Varistor control of inductive transients

It is shown that the varistor, a nonlinear resistor with current-voltage characteristics of the form i=keⁿ , can be used to achieve superior limitation of inductive transients over that obtainable with a simple diode, or with a diode plus additional linear resistance. To this end a transient analysis is made of the circuit composed of the inductor, its internal linear resistance, and a shunt varistor when the source circuit is opened. The resultant differential equation, though nonlinear, is integrable in terms of elementary functions, and general results are presented in mathematical and graphical form for the current and voltage transients. For all n>1, the transient is found to reach zero in a finite time rather than asymptotically. For a given voltage rise when the source circuit is opened (a basic design parameter), the Zener diode yields the shortest transient. Except for the lowest values of n, the varistor is shown to approach the performance of the Zener diode, while offering practical advantages