Oscillator Modeling and Phase Noise

Brian Limketkai, 2004 Ph.D. Thesis

Advisor:  Robert W. Brodersen

Abstract:

Using a dynamical systems perspective, we develop a method to calculate phase noise in oscillators based on a particle diffusion model. Starting from the basic nonlinear equations of motion, a phase diffusion equation is formulated by viewing the system in state space. The resulting phase diffusion solution is then found approximately by using multiple scale perturbation theory to get closed-form analytical expressions. In this way, the effects of the nonlinearities on the phase diffusion become evident. Similar techniques are then also applied to finding the locking bandwidth of a 2:1 injection-locked frequency divider.