Two problemsThere are two calibration problems.
One is to control the phases of the signals entering the two antennas during transmit and to control the phases when two signals are added during receive. Of course the amplitudes have to be controlled also, but that is easy.
The other problem is to make sure the antennas are really orthogonal to each other. This is very important when a cross yagi is used in the " + " configuration because errors cause loss of gain with a small effect on SWR. In the " X " configuration poor orthogonality causes poor SWR, but no loss of gain. Another very good reason to use the " X " configuration.
(Of course the " + " is better than the " x " if a linear polarisation at 45 degrees angle is desired. The two configurations are the same antenna, just twisted by 45 degrees.)
The orthogonality problem is treated at some length below because I think it is often neglected. Orthogonality adjustments have to be performed if there is any asymmetry in the antenna system and it is particularly important if a simple select one or the other antenna is used for polarisation adjustment.
When separate pre- amps are used for the two antennas, it is no longer possible to make sure the phase relation is correct just by cutting cables accurately. Phase and Amplitude calibration has to be performed.
Orthogonality problemsWhen two antennas are mounted more or less in the same physical space, but with orthogonal polarisation, such as a cross yagi, insufficient orthogonality can easily become a problem. It is a good idea to make everything symmetric with good accuracy because then such problems will automatically be absent.
The 4 x 14 element cross yagi array I am presently using is far from symmetric. The boom tubes are made from thin walled 50 mm soft aluminium tubes, and I decided 10 mm holes would weaken them too much. I have had to bring the array down two times each year on the average to straighten the boom tubes anyway, and with 10 mm holes they might have become broken. The elements were first mounted by an omega shaped piece of aluminium with 14 mm space between boom tube and element. The elements were thus in good electrical contact with the boom tube. When I checked the first cross yagi, the SWR was very high, and did not have even a close resemblance to the SWR vs frequency curve that I had measured before when evaluating the boom correction for this particular mounting method.
Removing one set of elements, to get back to a conventional yagi restored correct SWR vs frequency. It turned out that one single element in any perpendicular position was enough to destroy the antenna. Fortunately, as it turned out, 1 mm thick teflon between each element and its omega-shaped clamp provided enough series impedance to reduce the undesired coupling to a reasonably small level despite the relatively high capacitance across about 3 square centimetres of 1 mm teflon.
The elements of my cross yagis are mounted at their midpoints. At right angles some coupling still remains despite the teflon isolation - the line joining the centres of the elements of one part is 62 mm away from the line joining the element centres of the other. This coupling is small, and it is removed by making the angle between the two element sets slightly smaller than 90 degrees.
If you consider a cross yagi design, through hole mounting is a good idea. All element mid points are then on a single straight line, and the coupling is zero at precisely 90 degrees. Still there may be some asymmetry, for example originating in the use of folded dipoles, so it is a good idea to verify the orthogonality and possibly adjust it, which is an easy thing to do.
Effects of poor orthogonalityPoor orthogonality, which is the same as poor isolation between the two supposedly orthogonal antennas has some unpleasant but not disastrous effects on performance as long as the coupling is reasonably small.
First some simple arguments on what to expect when the undesired coupling is -10 dB. The undesired coupling will show up in different ways depending in which way the (not so) orthogonal antenna pair is used
One or the other of two orthogonal antennas is used.This is the most common way of using cross yagis today. (March 1997) The antennas are in the " + " configuration, one horizontal and one vertical. Sending 100 W into the horizontal antenna leads to 10 W coming out from the feed point of the vertical. This is simply the definition of an undesired coupling of -10dB. If the vertical antenna was terminated in a 50 ohm resistor, these 10 W would be converted to heat and lost. To produce these 10 W as a receiving antenna, the vertical antenna will have to emit 10 W as radiation because of the currents in the elements needed for a receive antenna send 10 W out from the feedpoint.
It would be quite unconventional to terminate the vertical feed line in a matched resistor. The unused antenna is left open (or shorted), so those 10 W sent into the feeder is reflected and sent back to the vertical antenna. Sending 10 W into the vertical antenna will of course result in 1 W being sent down the feeder of the horizontal antenna, contributing to the SWR, and 1 W radiated as part of the horizontal radiation. (The coupling is of course the same in both directions.) In total 81 W is emitted by the horizontal antenna and 18 W by the vertical.
If this antenna is used for tropo scatter, with the other station using an horizontal antenna, all radiation that leaves the vertical antenna is useless. Tropo scatter conserves polarisation very well, and the vertical component is useless.
For EME, the power leaving through the vertical antenna may be useful. If it is or not depends on the optimum polarisation for the incoming or outgoing wave at the particular time. The radiation from the unused vertical antenna may twist the polarisation plane, or add a circular component depending on the phase between the two radiated components.
