An Unconstrained Architecture for Systematic Design of Higher Order $\Sigma \Delta$ Force-Feedback Loops

Nowadays, SigmaDelta-modulation is a widely used technique for analog-to-digital (A/D) conversion, especially when aiming for high resolutions. While being applied initially for purely electrical A/D converters, its application has been expanded to mixed mechanical-electrical systems. This has led to the use of SigmaDelta force-feedback for digital readout of high-performance inertial sensors. However, compared with their electrical counterpoint, SigmaDelta force-feedback loops often have to deal with three additional issues: 1) an increased stability problem due to phase-lag occurring in the sensor; 2) the injection of relatively high levels of readout noise in the loop; and 3) the lack of degrees-of-freedom of many SigmaDelta force-feedback architectures for implementing an arbitrary noise transfer function. As a result, SigmaDelta force-feedback loops found in literature are designed in a much less systematic way as compared with electrical SigmaDelta modulators. In this paper, we address these issues and propose a new unconstrained architecture. Based on this architecture, we are able to present a systematic approach for designing SigmaDelta force-feedback loops. Additionally, the main strengths and weaknesses of different SigmaDelta force-feedback architectures are discussed.