谐波振荡器稳定性分析

Stability Analysis of Harmonic Oscillators

提出一种基于非线性系统稳定性理论的谐波振荡器一般稳定性判别方法。在分析中,首先由谐波振荡器等效电路建立起振荡平衡方程,并利用Taylor级数和微分算子使方程得到简化。通过求解动态振荡方程在平衡点的Jacobian矩阵,根据其特征根可判定振荡器的稳定与否。分析结果表明:该方法具有理论严密、准确性高、适用范围广等特点,可指导工程应用。

A general method is proposed for the stability of a harmonic oscillator based onthe stability theory of non-linear system. In the process of analysis, the harmonic oscillation equivalent circuit is used to establish oscillation equilibrium equations, which is simplified by using Taylor Series and differential operators. The Jacobian matrices of dynamic oscillation equations are solved in the operating point, and its eigenvalues is used to determine the operating state of the circuit. The result shows this method has the features of rigorous theory, a high accuracy, a wide range of application and so on, and it is statable for project application.