#### Antenna polarization mismatch

Joseph (Joe) Gray, W5JG

Just thought I'd share some recent thoughts and discoveries.

Do you hold your HT straight up and down when talking through the repeater? Most of us don't. We hold it at an angle. That means that there is some signal loss between our HT and the vertically polarized antenna at the repeater. This applies to your cell phone as well.

How much loss is there, and is it worse at certain angles? I have always heard the rule-of-thumb that between a vertical antenna and a horizontal antenna (one antenna oriented 90 degrees to the other), there is 20 dB of loss.

I just came across the formula for actually calculating the loss at any angle between the two antennas. Expressed as an Excel formula, it looks like this:

I have attached an Excel spreadsheet, with the calculation for angles from 0 to 90 degrees. The spreadsheet cosine function wants radians, thus the conversion from degrees.

This formula only applies to linearly polarized antennas. Circularly polarized antennas have a different formula.

Note that these calculations are for "ideal" antennas, and "ideal" RF propagation between them. The real world is a little different.

We can see from the spreadsheet that for angles up to 30 degrees, there isn't a significant signal loss between the two antennas. At 45 degrees, we lose half our signal. Being a logarithmic function, things get rapidly worse. At 90 degrees, we should have almost total signal loss between the two antennas.

That is theory. In the real world, antennas are not perfectly polarized either vertically or horizontally. We also have some reflection and refraction of part of our signal, which may change the polarization of those components.

So, is that rule-of-thumb figure of 20 dB any good for 90 degree, cross polarized antennas? Various internet sources say that in the real world, the loss is 20-30 dB.

For those who need to brush up on their Decibels, that means that if you hold your HT horizontal, only 1/100 to 1/1000 of your transmitted signal is reaching the repeater. Keep it under 30 degrees from vertical.

This might be a good demonstration for someone to do at a club meeting. You could use anything from a simple field strength meter, to a spectrum analyzer to see the effect. You'd probably have to attenuate the transmitted signal quite a bit, at such close range, however. I'd volunteer, but I live in Carson City, NV now. Too long a drive :-)

BTW, since almost all of us have a rubber duck antenna on our HT's, you might be thinking that since the antenna is made from a spiral of wire (a helical antenna) the polarization of a rubber duck is not vertical. It turns out that since both the diameter of the helix and the spacing of the turns is significantly less than 1/4 wavelength, the rubber duck antenna acts like a base-loaded monopole, and has a vertical radiation pattern.

Joe Gray
W5JG

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