Theoretical models of voltage controlled oscillators and the effects of non-linearity

Restricted until 11 Oct. 2009.This thesis presents mathematical models and performance evaluations of voltage-controlled oscillators when noises are included in the model. There are two main parts of the research. The first part introduces a novel mathematical model of a voltage-controlled oscillator (VCO) based on physical dynamics with noise. The effects of noise in this oscillator model are shown and the analytical forms of the resulting phase noise are obtained using the stochastic integrals. It is shown that the VCO has phase noise contributed from the internal noise of the clock and the clock drift caused by tuning plus tracking loop noises. Moreover, a two-pole filter is designed to constrain tracking loop noise. A timing jitter estimate is proposed. Analysis of the resulting phase noise along with the simulation suggest that the timing jitter process has a random walk behavior with restoring force and the upward zero-crossing jitter is normally distributed. The cycle-to-cycle jitter statistics are shown to be Gaussian distributed and independent.; The second part of the research is focused on oscillators with non-linearity. The oscillator model proposed is based on Robinson's oscillator. Two cases are studied, noise-free and noise-present conditions. Three types of oscillator models are introduced when noise is present. Noise effects on the oscillators and the non-linearity effect on the noise are analyzed. A new oscillator phase noise model which indicates the effect of a non-linearity is proposed. The results show that the newly defined phase noise is a modified Wiener process whose variance increases with time. The phase noise process is shown to be Gaussian distributed. Furthermore, the spread of the variance of the phase noise is reduced if the hard-limiter non-linearity used in the oscillator model is replaced by a soft-limiter with small slope. Similar effects are seen by reducing the system gain parameters. Further system performance improvement is achieved by the introduction of a soft-limiter in the outer-loop of the model, which further reduces the degradation of the noise on the steady state response