Calculation of Mutual Inductance between Circular and Arbitrarily Shaped Filaments via Segmentation Method

TL;DR

This paper introduces two analytical formulas and a segmentation-based method for calculating mutual inductance between a circular filament and arbitrarily shaped filaments, validated through numerical examples and software comparisons.

Contribution

It presents a novel segmentation method using derived formulas to compute mutual inductance with arbitrary filament shapes, expanding practical calculation capabilities.

Findings

Formulas accurately compute mutual inductance for various shapes.

Method validated against FastHenry software and literature examples.

Results show high agreement with reference data.

Abstract

In this article, two analytical formulas for the calculation of mutual inductance between a circular filament and line segment arbitrarily positioning in the space are derived by using Mutual Inductance Method (MIM) and Babic's Method (BM), respectively. Using the fact that any curve can be interpolated by a set of line segments, a method for calculation of mutual inductance between a circular filament and filament having an arbitrary shape in the space is proposed based on the derived analytical formulas. The derived two formulas and the proposed method (Segmentation Method) were numerically validated by using FastHenry software and reference examples from the literature. In particular, the proposed method was successfully applied to the calculation of mutual inductance between the circular filament and the following special curves such as circle, circular arc, elliptic arc, ellipse, spiral, helices and conical helices. All results of the calculation are in good agreement with the reference examples.