An Exact Series Solution of Fields Radiated From a Magnetic Frill Source Using Lommel Expansions

This paper presents an exact series solution for fields radiated from a magnetic-frill source that is valid everywhere above the plane of the magnetic-frill. The derivation of the field expressions is based on Lommel expansions and direct integration of the vector potential. The field expressions presented in this study were in excellent agreement with the corresponding fields available in the literature. The known expressions for fields radiated from the magnetic-frill on its axis and those radiated from magnetic current rings are obtained as special cases from the field expressions presented in this study. These expressions can be used to accurately compute the tangential component of the incident electric field on the surface of an antenna needed in the MoM solution for a thick as well as a thin antenna input impedance computation, in addition to the analysis of the characteristics of coaxial wave-guides, cables, antennas mounted on ground planes, and in the analysis of electromagnetic compatibility problems and assistance in estimating human exposure to radiation from the apertures of coaxial cables.