A Closed-Loop Digitally Controlled MEMS Gyroscope With Unconstrained Sigma-Delta Force-Feedback

In this paper, we describe the system architecture and prototype measurements of a MEMS gyroscope system with a resolution of 0.025 $^{\circ}$/s/ $\sqrt{{\rm Hz}}$. The architecture makes extensive use of control loops, which are mostly in the digital domain. For the primary mode both the amplitude and the resonance frequency are tracked and controlled. The secondary mode readout is based on unconstrained $\Sigma\Delta$ force-feedback, which does not require a compensation filter in the loop and thus allows more beneficial quantization noise shaping than prior designs of the same order. Due to the force-feedback, the gyroscope has ample dynamic range to correct the quadrature error in the digital domain. The largely digital setup also gives a lot of flexibility in characterization and testing, where system identification techniques have been used to characterize the sensors. This way, a parasitic direct electrical coupling between actuation and readout of the mass-spring systems was estimated and corrected in the digital domain. Special care is also given to the capacitive readout circuit, which operates in continuous time.