Modeling of a Magnetic Coupler Based on Single- and Double-Layered Rectangular Planar Coils With In-Plane Misalignment for Wireless Power Transfer

This article proposes an analytical model that provides accurate self-inductance and mutual inductance calculations for two mutually coupled rectangular, planar, and spiral coils with an air core, which are equal and parallel, including the possibility of a lateral misalignment. Both single- and double-layered coil geometries were modeled by considering an arbitrary number of turns with a circular cross section per layer. The model equations, which can be readily implemented in software, are the results of a systematic approach that starts from the equations for the self-inductance of a wire and the mutual inductance of two parallel and misaligned wires that lie on the same plane. Accuracy is guaranteed by considering all the magnetic interactions among the individual turns in the two coils, while the simplifications involve only the calculations made at the corners of the coils. The model was validated by taking as reference experimental measurements carried out on a rectangular and a square magnetic coupler. A second analytical model, based on equivalent single-turn coils, was also tested for comparison purposes. The validation was extended with finite-element analysis tools by considering a wide range of coil side lengths, air gaps, number of turns, and lateral misalignments. The proposed model can, therefore, be regarded as a reliable tool to aid in the design of rectangular-shaped air-core magnetic couplers with applications in the contactless transfer power that are not necessarily limited to vehicle electrification.