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Efficient computation of the surface fields of a horizontal magnetic dipole located at the air‐ground interface
Author(s) -
Parise M.
Publication year - 2015
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2120
Subject(s) - computation , series (stratigraphy) , boundary value problem , surface (topology) , boundary (topology) , numerical integration , benchmark (surveying) , antenna (radio) , plane (geometry) , magnetic dipole , interface (matter) , computer science , field (mathematics) , ground plane , dipole , mathematical analysis , geometry , mathematics , physics , algorithm , telecommunications , geology , paleontology , geodesy , bubble , quantum mechanics , maximum bubble pressure method , parallel computing , pure mathematics
Summary In this paper, the classic problem of determining the fields of a vertically oriented current‐carrying small circular‐loop antenna located near a plane air–earth boundary is revisited. It is well known that the Sommerfeld integrals describing the field components generated by the loop source cannot be exactly evaluated and that their numerical integration is made difficult by the presence of highly oscillatory terms in the integrands. Here, for both source and observation points on the interface, a rigorous method is developed that allows analytical integration of the Sommerfeld integrals, providing fast‐convergent series representations for the surface fields. The obtained formulas permit to overcome all the drawbacks of the previously published approximate solutions to this problem, and to avoid the necessity of using purely numerical approaches when high computational accuracy is required. At the same time, the proposed series representations constitute an analytical benchmark for numerical procedures employed to solve electromagnetic boundary value problems, with applications in antenna design and close‐to‐the‐surface communication. Copyright © 2015 John Wiley & Sons, Ltd.