Radiation of a Vertical Dipole over Flat and Lossy Ground using the Spectral Domain Approach: Comparison of Stationary Phase Method Analytical Solution with Numerical Integration Results

Abstract

In this paper we re-consider the problem of radiation from a vertical short (Hertzian) dipole above flat lossy ground, which represents the well-known in the literature ‘Sommerfeld radiation problem’. Particularly, we expand on the problem’s solution in the spectral domain, which ends up into simple one dimensional (1-D) integral expressions for the received EM field and represent the exact EM solution to the aforementioned problem. The advantage of the derived expressions is based on the fact that they can be analytically evaluated through the use of the Stationary Phase Method (SPM), which however is valid in the high frequency regime. To our knowledge, the literature lacks specifying the exact frequency range over which the SPM method is applicable. Hence, in this paper numerical integration on the above mentioned integral expressions is applied and the results are compared with those obtained through the SPM. These comparisons are then used as the basis of determining the frequency limits of applicability of the SPM solution. In fact it is shown that due to the specific peculiarities of the integrated expressions, which possess certain singularities, it is often preferable to use the SPM method as the best estimate for the received signal level, especially for most practical frequencies of interest in the area of wireless telecommunications. Additional practical implications that these findings suggest, as well as further research to be triggered, as a result of the overall progress that has been made by our research group so far on the specific subject, are provided as well.

DOI: http://dx.doi.org/10.5755/j01.eee.21.3.10268