Analytic Hysteresis Function

An analytic function is proposed in a parametric form which displays the character of an adjustable hysteresis loop. The type of function used was suggested by the phase-frequency characteristic of a conventional phase shift network. There are two parameters in the analytic function, one of which controls the width of the loop, and the other, the steepness of the sides of the loop. These two parameters are related to the conventional magnetic parameters such as coercivity, residual induction, etc., so that one may construct a synthetic loop corresponding to a given experimental loop. The analytic function was used to produce equations for the Fourier series components of $b$ and $h$ in terms of the two parameters. The mathematics is omitted in the paper but the results are given, and an application of the results is made to some experimental data. A typical set of CRO photographs is used to display a family of synthetic loops produced by an analog computer arranged to generate voltages corresponding to the analytic function.