The describing function method and the analysis of the magnitude stabilization phenomenon in a nonlinear OSC

Abstract

We present a nonlinear analysis of a nonlinear oscillator which uses an operational transconductance amplifier (OTA), a second generation current conveyor (CCII), or a current feedback operational amplifier (CFOA) as a nonlinear element. Nonlinear oscillators are nonlinear systems that can display oscillations of fixed amplitude and fixed period without external excitation. These oscillations are called limit cycles, or self-excited oscillations. The magnitude stabilization phenomenon in a nonlinear oscillator is one of the characteristics of stable limit cycles. An equivalent feedback configuration of an oscillator circuit with a nonlinear feedback element is used. The essential tool here is the describing function method used for predicting the existence of limit cycles and, more generally, used to analyze the magnitude stabilization phenomena. We motivate this method for the physical insights into the analysis and design of nonlinear oscillator circuits based on nonlinear devices such as OTA, CCII, CFOA, etc. The describing function method offers also a way for finding the magnitude of an oscillation via an integral equation. Simulation results using MATLAB and PSPICE agree well with the theory.