Antenna radiation patterns

Information in antenna data sheets usually contains two radiation pat- terns: vertical and horizontal. For a microwave ‘dish’ antenna the vertical and horizontal radiation patterns are usually nearly identical: the radi- ation pattern has circular symmetry.

The radiation pattern does not consist of a single ‘beam’. There will be additional smaller beams known as side lobes. These are particularly noticeable with antennas that transmit with a very narrow beam, such as those used for microwave point-to-point links. These side lobes are gen- erally problematic in radio communications because they represent the fact that not all of the energy travels in the direction intended (and also, that antennas can receive signals from directions other than that in which they are pointed). This is a highly significant factor contributing to the level of interference in a radio network. The ratio of the gain in the main beam (what we have simply been calling the antenna gain) and the gain in the most significant side lobe is a significant antenna parameter in allowing the planner to assess how much interference will be caused in a network. 3.6.1 The radiation pattern of an aperture antenna

In chapter 2 we examined the vertical radiation pattern of an omni- directional antenna. This pattern was predicted by determining the phase difference between contributions from the various half-wave dipoles that

made up the antenna. Although there are no elements as such with an aperture antenna, Huygens’ principle allows us to adopt a similar approach when considering the radiation pattern of these antennas. We will attempt to predict the ‘far-field’ radiation pattern. This is the radiation pattern that would be measured at a great distance from the antenna (in theory, at an infinite distance). One assumption that is a great help in predicting this radiation pattern is that of the equivalence between a parabolic dish illuminated by a source at its focus and an aperture illu- minated from behind by a uniform plane wave. This equivalence is illustrated in figure 3.13. The important feature of the paraboloid shape of the reflecting dish is that it equalises the path lengths from the focus to points on a plane in front of the dish perpendicular to the principal direction. Because the path lengths are equal, the wave travelling for- wards immediately in front of the dish is similar to a uniform plane wave. This is the same as the wave immediately in front of the aperture that is illuminated from behind by a ‘genuine’ uniform plane wave. In both cases the wave will disperse as it progresses.

If we consider a side view of the aperture illuminated from behind, it gives an idea of the way in which side lobes will be produced. If we

Figure 3.13 The equivalence of an aperture illuminated from behind by a plane wave and radiation from a parabolic dish antenna.

divide the plane wave into wavelets in the plane of the aperture, we can approach the problem in a similar manner to that used to predict the radiation pattern of an array of half-wave dipoles. In the principal direction, all the contributions from the wavelets will add in phase. However, there will be a null in a direction such that the variation in path length over the face of the aperture equals one wavelength. In this dir- ection, each wavelet will have a corresponding wavelet for which the path-length difference is half a wavelength and they will therefore cancel out. This will occur when the angle is such that

sin h¼ k=d: ð3:12Þ

As the angle increases we come out of the null. There is a second null when

sin h¼ 2k=d ð3:13Þ

(in general there is a null where sin h¼ nk=d, where n is any integer). Between these two nulls, there is a peak in signal strength, the first side lobe. In the direction of this peak, the contributions from each wavelet do not add in phase and therefore the peak will not be as strong as that in the principal direction, but neither do the contributions cancel out. Figure 3.14 shows the radiation pattern for an evenly illuminated aper- ture where the aperture width is approximately four wavelengths.

Two side lobes on either side of the main beam are clearly visible. The peak of the first side lobe shows that it would produce a field strength of approximately 21% of that produced in the principal direction. That corresponds to a power density 14 dB less than that in the principal direction. The amount of energy in the side lobes can be reduced by tapering the illumination of the aperture towards its edge. In a practical dish antenna, the feeder at the focus will illuminate the aperture and designing the optimum illumination of the dish is a necessary activity if

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Figure 3.14 The radiation pattern of an evenly illuminated aperture antenna with diameter approximately equal to four wavelengths.

the antenna itself is to have good performance. Figure 3.15 shows the radiation pattern for a similar antenna to that of figure 3.14 but with an aperture illuminated such that the contributions from wavelets near the edge of the aperture will be less than those from wavelets near the centre. Notice that the side lobes are much smaller than when the aperture illumination is tapered. The two radiation patterns are drawn to the same scale and reveal that the gain in the principal direction has been reduced (by about 0.8 dB) by tapering the illumination of the aperture.