Digitally Tuned Low Power Gyroscope Bernhard E. Boser & Chinwuba Ezekwe Berkeley Sensor & Actuator Center Dept. of Electrical Engineering and Computer Sciences University of California, Berkeley B. Boser 1
Outline Objective: 100x power reduction in MEMS gyroscope What are gyroscopes? Power reduction techniques Mechanical gain Low power, low noise amplification Results B. Boser 2
Accelerometer flexture anchor N Unit Cells 2 2π 10kHz Fixed Plates xcell x a 2 2.5pm 1 40 1mG Angstrom B. Boser 3
Vibratory Gyroscope Vibrate along drive axis with oscillator @ f drive Detect vibration @ f drive about sense axis with accelerometer x 1 4000 Angstrom B. Boser 4
Gyroscope Design Electrostatic Drive Electrostatic Sense Pickup B. Boser 5
Power / Accuracy Tradeoff 2 1 1 vn gm I D signal SNR noise const Design options: 1) Lower amplifier noise 2) Increase signal Dv gyro without power penalty B. Boser 6
Outline Objective: 100x power reduction in MEMS gyroscope What are gyroscopes? Power reduction techniques Mechanical gain Low power, low noise amplification Results B. Boser 7
Mode-Matching Drive Amplitude Drive Axis Response f drive Frequency B. Boser 8
Mode-Matching Amplitude get Q times the deflection Fabrication tolerance ~ 2% Match by active tuning Drive Axis Response Sense Axis Response B. Boser 9
Frequency Error Estimation open loop response: X Y Response bandwidth feedback ( closed loop ): Pilot Tones f r /2 sense frequency X + S - S Y Response T(s) >> 1 frequency B. Boser 10
Sense Resonance Estimation H m 1 s f sense Frequency B. Boser 11
Key Idea 1 K H f m s two pilot tones locked to the drive frequency amplitudes depend on frequency mismatch! f drive force amplitude difference to zero B. Boser 12
Electrostatic Tuning V tune x s Voltage-Tunable Spring Net Stiffness k s k Mechanical m C 2 tune V 2 tune gap Electrostatic Spring B. Boser 13
Electrostatic Force Feedback v fb x s V bias v fb F e C gap Voltage-To- Force Gain C v gap SignalDependent Stiffness s0 s0 2 2 Vbias v fb 2 V bias 2 2 fb x s 2-level feedback (Sampled Data SD ) B. Boser 14
Sensor Frequency Response Main mode near 15kHz Big parasitic modes near 95kHz and 300kHz Smaller parasitic modes all over Feedback? B. Boser 15
Parasitic Resonances Normalized Magnitude (db) Normalized Magnitude (db) Phase ( ) Phase ( ) Frequency (Hz) Non-collocated Control (separate electrodes) Frequency (Hz) Collocated Control (same electrode) B. Boser 16
Sampled Data System Normalized Magnitude (db) Aliased Resonance Phase ( ) Excess Lag Frequency (khz) B. Boser 17
Negative Feedback Magnitude (db) Phase ( ) Unstable Large Negative Margin Frequency (khz) B. Boser 18
Positive Feedback Magnitude (db) DC gain < 0 Phase ( ) Small But Enough Margin Huge Positive Margins stable Frequency (khz) B. Boser 19
Mode-Matching Summary >100x increased signal 100x power savings Fabrication tolerances, drift mismatch Background calibration Electrostatic tuning Sensitivity = f(q, environment) Force feedback Stability positive feedback B. Boser 20
Sampling Noise Closed Loop Open Loop V m C S+ v 2 n C C i P CL Δf V x Ideal Sampler V o V m C S+ C P v 2 n Δf G m V x C L Ideal Sampler V o C S- C P C i C L T s C S- C P C L T s V m V x Signal V m V x Signal sample sample B. Boser 21
Boxcar Sampler versus Charge Integrator SNR SNR BS CI 1 feedback penalty 2 1 F n τ 2 settling penalty n = T s / amp of charge integrator F = feedback factor of charge integrator Typical SNR improvement ~10dB 10x power savings! B. Boser 22
System Block Diagram V tune 1 Accumulator Mode Matching, Dither and Offset Compensation (Digital, Off-Chip) PI Estimate ΣΔ Filter Mode-Mismatch Pilot Tones Estimator ΣΔ Dither and Offset Comp Digital background calibration Negligible power penalty Coriolis Acceleration Drive Motion V m 3 FE 3 rd -Order SC Filter Digital Output Sense/FB Switch 1-Bit Quantizer Sense Element Two-Level Feedback Coriolis Readout B. Boser 23
Chip Photo B. Boser 24
Chip Micrograph B. Boser 25
Output Spectrum PSD Relative to Full Scale (db) Frequency (khz) B. Boser 26
Angular Rate ( /sec) Output Spectrum Without calibration Noise Floor: 0.03 /s/ Hz Mismatch: ~400Hz (2.6%) 10 3 Pilot Tones 10 2 10 1 10 0 ~400Hz 10-1 10-2 10-3 14800 15000 15200 15400 15600 15800 16000 16200 Frequency (Hz) B. Boser 27
Angular Rate ( /sec) Output Spectrum Without calibration Noise Floor: 0.03 /s/ Hz Mismatch: ~400Hz (2.6%) With Calibration Noise Floor: 0.004 /s/ Hz Mismatch: << 50Hz (0.3%) Capacitance resolution 1Hz bandwidth 0.3aF/12.5pF = 24ppb 10 3 Pilot 10 2 Tones 10 1 10 0 10-1 10-2 10-3 14800 15000 15200 15400 15600 15800 16000 16200 Frequency (Hz) B. Boser 28
Tuning Voltage Startup Transient 300ms B. Boser 29
Results Summary Power dissipation: 1mW (excluding drive) Front-end power reduction: Mode-matching: 100x Boxcar sampling: 10x 1000x combined power savings! B. Boser 30
Comparison to previous work Reference Power (mw) Noise ( /sec/ Hz) BW (Hz) Tuning Time (sec) [1] 30 0.05 20 - [2] 13 1 40 - [3] 31 0.05 36 - [4] 6-0.2 140 This work 1 0.004 50 0.3 [1] Geen, JSSC 2002 [2] Petkov, ISSCC 2004 [3] Saukoski, ESSCIRC 2006 [4] Sharma, ISSCC 2007 B. Boser 31
Conclusions Power savings Mechanical gain 100x reduction Open-loop charge amplifier 10x reduction Digital processing occurs minimum power overhead Techniques Background calibrated mode matching insensitive to process variations Positive feedback insensitive to parasitic modes B. Boser 32
Acknowledgements Christoph Lang & Vladimir Petkov Robert Bosch Corporation Gyroscope and financial support B. Boser 33