resonant strain sensor

© 2005 B. Boser 1

Resonant Strain Sensor

K. E. Wojciechowski and Bernhard E. Boser Berkeley Sensor & Actuator Center

Dept. of Electrical Engineering and Computer Sciences

University of California, Berkeley

© 2005 B. Boser 2

Outline

• Strain sensor

• Resonant force sensing

• Oscillator analysis

– Phase and frequency noise

– Design for minimum noise

• Oscillator sustaining circuit

• Frequency-to-digital conversion

• Conclusions

© 2005 B. Boser 3

Strain Sensor Applications

© 2005 B. Boser 4

Strain Sensor Specifications

Lbeam ≤ 200 mm

g

g

L

L :Strain

• Resolution: 0.1 m

• Full-scale: ±1000 m

• Bandwidth: 10 kHz

• Gauge length: ≤200 mm

m102.0

20pm

μm200μ1.0

10

gg LL

© 2005 B. Boser 5

Resonant Strain Sensor

d

dfff o :Modulation Frequency

38Hz/μ 217kHz :design This d

dffo

Oscillator

Circuit

Frequency

to

Digital

Converter

f

DETF

© 2005 B. Boser 6

Frequency Modulation P

ow

er

Frequency f

d

df

Phase Noise!

© 2005 B. Boser 7

Phase Noise

1 10 100 1 103

1 104

1 105

130

120

110

100

90

80

7070

130

dB10 L f L o f co

100f cof co

100

f

Frequency Offset f [Hz]

Ph

as

e N

ois

e D

en

sit

y

L(

f)

[dB

c/H

z]

Power-Carrier

Bandwidth / Power-NoisefL

Bandwidth f

Noise-Power / Bandwidth

Lnear(f)

Lfar

© 2005 B. Boser 8

Frequency Noise

Bc/Hzd110kHz102

Hz8.35.1

5.1 Noise Phase

3

2

for 2

2 Noise Total

2)( NoiseFrequency

2

2

3

3

2

2

B

SL

LB

fBfdLf

fdfSS

fLffS

fTfar

far

co

B

far

B

ffT

f

© 2005 B. Boser 9

Prior Art MEMS Resonators

• Vacuum encapsulation

• Integrated electronics

• Much worse than quartz – why?

[T. Roessig , 1997]

dB702

NF

[A. Seshia , 2002]

Q = 10000 Q = 17000

dB75

© 2005 B. Boser 10

MEMS Oscillator Noise Roessig

1997

Nguyen

1999

Seshia

2002

Seth

2004

Goal

(This Work)

Noise Lfar [dBc/Hz] -70 -70 -75 -83 < -110

Vacuum

Monolithic

Frequency, fo 175 kHz 16.5 kHz 145 kHz 57 kHz 217 kHz

Motional Res., Rx ? 3.8 M ? 2.5 M

Q 17000 51000 10000 14000

Amplitude VDrive ? ~ 34 mV ~36 mV 5.3 mV

Need oscillator with 1000x lower noise than prior art!

© 2005 B. Boser 11

Low-Noise Oscillator Design

Power-Carrier

Bandwidth / Power-NoisefL

BIG!

small

What is the noise power?

Constrained by gap,

nonlinearity

© 2005 B. Boser 12

Mass m

Spring

k

Damper

b

-x

Fext

Electro-Mechanical Oscillator

xmxbkxFext

© 2005 B. Boser 13

Mass m

Spring

k

Damper

b

-x

V

Fext

Cx

Lx

Rx

Electro-Mechanical Oscillator

xmxbkxFext

© 2005 B. Boser 14

Oscillator Sustaining Circuit

Rx Lx

Cx

V1

I1

Unity-gain feedback

at resonance

© 2005 B. Boser 15


Rx

Rf = Rx

V1 V2 = -V1

Resonator at resonance

Output = Input

(inverted)

© 2005 B. Boser 16


Rx

Rf = Rx

V1 V2 = -V1-1x

© 2005 B. Boser 17

Oscillator Noise Voltage

Rx

Rf = Rx

V1 V2 = -V1-1x

+

+

4kBTrRxf

4kBTrRxf

dffQ

fRTkv oxRBn

2

2

12

214High Q?

