Using Linrad to evaluate mutual coupling between polarizations in cross Yagi antennas.
(Feb 27 2011)

Mutual coupling in cross Yagi antennas.

A Yagi antenna is a resonator with a fairly high Q. Resonators are sensitive to mutual coupling. In cross Yagis even small deviations from symmetry can cause fairly large transfers of power from one polarization to the other.

If a transmitter is connected to the feedpoint for one polarization, mutual coupling would transfer some fraction of the power to the other polarization from where it would be radiated. The system would then generate elliptic polarisation or possibly a tilted linear polarization. Whether the part emitted in the unintended polarization is useful or lost depends on the circumstances. Look here for more info and some NEC simulations. How to calibrate an adjustable polarisation antenna.

Linrad with two RF channels.

When using Linrad with two RF channels and a cross-Yagi antenna mutual coupling will lead to different sensitivity for different polarizations. In a good system where most of the noise is sky noise the S/N ratio will not be affected when CW is received with adaptive polarization. The waterfall sensitivity will become different for different polarizations however.

It is a very good idea to have a system that is set up for equal sensitivity in all polarizations. That means that the waterfall colour scale and the various dB scales become equally calibrated for all polarizations. They would give give the antenna temperature independently of the polarization. Under normal circumstances the antenna temperature would be the same for all polarizations. Deviations from normal are easily seen and one would be alerted for any problem causing a system degradation. Local interferences typically have a defined polarization and therefore one can observe even small degradations of the noise floor by comparing different polarizations or by looking at the correlation spectrum, but only if antenna orthogonality is good.

Typical results for tests on good cross Yagi systems.

Figure 1 shows Linrad playing the file frh1135.bz2 213032622 bytes from sm5bsz.com. The file was recorded during the ARRL EME contest 2001 using the system of 32 cross yagi antennas of SM5FRH. Some more info about this file and some similar files is available here: ARRL2001





Figure 1 The file frh1135 with 100000 averages for correlation. The baseband and S-meter graphs show H and V. H is about 0.5 dB stronger than V.

By setting the linear polarisation angle to 45 degrees by clicking at the line showing the angle Linrad is instructed to take the sum and the difference of the two channels H and V.

When the phase ruler is set to about 135 degrees the sum and the difference become nearly equal. This is shown in figure 2. The phase ruler is the upper green band in the polarization graph. It goes from 270 to 90 degrees with zero at the center. It sets the phase shift between the two RF channels before they are combined. By twisting the phase between the two channels by 90 degrees from 135 to 45 degrees one would get the largest possible difference between the sum and difference between H and V. This is shown in figure 3.





Figure 2 The file frh1135 with 1000 averages for correlation. The baseband and S-meter graphs show H+V and H-V with a phase angle between H and V of about 135 degrees. The sum and the difference are equal.





Figure 3 The file frh1135 with 10 averages for correlation. The baseband and S-meter graphs show H+V and H-V with a phase angle between H and V of about 45 degrees. H+V is about 0.5 dB stronger than H-V.

The stack of 32 cross yagi antennas that Tobbe, SM5FRH was using around year 2000 had a good isolation between V and H. The images above that were produced 10 years later from a wideband recording allows us to evaluate how large the crorr-polarization coupling was.

Let us denote the incoming radio wave as H and V. Two orthogonal linearly polarized waves. H is horizontal and V is vertical. We assume that they are galactic noise and therefore totally uncorrelated. When those electromagnetic fields are received by a crossed yagi antenna having two output signals X and Y, the output would be like this:

X=H+c*V
Y=V+c*H


c is a complex coefficient telling how much the antennas see of each other.

the power of (X+Y) becomes (H2+V2) if the phase of c makes the mutual coupling phase shifted by 90 degrees while the power would be (H2+V2) + 4*c*H*V if the mutual coupling is in phase. The above is sloppy. If you can supply a more stringent text to place here, please send me an E-mail...

Assuming the power of H equals the power of V we get the power of H+V as (1 + 2*c) * 2 * H2

The term 2*c goes from zero to 2*c depending on the phase angle at which the sum of H and V is taken. In the figures above we can see that a phase angle of 45 degrees makes the sum and difference deviate by 0.5 dB (=1.123 times). (The difference at 45 degrees is the sum at 225 degrees) From that we can conclude that c=0.0615. Feeding 1 kW into the H antenna should give 61W (-12.1 dB) power at the V connector.

