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Ground-Reflection Factors

The radiation patterns of Fig. 13 are for free space and apply in practice only if all reflections are neglected. When antennas are near the earth, as they often are, the effect of reflections from the earth must be considered. To obtain an approximate idea of the actual radiation pattern, several assumptions are made: first, that vertically polarized waves are reflected from the earth without a change in phase; second, that horizontally polarized waves are reflected from the earth with a change in phase of 180°; and, third, that no energy is lost during reflection. If these assumptions are made, it is then possible to determine theoretical ground-reflection factors, which when applied to the free-space radiation pattern give the (theoretical) antenna radiation pattern in the presence of the earth. Note in particular that in this section plots of ground-reflection factors and not antenna radiation patterns are being developed.

Because the reflected wave is assumed to be shifted in phase either 0° or 180° at the surface of the earth, it is possible to represent a reflected wave as coming from an image antenna as in Fig. 14. Halfwave antennas are employed as illustrations because they are relatively simple. The method can be extended to longer antennas and to antennas that are other than vertical or horizontal.6,21

In Fig. 15 are shown plots of ground-reflection factors for various conditions. As an illustration of how these are determined, typical calculations will be made for a horizontal half-wave antenna λ/4 (or 90°) above the surface of the earth and at an angle of 30° with the horizontal. The relative radiation at some distant point, where the rays

Figure 14. Because a horizontally polarized wave is assumed to be reflected with a 180° shift in phase and a vertically polarized wave is assumed to be reflected with 0° shift in phase, the action of the reflected wave for horizontal and vertical antennas can be represented as if an image of the antenna, or an ''image antenna," were an equal distance below the surface of the earth. The polarity of an image antenna is the same as would be induced in a wire at that point. To reach a distant point, the reflected ray, assumed to come from the image antenna, must travel a distance 2H sin θ farther than the direct ray. Half-wave antennas are shown because they are common.

are assumed to arrive parallel, will be computed. The ground-reflected ray travels (Fig. 14) 2H sin θ = 2 x 90° sin 30° = 90° farther than the direct ray; also, there is an assumed 180° shift in phase at the instant of reflection. (An alternate viewpoint is that the signal from the image antenna of Fig. 14 is 180° out of phase.) Thus, at the distant point, at 30° with the horizontal, the ground-reflected ray is 90° + 180° = 270° behind the direct ray which is equivalent to leading by 90°. Assuming no loss at reflection and that the magnitude of each ray is 1.0, the magnitude of the signal is the vector sum of these two rays or 1.414. This is plotted at 30° in the lowest diagram of Fig. 15(a). Other factors are determined in a similar manner. For the lowest diagram of Fig. 15(b), at 30° the ground-reflected ray will

Figure 15. Ground-reflection factors for the vertical and horizontal half-wave antennas of Fig. 14. The wavelength notations on each figure are the height of the antenna above the surface of the earth. These are not radiation patterns.

travel 2H sin θ = 90° farther, and, since there is an assumed shift of 0° at the surface, the reflected ray will arrive at the distant point 90° behind the direct ray. Assuming no loss at reflection, the resultant field will be the sum of two vectors of magnitude 1.0 and 90° out of phase, and the reflection factor will be 1.414 as before.

Equations can be written which will give the reflection factors. For the diagrams of Fig. 15 (a) the equation is

which applies to horizontal half-wave antennas of any height H in degrees above the earth. For the diagrams of Fig. 15(b) the equation is

which applies to vertical half-wave antennas with centers at any height H above the surface of the earth. Plots of reflection factors for many heights are available.37



Last Update: 2011-05-30