High-precision frequency measurement for microresonant sensors based on improved modified multi-phase clock method

Microelectromechanical system resonant sensors are widely used in high precision applications. Frequency measurement plays an important role in such frequency readout sensors. This paper proposed an improved modified frequency measurement method based on the multi-phase clock (MPC), which can effectively improve the measurement accuracy but does not reduce the output rate. Innovative claims include (1) building a model of measurement error for MPC in which the probability of triggering error under different conditions is calculated, (2) improving the accuracy of the MPC measurement by phase reverse, and (3) proposing an algorithm to eliminate jitters of the measured signal. We compared the measurement results of this optimized MPC realized by the field programmable gate array (FPGA) device with those of the conventional MPC, spectral measurement, and equal precision measurement implemented with the National Instruments acquisition equipment PXI-4461 and USB-6366, respectively. The results show that the bias instability of the adopted method is ∼10 µHz obtained by Allan variance analysis, which is better than that of the other three methods. It can meet the accuracy requirements for the resonant frequency measurement of state-of-the-art resonant accelerometers. In addition, an algorithm running in FPGA is proposed to eliminate jitters caused by the noise of the measured signal for enhancing the robust of optimized MPC. The results demonstrate that the optimized MPC has features of high accuracy and anti-interference capability and can be easily transferred to the application specific integrated circuit in the future due to its full digital circuit version.