An analysis is presented of the effect of the protective cover on the acoustic response of a miniature silicon microphone. The microphone diaphragm is contained within a small rectangular enclosure and the sound enters through a small hole in the enclosure's top surface. A numerical model is presented to predict the variation in the sound field with position within the enclosure. An objective of this study is to determine up to which frequency the pressure distribution remains sufficiently uniform so that a pressure calibration can be made in free space. The secondary motivation for this effort is to facilitate microphone design by providing a means of predicting how the placement of the microphone diaphragm in the package affects the sensitivity and frequency response. While the size of the package is typically small relative to the wavelength of the sounds of interest, because the dimensions of the package are on the order of the thickness of the viscous boundary layer, viscosity can significantly affect the distribution of sound pressure around the diaphragm. In addition to the need to consider viscous effects, it is shown here that one must also carefully account for thermal conductivity to properly represent energy dissipation at the system's primary acoustic resonance frequency. The sound field is calculated using a solution of the linearized system consisting of continuity equation, Navier-Stokes equations, the state equation and the energy equation using a finite element approach. The predicted spatial variation of both the amplitude and phase of the sound pressure is shown over the range of audible frequencies. Excellent agreement is shown between the predicted and measured effects of the package on the microphone's sensitivity.

中文翻译：

---

微声学分析，包括粘度和热导率，以模拟保护帽对 MEMS 麦克风声学响应的影响。

分析了保护罩对微型硅麦克风声学响应的影响。麦克风振膜包含在一个小的矩形外壳内，声音通过外壳顶部表面的一个小孔进入。提出了一个数值模型来预测声场随外壳内位置的变化。本研究的一个目的是确定压力分布保持足够均匀的频率，以便可以在自由空间进行压力校准。这项工作的第二个动机是通过提供一种预测麦克风振膜在封装中的位置如何影响灵敏度和频率响应的方法来促进麦克风设计。虽然封装的尺寸相对于感兴趣的声音的波长通常很小，但由于封装的尺寸与粘性边界层的厚度相当，因此粘性会显着影响振膜周围的声压分布. 除了需要考虑粘性效应外，这里还表明，还必须仔细考虑热导率，以正确表示系统主要声学共振频率下的能量耗散。声场是使用由连续性方程、纳维-斯托克斯方程、状态方程和能量方程组成的线性化系统的解来计算的，使用有限元方法。声压的幅度和相位的预测空间变化显示在可听频率范围内。封装对麦克风灵敏度的预测和测量影响之间显示出极好的一致性。