Dynamic Characteristics of a Biharmonic Self-Oscillator

Abstract

Introduction. Modern methods of stabilizing a frequency of self-oscillations use an improvement of the stability of reactive parameters of the self-oscillators circuit and an increase in the quality factor of an oscillating system. It is also possible to improve the frequency stabilization based on the phenomenon of mutual synchronization of the self-oscillator modes using a multi-loop oscillation system. Previously, a method for reducing a phase noise of an auto-oscillator with synchronization of two modes in a biharmonic auto-oscillator with multiple frequencies was described. The method was developed under the assumption that an active element is inertialess. The idea of the method of synchronizing of the main oscillation with its 2-nd harmonic using an additional loop is based on the consideration that internal fluctuation processes in the active element modulate in-phase all current har-monics. Therefore, it is possible to use this natural cross-correlation of noise processes to neutralize their influence. Aim. Building and analysis of a mathematical model of a biharmonic oscillator in order to analyze the operating modes of such generator and reduction of the phase noise of its output oscillation. Materials and methods. The mathematical model was developed by the method of slowly changing amplitudes, and the analysis was performed by methods of numerical integration and differentiation. Results. It was demonstrated that synchronization of two oscillations at multiple frequencies in the active element reduced the phase noise of the main oscillation. Conclusion. In the paper dynamic modes of a biharmonic Colpitts oscillator operating in the phase synchronization of two waves were analyzed. It was shown that with an increase in an inertia of the active element, the synchronous was preserved. Shortened differential equations of the system for slowly changing amplitudes and phases of oscillatory modes were obtained. The study of nonlinear dynamics and of stationary synchronous of the system was carried out by the method of phase space in coordinates of mode amplitude – phase difference. The conducted field experiment allows one to conclude that it is possible to reduce the phase noise in a stationary synchronous biharmonic mode. It can be used in the frequency stabilization task.