Abstract
Self-sustained vibrations are significant in high sensitivity detection and frequency standards using microelectromechanical (MEMS) resonators. To achieve optimal performance in these applications, it is crucial to maintain phase coherence and minimize phase noise of the vibrations. However, self-sustained oscillations lack a reference at their vibration frequency, making the phase easily agitated by stochastic noise and thus diffuse with time, leading to phase decoherence.
In this dissertation, I investigate phase coherence in two-mode MEMS resonators when driven into self-sustained oscillations. Nonlinear mode coupling in two-mode systems allows efficient energy exchange, and self-sustained oscillations occur on both modes by parametrically modulating the mode coupling at a sideband of the higher mode through a pump current. I study basic properties of phases in these self-sustained oscillations, including phase diffusion and anti-correlation.
I design and implement feedback scheme in the two-mode system, although the phase is arbitrary, the feedback enable us to stabilize the phase of one mode by measuring the phase of the other mode and then compensating for the phase diffusion by adjusting the phase of the pump. Notably, the phases of both two modes can be stabilized via the similar feedback scheme. The engagement of such feedback thus maintains the phase coherence of self-sustained oscillations. On the same system, I also investigate the phase decoherence induced by thermal agitation. By quantifying the extent of decoherence, I find this property can be used to study thermal noise which inevitable exists in the vibration systems.
I design and implement a feedback scheme in the two-mode system to stabilize the phase of one mode by measuring the phase of the other mode and compensating for phase diffusion by adjusting the phase of the pump. The phases of both modes can be stabilized via similar feedback schemes, maintaining the phase coherence of self-sustained oscillations. I also investigate phase decoherence induced by thermal agitation in the same system. By quantifying the extent of decoherence, I find that this property can be used to detect thermal noise, which inevitably exists in vibration systems.
Additionally, I explore another two-mode microelectromechanical system where self-sustained oscillations are modulated by 1:3 internal resonance. This novel system provides a platform to study limit cycles, period doubling transitions, frequency combs, and chaotic behavior. Particularly, I find that the phase diffusion of spectral components of a limit cycle is determined by the component's position in frequency. With the help of a secondary drive, the phases of self-sustained oscillations are fixed, maintaining coherence.