Accurate Modeling of Coil Inductance for Near-Field Wireless Power Transfer

This paper presents closed form expressions for self-inductance and mutual inductance of circular wire-wound coils (WWCs) used in near-field wireless power transfer systems. The calculation of the radius of the coils, inspired from the Archimedean spiral found in many biological organisms, is used to model the self-inductance of single- and multilayer spiral coils. The value of the mutual inductance is determined by expressing the Taylor expansion of Neumann's integral for constant current-carrying wires. Formulas for the mutual inductance are also derived for misaligned magnetically coupled coils enabling the rapid but accurate calculation of power transfer efficiency in real-life applications. Self-inductance and mutual inductance values are computed using the 3-D electromagnetic software package Maxwell 3D, and these values demonstrate excellent agreement compared with the proposed models. WWCs of different geometrical configurations have been manufactured to validate experimentally the accuracy of the proposed models. Comparison of analytical and experimental results indicates that the proposed models are capable to accurately predict the self-inductance and mutual coupling rapidly. The proposed modeling paves the way for the time efficient optimization of near-field wireless power transfer links.