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 dom...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.展开更多
For d particular Riccati equation on torns T2,an exact relation (28) between the generators of its monodromy group and theparameter A E R is obtained, so that the dependence of the properties of themonodromy group on ...For d particular Riccati equation on torns T2,an exact relation (28) between the generators of its monodromy group and theparameter A E R is obtained, so that the dependence of the properties of themonodromy group on the parameter A can be discussed globally. It is provedthat the limit set of the monodromy group has a fractal structure if and only if展开更多
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)
文摘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.
文摘For d particular Riccati equation on torns T2,an exact relation (28) between the generators of its monodromy group and theparameter A E R is obtained, so that the dependence of the properties of themonodromy group on the parameter A can be discussed globally. It is provedthat the limit set of the monodromy group has a fractal structure if and only if
