Harmonic Distortion Analysis for Switched-Capacitor Electromechanical Sigma–Delta Modulators

As the conversions between the sensing element and interface in the feedback loop and forward path are nonlinear, harmonic distortions appear in the output spectrum, which will decrease the signal-to-noise and distortion ratio. Nonlinear distortions are critical for a high-resolution electromechanical sigma-delta (ΣΔ) modulator. However, there exists no detailed analysis approach to derive harmonic distortion results in the output signal for electromechanical ΣΔ modulators. In this paper, we employ a nonlinear op-amp dc gain model to derive the nonlinear displacement to voltage conversion in the forward path, and the nonlinear electrostatic feedback force on the proof mass is also computed. Based on a linear approximation of the modulator in the back end, the harmonic distortion model in the output spectrum of the proposed fifth-order electromechanical ΣΔ modulator is derived as a function of system parameters. The proposed nonlinear distortion models are verified by simulation results and experimental results.