In this paper, an analytical model of a micro-electromechanical (MEM) resonator used as a 4-bit digital-to-analog converter (DAC) is presented. First, we derive the dynamic equation of the 4-bit DAC device, and the nonlinear governing equation is solved by the Galerkin method combined with a shooting technique to simulate the static response, linear eigenvalue problem, and forced vibration response of the device for various electrostatic actuation cases. Also, we optimize the air gaps in the linear domain to ensure enhanced performance of the DAC. Further, to analyze the operation of the DAC in the nonlinear regime, two experimental samples powered by −2 dBm and −12 dBm AC inputs are examined. Forward and backward frequency sweeps are conducted experimentally and analytically. The proposed analytical results are validated by comparison with experimental data. The results indicate that the presented modeling, simulations, and optimization are effective tools for the design of MEM resonator-based circuits.

在本文中，提出了用作 4 位数模转换器 (DAC) 的微机电 (MEM) 谐振器的分析模型。首先，我们推导了4位DAC器件的动态方程，通过伽辽金法结合射击技术求解非线性控制方程，模拟器件在各种情况下的静态响应、线性特征值问题和强迫振动响应。静电驱动案例。此外，我们优化了线性域中的气隙，以确保增强 DAC 的性能。此外，为了分析 DAC 在非线性状态下的操作，检查了由 -2 dBm 和 -12 dBm 交流输入供电的两个实验样本。前向和后向频率扫描通过实验和分析进行。通过与实验数据进行比较，验证了所提出的分析结果。结果表明，所提出的建模、仿真和优化是设计基于 MEM 谐振器的电路的有效工具。