Method of moments analysis of active thin circular loop antennas with closed-form currents and validity

Abstract

This paper presents an analysis of electromagnetic radiation due to thin circular loop antennas of arbitrary radii a. The electric type of dyadic Green's function expanded in terms of spherical wave functions is employed in this study. The Galerkin's method of moments is applied in the derivation of current distributions along the thin circular loop wires. With an advantage over others, the present analysis is quite general, compact and straightforward; most importantly, the current distributions are obtained analytically and expressed in a closed and simple form. Resulted from these currents, radiated fields in both near- and far-zones and both inside and outside the sphere of radius a are expressed in terms of the spherical vector wave functions. Also discussed in this paper is the validity of definitions of far-zone and electrically small size. The maximum radius of an electrically small circular loop antennas is found from a quantitative error analysis of both loop currents and the far-zone fields.