为了准确表征微电子机械系统(MEMS)谐振器在大振幅运动时的行为特性, 建立了刚度非线性MEMS谐振器集**数模型, 并创建了一整套MEMS谐振器非线性特性的表征方法和测试系统。搭建了基于锁相环和自动增益控制的MEMS谐振器闭环工作电路, 分析了不同驱动振幅下, MEMS谐振器的工作状态。推导建立了工作振幅、工作频率与MEMS谐振器刚度非线性之间的数量关系。最后, 基于衰减模式和稳定振荡模式两种工作形态, 实际测量了MEMS谐振器的无阻尼自然谐振频率和刚度非线性。结果显示: 无阻尼自然谐振频率和刚度非线性系数的测量重复性分别为18.6×10-6和1.50%。针对实测的MEMS谐振器无激励振幅自衰减曲线, 分别用理想二阶系统谐振器模型和刚度非线性谐振器模型进行残差分析。结果显示后者的残差要比前者的残差小9.5%, 表明刚度非线性MEMS谐振器模型更接近真实情况, 也验证了该刚度非线性特性表征方法的准确性。基于该方法, 测量了MEMS谐振器刚度非线性系数和无阻尼自然谐振频率的温度特性, 得到的无阻尼自然谐振频率的温度系数为-0.487 Hz/℃, 线性拟合度达99.964%。

To describe the behavior characterization of a MEMS(Micro-electro-mechanical System) resonator with a large amplitude accurately, a lumped parameter model of the nonlinear stiffness MEMS resonator was established and an innovative method to measure and characterize the nonlinear coefficient of the resonator was presented. A closed loop control circuit was designed and manufactured based on a Phase Locked Loop (PLL) and an Automatic Gain Controller (AGC) and the quantity relationship between the vibration amplitude, vibration frequency, and the nonlinearity coefficient was given. Finally, according to the the given relationship, the natural resonant frequency and the stiffness nonlinear coefficient were measured by curve fitting in both of decaying mode and stable mode. The results indicate that the repeatabilities of the two measured results are 18.6×10-6 and 1.5%, respectively. With the measured amplitude self-decaying curve, the residuals were measured by an ideal second-order system resonator model and a stiffness nonlinear resonator model, and the results show that residuals from the latter is less 9.5% than that of the former. The results demonstrate that the stiffness nonlinear resonator model is more close to the actual situation and verify the validity of the measured nonlinearity characteristics by the proposed method. Moreover, the temperature characteristics of nonlinear coefficient and natural resonating frequency were also investigated. The temperature coefficient of the natural resonant frequency is -0.487 Hz/℃, and the goodness of linear fitting is up to 99.964%.