A closed — Form analytical solution to the radiation problem from a short dipole antenna above flat ground using spectral domain approach

Abstract

In this paper we consider the problem of radiation from a vertical short (Hertzian) dipole above flat ground with losses, which represents the well -known in the literature 'Sommerfeld radiation problem'. We end -up with a closedform analytical solution to the above problem for the received electric and magnetic field vectors above the ground in the far field area. The method of solution is formulated in the spectral domain, and by inverse three -dimensional Fourier transformation and subsequent application of the Stationary Phase Method (SPM) the final solutions in the physical space are derived. To our knowledge, the above closed -form solutions are novel in the literature for the Sommerfeld radiation problem.

Sommerfeld half-space problem revisited: Short-wave asymptotic solutions

“…In the vicinity of the observation angle θ 1 = θ t the formula is unjust, it should be substituted by the formula (28), which follows from (25) and is expressed by E LOS with a constant unit vector e θ (θ t ) in (29).…”

“…Transmitted Wave It is obvious that the intensity of the lateral wave at the observation point B (see Fig. 3) is greater than at the observation point A, as can be seen from ( 26) and ( 27) or (29).…”

“…This work is a continuation of a series of papers [28,29,30,31,32] devoted to a novel method for solving the classical Sommerfeld problem of a vertical electric dipole radiating in an imperfectly conducting half-space. Where occurs the quantitative estimation carried out by various numerical methods of the short-wave asymptotic solutions, obtained by the steepest descent or saddle point method (SPM) using an etalon integral concerning, in the main, the reflected and surface waves.…”

The Radiation Problem from a Vertical Short Dipole Antenna above Flat and Lossy Ground: Novel Formulation in the Spectral Domain with Closed – Form Analytical Solution in the High Frequency Regime

“…Here the relative complex permittivity of the ground (medium 2) is ε΄ r =ε΄/ε 0 =ε r +ix , where x=σ/ωε 0 =18×10 9 σ/f , σ being the ground conductivity, f the frequency of radiation and ε 0 =8.854 ×10 -12 F/m is the absolute permittivity in vacuum or air. Then the wavenumbers of propagation of EM waves in air and lossy ground, respectively, are given by the following equations: EXPRESSIONS FOR THE RECEIVED ELECTROMAGNETIC (EM) FIELD OBTAINED THROUGH THE FORMULATION IN THE SPECTRAL DOMAIN Following [5], [7], [8] and [9], we find the following expressions for the received EM fields [in the higher halfspace, x>0, i.e. Line of Sight (LOS) field and field scattered from the ground, for receiver positions above it], as given below :…”