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

Fixed Plates

Angstrom40

1

pm5.2

10kHz2

mG12

2

π

ax

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xcell

Vibratory Gyroscope

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• Vibrate along drive axis with

oscillator @ fdrive

• Detect vibration @ fdrive

about sense axis with

accelerometer

Angstrom

4000

1x

Gyroscope Design

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Electrostatic

Drive

Electrostatic

Sense Pickup

Power / Accuracy Tradeoff

Dm

nIg

v112 const

noise

signalSNR

Design options:

1) Lower amplifier noise

2) Increase signal Dv

without power penalty

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gyro

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 Axis Response

fdrive Frequency

Drive

Amplitude

B. Boser 8

Mode-Matching

Fabrication tolerance ~ 2%

Match by active tuning get Q times the deflection

Drive Axis Response Sense Axis Response

Amplitude

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Frequency Error Estimation

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frequency

Re

spo

nse

r/2

bandwidth

open loop response:

X Y

frequency

Re

sp

on

se

|T(s)| >> 1

feedback (“closed loop”):

X Y S +

-

S

Pilot Tones fsense

Sense Resonance Estimation

sH

1

m

Frequency fsense

B. Boser 11

Key Idea

sHK

1

mf

two pilot tones locked

to the drive frequency

fdrive

amplitudes depend on

frequency mismatch!

force amplitude difference to zero

B. Boser 12

Electrostatic Tuning tuneV

sx

tuneV

sx

ticElectrosta

2

tune2

tune VC

kk msgap

Mechanical

Net Stiffness

Voltage-Tunable

Spring

Spring

B. Boser 13

Electrostatic Force Feedback

sx

biasV

fbv

fbv

sx

biasV

fbv

fbv

sfbbiass

fbbiass

e xvVC

vVC

F

StiffnessDependent Signal

Gain Force--ToVoltage

2200 22 2gapgap

B. Boser 14

2-level feedback (Sampled Data “SD”) feedback

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

Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Collocated Control (same electrode)

Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Non-collocated Control (separate electrodes)

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Sampled Data System

Excess Lag

Aliased

Resonance

Frequency

(kHz)

Normalized

Magnitude

(dB)

Phase

(°)

Excess Lag

Aliased

Resonance

Frequency

(kHz)

Normalized

Magnitude

(dB)

Phase

(°)

B. Boser 17

Negative Feedback

Frequency

(kHz)

Magnitude

(dB)

Phase

(°)

Large Negative Margin

Frequency

(kHz)

Magnitude

(dB)

Phase

(°)

Large Negative Margin

Unstable

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Positive Feedback

Frequency

(kHz)

Magnitude

(dB)

Phase

(°) Small But

Enough

Margin Huge Positive

Margins

Frequency

(kHz)

Magnitude

(dB)

Phase

(°) Small But

Enough

Margin Huge Positive

Margins

B. Boser 19

stable

DC gain < 0

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

Δf

v2n

Ci

IdealSampler

CS-

CS+

CP

CPCi CL

VoVm Vx

Vx

Ts

Vm

sample

CL

Signal

Δf

v2n

CS-

CS+

CP

CP

CL

CL

Vm VxGmIdeal

SamplerVo

Vx

Ts

Vm

Signal

sample

B. Boser 21

Boxcar Sampler versus Charge Integrator

• n = Ts/ amp of charge integrator

• F = feedback factor of charge integrator

• Typical SNR improvement ~10dB

• 10x power savings!

penaltysettling

penalty feedback

2

CI

BS

2

n

F1

1

SNR

SNR

τ

B. Boser 22

System Block Diagram

Sense/FB

Switch

FE

Two-Level

Feedback

3rd-Order

SC Filter

1-Bit

Quantizer

3

Accumulator

ΣΔDither and

Offset Comp

Mode-Mismatch

EstimatorPilot Tones

EstimateΣΔ

Vtune1

Digital

Output

Mode Matching, Dither and Offset Compensation

(Digital, Off-Chip)

Sense Element

Coriolis

Acceleration

VmDrive

Motion

PI

Filter

Coriolis Readout

Sense/FB

Switch

FE

Two-Level

Feedback

3rd-Order

SC Filter

1-Bit

Quantizer

3

Accumulator

ΣΔDither and

Offset Comp

Mode-Mismatch

EstimatorPilot Tones

EstimateΣΔ

Vtune1

Digital

Output

Mode Matching, Dither and Offset Compensation

(Digital, Off-Chip)

Sense Element

Coriolis

Acceleration

VmDrive

Motion

Sense Element

Coriolis

Acceleration

VmDrive

Motion

PI

Filter

Coriolis Readout

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Digital background

calibration

Negligible power

penalty

Chip Photo

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Chip Micrograph

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Output Spectrum

Frequency

(kHz)

PSD

Relative to

Full Scale

(dB)

Frequency

(kHz)

PSD

Relative to

Full Scale

(dB)

B. Boser 26

Output Spectrum

Without calibration

• Noise Floor:

0.03°/s/Hz

• Mismatch:

~400Hz (2.6%)

14800 15000 15200 15400 15600 15800 16000 1620010

-3

10-2

10-1

100

101

102

103

Pilot

Tones

~400Hz

An

gu

lar

Ra

te (°/

se

c)

Frequency (Hz)

B. Boser 27

Output Spectrum

14800 15000 15200 15400 15600 15800 16000 1620010

-3

10-2

10-1

100

101

102

103

Pilot

Tones

An

gu

lar

Ra

te (°/

se

c)

Frequency (Hz)

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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

Tuning Voltage Startup Transient

300ms300ms

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