Analysis of an iterative approach to determine the current on the straight infinite wire above ground

Abstract

An iterative approach which was recently applied to approximate the reflection and scattering coefficients of transmission line ports is analyzed. The iterative solution for the current on an infinite wire above ground is compared to the exact solution. The example is chosen since it is one of the few problems where an exact solution exists. The wire is excited by a lumped voltage source or a plane wave. The convergence of the iterative approach is shown. It can be concluded that the zeroth iteration, which is the classical transmission line solution, coincides with the general transverse electromagnetic mode. Furthermore, it is shown that the first iteration is a very good approximation of the radiation and leaky modes, that occur in the close neighborhood around the lumped source.