Accurate Expressions of Mutual Inductance and Their Calculation of Archimedean Spiral Coils

Abstract

Considering the helicity of Archimedean spiral coils, this paper proposes accurate expressions of mutual inductance and their numerical calculation methods, which can be applied in the wireless power transmission field, etc. Accurate expressions of mutual inductance are deduced respectively for two coils that are coaxial, laterally misaligned, or non-parallel, and numerical calculations are performed using Gaussian integration as well. In the case of coaxial coils, the calculation results are verified by the 3D finite element method (3D FEM) and compared with the results gained by the traditional method that approximates two spiral coils to two clusters of series-connected circular coils ignoring helicity. The comparison of the three methods shows that results achieved by the proposed expression are close to that of 3D FEM, while there is increasing error with the screw pitches of the coils when using the traditional circular coil approximation method. The influence of relative position on the mutual inductance of the two coils is also studied and it is further explained through magnetic field distribution. Finally, the validity of the proposed expressions of mutual inductance is verified by experimental results.

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“…where Mx,y+1 is the mutual inductance between coil at coordinate (x,y) and an edge adjacent coil (Figure 2). For calculation of Mx,y+1, the formula introduced by Siu, Su, and Lai [30] is suitable: In the periodic grid, coils are adjacent; hence, it is necessary to include magnetic coupling between them. Mutual inductance Mperiod, which came directly from periodic distribution of coils arranged on the surface xy, is a sum of all mutual inductances [28,29]:…”

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