Losses in cylindrical ferromagnetic cores including hysteresis and eddy-current effects

Cylindrical cores of ferromagnetic material with steady-state sinusoidal excitation in either a circumferential or an axial direction are defined in terms of an equivalent orthogonal coordinate system thus facilitating the computation of flux penetration and losses in such configurations by a multi-layer theory. By neglecting all harmonic components in the field quantities and assuming an elliptical magnetization B/H loop, both hysteresis and eddy-current effects are included in the treatment. The concept can be extended to cores with nonlinear magnetization characteristics, and examples are given for solid cylindrical and annular cores.