Synthesis of wideband linear array antennas with Taylor distributed element positions

Abstract

In this work, a technique for synthesizing wideband linear array antennas with equally excited elements positioned according to a Taylor distribution function g(p) is developed. The discrete element array is considered to be a radiating aperture; hence, an equivalence for the far field pattern |S(V)| of an array and that of a radiating aperture is derived with the use of Fourier transform theory. In order to investigate the limitations on the sidelobe levels and the directivity of the array, two regions of the average field pattern are considered. Region 1 is defined as the region of equal sidelobe levels in the average field pattern and Region 2 as the region of decaying sidelobe levels in the average field pattern. Expressions for the probability distribution function of |S(V)| in Regions 1 and 2 are derived. An expression for a bounding value of the directivity of the array is derived. The resulting expressions are functions of the distribution function g(p), the number of elements in the array and the length of the array. The method of spacing the elements in the array is based on an approximation of the area under the g(p) selected. Equal area increments are computed and one element per area increment is used in order to establish an aperture distribution of electric field. Numerical values of the probability distribution functions, the bounding values of directivity, and the peak sidelobe levels are computed with the aid of an IMB 7094 computer for design sidelobe levels of 15 and 25 decibels.