Séminaire Michele Bonnin

Jeudi 24 Septembre 2015 (14h00, salle G001)

Michele Bonnin, Department of Electronics and Telecommunications Politecnico di Torino.

Titre : A mathematical framework for the analysis of phase and amplitude noise in oscillators.

Résumé : Nonlinear oscillators play a major role in many natural and manmade systems. Noise may significantly affect the performance of oscillators, which in turns influence the functionality of the whole system. A wide variety of heuristic, mainly design oriented modelling techniques are available, but a rigorous general theory for the phase noise problem in oscillators is still absent. This talk presents a mathematical framework for the analysis of the phase noise and amplitude noise in nonlinear oscillators subject to white Gaussian noise.

After introducing the basic elements of the theory of stochastic differential equations and Ito calculus, a rigorous set of equations will be derived, to describe the influence of noise on the phase and amplitude of nonlinear oscillators of any order. It will be shown that the phase noise problem is a convection-diffusion process. Using Floquet’s theory, it will be shown that a partial decoupling between the phase and the amplitude dynamics can be obtained, and how reduced order models can be derived. The implications in some practical applications such as stochastic resonance and energy harvesting will be briefly discussed.