A method for the calculation of properties of wire antennas

The properties of a symmetrically-fed dipole antenna are examined by methods of an integral equation and a modified transmission line approach. The kernel of the integral equation is explored, including a modification due to a hypothetical filamentary source along the antenna axis. An iterative form is developed for the antenna current, and transmission line equations are defined which are equivalent at the first iteration. A second order solution for the dipole antenna is formulated, along with an expression for the Hertzian vector and the input impedance. The delta-function feed and the approximate kernel are found to be mathematically imcompatible. Further conclusions are drawn on the form of the quasi-static current near the origin, an explicit expression for the line reactance, and the use of a circuit equivalence to determine the amplitude for the iterative process.