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From Direction and Polarization to Phase Difference


We need a minimum of two antennas to achieve a directional phase difference. Two antennas that are small with respect to the wavelength are a good choice. See Figure 3. For example, active small “magnetic” loop antennas work well (see Note 1). They are wideband, optimally balanced and there is a negligible mutual coupling between both antennas.

Figure 3 — Three configurations with the antennas a) in the same direction b) at right angles to one another and c) above one another.

Figure 4 — Two antennas show an arc of directions with the same difference in phase.

Figure 5 — Phase difference as a function of the azimuth direction for a 0° elevation angle.



Loop Antennas in the Same Direction

It is obvious we are about to use both loop antennas as an array, as we are mainly interested in the direction from which the signals enter. In this array, all antennas must have identical radiation patterns and the polarization must also be the same in all directions. The resulting radiation pattern of an array is determined by adding the fields of the antennas with suitable amplitude ratios and phase differences.

In our case, however, we are not going to add the fields, but decompose one field into two components (signals) with their own amplitude and phase. In this specific case, we look at the difference in phase between the signals received by both antennas. This actually concerns time difference of arrival (delay) differences. One antenna receives the signal earlier in time than the other antenna. We may convert this into a phase, as the bandwidth of the channel is small with respect to the carrier frequency.

This phase difference is simple to calculate. We already know the wavelength of the carrier frequency. Now we only have to work out the difference in distance between both antennas for the respective direction. A wavelength corresponds to 360° (a complete sine period). The phase difference is therefore this 360° times the ratio of the difference in distance and the wavelength. Depending on which antenna first receives the signal, this phase difference will be positive or negative.

Remember, the direction also includes elevation as well as azimuth. We get the same phase difference for an arc of direction, as shown in Figure 4.

Each arc is formed by all directions having the same angle with the axis on which both antennas are situated (X-axis). We can therefore make no distinction between signals on the opposite side of this axis. We need more antennas for this. Only in the extension of this axis and at 0° elevation do we find a single point where the phase difference is at a maximum. Figure 5 shows the phase difference as a function of the azimuth direction for an elevation angle of 0° and an antenna distance of 7 m for each band. With increasing elevation angle, these phase differences become smaller. Apart from the phase difference, we therefore also need the elevation angle in order to determine the azimuth direction. We cannot determine this elevation angle with two antennas, and can only estimate this based on the distance to the transmitter.



Loop Antennas at Right Angles to One Another

Here also, we are still looking only at the far field. When both antennas are at a relatively short distance from one another, a wave will arrive almost simultaneously. Ground waves and local interfering sources are linearly polarized. With small antennas, this can only result in a phase difference of 0° or 180°. I will elaborate on this in the “Near Field” section.

Radio amateurs normally do not dwell on it, but sky waves can be circularly (mostly elliptical) polarized. At 160 and 80 meters, this circular polarization can be highly constant and predictable. This leads to phase differences of about –90° or +90°. On the higher-frequency bands, polarization is normally linear and variable in direction. The phase difference wanders unpredictably over the entire 360°.

We can make use of this circular polarization. At 160 and 80 meters, there are now unexpected possibilities, as it is difficult on a residential location for those bands to have sufficient distance between both loop antennas. With the loop antennas in the same direction, the maximum phase difference on those bands is then quite small. In the case of local stations, this is further reduced by the high elevation angle (NVIS). The smaller the phase difference, the more difficult it is to separate the signals. Thanks to circular polarization, and with the loop antennas at right angles to one another, we can still separate local interfering sources and ground-wave signals from desired sky-wave signals.


Loop Antennas above One Another

It would be a fine thing if we could select the signals based on the elevation angle. Local interference arrives at a very low elevation angle. The same, however, also applies to the true DX signals. Many other signals enter under a steeper elevation angle. These can then be separated from local interference.

This is simple in free space. You place the two antennas at a distance above one another. Depending on the elevation angle, we measure a phase difference. In practice, the (loop) antennas are generally, with respect to the wavelength λ, placed on a low height (< ¼ λ) above the ground. The elevation angle cannot be easily determined with two antennas in this condition.


Figure 6 — Phase with low level antennas independent of height as a result of far field

ground reflection.


Figure 6 shows the contribution made by ground reflection. We find this picture in Chapter 3 of The ARRL Antenna Book and other Amateur Radio handbooks.2 The wave reflected by the ground appears to have been received or transmitted by a mirror antenna in the ground. Let us assume the ground reflects 100%. Then the mirror antenna receives the same signal strength, but at a distance BC, later. The real antenna receives the total of both signals, the direct and the reflected wave. The net phase is then precisely between the phases of the real and the mirror antenna. This is exactly the phase that we receive at a height of 0 meters (half

the distance A – B between the real and the mirror antenna).

The phase we measure is therefore independent of the height at which we place the antenna. In reality, the ground is not ideal and we will measure phase differences. But these will be of no use until we have placed one antenna at a height of ¼ λ or higher. On a residential location, neighbors may find as little as 10 meters to be too high. This option will therefore be mainly applicable for the higher-frequency bands, 30 meters and higher.



Last update: September 24, 2006