system and circuit design for a capacitive mems gyroscope - Aaltodoc

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Hprictrl(s), Hprictrl(z) Primary resonator amplitude controller, either continuous- time or discrete-time Hqcctrl(s), Hqcctrl(z) Quadrature compensation controller, either continuous- time or discrete-time Hqcomp(s) Transfer function from quadrature compensation voltage xix to force in electrostatic quadrature compensation performed with a dc voltage H V/q(s) Transfer function from charge to voltage, part of H V/y(s) H V/x(s) Transfer function from primary resonator displacement to voltage H∗ V/x (s) Transfer function from primary resonator displacement to voltage after frequency transformation to dc H V/y(s) Transfer function from secondary resonator displacement to voltage H x/F(s) Primary resonator transfer function from force to displacement H∗ x/F (s) Primary resonator transfer function from force to displacement after frequency transformation to dc Fy,all All forces acting on the y-directional resonator H y/F(s) Secondary resonator transfer function from force to dis- IBCOMP1, IBCOMP2 IBCORE IBIAS ICT RL ID placement Biasing currents of the comparator of CCO CCO static biasing current Biasing current CCO control current Drain current Iin,pri, Iin,pri(t) In-phase component of the input of the synchronous de- Iin,sec modulator in the primary resonator readout In-phase component of the input of the synchronous de- modulator in the secondary resonator readout
xx Iin,sec Ileak In-phase component of the input of the synchronous de- modulator in the secondary resonator readout, normal- ized with respect to the primary signal Leakage current Iout,pri, Iout,pri(t) In-phase component of the output of the synchronous de- modulator in the primary resonator readout Iout,sec, Iout,sec(t) In-phase component of the output of the synchronous de- Iout,sec,n Iset,pri modulator in the secondary resonator readout Spectral density of the mechanical-thermal noise in the in-phase component of the output after demodulation Target value for the primary resonator vibration amplitude Iout,pri j Imaginary unit, commonly also denoted by i K Word length at the output of the interpolation filter, en- tering the noise-shaping loop k, k Spring constant; spring matrix K(z) Transfer function of a compensator kB keff kes KF kxx kxy, kyx kyy Boltzmann constant, 1.38066 · 10 −23 J/K Effective spring constant after electrostatic spring soft- ening Electrostatic spring constant Flicker (1/f) noise coefficient Spring constant in the x-direction Anisoelastic terms in the 2-D EoM Spring constant in the y-direction L Channel length in a MOS transistor M Word length at the input of the DAC m, m Mass; mass matrix mIF Interpolation factor
Page 1 and 2: TKK Dissertations 116 Espoo 2008 SY
Page 3 and 4: Distribution: Helsinki University o
Page 6: VÄITÖSKIRJAN TIIVISTELMÄ TEKNILL
Page 9 and 10: ii introduced on a more general lev
Page 11 and 12: iv Muut tarvittavat piirilohkot - k
Page 13 and 14: vi I would like to express my grati
Page 15 and 16: viii 2.4.3 Single- and Two-Chip Imp
Page 17 and 18: x 8.4.2 High-Voltage DAC . . . . .
Page 19 and 20: xii ΔVDC ε0 εr ζI, ζQ ηI, ηQ
Page 21 and 22: xiv ω0y ωc ωcw ωe ωexc ωUGF
Page 23 and 24: xvi Cn,sw,rms COX CP Cpar Input-ref
Page 25: xviii G V/Ω G V/x G V/y G y/Ω G y
Page 29 and 30: xxii RB RCOMP Rcorr Reff R f RGM Re
Page 31 and 32: xxiv Vin,sec,de(t) Output of the se
Page 33 and 34: xxvi AGC Automatic Gain Control ALC
Page 35 and 36: xxviii ICMR Input Common-Mode Range
Page 37 and 38: xxx VRG Vibrating Ring Gyroscope XO
Page 39 and 40: 2 Introduction with more details in
Page 41 and 42: 4 Introduction effect couples vibra
Page 43 and 44: 6 Introduction mary resonator excit
Page 46 and 47: Chapter 2 Micromechanical Gyroscope
Page 48 and 49: 2.1 Operation of a Vibratory Microg
Page 60 and 61: 2.2 Mechanical-Thermal Noise 23 2.1
Page 62 and 63: 2.3 Excitation and Detection 25 req
Page 64 and 65: 2.4 Manufacturing Technologies 27 b
Page 66 and 67: 2.4 Manufacturing Technologies 29 E
Page 68 and 69: 2.5 Published Microgyroscopes 31 2.
