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1
EE 245: Introduction to MEMSLecture 26m1: Gyros, Noise & MDS
EE C245: Introduction to MEMS Design LecM 15 C. Nguyen 11/18/08 7
Principle of Operation• Tuning Fork Gyroscope:
InputRotation
DrivenVibration
@ fo
Coriolis(Sense)
Response
CoriolisTorque
z
ω
Am
plitu
de
fo (@ T1)
SenseResponse
DriveResponse
Drive/Sense Response Spectra:
z
xy
Ω×=rrr
vac 2
2r
ccc akam
kFx
ω
rrrr
===
vr
CoriolisAcceleration
Driven Velocity
Rotation Rate
CoriolisDisplacement
CoriolisForce
Beam Stiffness
Beam Mass
Sense Frequency
car
Ωr
Basic Vibratory Gyroscope Operation
EE C245: Introduction to MEMS Design LecM 15 C. Nguyen 11/18/08 8
Principle of Operation• Tuning Fork Gyroscope:
InputRotation
DrivenVibration
@ fo
Coriolis(Sense)
Response
CoriolisTorque
z
z
xy
Ω×=rrr
vac 22r
ccc akam
kFx
ω
rrrr
===
vr
Driven Velocity
Beam Stiffness
Beam Mass
Sense Frequency
car
Ωr
Vibratory Gyroscope Performance
• To maximize the output signal x, need:
Large sense-axis massSmall sense-axis stiffness(Above together mean low resonance frequency)Large drive amplitude for large driven velocity (so use comb-drive)If can match drive freq. to sense freq., then can amplify output by Q times
EE C245: Introduction to MEMS Design LecM 15 C. Nguyen 11/18/08 9
MEMS-Based GyroscopesVibrating Ring GyroscopeVibrating Ring Gyroscope
EE C245: Introduction to MEMS Design LecM 15 C. Nguyen 11/18/08 11
Sense Electrodes
Tuning Electrodes
Sense Electrodes
Tuning Electrodes
Drive Electrode
zΩr
Drive
Sense
[Zaman, Ayazi, et al, MEMS’06]
Drive Voltage Signal
(-) Sense Output Current
(+) Sense Output Current
Drive Oscillation Sustaining Amplifier
Differential TransRSense
Amplifier
MEMS-Based Tuning Fork Gyroscope
EE C245: Introduction to MEMS Design LecM 15 C. Nguyen 11/18/08 12
• Drive and sense axes must be stable or at least track one another to avoid output drift
Sense Electrodes
Drive Electrode
Tuning Electrodes
Tuning Electrodes
Quadrature Cancellation Electrodes
Drive Electrode
ω
Am
plitu
de
DriveResponse
T1
T2
fo (@ T1) fo (@ T2)
Problem: if drive frequency changes relative to sense frequency, output
changes bias drift
Problem: if drive frequency changes relative to sense frequency, output
changes bias drift
Drive
Sense
Need: small or matched drive and sense axis temperature
coefficients to suppress drift
Need: small or matched drive and sense axis temperature
coefficients to suppress drift
SenseResponse
Sense Electrodes
MEMS-Based Tuning Fork Gyroscope
EE C245: Introduction to MEMS Design LecM 15 C. Nguyen 11/18/08 13
Mode Matching for Higher Resolution• For higher resolution, can try to match drive and sense axis resonance frequencies and benefit from Q amplification
Sense Electrodes
Drive Electrode
Tuning Electrodes
Tuning Electrodes
Quadrature Cancellation Electrodes
Drive Electrode
ω
Am
plitu
de
DriveResponse
T1
T2
fo (@ T1) fo (@ T2)
Problem: mismatch between drive and
sense frequencies even larger drift!
Problem: mismatch between drive and
sense frequencies even larger drift!
Drive
Sense
Need: small or matched drive and sense axis temperature
coefficients to make this work
Need: small or matched drive and sense axis temperature
coefficients to make this work
SenseResponse
EE C245: Introduction to MEMS Design LecM 15 C. Nguyen 11/18/08 14
Issue: Zero Rate Bias Error• Imbalances in the system can lead to zero rate bias error
Drive imbalance off-axis motion
of the proof mass
Drive imbalance off-axis motion
of the proof mass
Output signal in phase with the
Coriolis acceleration
Output signal in phase with the
Coriolis acceleration
Sense Electrodes
Drive Electrode
Tuning Electrodes
Sense Electrodes
Tuning Electrodes
Quadrature Cancellation Electrodes
Quadrature Cancellation Electrodes
Mass imbalance off-axis motion
of the proof mass
Mass imbalance off-axis motion
of the proof mass
Quadrature output signal that can be confused with the
Coriolis acceleration
Quadrature output signal that can be confused with the
Coriolis acceleration
Drive Electrode
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EE 245: Introduction to MEMSLecture 26m1: Gyros, Noise & MDS