Representation of magnetisation curves over extensive range by rational-fraction approximations

Abstract

The paper presents a simple mathematical expression which enables representation of all types of magnetisation curves over a very wide range. The equation given is ideally suited for problems which require use of the B/H curve many times, since calculations using it require only a few operations of the basic arithmetic adding, multiplying and dividing.Although the equation is not linear in all the parameters, a method for obtaining the best parameters, in which the problem is first linearised and then restored to its original nonlinear form by a system of iteration, is described.A discussion of the meaning of the best parameters of the equation to fit the data curve, whether it is to be read fromB to H, or H to B, or both ways, is given.Comparison is given between several saturation curves and their mathematical counterparts over magnetising m.m.f. from zero to, in one case, 300000AT/m.