© 2005 B. Boser 18

Phase Noise

near

far

L

o

LoB

rB

o

oB

rB

oB

x

n

f

f

QQ

xk

Tk

fQ

fQ

xk

Tk

Q

xk

Rv

fL

2

2

2

2

spring in storedenergy

2

2

1

2

22

221

2

oscillator to delivered power

power-noise

tradeoff

(for high bandwidth optimal Q < 100)

for given mechanical amplitude

Qxk

TkL

oB

rBfar

2

2

2

2 2

14

f

f

Qxk

TkL o

oB

rBnear

© 2005 B. Boser 19

Phase Noise Floor – Interpretation

QResonator in StoredEnergy

Energy Thermal

sElectronicby dReplenisheEnergy

Energy Thermal

22

Qxk

TkL

oB

rBfar

Set by thermodynamics

Resonator properties (size) Resonator quality

Sets long-term stability

MEMS versus Quartz Resonators

1. Maximum power limited in “small”

MEMS oscillators – Increasing resonant frequency helps

– Bulk acoustic waves store more energy

2. High motional impedance Rx – Loaded Q ≈ intrinsic Q

© 2005 B. Boser 20

© 2005 B. Boser 21

Prototype DETF Strain Sensor

Double-ended tuning fork (DETF).

Strain Actuator

Comb drive interface

capacitors for

sustaining circuit

Gauge Length (Lbeam) 200 mm

Width, (Wbeam) 6 mm

Measured Resonant

freq. (fr) 217kHz

Measured Q

(atmospheric

pressure)

370

Measured sensitivity 38Hz/m

© 2005 B. Boser 22

Problem with Low Q Operation

• No vacuum packaging (Q ~ 370)

• Large feature spacing ~3mm gaps

• Modest Vbias = 30V

• No integration: PCB parasitics

Large Rx

18 M 5 kH 0.1 fF

Rx Lx Cx

Cft = 70fF

Large Cft

© 2005 B. Boser 23

Effect of Cft on Sustaining Circuit

Rx

Rf = Rx

-1x

Cft

Isense

(Isense)

f/fo

Cft = 0

0.98 0.99 1 1.01 1.02 -100

-50

0

50

100

Cft = 70 fF

Cft = 20 fF

© 2005 B. Boser 24

Time-Variant Sustaining Circuit

• Undesired ICft decays quickly

• Sinusoidal IDETF decays slowly

• Zero crossings set by DETF, not Cft

VDrive

Cft

IDETF

ICft

VDETF = IDETF *Rt

VCft = ICft*Rt

ISense Rt

VSense +

© 2005 B. Boser 25

Time-Variant Oscillator (TVO) Itot IRES

VDrive

Cft

Ift comparator

Itot

time

IRes

Ift

time

VDrive

© 2005 B. Boser 27

Measured TVO Phase Noise

• Resolution

– 20-n in 10kHz

– 200-p/rt-Hz

– 40-fm/rt-Hz

• Test equipment:

Agilent 5501A

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

1 10 100 1000 10000 100000

dBc/

Hz

offset from carrier, f [Hz]

© 2005 B. Boser 28

MEMS Oscillator Noise

Roessig

1997

Nguyen

1999

Seshia

2002

Seth

2004

This Work

2004

Noise Lfar [dBc/Hz] -70 -70 -75 -83 -120

Vacuum

Monolithic

Frequency, fo 175 kHz 16.5 kHz 145 kHz 57 kHz 217 kHz

Motional Res., Rx ? 3.8 M ? 2.5 M 18 M

Q 17000 51000 10000 14000 370

Amplitude VDrive ? ~ 34 mV ~36 mV 5.3 mV 10 V

© 2005 B. Boser 29

Frequency-to-Digital Conversion

Oscillator

Circuit

Frequency

to

Digital

Converter

f

DETF

Methods:

