AC Power Losses Model for Planar Windings With Rectangular Cross-Sectional Conductors

In this letter, a method to calculate the ac losses, including skin effect and proximity losses, in planar windings with rectangular cross-sectional conductors is proposed. The aim is proposing proper ac losses expressions similar to the formulas available for round cross-sectional wires, to be used for the calculation of the ac losses and the optimization of planar magnetic windings implemented in the printed circuit board. The proposed model is based on the decomposition into conduction and proximity losses. Conduction losses only depend on the properties of the conductor, whereas proximity losses are calculated by using the orthogonal decomposition of the magnetic fields in which the conductors are immersed. Functions including the frequency and geometrical dependences of the both types of losses are extracted by means of finite element method simulation. Finally, several prototypes are used to verify the proposed expressions and some design considerations are also outlined.