Analytical winding foil thickness optimisation of inductors conducting harmonic currents

This study presents analytical winding power loss minimisation of foil inductors conducting ac harmonic currents with and without dc offset. The approximated equation for the ac winding power loss is derived and used to determine the optimum foil thickness of inductors operating with multi-harmonic ac currents. An approximated equation for the total winding power loss is also derived and used to determine the optimum foil thickness of inductors operating with multi-harmonic ac currents superimposed on the dc current. The design procedure for inductors with minimum total winding power loss is presented for a pulsewidth-modulated dc-dc boost converter operating in discontinuous conduction mode. The theoretical predictions have been verified by measurements of inductors with four different foil thicknesses.