Calculation of Self-Resonant Spiral Coils for Wireless Power Transfer Systems With a Transmission Line Approach

A mathematical model is presented for the calculation of self-resonant planar coils with an arbitrary winding function. It consists of a transmission line model and allows for a fast computation. It is used to determine the resonant frequencies and current distributions of given geometries and optimize them with respect to their quality factors. Thereby, compact high-quality resonators for resonant wireless power transfer systems can be found.