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[linrad] Re: Polarization question
- Subject: [linrad] Re: Polarization question
- From: Joe Taylor <Princeton.EDU; joe@xxxxxxxxxxxxxxxx>
- Date: Mon, 25 Jun 2007 14:22:46 -0400
I have been thinking more about the Linrad polarization
questions that I raised here two weeks ago.
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.
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
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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