The effect of the temperature-dependent nonlinearities on the temperature stability of micromechanical resonators

Micromechanical resonators show a discrepancy between the frequency-temperature (f-T) characteristics they have in open-loop and closed-loop measurements, and this discrepancy adversely affects resonator's temperature stability performance. We explain the discrepancy with a model that combines the temperature-dependent quality factor (Q) with the nonlinear amplitude-frequency (A-f) effect; we then experimentally verify the model using two types of double-ended tuning fork resonators. In addition, we present an improved closed-loop system that removes the discrepancy, thus improving the temperature stability.