Analytical method for multimode oscillators using the averaged potential

Abstract

Abstract A method using the averaged potential is proposed for analyzing the oscillation in a multimode negative resistance oscillator. the averaging method is applied to the mixed potential defined by Brayton and Moser and a function called the averaged potential is introduced that expresses the average of the loss (dissipation) of the system. the averaged equations derived by applying the averaging method to the network equations can be expressed as the gradient system of the averaged potential. Hence, stable oscillation corresponds to a minimum of the averaged potential. the analysis of the system is reduced to constructing the averaged potential and to finding the minima. the physical meaning is clarified for the phenomenon of minimal loss of the system in a stable oscillation system. General rules of initiation of nonresonant multimode oscillations are derived because the averaged potential becomes a quadratic form when the chracteristic of an active device is expressed in terms of a polynomial of order three.