This work provides an analytical non-linear model for the capacitive transduction in MEMS transducers with perforated counter-electrodes, especially applicable to capacitive MEMS microphones. Starting from an electrostatic description of a perforated unit cell of the transducer, analytical formulations of the variable capacitance and electrostatic forces are derived, accounting for the deflection profile of a clamped circular plate. A lumped implementation into conventional circuit simulations tools is enabled via behavioral modeling based on hardware description languages, such as Verilog-A. Therefore, the analytical model is approximated via Taylor series expansions, allowing for a stable and non-linear behavioral implementation. The resulting model finally enables both a small- and large-signal analysis of capacitive MEMS microphones, precisely accounting for non-linearities in the capacitive transduction. This allows to simulate the harmonic distortion of the microphone's output signal and to account for electrostatic spring-softening in simulations of its bias voltage dependent sensitivity.

中文翻译：

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电容式 MEMS 麦克风中机电耦合的非线性集总模型


这项工作为带有穿孔反电极的 MEMS 换能器中的电容式传导提供了一个分析非线性模型，特别适用于电容式 MEMS 麦克风。从换能器的穿孔单元的静电描述开始，推导出可变电容和静电力的分析公式，解释了夹紧圆板的偏转轮廓。通过基于硬件描述语言（例如 Verilog-A）的行为建模，可以实现传统电路仿真工具的集总实现。因此，分析模型通过泰勒级数展开来近似，从而实现稳定和非线性的行为实现。由此产生的模型最终能够对电容式 MEMS 麦克风进行小信号和大信号分析，精确地考虑电容换能中的非线性。这允许模拟麦克风输出信号的谐波失真，并在模拟其偏置电压相关灵敏度时考虑静电弹簧软化。