Capacitive Interface Electronics for Sensing and Actuation

B. E. Boser 1

Capacitive Interface Electronics

for Sensing and Actuation

Bernhard E. Boser

University of California, Berkeley

[email protected]


mailto:[email protected]

B. E. Boser 2

Outline

• Capacitive Sensors

– Applications

– Displacement sensors

• Readout electronics

– Sensor interface

– Circuit topologies

– Electronic noise

• Feedback

– Electrostatic force feedback

– Stability

– Sigma-delta conversion

• Conclusions


B. E. Boser 3

Applications


B. E. Boser 4

flexture

anchor

N Unit CellsFixed Plates

Accelerometer


2 2

1mG

2 10kHz

2.1

Angs5pm trom40

ax

π

acceleration

B. E. Boser 5

Gyroscope


• Vibrate along drive axis with

oscillator @ fdrive

• Detect vibration @ fdrive

about sense axis with

accelerometer

20 fmtypx

Classical radius of

electron: 2.8 fm

B. E. Boser 6

Capacitive Displacement Sensors

Gap closing Overlap


x

xo

x xo

oo

o

xC x C

x x

o

o

o

x xC x C

x

0

1 1

o o x

dC x

C dx x

1 1

o o

dC x

C dx x

Cap closing actuator has higher sensitivity

B. E. Boser 7

Capacitive Displacement Sensors

Gap closing

High sensitivity

Limited travel range

Nonlinear

Pull-in

Overlap


x=20fm

xo=2mm

x=20fm

xo=20mm

20C 10 zF 10 Fo

Low sensitivity (large xo)

Large travel range

Linear (first order)

No pull-in (first order)

Co = 1pF Co = 1pF

21C 1 zF 10 Fo

B. E. Boser 8

Alternative Geometries


Gap Closing Design • high sensitivity

• small travel range

Overlap Sensor Design • low sensitivity

• large travel range

Dis

pla

cem

ent

Compromise

B. E. Boser 9

Outline


– Applications


Readout electronics




• Feedback


– Stability


• Conclusions


B. E. Boser 10

Capacitance to Voltage Conversion


A A

x

Anchor

AA

x = 0

x > 0

t

L

N movable fingers

x0+x

sense capacitor Cs reference capacitor Cref

+Vs = 1V

-Vs = -1V

Vx =Vs C/Co = 10 nV

Cs1 = Co + C

Cs2 = Co - C

Co = 1 pF

C = 10 zF

• maximize C

• minimize Co

• maximize Vs

B. E. Boser 11

Parasitics


Cs1

Cs2

substrate shield

ParasiticElements

B. E. Boser 12

Capacitive Transducer Interface


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Interference


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Differential Interface

Single-Ended Pseudo-Differential


Interference common-mode signal

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Modulation


• Low frequency acceleration signal

– Subject to low-frequency interference

E.g. 1/f noise

– Capacitors do not pass DC

• Solution: modulate signal before it can be corrupted

B. E. Boser 16

Modulation in 2-Chip Sensors


Reject drift in bond-wire capacitance

Sense Voltage Modulation

Ref: Lang et al, Cancelling low frequency errors in MEMS systems, 2009.

B. E. Boser 17

Mechanical Modulation


Ref: P. Lajevardi, V.P. Petkov, and B. Murmann, "A ΣΔ Interface for MEMS Accelerometers using Electrostatic Spring-

Constant Modulation for Cancellation of Bondwire Capacitance Drift," in Digest ISSCC 2012, pp. 196-197.

B. E. Boser 18

Capacitive Interface Circuits

Continuous Time Sampled Data


• Output modulated

• High valued bias resistor

• No bias resistor, direct interface to ADC

• Noise folding

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Noise Folding


B. E. Boser 20

“Boxcar” Sampling


• ~ 10dB noise / power reduction possible

• sensitive to clock jitter & nonlinearity

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Outline


– Applications






Feedback


– Stability


• Conclusions


B. E. Boser 22

Electrostatic Force Feedback

Benefits:

• Reduced sensitivity to transducer

nonlinearity

• Increased bandwidth (gyroscopes)

Challenges:

• Need accurate feedback force

• Stability

• Increased noise


A ain Vout

F

S +

-

B. E. Boser 23

Scale Factor

Openloop Feedback


2 2s s

out

o or r

x

C

V Vx dC xV

dx C x

2

ADC output scale factor

ˆo r ox D x

Vs

xcell ADC out

o

s

VD

V

2

acceleration force

feedback force

1

2fb

dCV mx

dx

21ˆ2

fbdC Vx

dx m

• Final measurement depends on

absolute voltage

• Need precision reference for good

scale factor accuracy

• Feedback is nonlinear

B. E. Boser 24

Stability

Challenges:

• 2nd order system

• High Q 180o phase lag at resonance

• Higher order resonances

• Additional loop delay (e.g. DAC)


typical high

performance gyroscope

frequency response

Sense mode

“Parasitic” modes

B. E. Boser 25

Feedback Actuator

Non-Collocated

separate electrodes for

sense and feedback

Collocated

same electrodes for

sense and feedback


Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Frequency

(Hz)

Normalized

Magnitude

(dB)

Phase

(°)

Stabilize with lead compensator?

B. E. Boser 26

Sampled Data System Loop Gain


B. E. Boser 27

Frequency

(kHz)

Magnitude

(dB)

Phase

(°) Small But

Enough

Margin Huge Positive

Margins

Frequency

(kHz)

Magnitude

(dB)

Phase

(°) Small But

Enough

Margin Huge Positive

Margins

Positive Feedback


stable

DC gain < 0

B. E. Boser 28

Sigma-Delta A/D Conversion


• Very low overhead: only comparator (and 1-bit DAC)

• Sensor acts as loop filter

• Or so it seems …

x x̂

B. E. Boser 29

Broad-band Noise


ONLY Electronic Noise

ONLY Quantization Noise

Quantization + Electronic Noise

Inp

ut

Noise

Frequency

Po

we

r

B. E. Boser 30

Noise Filter with Feed-forward for Stability


B. E. Boser 31

Lead Compensator


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Outline


– Applications






• Feedback


– Stability


Conclusions


B. E. Boser 33

Conclusions

• Capacitive sensor interfaces can resolve

femto-meter displacements

• Challenges

– Transducer:

• Parasitic capacitance, resistance

• Interference pseudo differential interface

• Nonlinearity

– Electrostatic Force-Feedback

• Scale-factor sensitivity to absolute voltage

• Stability: 2nd order system, parasitic resonances

• Sigma-delta ADC: noise enhancement


Capacitive Interface Electronics for Sensing and Actuation

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