Field and inductance calculations for coaxial circular coils with magnetic cores of finite length and constant permeability

Abstract

A circular coil equipped with magnetic core of finite length and constant permeability is difficult to analyse by traditional analytical methods in consequence of the complicated boundary conditions. The difficulties can be overcome by using the truncated region eigenfunction expansion method, and with the aid of a special source function K ( z ) introduced in the work, this method can be simplified remarkably and concise expressions of the inductance of coils with magnetic cores are obtained. In addition, the calculations can be extended readily to a pair of coaxial coils with magnetic cores of finite length and different permeability. The eigenvalues and inversions of matrices are implemented numerically in the solving process, while most of calculations are accomplished by analytic integrations and matrix algebra, by which the deduced expressions are quite suitable for numerical evaluations. The proposed method is verified by the numerical results compared with those of finite-element method simulations, from which it is confirmed that the proposed method is much faster and more memory efficient.