Analysis of resonant pull-in of micro-electromechanical oscillators

Abstract

International audienceIn this paper, the equations governing the pull-in of electrostatic MEMS (micro-electromechanical systems) oscillators are established and analyzed. This phenomenon defines the maximal oscillation amplitude that can be obtained without incurring instability and, hence, an upper limit to the performance of a given device. The proposed approach makes it possible to accurately predict pull-in behaviour from the purely resonant case, in which the electrostatic bias is very small, to the static case. The method is first exposed in the case of a parallel-plate resonator and the influence of the excitation waveform on the resonant pull-in characteristics is assessed. It is then extended to the more complex case of clamped-clamped and cantilever beams. The results are validated by comparison with transient simulations

Synchronization of a micromechanical oscillator in different regimes of electromechanical nonlinearity

“…Electrostatically actuated micromachined resonators can operate at large amplitudes (up to 64% of the capacitive gap) using sinewave actuation without exhibiting electrostatic pull-in instability. [31][32][33] While complete analysis of electromechanical nonlinearity can be found in the literature (e.g., Refs. 34 and 35), assuming stable oscillation at large amplitudes and using a Taylor series expansion for the electrostatic and mechanical forces, a simplified, forced equation of motion, also used elsewhere, 36,37 including only odd-power stiffness nonlinearities due to the symmetry of the structure, 3 can be written as…”

Noise Evasion Properties of Electrostatic Gap-Closing MEMS Resonators with Pulsed Excitation Waveforms

“…Because of the dependence on of the multiplicative coefficient on the right-hand side of (1), these two driving schemes have fundamentally different properties with respect to frequency stability. On the other hand, they are both immune to resonant pull-in [8][9] provided ≫ 1 and ≪ 4/27 (this limiting value corresponds to static pull-in), meaning that they can be used to make the resonator oscillate at an arbitrary amplitude without risk. In what follows, we study the impact on frequency stability of fluctuations of the feedback phase from the nominal 90° value.…”