Phase noise analysis of oscillators with Sylvester representation for periodic time-varying modulus matrix by regular perturbations  

作　　者：FAN JianXing YANG HuaZhong WANG Hui YAN XiaoLang HOU ChaoHuan 

机构地区：[1]Department of Electronic Engineering, Tsinghua University, Beijing 100084, China [2]Institute of VLSI, Zhejiang University, Hangzhou 310027, China [3]Institute of Acoustics, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《Science in China(Series F)》2007年第4期587-599,共13页中国科学（F辑英文版）

基　　金：the National Fundamental Research Project (Grant Nos. G1999032903 and 90307016);the National Natural Science Founda-tion of China (Grant No. 60025101);and the "863" Program (Grant No. 2003AA1Z1390)

摘　　要：Phase noise analysis of an oscillator is implemented with its periodic time-varying small signal state equations by perturbing the autonomous large signal state equations of the oscillator. In this paper, the time domain steady solutions of oscillators are perturbed with traditional regular method; the periodic time-varying Jocobian modulus matrices are decomposed with Sylvester theorem, and on the resulting space spanned by periodic vectors, the conditions under which the oscillator holds periodic steady states with any perturbations are analyzed. In this paper, stochastic calculus is applied to disclose the generation process of phase noise and calculate the phase jitter of the oscillator by injecting a pseudo sinusoidal signal in frequency domain, representing the white noise, and a δcorrelation signal in time domain into the oscillator. Applying the principle of frequency modulation, we learned how the power-law and the Lorentzian spectrums are formed. Their relations and the Lorentzian spectrums of harmonics are also worked out. Based on the periodic Jacobian modulus matrix, the simple algorithms for Floquet exponents and phase noise are constructed, as well as a simple case is demonstrated. The analysis difficulties and the future directions for the phase noise of oscillators are also pointed out at the end.Phase noise analysis of an oscillator is implemented with its periodic time-varying small signal state equations by perturbing the autonomous large signal state equations of the oscillator. In this paper, the time domain steady solutions of oscillators are perturbed with traditional regular method; the periodic time-varying Jocobian modulus matrices are decomposed with Sylvester theorem, and on the resulting space spanned by periodic vectors, the conditions under which the oscillator holds periodic steady states with any perturbations are analyzed. In this paper, stochastic calculus is applied to disclose the generation process of phase noise and calculate the phase jitter of the oscillator by injecting a pseudo sinusoidal signal in frequency domain, representing the white noise, and a δcorrelation signal in time domain into the oscillator. Applying the principle of frequency modulation, we learned how the power-law and the Lorentzian spectrums are formed. Their relations and the Lorentzian spectrums of harmonics are also worked out. Based on the periodic Jacobian modulus matrix, the simple algorithms for Floquet exponents and phase noise are constructed, as well as a simple case is demonstrated. The analysis difficulties and the future directions for the phase noise of oscillators are also pointed out at the end.

关 键 词：phase noise periodic time-varying Sylvester theorem power-law spectrum Lorentzian spectrum Floquet exponent stochastic calculus 

分 类 号：TN752[电子电信—电路与系统]