An Efficient Algorithm To Calculate the Current Distribution Along a Perfectly Conducting Circular Loop Antenna

Abstract

A new method and formulation are presented to calculate the time-dependent current along a circular loop antenna which is either voltage driven or excited by an incident field. One-dimensional integral equations for the total current are derived from an integral representation for the magnetic vector potential in the time-Laplace domain. In analogy with the case of a straight thin wire, these equations are referred to as Pocklington's and Hallén's equation, respectively. In contrast with open-ended wires, where the unknown current must vanish at the end points, periodic boundary conditions are required. After an angular discretization of Hallén's equation, this periodicity can be used very efficiently to calculate the current with a Discrete Fourier Transformation. The spectral properties of the current are investigated. Special attention is devoted to the location of natural frequencies (poles of the complex current) in the complex plane, its dependence on the discretization and the consequences for the accuracy of the time-dependent current. Several alternatives are proposed for dealing with a zero natural frequency. Results of the calculated current and the induced electric field are given for the case of a Gaussian voltage pulse and an incident plane wave.