Electrical circuit models of the HF initial permeability spectra of soft ferrite lead to revised definition of fundamental material properties

Engineers are usually interested in the relative magnetic permeability of a soft ferrite μ_r, whereas physicists and material scientists are more interested in the magnetic susceptibility χ. The magnetostatic relationship between these dimensionless scalars is simply μ_r = χ +1. But ferrite for HF must be considered in magneto-dynamic terms. The simplest physical approach to this is to apply Debye´s mathematical model of simple relaxation. This gives an expression for the complex susceptibility spectrum χ(ω), in which the imaginary term represents the loss. However, complex susceptibility and permeability can be expressed in either series or parallel terms, the latter having primacy. Electrical circuit models show that we cannot conclude that μ_r(ω) = χ(ω) +1. This leads to a clarification of the relationship between the susceptibility and permeability in the presence of loss. A parallel model for the initial permeability spectra of ferrites is presented, the variables being the static susceptibility, Snoek´s Product and the maximum Q. The relative loss factor, tanδ_m/μ_i is shown to be an approximation for the reciprocal of the imaginary part of the parallel permeability.