A Data-Driven, Gain-Scheduled Equivalent Circuit for the B-H Behavior of Power Ferrites

Abstract

An equivalent circuit for the dynamic B-H behavior of power ferrites is identified from measured transients. It consists of classical elements of hysteresis modeling: a nonlinear inductor for the reversible curve, six viscous play branches (inductors in series with diode-bridge sliders) that form a Prandtl-Ishlinskii model, two R-L branches for the magnetic after-effect, a mean-field feedback of H as in the Jiles-Atherton model, and a measurement path. All elements are positive apart from the feedback sources, and the circuit can run in SPICE. Discretized at the sampling step, the circuit is a difference equation with 32 parameters per material, fitted by backpropagation through time. On the 15 materials of the MagNet Challenge 2, the mean sequence relative error is 7.33 % against 7.77 % for the challenge-winning recurrent network with 336 parameters, and the circuit is more accurate on 12 of the 15 materials. The accuracy can be scaled up by gain scheduling, where a small network per material sets the element values at every step from the excitation, while the hysteresis memory stays in the circuit, such that the error drops to 5.25 % with 656 parameters per material. Thus, an interpretable model is demonstrated that achieves state-of-the-art accuracy.