Tutorial: Experimental Nonlinear Dynamical Circuit Analysis of a Ferromagnetic Inductor

We analyzed ac electrical measurements of a ferromagnetic inductor as a dynamical nonlinear circuit element and observed a pinched hysteresis loop in the plot of the time derivative of its current di/dt versus voltage v. Using the classifications of Chua, we constructed a model of an ideal voltage-controlled non-linear (-1,0) element to compare with the measured characteristics. Deviations of the ideal model from the experimental data indicated the presence of a second state variable or parameter, identified as temperature, which depends upon the power dissipated in the inductor. After installing a normal linear inductor in parallel with the ferromagnetic inductor, the latter displayed two regions of negative differential inductance accompanied by a significant decrease in power dissipation, while the former displayed a sharp negative power spike. We provide a simple extension of the ideal model that agrees well with the experimental data.