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Evaluation of the Flux Linkage Between Equally Sized Circular Loops Placed on a Layered Soil

By Mauro Parise
Progress In Electromagnetics Research Letters, Vol. 89, 127-132, 2020


This paper presents an efficient method for evaluating the flux linkage between two circular loops located on the top surface of a plane multilayer soil. The method consists of a rigorous procedure, which leads to expressing the flux as a sum of products of Bessel functions. First, the integral representation for the mutual inductance is cast into a form where the integration range is continued to the negative real axis. Subsequently, the non-oscillating part of the integrand is replaced with a rational approximation, arising from using a well-known least squares-based fitting algorithm. Finally, analytical integration is performed by applying the theorem of residues. As a result of the proposed method, the flux linkage between the loops is expressed as a finite sum of products of Bessel functions. Since no assumptions are made in the mathematical derivation, the obtained explicit expression is valid regardless of the operating frequency. Numerical tests are performed to show the advantages of the proposed method with respect to standard numerical integration techniques. In particular, it is seen how the use of the derived series representation for the inductance with 50 terms permits to achieve the same accuracy as conventional Gauss-Kronrod numerical integration technique, with the advantage of reducing the computation time by at least 8 times.


Mauro Parise, "Evaluation of the Flux Linkage Between Equally Sized Circular Loops Placed on a Layered Soil," Progress In Electromagnetics Research Letters, Vol. 89, 127-132, 2020.


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