6.10 Magnetic Losses and Frequency Dependence
This is important mainly for ferromagnetic and ferrimagnetic materials when they are placed in an alternating magnetic field. Associated with frequency response are magnetic hysteresis losses and frequency response of magnetic permeability.
6.10.1 Magnetic Losses
We imagine a ferromagnetic or ferrimagnetic material with a hysteresis curve is subjected to an alternating magnetic field, H = H0 exp (iωt). The frequencies are kept such, typically low, such that switching of magnetization of the material keeps pace with the magnetic field switching. In an analogy to the dielectric materials, two loss mechanisms are of importance:
Eddy current losses induced by the alternating magnetic field which are quite dependent on the resistivity of the material; and The domain wall motion requires as well as dissipates some amount of energy resulting in what are called as intrinsic magnetic losses or hysteresis losses.
Both of these effects add up and energy loss is dissipated as heat. While frequency, magnetic field strength and maximum magnetic flux increase both types of losses, increasing the resistivity (ρ) decreases eddy current losses in particular, losses are more when the material is conducting and many ferromagnets tend to be quite conductive.
Hysteresis loss is the energy loss per cycle times number of cycles and is given as
where f is the frequency of applied field, Hc is the coercive field strength and Br is magnetic remanence.
Eddy current power losses can be expressed as
The total power loss is the sum of these two losses.
These two equations can help a user to choose a material carefully so that losses can be minimized. |