Equal power is fed into both antennasThis would be normal for a cross yagi in the " x " configuration. Sending 50 W into antenna 1 and 50 W into antenna 2 will create horizontal or vertical polarisation when the phase difference is 0 respectively 180 degrees.
In this case, 5 W will be sent from one antenna into the feedline belonging to the other due to the -10 dB coupling. These two signals will add, and produce a high SWR in the main feed line. Both with 0 and 180 degree phase difference, the signals will add to the same amplitude. The reflected wave will differ by 180 degrees with respect to the wave sent out from the transmitter depending on if the antennas are fed for horizontal or vertical polarisation.
Receive system with separate pre- amplifiersIn this case a wave enters the antenna, and some part of the total signal will come out from one of the feed points, and the rest of the signal will come out from the other.
When a undesired coupling is present, the polarisation required for all signal to come out from one of the antennas is no longer the linear polarisation parallel with the elements, but some other, in general elliptic polarisation.
The polarisation required for all signal to come out from the second antenna will also be different from parallel to the elements of the second antenna in a similar fashion.
The important thing is that the two different polarisations that match the two different feed points are NOT orthogonal. They contain a common component.
With two non-orthogonal antennas (non- zero coupling) the outputs from the two pre- amplifiers are not orthogonal. This means that when the two amplifiers are set for equal gain, adding and subtracting the signals from them will result in different output levels. (Of course adding or subtracting two orthogonal signals gives the same result, +3 dB. For uncorrelated signals, phase has no meaning.)
My present system with two independent pre- amplifiers shows this effect very clearly when the birds have been changing the inter- element angle too much. (Very little in fact) I regularly bring the antenna down for adjustment due to bent booms but sometimes also for too big changes in SWR when switching from H to V. The level when I can no longer tolerate the reflected wave phase change (because changed tuning is needed for V and H) is the same level as when adding the signals produces 2dB only, while subtracting them produces +4dB.
NEC2 Simulations of poor orthogonalityThe discussion above indicates that poor orthogonality may be a problem with cross yagis. To further illustrate the problem, I have made some NEC2 calculations on a cross yagi, very similar to my 14 element system. All the elements have their midpoints on a common straight line. The two "orthogonal" yagis are separated by 5 cm along the boom, and the angle between them is varied in steps of 0.5 degrees.
Calculations are made for the following configurations:
The tables below show the results of these NEC simulations:
Table 1. Angle between antennas is 90.0 degrees. Power is fed into the horizontal antenna. The emitted wave is a pure horizontal wave. The result is completely independent on how the vertical antenna is terminated: 50 ohms, open or shorted.
Table 2. (50 Ohms). Angle between antennas is 89.5 degrees. Power is fed into the horizontal antenna. The vertical antenna is connected to a 50 ohm resistor. The signal radiated by the vertical antenna is nearly 90 degrees out of phase, and it is more or less useless. If the useless vertical component is not included in the gain figure, a real gain of 17.48 dB is obtained. With 1.45% of the power reaching the 50 ohm termination at the vertical antenna, the coupling between the antennas is -18.4 dB.
Table 3. (50 Ohms) Angle between antennas is 89.0 degrees. See table 2 for explanation.
Table 4. (50 Ohms) Angle between antennas is 88.5 degrees. See table 2 for explanation.
Table 5. (Open) Angle between antennas is 89.5 degrees. Power is fed into the horizontal antenna. The feed point of the vertical antenna is left open. The signal radiated by the vertical antenna is 139 degrees phase shifted from the signal radiated from the horizontal antenna. For tropo the vertical component is useless, but for EME half the energy constitutes an in phase component that will be useful (when the twisted linear polarisation plane coincides with the desired polarisation plane)
Table 6. (Open) Angle between antennas is 89.0 degrees. See table 5 for details.
Table 7. (Open) Angle between antennas is 88.5 degrees. See table 5 for details.
Table 8. (Shorted) Angle between antennas is 89.5 degrees. Power is fed into the horizontal antenna. The feed point of the vertical antenna is shorted. The signal radiated by the vertical antenna is 63 degrees phase shifted from the signal radiated from the horizontal antenna. Compare with table 5. The amount of power radiated by the second antenna has changed and so has the phase relation. The phase of the currents in the vertical antenna can be controlled by the length of cable between the feed point and the relay used to select antenna, but it is much better to remove the undesired coupling. With larger deviations from 90.0 degrees, the result becomes worse just as for the "Open" cases, table 5 to 7.
Table 9. (In phase) Angle between antennas is 89.5 degrees. Power is fed into both antennas and the signals are phase shifted to compensate for the 5 cm the antennas the antennas are separated on the boom. The whole system is rotated by 45 degrees, and when the angle between the antennas is 90.0 degrees, the gain, impedance and polarisation is identical to the result from a single antenna as in table 1. Note that the undesired coupling causes poor SWR but that it does not affect the radiation by the antenna which retains the desired polarisation.
