Temperature compensation method for the resonant frequency of a differential vibrating accelerometer using electrostatic stiffness control

Differential vibrating accelerometer (DVA) is a resonant-type sensor which detects the change in the resonant frequency in the presence of acceleration input, i.e. inertial loading. However, the resonant frequency of micromachined silicon resonators is sensitive to the temperature change as well as the input acceleration. Therefore, to design a high-precision vibrating accelerometer, the temperature sensitivity of the resonant frequency has to be predicted and compensated accurately. In this study, a temperature compensation method for resonant frequency is proposed which controls the electrostatic stiffness of the dual-ended tuning fork (DETF) using the temperature-dependent dc voltage between the parallel plate electrodes. To do this, the electromechanical model is derived first to predict the change in the electrostatic stiffness and the resonant frequency resulting from the dc voltage between the resonator and the electrodes. Next, the temperature sensitivity of the resonant frequency is modeled, estimated and compared with the measured values. Then it is shown that the resonant frequency of the DETF can be kept constant in the operating temperature range by applying the temperature-dependent driving voltage to the parallel plate electrodes. The proposed method is validated through experiment.