Optimum foil thickness of inductors conducting DC and non-sinusoidal periodic currents

This study presents a derivation of an expression for the optimum thickness of foil inductors operating under DC and AC non-sinusoidal periodic currents. The exact equation for the DC winding power loss and approximated equations for the AC winding power loss are used to determine the optimum thickness of the foil for the single-layer and multi-layer inductors, operating with multi-harmonic AC currents superimposed on the DC component. The design procedure for inductors with minimum winding power loss is presented for a pulsewidth-modulated DC-DC buck converter operating in discontinuous conduction mode (DCM). The comparison of the total winding power loss of the designed inductor with optimum foil thickness to the total winding power loss of the inductor with non-optimised round conductor is also given. The theoretical predictions have been verified by measurements of inductors with three different foil thicknesses.