Synthesis of planar continuous current sources with arbitrary shapes for generation of desired radiation patterns by methods of moments and least squares

Abstract

Synthesis of planar continuous current sources (planar CCSs) with arbitrary shapes is developed for the generation of specified radiation patterns by method of moments (MoM) and method of least squares (MLS). First, an integral equation is expressed, which relates planar CCS current distribution to its radiation pattern. Second, the planar CCS region is divided into several segments and its current distribution is expressed in terms of the pulse expansion functions to discretise the integral equation. Third, the resulting discretised integral equation is converted to a linear equations system by MoM and MLS. Fourth, the resulting linear equations system is solved to determine unknown coefficients of planar CCS current distribution. To evaluate and compare the efficacy of proposed methods, two parameters of synthesis error (SE) and superdirectivity ratio (SR) are used. It is shown that the number of segments should be properly determined to achieve specified SE and SR. If resulting radiation pattern does not meet design goal, a perturbation procedure is applied to current distribution in order to improve the characteristics of radiation patterns of the planar CCS, such as side-lobe level and pattern ripple. Several examples are given to validate the efficacy of the proposed methods.