We predict the contribution of eddy currents to power losses in polycrystalline Mn-Zn ferrites and apply it to experimental results obtained on a broad frequency range in different commercial materials and differently sized ring samples. It is verified by theory and experiment that the eddy currents can, in sufficiently large specimens, measurably contribute to the energy dissipation, in conjunction with spin damping mechanisms. In this context, the direct role of the domain wall processes is shown to be negligible, with the so-called classical losses, chiefly associated with the rotations, accounting for all of the eddy-current losses. To predict the frequency dependent classical loss W_eddy^(cl)(f) in the actual heterogeneous material, the electromagnetic field equations are formulated under a variational multiscale approach, with fine and coarse scales identified with the thickness of grain boundary layers and grain size, respectively. The eddy-current patterns are correspondingly observed to evolve, on increasing the magnetizing frequency, from mostly grain-confined to circulating on the scale of the sample cross-section. Based on the measurement of the electrical resistivity versus frequency and knowledge of the average grain size, an overall frequency dependence of the classical loss W_eddy^(cl)(f) is formulated. With the energy loss W(f) measured from dc to 10 MHz in different types of commercial Mn-Zn ferrites having different cross-sectional areas, it is found that the W(f) behaviors in a given material all tend to fall onto a single W(f) curve once purged of the calculated W_eddy^(cl)(f). The residual size-independent loss is the one associated with the damping of the precessional spin motion, which can separately be accounted for.

Magnetic losses under triangular symmetric and asymmetric induction waveforms, like the ones found in power electronics devices, have been measured over a broad range of frequencies and predicted starting from standard results obtained with sinusoidal induction. Non-oriented Fe-Si and Fe-Co sheets, nanocrystalline Finemet ribbons, and Mn-Zn ferrites have been investigated up to f = 1 MHz and duty cycles ranging between 0.5/f and 0.1/f. The intrinsic shortcomings of the popular approach to loss calculation of inductive components in power electronics, based on the empirical Steinmetz equation and its numerous modified versions, are overcome by generalized application of the Statistical Theory of Losses and the related concept of loss separation. While showing that this concept applies both to ferrites and metallic alloys and extracting the hysteresis (quasi-static), excess, and classical loss components, we relate in a simple way the magnetic energy losses under symmetric triangular induction (square wave voltage) and sinusoidal induction. The loss behavior under asymmetric triangular induction is directly retrieved from the symmetric one, by averaging the energy losses pertaining to the two different semi-periods. Good comparison with the experimentally measured energy loss versus frequency behavior is verified in all materials.

We review the basic phenomenology of magnetic losses from DC to 1 GHz in commercial and laboratory-prepared soft ferrites considering recent concepts regarding their physical interpretation. This is based, on the one hand, on the identification of the contributions to the magnetization process provided by spin rotations and domain walls and, on the other hand, the concept of loss separation. It additionally contemplates a distinction between the involved microscopic dissipation mechanisms: spin damping and eddy currents. Selected experimental results on the broadband behavior of complex permeability and losses in Mn-Zn ferrites provide significant examples of their dependence on sintering methods, solute elements, and working temperature. We also highlight the peculiar frequency and temperature response of Ni-Zn ferrites, which can be heavily affected by magnetic aftereffects. The physical modeling of the losses brings to light the role of the magnetic anisotropy and the way its magnitude distribution, affected by the internal demagnetizing fields, acts upon the magnetization process and its dependence on temperature and frequency. It is shown that the effective anisotropy governs the interplay of domain wall and rotational processes and their distinctive dissipation mechanisms, whose contributions are recognized in terms of different loss components.