In this paper we describe the system architecture and prototype measurements of a MEMS gyroscope system with a resolution of 0.025The 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 Σ∆ 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 set-up 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.
Nowadays, 61-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 61 force-feedback for digital readout of high-performance inertial sensors. However, compared with their electrical counterpoint, 61 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 61 force-feedback architectures for implementing an arbitrary noise transfer function. As a result, 61 force-feedback loops found in literature are designed in a much less systematic way as compared with electrical 61 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 61 force-feedback loops. Additionally, the main strengths and weaknesses of different 61 force-feedback architectures are discussed.
Index Terms-A/D-conversion, force-feedback, MEMS inertialsensors, sigma-delta (61) modulation, systematic design.
61-modulation is a proven method to realize high-and very high-resolution analog-to-digital converters. A particularly efficient way to implement such a modulator uses double-sampling where the circuit operates during both clock phases of the master-clock. Hence, the sampling frequency is twice the master-clock frequency. Unfortunately, path mismatch between both sampling branches causes a part of the quantization noise to fold from the Nyquist frequency back in the signal band. Therefore, the performance is severely degraded. In this paper, we show that the problem is reduced but not eliminated by employing multibit quantization. Next, we present an indepth solution for the problem. The approach consists of modifying the quantization noise transfer function of the overall modulator to have one or several zeros at the Nyquist frequency. This way the effect of noise folding can nearly be eliminated. It is shown that this can be implemented by a simple modification of one of the integrators of the overall modulator circuit. Finally, several design examples of single-bit and multibit modulators are discussed.
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