Wideband Approximate Solutions for the Sommerfeld Integrals Arising in the Wire over Earth Problem

Abstract

Approximate solutions for the spatial Fourier transform (in the axial direction) of the Sommerfeld type integrals for the axial and vertical electric fields from a current on a thin wire of infinite length above lossy earth are derived. These solutions are valid over a wide band of frequencies (1 Hz - 1 GHz) and for distances from field points to the wire which are essentially unrestricted, as well as for a wide range of values of the Fourier transform variable, γ. Calculations based on these solutions are shown to be consistent with numerical integrations of the exact integrals. The method used in this paper can be easily used to find solutions for other field components.