An analytical synthesis method for linear, ring and planar antenna arrays based on ultra-spherical polynomial

Abstract

An analytical method is proposed to synthesize arbitrary patterns for linear, ring and planar antenna arrays. It is well-known that the radiation pattern of an antenna array can be described by the ultra-spherical polynomials. Some ultra-spherical functions such as the Tschebyscheff and Legendre polynomials have been introduced in the literature. Using the orthogonality property of ultra-spherical functions, a closed form expression can be obtained for any arbitrary array factor. The array’s excitation coefficients are then determined using a matrix-based system of equations. This system is solved using the Moore-Penrose pseudo-inverse principle, and the excitations of the array elements are calculated. The proposed method is demonstrated to be capable of designing linear, circular, and planar arrays. To validate the performance of the introduced method, several practical arrays are considered. The obtained results validate the benefits of the presented method in synthesizing radiation patterns for various types of linear and planar arrays.