Exact Fields Expressions for a Circular Loop Antenna above a Perfect Electric Conducting Ground Plane

Abstract

This paper presents exact electromagnetic fields expressions of a circular loop antenna (CLA) with an arbitrary current and dimensions placed over a perfect electric conducting ground plane. Fields derivations are based on the spherical Bessel functions (SBFs) and associated Legendre polynomials (ALPs) expansion. These expressions are valid everywhere above the ground plane except on the loop. The field expressions presented in this paper reduces to the known far-field expressions of the loop antenna over ground plane when large argument approximations for SBFs are applied. Moreover, approximate expressions in the near-fields region are derived from the exact fields. Fields of the uniform CLA over ground plane and that on the axis of the loop are obtained as special cases. The results from the simulation software AN-SOF are in excellent agreement with the results obtained using the field expressions presented in this paper which reveals the correctness of these expressions.