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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Analysis of noise in quartz crystal oscillators by using slowlyvarying functions method
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Analysis of noise in quartz crystal oscillators by using slowlyvarying functions method

机译：慢变函数法分析石英晶体振荡器中的噪声

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By using formal manipulation capability of commercially availablensymbolic calculation code, it is possible to automatically derive thencharacteristic polynomial describing the conditions for oscillation of ancircuit. The analytical expression of the characteristic polynomial isnobtained through an encapsulation process starting from the SPICEnnetlist description of the circuit: by using a limited number of simplentransformations, the initial circuit is progressively transformed in ansimplified standard form. In this method, the nonlinear component isndescribed by its large signal admittance parameters obtained from a setnof SPICE transient simulations of larger and larger amplitude. Thenencapsulation process involving linear and nonlinear components as wellnas noise sources leads to a perturbed characteristic polynomial. In thentime domain, the perturbed characteristic polynomial becomes a nonlinearnnonautonomous differential equation. By using an extension of the slowlynvarying functions method, this differential equation is transformed intona nonlinear differential system with perturbation terms as thenright-hand side. Eventually, solving this system with classicalnalgorithms allows one to obtain both amplitude and phase noise spectranof the oscillator
机译：通过使用市售的符号计算代码的形式操作能力，可以自动得出描述电路振荡条件的特征多项式。从电路的SPICEnnetlist描述开始，通过封装过程无法获得特征多项式的解析表达式：通过使用有限数量的simplen转换，初始电路以简化的标准形式逐步转换。在这种方法中，非线性分量由从一组越来越大的幅度的SPICE瞬态仿真中获得的大信号导纳参数来描述。然后，以线性和非线性分量作为井壁噪声源的封装过程将导致扰动的特征多项式。在时域中，被摄动的特征多项式变为非线性非自治微分方程。通过使用慢变函数方法的扩展，该微分方程被转化为一个非线性微分系统，其摄动项为右手边。最终，用古典算法求解该系统将使人们获得振荡器的幅度和相位噪声频谱

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