Fourier Current Distributions

Author: Edmund A. Laport

By the Fourier analysis of a specified radiation pattern, it is possible to find a combination of pairs of radiators with current distributions in accordance with the Fourier coefficients which will produce that pattern, as discussed in Sec. 2.18. When applied to broadside arrays of dipoles with half-wavelength spacings the analysis is made very simply by the well-known methods of alternating-current harmonic analysis, except that in this case the harmonic term is the spherical harmonic, which is the pattern for a symmetrical pair of radiators. Therefore

Figure 3.64 shows the manner in which the Fourier coefficients are applied to the cophased currents in a symmetrical series of radiator pairs.

The special advantage of Fourier distributions is that a distribution can be found which will produce a pattern of any specified symmetrical shape, the number of pairs used determining the degree of realization of the specified pattern.

FIG. 3.64. Fourier current distributions for broadside patterns.

The above equations apply only to the case where f(β) is an even function, though the method may be applied to odd functions or to asymmetric functions that are combinations of both types. One specified characteristic of the desired pattern may be the suppression of secondary lobes over certain ranges of angles and a specified shape of pattern within those angles where radiation is wanted.