The minimization of copper losses in core-less inductors: application to foil- and PCB-based planar windings

Core-less magnetic components have only winding losses and show a much more pronounced size reduction with increasing frequency. Therefore air coils have a size advantage in the MHz range used for energy-storage in switch-mode power supplies. The use of high switching frequencies causes eddy currents in the windings with the consequence of significantly increasing copper losses. The paper describes how to calculate the copper losses of foil-windings using a simple state space model and based on the results, it outlines the possibilities to reduce the winding losses by proper component design