Semi-Analytical Approach for Finite-Element Analysis of Multi-Turn Coil Considering Skin and Proximity Effects

Native application of finite-element method (FEM) to the analysis of skin and proximity effects in multi-turn coils results in large equation systems, whose solution needs long computational time. This paper proposes a semi-analytical approach to overcome this problem. For the analysis of the proximity effect, the complex permeability of a round conducting wire immersed in uniform time-harmonic magnetic fields is represented in a closed form. Then, the homogenized complex permeability over the cross section of the multi-turn coil is analytically evaluated using the Ollendorff formula. The magnetoquasistatic problem is thus replaced by the magnetostatic one, in which the multi-turn coil is treated as a uniform material with the homogenized complex permeability. The skin effect is taken into consideration by introducing the corresponding impedance in the circuit equation. The proposed method is shown to give the impedance of multi-turn coils, which is in good agreement with that obtained by the conventional FEM as well as experiments.