How can cross-polarization loss be determined given the angle between two antennas?

This question addresses the case where two antennas are exactly 90° cross-polarized, but not other angles.

How can I determine the theoretical, and estimate the actual, attenuation from cross-polarization between two antennas given the angle between them?

2 Answers

For two linearly-polarized antennas, the response just the square of the cosine of the angle between them (in the plane orthogonal to the direction of propagation), also known as the "tilt angle". So:

$$\cos^{2} 0^{\circ} = 1$$ (no loss)
$$\cos^{2} 20^{\circ} \approx 0.88$$ (0.5dB loss)
$$\cos^{2} 45^{\circ} = 0.5$$ (3dB loss)
$$\cos^{2} 60^{\circ} = 0.25$$ (6dB loss)
$$\cos^{2} 80^{\circ} \approx 0.03$$ (15dB loss)
$$\cos^{2} 90^{\circ} = 0$$ (total loss)

For one linear and one circular antenna, the theoretical polarization loss is always 3dB, no matter the orientation of the linear antenna.

For two circular-polarized antennas, the theoretical loss is 0 if you got the handedness correct, and infinite if you got it wrong.

For elliptical polarization, the formula is not so trivial, but it acts like a mix of the linear and circular cases — actually, linear and circular polarization are just special cases of elliptical polarization where a lot of the terms drop out.

It's not really practical to estimate how far from theoretical things will be in the real world, without a lot of information you're unlikely to have. The main causes of deviation from the theoretical behavior are:

1. The radiated or received polarization isn't pure linear or circular, because of imperfections in the antenna geometry or interaction with the feedline or other conductive objects in the near-field. You can't figure that accurately unless you have to-the-millimeter knowledge of where the antenna will be installed, the location and composition of everything nearby, and any bends or wiggles in the antenna elements.

2. The signal was reflected or refracted off of something in the environment, causing it to be received by multiple paths, with differing polarization. You can't figure this one out without knowing everything, maybe out to a distance of many miles, that could contribute to multipath.

• Is there any way to estimate the actual loss without just measuring it? Jan 1, 2023 at 3:51
• @kj7rrv see edit. Jan 1, 2023 at 4:34
• This loss is only theoretically applicable for direct line of sight signals. ANY non-uniform bouncing(reflection) or bending(refraction) of the signal wavefront results in a change of polarization, making these equations mostly useless in the practical world. The closest to "cos290∘=0 (total loss)" has an absolute maximum about 70db isolation., under ideal conditions.(circular polarization to a satellite through a cloudless sky >10 GHz with zero solar index with a 10M parabolic dish.) There are no absolutes for this calculation based in reality.
– user23328
Feb 25, 2023 at 3:37

Loss can be gain, given the input signal. Reciprocity always applies.

There is no magic "formula" only the bubble and the polarization/direction it fits.

The only firm rule is a 3db "loss" per 2 way splitter. Unless reflected via swr, where the excess power is burned off as heat, and/or reflected to the transmitter or tuner(which bounces it back to the antenna...), the power is transmitted into the air. The power supplied must be either burned off or transmitted. This is the law of conservation of energy.

I stipulate that there can be no loss of power of a properly tuned(1:1 swr) antenna or multiples of the same no matter the orientation.

The emitted pattern and polarization are the only constraints given to the power output.

Given the distance between antennas this can create nulls a cancellation of a signal in a direction, or an elliptical(or circular) polarization pattern, if mixed polarity(H,V) antennas are used. The same amount of power is radiated not matter the polarity or direction of the output waveform bubble.

The bubble is formally defined as the energy pattern of a sphere about an isotropic radiating point. It can be enlogated by nulls to fit certain directions, once airborne never quashed only fortified on the opposite direction by nulls, cancellation of the waveform in a direction.