Note that the theory above is not verified and that there could be a missed factor of two somewhere. If you know for sure what is correct, please send an E-mail.

The correlation spectra, the yellow curves in the main spectrum would coincide with the white curve, the normal spectrum, if the same signal were sent to the two RF inputs or if no averaging were done. The correlation spectra give the following info:
No of averages     Corr level
                     (dB)
   99990             -11.3
    1000             -11
      10             -5

Increasing the number of averages in correlation spectra by a factor of 100 should lower the correlation noise floor by a factor of 10 (10 dB.) It is obvious that the correlated spectrum of the SM5FRH antenna gives a correlated power 11.3 dB below the summed power of H and V. It is obvious that 1000 averages is enough going from 10 to 1000 averages lowers the correlation by 6dB only, not the expected 10 dB.

Figure 4 shows a screen dump with Linrad playing a recording from about 1998. The hardware was a two channel SDR with crystal filters. connected to the 4 x 14 cross yagi I used at that time.





Figure 4 The 4x14 antenna with 100000 averages for correlation. The two polarizations +45 and -45 differ by a few tenths of a dB only.

The biggest difference between the sum and difference of the two RF channels is at a phase angle of about 135 degrees. Figure 5 shows that.





Figure 5 The 4x14 antenna with 1000 averages for correlation. The two polarizations +45 and -45 are summed at 135 degrees and at 315 degrees. Those angle give the largest difference, about 0.3 dB. Angles are set with the phase ruler, the white line in the upper green bar of the polarization graph.

At 45 degrees the difference is very small as can be seen in figure 6.





Figure 6 The 4x14 antenna with 1000 averages for correlation. The two polarizations +45 and -45 are summed at 45 degrees and at 135 degrees. Those angle give the same power because the component of the signal from the other antenna is at 90 degrees.

The correlation spectra give the following info:
No of averages     Corr level
                     (dB)
   99990             -18
    1000             -12

The correlation spectrum does not only show the coupling between the orthogonal polarizations of the antenna. It also shows the level of various signals (interferences) that reach both of the orthogonal antennas.

The correlation is small and that means that the two polarizations are orthogonal and that no interference source is reaching both antennas.

Figure 7 is a recording from year 1999. with the same hardware as the previous recording. A 4x14 elements cross yagi and a two channel 20 kHz wide receiver. The recording was made on a DAT recorder.





Figure 7 The 4x14 antenna with 40000 averages for correlation.

When there is interference that reaches both antennas there will of course be correlation. Figure 8 is the same recording as figure 7 but after some interference pulses.





Figure 8 The 4x14 antenna with 40000 averages for correlation after an interference pulse that is present in both antennas.

Test results for a less good cross yagi system.

Figures 9 and 10 show a very short recording from a cross yagi array that suffers from strong mutual coupling between the two polarizations H and V. The fixed polarization is set to 45 degrees which will result in (H+V) and (H-V) blue and red in the S-meter graph. With the phase ruler set to about 135 degrees as in figure 9 the two combinations which can be denoted (H+V) at 135 degrees and (H+V) at 315 degrees have the same power.





Figure 9 A cross yagi with poor isolation between H and V. at 135 and 315 degrees phase shift between H and V the power level is the same for H+V. (Which is the same as to say (H+V) equals (H-V) at 135 degrees.)

When the phase ruler is set to 45 degrees in the polarization graph the difference between (H+V) and (H-V) amounts to about 4 dB. This explains the strong correlation spectrum. Only about 3 dB below the summed power of H and V.





Figure 10 A cross yagi with poor isolation between H and V. at 45 and 225 degrees phase shift between H and V the power level differs by about 4 dB for H+V. (Which is the same as to say (H+V) differs from (H-V) by 4 dB at 135 degrees.)

Poor orthogonality can be caused by various things. Figure 11 shows one of the possible causes.





Figure 11 Modest deviations from 90 degrees between the H and V elements can cause a surprisingly large coupling between H and V. How much cross-polarization coupling this particular bent element is causing is unknown. A rough estimate is that it could cause the coupling measured as the attenuation between the two feedpoints to go from infinity (better than 20 dB) to something in the order of 6 dB.

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