Cauer Circuit Representation of the Homogenized Eddy-Current Field Based on the Legendre Expansion for a Magnetic Sheet

Using the Legendre expansion of the magnetic field distribution, we derive the standard Cauer circuit representation of the frequency-dependent properties of magnetic sheets and discuss its physical meaning. The representation of non-linear inductors is derived so as to apply the Cauer circuit in the dynamic hysteresis modeling of silicon steel. This circuit accurately reconstructs the hysteretic property under pulsewidth modulation excitation using only one or two hysteretic elements.