Theoretical models of oscillators, phase noise and the effects of nonlinearity

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 based on Robinson are introduced when noise is present. A new oscillator phase noise model which indicates the effect of a nonlinearity is proposed. The results show that the newly defined phase noise is a modified Wiener process whose variance increases with time. The spread of the variance of the phase noise is reduced if the hard-limiter nonlinearity 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.