A novel characterization method for temperature compensation of composite resonators

We develop an efficient characterization method for temperature compensated micromechanical resonators by employing empirical data analysis with an a priori model. We have previously demonstrated that electrostatic-tuning of a composite resonator with an accurate lookup table can achieve a temperature stability of ±3.2 ppm, but this characterization method was not suitable for commercialization since it required measurements at every temperature point of interest. This paper presents a technique that can reduce the number of temperature points for calibration by 67% without compromising accuracy. We also demonstrate a one-point calibration method with which ±7 ppm calibration error can be achieved using a single temperature point measurement.