Study On Analyzing Methods Of Phase Noise In Oscillators Based On Dynamic System Models

A variety of oscillators are widely used with the rapid development of information technology. Most importantly, the specifications of oscillator are critical in improving the performance of whole equipments and systems. The specification of phase noise is the most important one among all the parameters of oscillator. Therefore, it is valuable to investigate the phase noise of oscillator. According to recent researches, there are general two methods including direct analysis with linear system or transferring the nonlinear system into linear domain. Since the close-loop gain of oscillator has to be larger than one at the beginning stage of oscillate to amplify the both internal and external noise of oscillator, the output amplitude of oscillator can be increased. When the output amplitude is increased to some values, the close-loop gain will be decreased by the nonlinear characteristics of active components in the oscillator. The signal of oscillator can be stable only when the close-loop gain of oscillator is equal to one. Therefore, in order to make sure the oscillator can initialize oscillation and maintain stable status, all the oscillators have to be non-linear system. Any linear process will definitely change the physical characteristics of oscillator. This dissertation introduces the non-linear random dynamic system model of oscillator with noise. Additional researches about method analysis are investigated, which includes the following four sections.1) Deriving the non-linear random dynamic system model of oscillatorBased on the output pattern of ideal oscillator, the theory of non-linear dynamic system of oscillator is derived. The non-linear terms in the model are fully investigated. The properties of non-linear terms under verification process are obtained, which is constructional for analyzing the phase noise of oscillator based on non-linear random dynamic system.2) Deriving the numerical methods of non-linear random dynamic systemAt first, the method of s-scale Runge-kutta normal structures, which is proposed by Burrage is utilized. Using bi-colored rooted theory, the dissertation derives a four-stage semi-implicit Runge-Kutta method. In addition, the mean stability domain, precision, and convergence are all investigated. The results indicate our method has better performance than the four stage random corresponding response of Runge-kutta method. Then, the oscillator of Van der Pol is investigated based on the method. Under the additive and multiplying noise environment, the dissertation investigates the affect of white noise on the oscillator of Van der Pol and corresponding results are recorded. In addition, the phase noises of Van der Pol oscillator are analyzed based on white noise and chaotic noise. The results show that the phase noise of chaotic noise is quite larger than the counterpart of white noise.3) Analytical method of non-linear random dynamic system model is investigated.The Fokker-Planck equation describing the relationship between the location of atoms and its variation of random distribution with time is introduced into the dissertation, which simplifies the analysis of phase noise change due to white noise. Based on the random numerical computations of Van der Pol oscillator, the plots of experiment approximate the results of theoretical derivations, which propose an innovative method in analyzing the phase noise of oscillator.4) Some related researched about the phase noise of oscillator?The theory of associated computations of phase noise is proposed. Based on the correlation operation theory, the phase noise of oscillator can be directly estimated without any external reference source.?For the popular phase instrumentation, the dissertation discusses the change of phase noise, when there has weak chaotic noise in the output signal. The result indicates the measured phase noise in experiments is better than one recorded in the practical field.?Concerning the popular usage of phase noise in harmonic balanced algorithm of circuit simulation software, the standard harmonic balanced algorithm is optimized based on genetic algorithm and rapid convergence characteristics.?For the dependence of oscillate parameters on field experience, the effectiveness of genetic algorithm optimized harmonic loop is verified by using Pierce crystal oscillator, which provides the actual proof for choosing optimized harmonic parameters.