Analytical Calculation of Proximity-Effect Resistance for Planar Coil With Litz Wire and Ferrite Plate in Inductive Power Transfer

Planar coils are popularly used in inductive power transfer applications. The coils' efficiency is improved with litz wire by eliminating the winding's skin-effect loss, but the proximity-effect loss still needs to be considered. To calculate the proximity-effect resistance, the magnetic fields across the windings are required. During the coils' optimization process, numerical methods of field calculation are too time-consuming due to the parametric sweep of physical parameters. The analytical calculation of the magnetic field is preferred in this scenario, but it becomes complex with the existence of the ferrite plate, which is used to increase the coils' coupling. In this paper, the method of image is applied to simplify the analytical calculation, in which the magnetic fields across the windings are derived from Ampere's law and Biot-Savart law. The proximity-effect resistance is then calculated with these fields. The study also proves that the size of the ferrite plate has negligible influence on the proximity-effect resistance as long as it is larger than the size of the winding. A planar coil was fabricated and measured to verify the analytical calculation of the proximity-effect resistance, using litz wire composed of 100 strands with 0.1 mm diameter. A square plate of 3C96 ferrite with the dimensions of 100 mm x 100 mm x 5 mm was placed below the winding. The difference between calculation and measurement is less than 15%.