A Rigorous Explicit Expression for the Mutual Inductance of Two Co-Axial Thin-Wire Coil Antennas Placed above a Layered Ground

Mauro Parise (), Giulio Antonini and Luisa Di Paola
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Mauro Parise: Department of Engineering, University Campus Bio-Medico of Rome, Via Alvaro del Portillo 21, 00128 Rome, Italy
Giulio Antonini: Department of Industrial and Information Engineering and Economy, University of L’Aquila, Via G. Gronchi 18, 67100 L’Aquila, Italy
Luisa Di Paola: Department of Science and Technology for Sustainable Development and One Health, University Campus Bio-Medico of Rome, Via Alvaro del Portillo 21, 00128 Rome, Italy

Energies, 2023, vol. 16, issue 22, 1-17

Abstract: This paper presents a quasi-analytical method that allows the derivation of a rigorous series-form representation for the mutual inductance of two co-axial coil antennas located above an arbitrarily layered earth structure. Starting from Biot–Savart law, which gives the integral representation for the primary vector potential generated by the source coil, the potential reflected by the layered ground is derived, and the resulting total vector potential is then integrated along the external circumference of the receiving coil to give the mutual inductance of the two antennas. The obtained representation for the flux is then evaluated analytically through the usage of the Gegenbauer addition theorem once an accurate, rational approximation is used in place of the factor of the integrand that exhibits branch cuts. It is shown how the resulting explicit solution exhibits the same degree of accuracy as purely numerical approaches like the finite-difference time-domain (FDTD) method and conventional numerical quadrature schemes, while it is less time-demanding than the latter methods.

Keywords: coil antennas; flux linkage; wireless power transfer; inductive coupling (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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