Homogenization of multi-turn coil with elliptic cross-section using complex permeability
ISSN: 0332-1649
Article publication date: 10 May 2019
Issue publication date: 3 June 2019
Abstract
Purpose
The tensor complex permeability of a multi-turn coil with elliptic cross-section is analytically expressed. In field analysis, a multi-turn coil can be modeled by the uniform material that has the present tensor complex permeability. It is shown that the frequency characteristic of the present tensor complex permeability is in good agreement with that evaluated by finite element method applied to a unit cell of the multi-turn coil region.
Design/methodology/approach
The authors introduce a new method to evaluate the complex permeability of a multi-turn rectangular coil. To obtain the complex permeability of a rectangular coil in a closed form, it is approximated as an elliptic coil. Because the rectangular coil has different complex permeabilities in the vertical and horizontal directions, the complex permeability have to be defined in a tensor form. It suffices to discretize the coil region into rather coarse finite elements without considering the skin depth in contrast to the conventional finite element method.
Findings
The proposed method is shown to give the impedance of multi-turn coils which is in good agreement with results obtained by the conventional finite element (FE) analysis. By extending the proposed approach, the authors can easily perform 3D FE analysis without difficulty in discretization of the coil region with fairly fine finite elements. Moreover, they found that the approximation of rectangular coils as the elliptic coils is valid for analysis of quasi-static fields using this homogenization method.
Originality/value
The novelty of this study is in the approximation of the rectangular coils with elliptic coils, and the complex permeability for them is formulated here in a closed form. The proposed formula includes that for the round coils. Using the present method, the authors analyze the rectangular coils without fine discretization.
Keywords
Acknowledgements
This work was supported in part by JSPS KAKENHI Grant Number 18J10778.
Citation
Fujita, S. and Igarashi, H. (2019), "Homogenization of multi-turn coil with elliptic cross-section using complex permeability", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 3, pp. 999-1008. https://doi.org/10.1108/COMPEL-09-2018-0356
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited