A Graphical Sinusoidal Analysis of a Nonlinear RC Phase-Shift Feedback Circuit

In certain nonlinear systems, a form of frequency response has been observed in which the peak is bent over to the right or left depending on the type of nonlinearity. It will be shown that a similar response may be obtained in the RC phase-shift feedback circuit by inserting a nonlinear resistor, such as a thyrite, in the feedback loop. This circuit is discussed with emphasis on a graphical sinusoidal analysis of some general applicability which predicts its frequency response. An informative physical interpretation is also obtained from the analysis of the triple-valued region in the response and of the "jump" phenomena. The method is essentially a graphical superposition of the voltageresistance characteristic of the nonlinear resistor upon the voltage-resistance characteristics (with frequency as a parameter) of the circuit between the two points where the nonlinear resistor is intended to be placed. The points of intersection satisfy both sets of characteristics, and therefore yield the response of the circuit. The method is also applied to a series RLC circuit containing a nonlinear iron core inductor, for which current-inductance curves are super-imposed.