Transformer winding loss caused by skin and proximity effects including harmonics in pulse-width modulated DC??DC flyback converters for the continuous conduction mode

High-frequency (HF) transformers used in pulse-width-modulated power converters conduct periodic non-sinusoidal HF currents, which give rise to additional winding losses caused by harmonics. This study presents expressions for winding power losses in a two-winding transformer with periodic non-sinusoidal primary and secondary current waveforms for flyback converters operating in the continuous conduction mode (CCM). Dowell´s equation, which takes into account both the skin and proximity effects, is used to determine the primary and secondary winding resistances as functions of frequency. Fourier series of the primary and secondary current waveforms and the winding resistances are used to determine the winding power losses at harmonic frequencies. The harmonic primary and secondary winding loss factors F_Rph and F_Rsh are introduced for CCM operation. The theory is illustrated by performance evaluation of the transformer in a flyback converter in CCM over the entire range of converter operation. Power losses in the primary and secondary transformer windings are illustrated as functions of the output power and the DC input voltage.