The dynamics of MEMS-Colpitts oscillators

Microelectromechanical systems (MEMS) based oscillators have been proposed for use in coupled arrays for many applications, including neuromorphic computing, clocks with reduced phase noise, and sensors. In many prior studies, the models for coupled oscillator behavior depended upon the phase dynamics of the individual oscillators, while the amplitude dynamics were assumed to be negligible. However, implementation of practical large-scale MEMS oscillator networks may involve systems with significant amplitude dynamics. This cannot be described by the commonly used phase models or by steady-state models that do not predict transient behavior. We present the design and analysis of a MEMS-Colpitts oscillator topology suitable for monolithic integration (resonators with integrated circuits). Applying multiple scales analysis to the dynamics results in significantly faster computation as compared to direct integration and enables the study of nonlinear behaviors (e.g. bifurcations) and both amplitude and phase dynamics. The strong correlation between the analytical and experimental results demonstrates the effectiveness of our modelling approach.