Dynamic behaviours of double-ended tuning fork based comb-driven microelectromechanical resonators for modulating magnetic flux synchronously

Microelectromechanical system (MEMS) resonators have been widely used in the magneto-resistive (MR) sensor for modulating the magnetic flux to enhance the detection limit. However, the manufacturing tolerances in MEMS fabrication processes make it challenging to fabricate the identical resonators with the same vibration frequency, which greatly decreases the detection limit of the MR sensor. To synchronize the MEMS resonators and improve the performance of the MR sensor, the double-ended tuning fork (DETF) based comb-driven MEMS resonators is proposed in this paper, making the system operate at the out-of-phase mode to complete the synchronization. The dynamic behaviour of the resonators is investigated through theoretical analysis, numerical solution based on MATLAB code and Simulink, and experimental verification. The results show that the transverse capacitances in the comb will significantly affect the resonance frequency due to the second-order electrostatic spring constant. It is the first time to observe the phenomenon that the resonant frequency increases with the increase of the bias, and it can also decrease with increasing the bias through adjusting the initial space between the fixed finger and the moving mass, they are different from the model about spring softening and spring hardening. Besides, the proposed DETF based comb-driven resonators can suppress the in-phase and out-of-phase mode through adjusting the driving and sensing ports, and sensing method, meanwhile make the magnetic flux modulation fully synchronized, and maximize the modulation efficiency, and minimize the detection limit. These characteristics are appropriate for the MR sensor, even other devices that need to adjust the resonance frequency and vibration amplitude. Furthermore, the model and the design can also be extended to characteristic the single end tuning fork based MEMS resonator and other MEMS-based MR sensors.