Second-Order Formulation for the Quasi-Static Field From a Horizontal Electric Dipole on a Lossy Half-Space

Abstract

Abstract-In a recent study, we proposed improved quasi-static approximations for the electromagnetic field components excited by a vertical electric dipole lying on the surface of a flat and homogeneous lossy half-space. The present paper introduces an analytical approach to derive analogous formulas for the case of the horizontal electric dipole. The approach is based on the expansion of the integral representations for the fields into power series of the ratio between the wavenumbers in free-space and in the conducting medium. Later, only the terms up to the second-order are retained, and term-by-term analytical integration is performed. Numerical results demonstrate that using the derived second-order approximations for the fields in place of the zeroth-order ones allows to reduce the maximum relative error in the calculation of the fields from about 23% down to less than 7%.