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*Subject*: [linrad] Re: Polarization question*From*: Leif Asbrink <sm5bsz.com; leif@xxxxxxxxxxxxxxxx>*Date*: Sun, 10 Jun 2007 18:54:01 +0200

Hi Joe, Zaba and all, > Ideally, I suppose, with an xpol antenna one would like to have > phase-matched preamps for the two polarizations and equal > electrical lengths for the two Rx feedlines. Sure:-) > Suppose they 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. Much more important would be the phase shift through very narrow filters in case you have such at the output of the preamplifier. A filter with 1 MHz bandwidth has a delay of something like 1us and in case the other channel has a filter with 1.5 MHz bandwidth, it would have much less delay and that could be a problem. When the phase is not matched, the polarisation indicator will not show the correct polarisation. That will not cause any loss of sensitivity, only make it more difficult to decide what tx polarisation to use. When it comes to the amplitude balance and similarity in NF I no longer remember how important it is for sensitivity. Not very important in relation to how important it is for getting correct polarisation readings in any case. The procedure to follow is like this: Connect everything. Compare the noise floor levels and insert an attenuator (or tweak the second RF amp tuning) for the noise floors of the two channels to become equal. 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. 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:-) Once the phase and amplitudes are properly set it will be a good idea to set the polarisation to + and -45 degrees with respect to the real orientations of the elements. The noise floor should ideally be exactly the same regardless of the phase. (plus, minus, circular or anything between.) In real life one might see significant differences in the noise floor and that would be caused by mutual coupling between the elements (to some extent the noise would then be correlated.) It is a good idea to verify that the isolation between polarisations is at least 20 dB in transmit mode:-) The procedure Linrad uses is to compute the powers in both channels as well as the complex correlation. Then like this: // ***************************************** //Now we have x2,y2 (real values) and xy (complex). //For explanation purposes, assume im_xy == 0, which corresponds to linear //polarization. The signal vill then be polarised in a plane. //a = angle between polarisation plane and the horisontal antenna. //Assume that the noise level n is the same in the two antennas, and that //the noise is uncorrelated. //We then find: // x2 = cos(a)**2 + n**2 // y2 = sin(a)**2 + n**2 // xy = sin(a)*cos(a) //From this we find: x2 * y2 - xy*xy = n**2 + n**4 //Neglect n**4: //cos(a)=sqr( x2 - ( x2 * y2 - xy*xy) ) //sin(a)=sqr( y2 - ( x2 * y2 - xy*xy) ) //The transformation formula to use for rotating the polarization //plane to produce new signals A and B, where A has all the signal and B //only noise, will then be: // A = X * cos(a) + Y * sin(a) // B = Y * cos(a) - X * sin(a) //Extending to im_xy != 0 the transformation becomes //re_A=C1*re_X+C2*re_Y-C3*im_Y //im_A=C1*im_X+C2*im_Y+C3*re_Y //re_B=C1*re_Y-C2*re_X-C3*im_X //im_B=C1*im_Y-C2*im_X+C3*re_X //C1 = cos(a) //C2 = sin(a) * re_xy / sqr( re_xy**2 + im_xy**2) //C3 = sin(a) * im_xy / sqr( re_xy**2 + im_xy**2) // ************************************** 73 Leif ############################################################# This message is sent to you because you are subscribed to the mailing list <linrad@xxxxxxxxxxxxxxxxxxxxx>. To unsubscribe, E-mail to: <linrad-off@xxxxxxxxxxxxxxxxxxxxx> To switch to the DIGEST mode, E-mail to <linrad-digest@xxxxxxxxxxxxxxxxxxxxx> To switch to the INDEX mode, E-mail to <linrad-index@xxxxxxxxxxxxxxxxxxxxx> Send administrative queries to <linrad-request@xxxxxxxxxxxxxxxxxxxxx>LINRADDARNIL