The evaluation of an asymptotic solution to the sommerfeld radiation problem using an efficient method for the calculation of sommerfeld integrals in the spectral domain
Bourgiotis S. Frangos P. Sautbekov S. Pshikov M.
1 June 2021MDPI AG
Electronics (Switzerland)
2021#10Issue 11
A recently developed high-frequency asymptotic solution for the famous “Sommerfeld radiation problem” is revisited. The solution is based on an analysis performed in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lossy ground. The paper is divided into two parts. We first demonstrate an efficient technique for the accurate numerical calculation of the well-known Sommerfeld integrals. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the surface wave. In the second part, we introduce the asymptotic solution and investigate its performance; we compare the solution with the accurate numerical evaluation for the received EM field and with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method. Simulations for various frequencies, distances, altitudes, and ground characteristics are illustrated and inferences for the applicability of the solution are made. Finally, special cases leading to analytical field expressions close as well as far from the interface are examined.
Asymptotic solution , Hertzian dipole , Numerical integration , Sommerfeld radiation problem , Surface wave
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School of Electrical and Computer Engineering, National Technical University of Athens, 9, Iroon Polytechniou Str., Zografou, Athens, 157 73, Greece
Department of Physics and Technology, Al-Farabi Kazakh National University, 71 Al-Farabi Ave., Almaty, 050040, Kazakhstan
School of Electrical and Computer Engineering
Department of Physics and Technology
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