An analytical method to calculate winding resistance for planar coil with ferrite plate and litz wire in inductive power transfer

Planar coils with litz wires are used a lot in inductive power transfer for electric vehicles. When the litz wire is properly selected for the coil, the winding resistance is composed of DC resistance and proximity-effect resistance. The calculation of DC resistance is simple, using the cross-sectional area and the length of the wire, but the calculation of proximity-effect resistance is complicated, in which the magnetic fields across the turns of the winding are essential. When the ferrite plate is added to the planar coil in inductive power transfer to improve the quality factor and the coupling coefficient, the analytical derivation of the magnetic fields is even more complicated. In this paper, the method of image is applied to obtain the magnetic fields across the winding turns of the planar coil with ferrite plate. The ferrite plate is replaced by mirror turns, and the magnetic fields are calculated with Ampere's Law and Biot-Savart Law. In order to verify the accuracy of this method, an exemplary planar coil with litz wire and ferrite plate was fabricated and its resistance was measured. The difference between the calculated resistance and measured resistance is less than 10%.