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University of Southampton Research Repository Eprints Soton University of Southampton Research Repository ePrints Soton Copyright © and Moral Rights for this thesis are retained by the author and/or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder/s. The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders. When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given e.g. AUTHOR (year of submission) "Full thesis title", University of Southampton, name of the University School or Department, PhD Thesis, pagination http://eprints.soton.ac.uk UNIVERSITY OF SOUTHAMPTON FACULTY OF PHYSICAL SCIENCES AND ENGINEERING Electronics and Computer Science Multi Stage Noise Shaping (MASH) Sigma Delta Modulator for Capacitive MEMS Inertial Sensors by Bader Almutairi Thesis for the degree of Doctor of Philosophy April 2015 UNIVERSITY OF SOUTHAMPTON ABSTRACT School of Electronics and Computer Science Doctor of Philosophy Multi Stage Noise Shaping (MASH) Sigma Delta Modulator for Capacitive MEMS Inertial Sensors by Bader Almutairi This research discusses the theoretical investigation, simulation and hardware implementation of the ElectroMechanical Multi-stAge noise SHaping (EM-MASH) sigma delta modulator (ΣΔM). The potential advantages of an EM-ΣΔM MASH compared to single-loop high-order ΣΔMs applied to inertial MEMS sensors are its inherent stability and high overload input level due to the use of lower order ΣΔMs in its individual stages. Furthermore, MASH has the advantages of high dynamic range and high noise shaping performance because of its overall high-order ΣΔM architecture. So far, the EM-MASH has not been sufficiently explored. This study is expected to serve as solid basis for the application of EM-MASH. In this research, various EM-MASH architectures (MASH21, MASH22, MASH211, MASH221 and MASH222) were theoretically studied, and the results were validated with simulations. A fourth order EM-MASH22-ΣΔM was theoretically examined and successfully implemented with a capacitive MEMS accelerometer, which includes a second order EM-Σ∆M loop cascaded with a purely electronic second order Σ∆M. The quantization noise from the first loop is digitised by the second loop and then cancelled by digital filters, whereas the quantization noise from the second loop is shaped by the second loop filter and a digital filter, which together provide fourth order noise shaping. The performance of EM-MASH22 was compared with that of a single-loop fourth order EM-Σ∆M (SD4). Both architectures were investigated by system level modelling and hardware implementation using surface-mount PCB technology. The results show that (a) both architectures achieve the same noise floor level of 19 μg/√Hz; (b) MASH22 is unconditionally stable, whereas SD4 is only conditionally stable; and (c) MASH22 achieves a higher overload input level and a higher dynamic range than does SD4. Furthermore, the research presents a novel EM-MASH-Σ∆M that employs a dual quantization technique and adopts a 2-0 structure (EM-MASH20). With a simpler and configurable composition, MASH20 is aimed at exhibiting a performance higher than that achieved with the MASH22 structure. The MASH20 does not require a second-stage ΣΔM, which reduces the complexity of the digital filters compared to those required for the MASH22; thus, the digital filter matching is more easily achievable. The study shows that the MASH20, like the MASH22, has an inherent stability, high overload input level, and high dynamic range compared to single-loop ΣΔM. However, the MASH20, with its simpler implementation, achieved a higher dynamic range and signal-to-noise ratio than the MASH22 and the SD4. A capacitive MEMS accelerometer was designed and employed with MASH20. Within a bandwidth of 1 kHz, the sensor achieves a noise floor level of 15 μg/√Hz, a full-scale acceleration of ±20 g and a bias instability of 20 µg for a period of three hours. The EM-MASH-Σ∆M is sensitive to the variation of the sensing element parameters and other analogue parameters, both of which are subject to manufacturing tolerance and imperfections. This causes a leakage of the quantization noise in the final output and degrades the modulator performance. The research explored a calibration method to solve this problem by utilizing the digital domain capabilities. The method is based on the optimization algorithm which was investigated using MATLAB. The research confirms the concept of the EM-MASH structure and proves that it is applicable as a closed-loop interface for high-performance capacitive MEMS inertial sensors. Table of Contents Table of Contents ............................................................................................................. i List of Tables ................................................................................................................... v List of Figures ................................................................................................................ vii DECLARATION OF AUTHORSHIP ........................................................................ xv Acknowledgements ...................................................................................................... xvii Abbreviations ............................................................................................................... xix Symbols ……………………………………………………………………………..xxii Introduction ......................................................................................... 1 1.1 Introduction ......................................................................................................... 1 1.2 Motivation and Contribution............................................................................... 2 1.3 Document Structure ............................................................................................ 4 Theoretical Background ..................................................................... 7 2.1 Introduction ......................................................................................................... 7 2.2 Mechanical Lumped Model of an Accelerometer .............................................. 7 2.3 Brownian Noise ................................................................................................ 10 2.4 Capacitive MEMS Control Strategies ............................................................... 11 2.4.1 Open-Loop Accelerometer ................................................................. 11 2.4.2 Closed-Loop Accelerometer ............................................................... 13 2.5 Sigma-Delta Principle ....................................................................................... 17 2.5.1 Quantization & Modulation Noise ...................................................... 17 2.5.2 Noise Shaping ..................................................................................... 19 2.5.3 Limit Cycle and Dithering .................................................................. 24 2.5.4 Higher Order Single-Bit ΣΔ Modulators ............................................ 24 2.6 Summary ........................................................................................................... 26 Literature Review ............................................................................. 27 3.1 State of the Art .................................................................................................. 27 3.2 Second Order Electromechanical Sigma-Delta Modulator............................... 30 3.3 Higher Order Single Loop EM-ΣΔM ................................................................ 31 3.4 Single-Loop High Order Electromechanical ΣΔM Design Methodologies ...... 36 i 3.5 Multi Stage Noise Shaping (MASH) Sigma Delta Modulator ......................... 43 3.6 Summary ........................................................................................................... 48 Design and Simulation of MASH ΣΔ Modulators for Inertial MEMS Capacitive Accelerometer ............................................................... 51 4.1 Introduction ....................................................................................................... 51 4.2 Analytical Investigation .................................................................................... 51 4.2.1 Second Order Electromechanical Σ∆ Modulator ................................ 52 4.2.2 Electromechanical MASH22-ΣΔM .................................................... 54 4.3 Electromechanical MASH-ΣΔM Stability Analysis ......................................... 57 4.4 Electrostatic Feedback Force and the Maximum Acceleration Input Level ..... 59 4.5 SNR Estimation ................................................................................................ 60 4.6 Design Procedure for Electromechanical MASH ............................................. 61 4.7 MATLAB and Simulink Modelling ................................................................. 63 4.7.1 Electromechanical MASH22 .............................................................. 63 4.7.2 Higher Order Electromechanical MASH............................................ 67 4.8 Summary ..........................................................................................................
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