Electromechanical Sigma–Delta Modulators (<inline-formula> <tex-math notation="LaTeX">$\Sigma \Delta {\mathrm{ M}}$ </tex-math> </inline-formula>) Force Feedback Interfaces for Capacitive MEMS Inertial Sensors: A Review

Abstract

Analog-to-digital converters based on sigma–delta modulators ( $\Sigma \Delta {\mathrm{ M}}$ ) are a popular choice for high resolution conversion from the analog to the digital domain. With relatively small modifications, they can also be used as electromechanical $\Sigma \Delta {\mathrm{ M}}$ (EM- $\Sigma \Delta {\mathrm{ M}}$ ) force feedback interfaces for capacitive micro-electromechanical systems (MEMSs) inertial sensors. Such interfaces are able to combine the benefits of force feedback and analog-to-digital conversion at relatively modest circuit cost. This paper provides a comprehensive review of EM- $\Sigma \Delta {\mathrm{ M}}$ interfaces for capacitive MEMS inertial sensors. The principle and the design methodology of EM- $\Sigma \Delta {\mathrm{ M}}$ interfaces are introduced. A classification of EM- $\Sigma \Delta {\mathrm{ M}}$ accelerometers and gyroscopes is presented, and a detailed analysis of different EM- $\Sigma \Delta {\mathrm{ M}}$ architectures is given. The most representative EM- $\Sigma \Delta {\mathrm{ M}}$ inertial sensors systems are discussed and compared with regard to their performance characteristics. In particular, the properties of various discrete and continuous-time techniques and a system parameter optimization methodology are illustrated through specific examples. Finally, current challenges and future development trends of EM- $\Sigma \Delta {\mathrm{ M}}$ interfaces for inertial sensors have been identified.