Mathematical model for nonlinear magnetic cores at low frequencies

A mathematical model is developed to define the nonlinear permeability of magnetic cores when eddy-current effects are negligible. The model is suitable for both numerical analysis by computer and for noncomputer studies of magnetic applications. The model has three basic flux-changing modes. These are 1) a switching mode resulting from irreversible domain-wall motion, 2) an elastic mode resulting from reversible domain-wall motion, and 3) an elastic mode resulting from domain rotation. All modes are defined by normal statistical distributions of permeability. The model is semi-empirical, that is, it results from a judicious combination of domain theory and measurable material properties such as incremental permeability and B-H characteristics. It is believed applicable to many nonconstricted loop materials and predicts the nonlinear characteristics of interest to magnetic material users. This is a dynamic model that depends on memory at field reversal to predict subsequent flux changes. This one model has good accuracy for field changes of any magnitude of either cyclic or pulse excitation.