system and circuit design for a capacitive mems gyroscope - Aaltodoc

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Symbols and Abbreviations α Parameter describing the magnitude of the error signal αrot caused by mechanical quadrature signal Angular acceleration of a rotating frame of reference with respect to an inertial frame of reference β Parameter describing the magnitude of the error signal caused by non-proportional damping; parameter describing the shape of the Kaiser window γ Parameter describing the magnitude of the error signal γn caused by electrical cross-coupling in the sensor element Excess noise factor in a MOS transistor δ Parameter describing the magnitude of the error signal caused by direct excitation of the secondary resonator Δφ Half of the difference between φUSB and φLSB Δω Frequency offset from the operating frequency ω0x ΔCD, ΔCD(t) Dynamic part of the detection capacitance ΔCD,pri ΔCD,sec ΔCexc ΔG y/Ω Dynamic part of the primary resonator detection capacitance Dynamic part of the secondary resonator detection capacitance Dynamic part of the primary resonator excitation capacitance Half of the difference between G y/Ω,USB and G y/Ω,LSB
xii ΔVDC ε0 εr ζI, ζQ ηI, ηQ Amplitude of the signal used to modulate VDC in ZRO measurement Permittivity of vacuum, 8.85418 · 10 −12 F/m Relative permittivity Parameters describing the magnitude of the error signal caused by variation in the middle electrode biasing voltage Parameters describing the magnitude of the error signal caused by cross-coupling of clock signals in the electronics θ Phase shift of the transfer function from the displacement θ1 θ1,pri θ1,sec θ2 θLPF,pri θLPF,sec ιI, ιQ of the secondary resonator to voltage; overall phase error in the synchronous demodulation resulting from the electronics Difference between phase shifts caused by primary and secondary channels Phase shift caused by the primary channel from CSA input to the output of the second HPF Phase shift caused by the secondary channel from CSA input to the output of the second HPF Phase shift from the output of the second HPF in the primary channel to the clock input of the ADC in the secondary channel Phase shift caused by the primary channel LPF Phase shift caused by the secondary channel LPF Parameters describing the magnitude of the error signal caused by cross-coupling of the primary resonator signal in the electronics κ Mode separation, κ = ω0y/ω0x µ Carrier mobility in the channel area
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: x 8.4.2 High-Voltage DAC . . . . .
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 and 26: xviii G V/Ω G V/x G V/y G y/Ω G y
Page 27 and 28: xx Iin,sec Ileak In-phase component
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.
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2.5 Published Microgyroscopes 33 gy
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2.5 Published Microgyroscopes 35 te
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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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Appendix F Microphotograph of the I
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