[linrad] Re: Polarization question

[Joe Taylor <Princeton.EDU; joe@xxxxxxxxxxxxxxxx>]

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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