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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Modeling nonlinearities in MEMS oscillators
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Modeling nonlinearities in MEMS oscillators

机译：MEMS振荡器的非线性建模

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摘要

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.
机译：我们提出了一个微机电系统（MEMS）振荡器的数学模型，该模型在单个数值建模环境中集成了MEMS谐振器和振荡器电路的非线性。这是通过将常规的非线性机械模型转换为电域同时考虑谐振器的突出非线性来实现的。通过将模拟的幅频响应与开环电寻址挠曲硅MEMS谐振器驱动到大运动幅度的测量值进行比较，验证了所提出的非线性电模型。接下来，研究了振荡器电路中的基本非线性，并提出了集成了谐振器非线性的MEMS振荡器的数学模型。针对基于MEMS跨阻放大器的方波和正弦波振荡器说明了这一概念。两种振荡器模型均得出稳态输出功率和输出频率的闭式表达式，并将其与实验和仿真结果进行比较，这三种情况下的预测趋势都非常匹配。

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