On Equations for Bent Thin-Wire Antennas

The Pocklington equation in its standard form can be considered a Fredholm integral equation of the first kind with a singular kernel. Managing the singularity during numerical simulations presents certain practical difficulties. In this article, an alternative form of the Pocklington equation for a thin, bent, ideally conducting wire is derived in the form of a Fredholm integral equation of the second kind with a regular kernel, which is better suited for numerical treatment. The kernel of the integral equation does not depend on the wire radius, which enters only through diagonal elements of the interaction matrix. Both cases of loop and open-ended wires are considered with loop wire antennas allowing for a particularly simple formulation. Numerical simulations confirm the validity of the derived equations. Numerical results calculated for a specific circular loop antenna match available experimental data.