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.

微机电系统 (MEMS) 谐振器已广泛用于磁阻 (MR) 传感器，用于调制磁通量以提高检测限。然而，MEMS制造工艺中的制造公差使得制造具有相同振动频率的相同谐振器具有挑战性，这大大降低了MR传感器的检测极限。为了同步MEMS谐振器并提高MR传感器的性能，本文提出了基于双端音叉（DETF）的梳状驱动MEMS谐振器，使系统工作在异相模式以完成同步。通过理论分析、基于 MATLAB 代码和 Simulink 的数值求解以及实验验证，研究了谐振器的动态行为。结果表明，由于二阶静电弹簧常数，梳子中的横向电容将显着影响谐振频率。第一次观察到谐振频率随着偏置量的增加而增加的现象，也可以通过调整固定手指和移动质量之间的初始间距随着偏置量的增加而降低，它们与模型不同关于弹簧软化和弹簧硬化。此外，所提出的基于 DETF 的梳状驱动谐振器可以通过调整驱动和传感端口以及传感方法来抑制同相和异相模式，同时使磁通量调制完全同步，并最大限度地提高调制效率，并最小化检测限。这些特性适用于 MR 传感器，甚至其他需要调整谐振频率和振动幅度的设备。此外，该模型和设计还可以扩展到基于单端音叉的 MEMS 谐振器和其他基于 MEMS 的 MR 传感器的特性。