A comparison of lumped and distributed solutions to nonlinear, transient, magnetic field problems

The transient magnetization of highly nonlinear materials is investigated using finite-element techniques and a multimode equivalent circuit approach. The use of constant eddy inductances in the equivalent circuit is shown to be correct only for linear materials or for small field perturbations in nonlinear materials. During large perturbations, the nonuniform permeability of nonlinear materials causes standard equivalent circuit techniques to be grossly inaccurate. Using numerical results, a field-dependent nonlinear eddy inductance has been defined that substantially increases the accuracy of nonlinear lumped analyses and is applicable to arbitrary forcing functions. This nonlinear inductance is a function of the differential permeability of the material surface and of a bulk differential permeability calculated from the average flux density in the material. To verify the accuracy of this approach, the transient total flux predicted by an equivalent circuit analysis incorporating nonlinear inductances is compared to the total flux from a transient finite-element analysis. Comparisons are given for the total flux versus time following the step application and the step removal of a surface field to an infinite flat plate and a long solid cylinder. The response of a toroidal coil with a saturable core to an instantaneous voltage change is also investigated using lumped and distributed techniques.