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振荡器的相位噪声分析是通过扰动自激大信号状态方程,导出周期时变小信号状态方程进行的.在振荡器的时域稳态解上应用传统的正则扰动方法,对周期时变系数Jacobi矩阵按照Sylvester定理进行分解,在它的周期向量构成的空间上,分析振荡器在扰动下能保持周期稳态的条件;注入表示白噪声的频域伪正弦信号和时域δ相关信号,应用随机微分方法,揭示相位噪声的产生过程,计算相位抖动;应用调频的原理分析幂律谱和Lorentz谱的形成以及它们之间的关系,并获得包含谐波的Lorentz功率谱.以周期系数Jacobi矩阵为基础,构造简单的计算Floquet指数和相位噪声的算法流程并给出简单实例.最后指出振荡器相位噪声分析的难点和发展方向.
The phase noise analysis of the oscillator is carried out by perturbing the state equation of the self-excited large signal and deriving the state equation of the small signal at the period. By applying the traditional regular perturbation method to the steady state solution of the oscillator, the periodic variable coefficient Jacobi The matrix is decomposed according to the Sylvester theorem, and the condition that the oscillator can maintain the periodic steady state under disturbances is analyzed in the space formed by its periodic vectors. The pseudo-sinusoidal signals in frequency domain and the signals in time domain δ are injected into the matrix, The phase noise is revealed and phase jitter is calculated, and the formation of the power-law spectrum and the Lorentz spectrum and the relationship between them are analyzed by applying the principle of frequency modulation, and the Lorentz power spectrum containing harmonics is obtained. The periodicity Jacobi matrix is Based on this, a simple calculation flow of Floquet exponent and phase noise is constructed and a simple example is given. Finally, the difficulties and development directions of oscillator phase noise analysis are pointed out.