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[linrad] Re: Polarization question

Hi Leif,

I have been thinking more about the Linrad polarization questions that I raised here two weeks ago.

I wrote:

Suppose they [the feedline lengths in X and Y channels] are not well matched. In other words, suppose that the complex gains and signal delays in the two polarization channels are not equal. Will Linrad's polarization-matching capability be compromised? As far as I can see, it still works well even with poorly matched feedlines. I suppose this must mean that Linrad solves for a differential complex gain, and that over a fairly narrow bandwidth a different delay can be treated as a phase shift.

You replied:

From a practical point of view the cables are well matched. I think
it is a safe assumption to guess that the length differences will be very small and of no concern.

Let's work in terms of the Stokes Parameters, with complex signals X and Y.

I = |X|^2 + |Y|^2     (total power)
Q = |X|^2 - |Y|^2     (horizontal linear component)
U = 2Re(X^* Y)        (vertical linear component)
V = 2Im(X^* Y)        (circular component)

L = sqrt(Q^2 + U^2)     (linear polarized component)
Theta = 0.5*atan(U/Q)   (polarization angle)

If I shift the phase of X relative to Y (say, by inserting an extra piece of cable in the X feedline), the values of U, V, L, and Theta will surely change.

I don't know what you meant when writing "From a practical point of view the cables are well matched." In my station, at present, it would be a complete accident if the downlines from the tower-mounted X and Y preamps were the same electrical length. They are just two pieces of coax that I had lying around.

Moreover, my xpol yagis have the H elements located forward of the V elements by some 10 inches or so (I forget the exact amount) -- maybe 1/8 of a wavelength. This will have a very significant effect, as well, no?

So, it seems to me that the only way to get things calibrated correctly is the one you outlined:

Listen to a linearly polarised signal that arrives with similar strength in both polarisations. (This is the strongest reason
why the X configuration is so much better than the + configuration.
It is easy to find a pure H-pol signal. Finding a 45 degree terrestrial signal is virtually impossible due to ground reflections so a + configured system has to be calibrated on EME signals.) Change cable lengths until the signal appears close to linear
on the pol meter. Fine tune by tweaking the second RF amplifiers.
(will affect both amplitude and phase, but there are two second
RF amplifiers so it should be possible to find both amplitude and
phase matching.

On the other hand, a strong practical reason to use the + configuration is that one wants to use the antenna for tropo as well as EME -- and therefore wants the ability to transmit a horizontal signal. My array, therefore, is in the + configuration.

It would of course be easy to add parameters for amplitude
and phase balance, but I have not done it since I found
it easy to do in hardware:-)

To me it seems much easier to do it in software, and perhaps I will try this within MAP65. Suppose the gains in the X and Y channels are already matched. Then, while receiving a 100% horizontally polarized signal, shouldn't it be sufficient to multiply the complex signal for X (or Y) by a complex constant e^(i*phi), with the phase shift "phi" chosen so as to minimize Stokes Parameter V ?

	-- Joe, K1JT

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