A Rational Approach to $B$ – $H$ Curve Representation

This paper introduces an approach to construct a rational function that fits the finite set of data points on the B-H plane representing the non-linear response of a permeable material, providing an approximation to the data well-suited for interpolation and extrapolation. Improving on previous methods, this approach provides a smooth, closed-form approximation to the data capable of representing the material's response from its Rayleigh region through to its saturation, appropriate for use with finite-element solvers. This is achieved by applying the method of vector fitting (as seen in the discipline of control systems) to the B-H data set, while taking care to remove pole-zero pairs that may occur between data points. The method is demonstrated to provide high-accuracy approximations to the data sets of a range of materials. Good agreement with measured data is obtained when the rational material representation is used in a finite-element software package to solve the TEAM 13 benchmark problem. A rational function expression for the TEAM 13 permeability is provided.