17.3.3 Radiation from arrays

Array antennas consist of a number of discrete elements which are usually small in size. Typical elements are horns, dipoles, and microchip patches. The discrete sources radiate individually but the pattern of the array is largely determined by the relative amplitude and phase of the excitation currents on each element and the geome­tric spacing apart of the elements. The total radiation pattern is the multiplication of the pattern of an individual element and the pattern of the array assuming point sources, called the array factor. Array theory is largely concerned with synthesizing an array factor to form a specified pattern. In communications most arrays are planar arrays with the elements being spaced over a plane, but the principles can be understood by considering an array of two elements with equal amplitudes, Figure 17.7(a). This has an array factor given by Equa­tion 17.12, where ψ is given by Equation 17.13.

The pattern for small spacingswill he almost omnidirectional and as the spacing is increased the pattern develops a maxima perpen­dicular to the axis of the array. At a spacing of half a wavelength, a null appears along the array axis. Figure I7.7(b). This is called a broadside array. If a phase difference of 180 degrees exists between the two elements then the pattern shown in Figure I7.7(c) results. Now the main beam is along the direction of the array and the array is called the end-fire array. This illustrates one of the prime advant­ages of the array, namely by changing the electrical phase it is possible to make the peak beam direction occur in any angular direction. Increasing the spacing above half a wavelength results in the appearance of additional radiation lobes which are generally undesirable. Consequently the ideal arrays spacing is half wave­length, though if waveguides or horns are used this is not usually possible because the basic element is greater than half a wavelength in size. Changing the relative amplitudes, phases and spacings can produce a wide variety of patterns so that it is possible to synthesise almost any specified radiation pattern. The array factor for an N element linear array of equal amplitude is given by Equation 17.14.

This is similar to the pattern of a line source aperture, Equation 17.5, and it is possible to synthesise an aperture with a planar array. There is a significant benefit to this approach. The aperture fields are determined by the waveguide horn fields which are constrained by boundary conditions and are usually monotonic functions. This constraint does not exist with the array so that a much larger range of radiation patterns can be produced. Optimum patterns with most of the energy radiated into the main beam and very low sidelobes can be designed.

17.4 Specific antenna types

17.4.1 Prime focus symmetric reflector antennas

17.4.1.1 Parabolic reflectors

The axi-symmetric parabolic reflector with a feed at the focus of the paraboloid is the simplest type of reflector antenna. The geometry is shown in Figure 17.8. The paraboloid has the property that energy from the feed at F goes to the point P on the surface where it is reflected parallel to the axis to arrive at a point A on the imaginary aperture plane. The equation describing the surface is given by Equation 17.15, where F is the focal length.

At the edge of the reflector, of diameter D, Equation 17.16 applies.

The depth of the paraboloid is usually specified by its F/D ratio. Common sizes are between F/D = 0.25 ( 6₍₁ = 90 degrees) to F/D = 0.4.