ON THE SOLUTION OF INVERSE EQUIVALENT SURFACE-SOURCE PROBLEMS

Abstract

Various formulations of the inverse equivalent surface-source problem and corresponding solution approaches are discussed and investigated. Starting from the radiation integrals of electric and magnetic surface current densities, the probe-corrected inverse equivalent source formulation is set up together with different forms of side constraints such as the zero-field or Love condition. The linear systems of equations resulting from the discretized forms of these equations are solved by the normal residual (NR) and normal error (NE) systems of equations. As expected and as demonstrated by the solution of a variety of inverse equivalent surface-source problems, related to synthetic as well as realistic antenna near-field measurement data, it is found that the iterative solution of the NE equations allows for a better control of the solution error and leads in general to a slightly faster convergence. Moreover, the results show that the incorporation of the zero-field condition into the solution process is in general not beneficial, which is also supported by the structure of the NE systems of equations. If desired, Love surface current densities, or just fields in general, can more easily be computed in a post-processing step. The accuracy of the obtained near-fields and far-fields depends more on the stopping criterion of the inverse source solver than on the particular choice of the equivalent surface-source representation, where the zero-field condition may influence the stopping criterion in a rather unpredictable way.