Analytical and experimental study of the dynamics of a micro-electromechanical resonator based digital-to-analog converter

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.