Precise Modeling of Mutual Inductance for Planar Spiral Coils in Wireless Power Transfer and Its Application

In magnetic coupling resonant wireless power transfer devices, planar spiral coils are often used as the coupling mechanism. In such application area, the coils are often wound sparsely with wide screw pitches and often under complex relative position. An accurate model of mutual inductance for planar spiral coils wound either densely or sparsely is established in this article. Utilizing Euler Angles, an exact expression of mutual inductance for a couple of planar spiral coils under arbitrary relative position is proposed. Based on this expression and geometric mean distance principle, a self-inductance expression for planar spiral coils is derived. Based on numerical calculation of the expressions proposed in this article, the influence of precession and spin angle on mutual inductance is studied; the method of determining radius of each turn when using traditional concentric circular filaments cluster approximation model for self- and mutual inductance calculation is studied; the difference of calculation results between the accurate model and the traditional approximation model is compared. Finite element simulation and experimental results verify the correctness of the proposed models.