On the solvability and application of numerical methods to Hallen´s equation

Certain fundamental mathematical properties of Hallen´s equation with the approximate kernel are discussed. Three cases are considered: (1) The delta-function generator, (2) the case of plane-wave incidence, and (3) the case of the frill generator. For a particular moment-method procedure (Galerkin´s method with pulse functions), the consequences to the numerical solutions are examined. Generalizations to other numerical methods with subsectional basis functions are mentioned. Many of the results in this paper come from studying the simpler problem of the antenna of infinite length analytically and applying the understanding thus obtained to the case of the finite antenna.