• Digital demodulation

• Analog PLL followed by ADC

• SPLL

© 2005 B. Boser 30

Digital Demodulation

Nyquist Rate or

Band Pass S A/D

Digital

Demodulator

15 bit,

fs = 20 kHz DETF

Oscillator

1Hz inSNR 1

2NF

rf frequency

Hz/Power

A/D noise floor

ADC Specs:

• 17 Bit A/D required

• Sample Rate fs ≥ 3fr = 651 kHz

• Bandwidth ≥ 2 x (Signal BW + Max change in fr) = 96 kHz

© 2005 B. Boser 31

PLL Demodulator

• Loop filter Bandwidth ≥ Signal Bandwidth (10kHz)

• VCO phase noise better than input phase noise (-120 dBc).

• Scale factor (Kvco) temp/supply dependence can be problem

• Needs extra ADC

DETF

OSCILLATOR

Kvco /s

Loop Filter

Fin

Ffb

VCO

Phase Det.

Kd

A/D: 15 bit,

fs = 20kHz

Phase Locked Loop

inv co

out fK

1V

© 2005 B. Boser 32

Solution: SPLL* Approach

• Performs demodulation and A/D conversion in same step

• Low complexity analog filter and A/D (4 bits) for 15 bit resolution

• Linearity and phase noise set by crystal reference

• Loop filter Bandwidth = Signal Bandwidth (10kHz)

Phase

Detector Digital

filter

Ref: Ian Galton. “A practical Second-Order Delta-Sigma Frequency to Digital Converter”, 1995 International Symposium on Circuits and Systems.

15 bit,

fs = 20kHz A/D

Counter

Kd

Crystal OSC,

Period =Tclk

DETF

OSC

Digitally Controlled OSC (DCO)

Fin

Ffb

Loop Filter

© 2005 B. Boser 33

Frequency-to-Digital Converter

Output:

Digitized frequency

strain

Input from: DETF Strain

Gauge Oscillator

Analog Filter

4bit

A/D Converter

FPGA

© 2005 B. Boser 34

101

102

103

104

105

10-8

10-6

10-4

10-2

100

102

Strain Resolution

Bandwidth (Hz)

mic

ro-s

train

number of points: 216

Simulated w/ 2% PFD mismatch and oscillator noise (red)resolution: 0.0294 microstrain

Measured (black) resolution: 0.0334 microstrain

Simulated 2% PFD mismatch and no oscillator noise (green) resolution: 0.027 microstrain

Measured Strain Resolution

mic

ro-s

trai

n, m

/rt

-Hz

Bandwidth (Hz)

© 2005 B. Boser 35

Test with Strain Actuator

Strain Actuator 10

1 10

2 10

3 10

4 10

5

10 -5

10 -4

10 -3

10 -2

10 -1

10 0

10 1

10 2 Strain Resolution

Bandwidth (Hz)

mic

ro-s

train

m

icro

-str

ain

Bandwidth [Hz]

DETF

100Hz

300Hz

1kHz 10kHz strain input

© 2005 B. Boser 36

Conclusions

• High resonator Q translates into – Low signal power delivered to resonator

– High phase noise

– Lowest phase noise is achieved for moderate Q

• High motional resistance, Rx – Typical for MEMS oscillators, exacerbated in low Q designs

– Incompatible with conventional oscillator circuits

– Overcome with time-variant sustaining circuit

• Strain sensor performance – 20-n (rms) resolution in 10kHz

– 200-mm gauge length

– 40-fm/rt-Hz displacement resolution

© 2005 B. Boser 37

Acknowledgements

• BSAC strain sensor research team under

Professor Albert Pisano

• Wayne Denny and Graham Mcdearmon of

Timken Company

• Bosch RTC for help with testing

• Bosch for fabrication

• Vladimir Petkov, Baris Cagdaser, Manu Seth

• Army Research Office grant # 19-02-1-0198

resonant strain sensor

Documents