Synthesis of Wire Antennas Using the Multipole Expansion Method

Abstract

A rigorous mathematical solution to the problem of synthesizing wire antennas using the multipole expansion method (MEM) is presented. The input current and required size of the antenna are estimated using the knowledge of the required field pattern. This solution is based on three steps. First, obtaining the expansion’s weighting coefficients that carry both the signature of the current and size of the antenna. In essence, the analysis of the direct modeling needs to be addressed first in order to define these coefficients. Second, extracting the coefficients from the required field pattern using the natural orthogonality property of the spherical harmonic functions. Finally, performing a numerical search for the argument of the spherical Bessel functions to satisfy the ratio between two successive moments. Once the size of the antenna is found, a recursive expression is used to obtain the input current. For the current distributions assumed herein, the odd order coefficients of the MEM are shown to be the only necessary coefficients to construct the radiation far-field. Also, it is found that the estimated model parameters are in excellent agreement with the analytical ones.