Page 70 and 71: 2.5 Published Microgyroscopes 33 gy
Page 72 and 73: 2.5 Published Microgyroscopes 35 te
Page 74 and 75: 2.5 Published Microgyroscopes 37 th
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2.5 Published Microgyroscopes 39 el
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2.5 Published Microgyroscopes 41 ar
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2.6 Commercially Available Microgyr
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1) User-selectable 2) Specified for
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12) Device has both analog and digi
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Chapter 3 Synchronous Demodulation
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3.1 Demodulation in Ideal Case 51 3
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3.3 Secondary Resonator Transfer Fu
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3.4 Nonlinearities in Displacement-
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3.5 Mechanical-Thermal Noise 63 Fig
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3.7 Discussion 65 non-idealities we
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68 Primary Resonator Excitation dis
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70 Primary Resonator Excitation The
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72 Primary Resonator Excitation and
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74 Primary Resonator Excitation 4.2
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76 Primary Resonator Excitation * H
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78 Primary Resonator Excitation dis
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80 Primary Resonator Excitation res
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82 Primary Resonator Excitation DAC
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84 Primary Resonator Excitation ac
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86 Compensation of Mechanical Quadr
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Figure 5.6 A feedback loop with Σ
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Chapter 6 Zero-Rate Output The zero
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6.1 Sources of Zero-Rate Output 99
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6.2 Effects of Synchronous Demodula
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6.3 Effects of Quadrature Compensat
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6.5 Discussion 109 source in the el
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112 Capacitive Sensor Readout Typic
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114 Capacitive Sensor Readout 7.1.1
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116 Capacitive Sensor Readout stati
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118 Capacitive Sensor Readout corre
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120 Capacitive Sensor Readout examp
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122 Capacitive Sensor Readout large
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124 Capacitive Sensor Readout DC an
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126 Capacitive Sensor Readout (a)
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128 Capacitive Sensor Readout In th
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130 Capacitive Sensor Readout suffi
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132 Capacitive Sensor Readout (a)
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134 Capacitive Sensor Readout negli
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136 Capacitive Sensor Readout reset
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138 Capacitive Sensor Readout incre
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140 Capacitive Sensor Readout is co
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142 Implementation such a way that
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144 Implementation 8.2 System Desig
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146 Implementation 8.2.1 Sensor Rea
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148 Implementation together with th
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150 Implementation approach require
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152 Implementation used for clock g
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154 Implementation Because of the d
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156 Implementation plied from the C
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158 Implementation of a PMOS transi
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160 Implementation R eff (MΩ) 1000
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162 Implementation R eff (MΩ) 1000
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164 Implementation effective resist
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166 Implementation is applied to th
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168 Implementation ther differences
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170 Implementation (a) (b) (c) V in
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172 Implementation V inp V inn V C2
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174 Implementation (a) -z -2 z -1 1
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Figure 8.19 Schematic of the implem
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178 Implementation teresis are equa
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180 Implementation From the silicon
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182 Implementation V inp V inn C 1p
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184 Implementation as an XOR operat
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186 Implementation triggered by the
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188 Implementation Θ 1 (°) 2.5 2
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190 Implementation R.m.s. noise (dB
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192 Implementation Quadrature outpu
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194 Implementation Signal (dBFS)
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196 Implementation itor towards gro
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198 Implementation Finally, the mea
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200 Implementation Root Allan varia
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202 Implementation Technology Table
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204 Conclusions and Future Work usi
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Bibliography [1] H. C. Nathanson an
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Bibliography 209 [20] L. Aaltonen,
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Bibliography 211 [45] J. M. Bustill
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Bibliography 213 [68] B. V. Amini,
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Bibliography 215 [88] S. R. Zarabad
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Bibliography 217 [113] Z. Y. Chang
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Bibliography 219 [138] ——, “N
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Appendix A Effect of Nonlinearities
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+ 3ABD · sin((ω0x − 2ωΩ)t + 2
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+ 3BC2 · cos((3ω0x + ωΩ)t − T
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Appendix B Effect of Mechanical-The
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lowing an identical path, the power
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232 Parallel-Plate Actuator with Vo
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234 Noise Properties of SC Readout
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Page 275 and 276:
Page 278 and 279:
Appendix F Microphotograph of the I
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