately 0.51 dB. That modest penalty explains why 3 dB became the accepted threshold for classifying an antenna as circularly polarized: exceeding it drives mismatch losses above 0.51 dB per link terminal, which is significant in precision geodetic, satellite, and low-noise receiver systems. When both terminals have 3 dB AR, worst-case mismatch loss rises to roughly 1.0 dB.

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

One of the most valuable practical consequences of a low axial ratio is improved multipath suppression. When a circularly polarized wave reflects off a surface (ground, building, or vehicle body), its handedness reverses: right-hand circular polarization (RHCP) becomes left-hand circular polarization (LHCP) and vice versa. A CP receive antenna naturally attenuates the opposite-sense signal by an amount proportional to its cross-polarization discrimination (XPD), which is directly linked to AR. In precision GPS surveying, improving boresight AR from 3 dB to 1 dB can increase ground-reflection multipath suppression by 20 dB or more, translating to centimeter-level improvements in position accuracy for static baselines. This is why geodetic-grade choke ring antennas, which achieve AR below 0.5 dB over a wide beamwidth, remain the gold standard for high-accuracy positioning despite their size and cost.

Applications and Industry Axial Ratio Requirements

GNSS and GPS: Circularly polarized signals are used for satellite navigation because CP is immune to Faraday rotation in the ionosphere and because reflected multipath reverses handedness, allowing CP antennas to inherently reject it. Precision geodetic receivers specify AR below 1 dB at boresight. Consumer GPS devices typically require AR below 3 dB. The L1 GPS signal at 1575.42 MHz is RHCP; mismatching sense between the satellite and ground antenna adds a 3 dB loss on top of any AR-related mismatch.

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 transmit and receive both horizontal and vertical linear polarizations to derive differential reflectivity (ZDR), which separates rain from hail and classifies precipitation type. The antenna's polarization purity in linear terms (equivalent to a very high AR in dB, typically > 40 dB, meaning a linear ratio above 100:1) directly limits ZDR accuracy. A 40 dB AR error floor produces a ZDR bias of roughly 0.017 dB, which is below the 0.1 dB calibration target of modern operational radars.

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: When a spherical near-field range measures both the right-hand (G_R) and left-hand (G_L) circularly polarized gain components at every point in the radiation pattern, the axial ratio at each angle follows from the amplitude ratio of the co-polarized and cross-polarized components. This yields a full AR pattern, including tilt angle, and is the most information-rich method available.

From cross-polarization discrimination (XPD): When XPD is measured in dB (the difference in dB between co-pol and cross-pol levels), axial ratio follows from AR (dB) = 20 log₁₀[(10^XPD/20 + 1) / (10^XPD/20 - 1)]. The calculator above includes a direct XPD-to-AR tab for this conversion. Note that a very high XPD (good isolation) corresponds to a low AR (good circular polarization), and the relationship is nonlinear: going from XPD = 20 dB to XPD = 30 dB reduces AR by only about 1.7 dB, whereas going from XPD = 6 dB to XPD = 20 dB reduces AR by nearly 12 dB.