Inductance Calculations for Circular Coils With Rectangular Cross Section and Parallel Axes Using Inverse Mellin Transform and Generalized Hypergeometric Functions

Abstract

The inductance integrals of air-core circular coils with rectangular cross section and parallel axes are difficult to tackle with analytical method due to the inclusion of Struve functions. Using the inverse Mellin transform, these Bessel-Struve integrals will be continued analytically to the complex plane, and then by virtue of contour deformation and residue theorem, they can be expanded to the series containing the generalized hypergeometric functions which are easy to execute in common mathematical software packages. The series solutions are preferable in case the difficulties arise in the evaluations of Bessel-Struve integrals, though they do not cover the whole region of coil geometric parameters. In addition, the obtained series were compared numerically with the corresponding integrals, complete consistency was shown clearly. By means of the proposed method, the computation efficiency can be improved by several orders of magnitude compared to that of the corresponding integral methods.