Fundamental Behavior Analysis of Single-Frequency Sine Wave Forced Oscillator based on Linear Model and Multi-Time Technique

Abstract

In this article, an excited oscillator which is analyzed by using a multi-time linear analytical model is proposed. An obtained closed-form solution can be exploited not only to explain phenomena in the beat and locked states that are mostly studied in literature but also in an additional state called the non-locked state. With the proposed analysis, it is found that the non-locked state of the oscillator behaves similarly to the up-conversion process. It provides a new point-of-view to the phase noise oscillator. Moreover, our principle indicates that the important factor defining the behavior in each state and state transition is the transfer function of the system. The proposed mathematical model is verified by the experimental and numerical results.