Maximum Directivity Index of a Linear Point Array

Abstract

The maximum directivity index of a symmetrical, linear point array has been calculated as a function of the number and spacing of the elements in the array. The excitation required to produce a maximum directivity index is not uniform, except for integral-half-wavelength element spacings, and in general the minor lobes of the directional response patterns produced are not of equal, nor of small, amplitude. For element spacings exceeding a half-wavelength, a conventional type of pattern and of excitation is found to produce the maximum directivity index. On the other hand, as the element spacing is reduced below a half-wavelength, the directivity patterns corresponding to the maximum directivity index become super-directive, and the directivity index may be improved relative to the value obtainable with uniform excitation. However, this improvement is obtained only at the expense of requiring large, reversed-phase excitation. Numerical results are presented for 3-, 5-, and 7-element arrays.