IEEE Circuits and Systems Magazine - Q2 2018 - 28
Feature
Tutorial: Experimental
Nonlinear Dynamical
Circuit Analysis of a
Ferromagnetic Inductor
suhas Kumar and r. stanley Williams
Abstract
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.
@IstOcKphOtO.cOm/BIrdlKpOrtfOlIO
c
hua has created a systematic framework for mathematically modeling electronic circuit elements
that he has termed a periodic table. [1] Within an
electronic circuit, a designer primarily cares about the
currents i (t ) passing through devices and voltages v (t )
Digital Object Identifier 10.1109/MCAS.2018.2821758
Date of publication: 21 May 2018
28
IEEE cIrcuIts and systEms magazInE
across them, which are properties that can be measured
experimentally versus time. Given these basic measurements, it is then possible to differentiate or integrate the
two signals, where a $ 0 refers to the a th derivative
while a 1 0 refers to the a th integral of voltage with respect to time, and similarly for b with reference to current. [1] The simplest model for an ideal circuit element is
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sEcOnd quartEr 2018
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