Table 10. (In phase) Angle between antennas is 89.0 degrees. See table 9 for details.
Table 11. (In phase) Angle between antennas is 88.5 degrees. See table 9 for details.
Table 12. (Antiphase) Angle between antennas is 89.5.0 degrees. Compared to table 9, the phase of one antenna is shifted by 180 degrees. See table 9 for further details.
Table 13. (Antiphase) Angle between antennas is 89.0 degrees. See table 12 for details.
Table 14. (Antiphase) Angle between antennas is 88.5 degrees. See table 12 for details.
Practical procedure for obtaining good orthogonality in a cross yagiThe NEC simulations above show that an isolation of 20 dB is sufficient. This means that the obvious way of checking a cross yagi is to connect one of the feed lines to a transmitter with known output, and a power meter and a dummy load to the other. The attenuation is then measured directly through the power arriving at the dummy load. If it is below -20 dB compared to the transmitted power everything is fine.
If the signal at the dummy load is too strong, bend all elements slightly so the angle between the two yagis deviates a little from 90 degrees. If the power at the dummy load increases, just bend the elements the other way. In my experience it is always be possible to find a zero. This procedure is illustrated by tables 2 to 4 above.
If your antenna is in the " X " configuration, and you have all connections well soldered and water tight like I have, the procedure above is not very attractive. The way I adjust my elements whenever necessary is as follows:
Connect directional couplers in the transmission line. Measure the phase and the amplitude of the reflected wave. It can be done with an oscilloscope for example. When the relays are switched between horizontal and vertical, the phase and amplitude of the reflected wave changes. Bend elements until the reflected wave does not change when switching between horizontal and vertical.
Simple switching needs no calibration
When the polarisation is adjusted by switching some different length feed lines close to the antenna, a reasonable mechanical accuracy is all that is needed once the coupling between the antennas is low enough as explained above.
Usually cross yagis are mounted at different positions along the boom, to get some free space around the feed points. It is a trivial thing to compensate for different mounting positions. Just imagine you are in front of an antenna. You know the speed of light, and the speed of waves inside your feed lines. Just make sure that the travel time through both cable and free space becomes equal when the delay cables are selected for equal phase.
Phase and amplitude calibrationThe need for a calibration procedure arises when two pre-amplifiers are used, one for each orthogonal antenna, and when the output signals from these amplifiers are added in order to produce a single signal that corresponds to an antenna with optimum polarisation.
Also if the transmit side uses long cables and/or some more sophisticated system for full polarisation control there may be a need for calibration.
When two pre- amplifiers are used, and the signals from them are used in a stereo system, there is no need for any calibration. The human brain will combine them in a near optimum way regardless of their relative phase. Not calibrating means not knowing the polarisation of the incoming wave, which means not knowing which polarisation will be optimum for the transmitted wave to arrive in line with the polarisation at the other end, so some calibration is good - but there is not much need for accuracy.
To calibrate the antenna, you need an incoming wave that will give the same signal from both antennas, and a known phase relation between those signals. It is then trivial to set the polarisation control(s) to fit a wave orthogonal to the incoming wave and tune phases and amplitudes for zero. Just one zero is needed, then everything is accurately tuned for all polarisations.
For a cross yagi system in the " X " configuration this is very easy. Tropo scatter conserves horizontal or vertical polarisation very well, but only if both stations point their antennas towards each other. What I do is simply to listen to a DX station when I know he points his antenna on me, switch polarisation to vertical, and adjust for zero. This adjustment is very stable, it is easy to do and to verify. The ease of calibration is another good reason for selecting the " X " configuration.
For a cross yagi system in the " + " configuration it is difficult to find a good signal source for calibration. One alternative could be a circularly polarised wave. I do not know any easy way to get it, and it has to be arranged for no ground reflections because the horizontal and vertical components are reflected differently. The same problem with ground reflections is present with a linearly polarised antenna at 45 degrees.
One safe way is to use the EME signals from a big station with linear polarisation. Wait for the signal to have similar S/N in both receive channels, and then adjust phase and amplitude for zero. This will lead to a correct phase adjustment, but it will of course work only for rather large systems in which EME signals are strong enough.
Afterwards the amplitude controls are adjusted for equal levels of the noise floor in the two channels.
The important calibration is the phase. During normal operation the phase is fixed at 0 or 180 degrees. A small phase error causing loss of 1 dB S/N is not easy to detect but it certainly makes EME contacts more difficult. With weak EME signals, it is not easy to see that the minimum when turning the linear polarisation control 90 degrees away is not as deep as usual, and it absolutely impossible to notice that the maximum is one dB below normal.
If the amplitude calibration is not accurate, it just means that the polarisation plane is slightly different from what you think, but you will get the optimum signal anyway.