Digitally Tuned Low Power Gyroscope - Peopleboser/presentations/gyro complete.pdfDigitally Tuned Low Power Gyroscope Bernhard E. Boser & Chinwuba Ezekwe Berkeley Sensor & Actuator

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

B. Boser 3

xcell

Vibratory Gyroscope

B. Boser 4

• Vibrate along drive axis with

oscillator @ fdrive

• Detect vibration @ fdrive

about sense axis with

accelerometer

Angstrom

4000

1x

Gyroscope Design

B. Boser 5

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

B. Boser 6

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

B. Boser 9

Frequency Error Estimation

B. Boser 10

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)

B. Boser 16

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

B. Boser 18

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

B. Boser 23

Digital background

calibration

Negligible power

penalty

Chip Photo

B. Boser 24

Chip Micrograph

B. Boser 25

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)

B. Boser 28

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