Power losses calculations in windings of gapped magnetic components: The extended 2-D method

An improved 2-D equivalent (i2D) analytical calculation method to estimate conductive losses in gapped magnetic components in a wide range of frequencies is presented. In the previous work, which is based on the superposition of losses mechanisms (skin, gap and proximity) in the winding of the component, several expressions to separately evaluate all components of losses were used and the total winding loss could be obtained by the addition of the calculated values. Although the obtained results were in good agreement with finite element analysis (FEA) and measurements this method is limited to conductors with smaller radius than the skin depth at the considered frequency. In this paper the dependence of the wire diameter is eliminated by means of the inclusion of the proximity magnetic field in the calculations while the number of required equations is reduced. The method is used to evaluate conduction losses in inductors for switched mode power supplies (SMPS) and the results are compared with FEA simulations.