Barkhausen criterion and another necessary condition for steady state oscillations existence

Abstract

Recent times have given rise to interesting discussions about the necessary and sufficient criteria for steady state oscillations of electronic circuits. The aim of this paper is to point out that the Barkhausen criterion (Bc), while a necessary condition for oscillations, but not a sufficient one, could be supplemented with another necessary condition. Here, we would like to take account of a feature of phase vs. frequency characteristics of linear feedback networks for oscillators. We analyze Twin-T (DT) oscillator and modified Wien (MW) oscillator according to [6], [7], from the point of linear circuit theory by means of open loop characteristic equations and root-locus diagrams for some parameters values where derivatives of the phase vs. frequency open loop feedback systems can be positive or negative, (in the vicinity of the frequencies where the Bc is fulfilled). Characteristic equations of both oscillators and their root-locus diagrams as a function of gain of ideal linear amplifier (AMP) are compared and estimated. For nonlinear amplifier, nonlinear ordinary differential equations have been solved and compared with the assistance of MATLAB, MathCAD and MICRO-CAP (MC10). In addition, we present experimental investigation of the impact of phase vs. frequency characteristic properties on steady state oscillation existence in feedback oscillators in other article as well [15]. All obtained results have confirmed that feedback systems with positive derivatives of phase vs. frequency characteristics (in the vicinity of frequencies where Bc is fulfilled) are incapable of producing steady state oscillations. So we can say that the requirement for negative derivatives of phase vs. frequency characteristic of the feedback network could be understood as a necessary condition for oscillations existence. It is a novel look at the role of this characteristic for steady state oscillations existence.