Full‐wave analytical explicit expressions for the surface fields of an electrically large horizontal circular loop antenna placed on a layered ground

Abstract

This study presents full-wave analytical explicit expressions for the time-harmonic surface fields of a large horizontal circular loop antenna located on a multilayer Earth. The expressions are derived by applying the following procedure. First, the complete integral representations for the EM field components are decomposed into three parts, that is, the residue contributions from the poles of the integrands and the two branch-cut integrals associated with the wavenumbers in free-space and in the bottom layer of the stratified medium. Next, the square-root term that generates the branch cut is extracted from the integrand of the generic branch-cut integral. Finally, the square-root algorithm-based partial fraction expansion is applied to each extracted square-root term, so as to convert the branch-cut integrals into closed-contour integrals around a set of pole singularities, which can be straightforwardly evaluated. As a result of the developed procedure, the fields are expressed as convergent sums of special functions. Numerical results are presented to validate the proposed formulation. In addition to being accurate, the derived formulas offer advantages in terms of computation time over standard numerical integration techniques.