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


B. E. Boser 13

Interference


B. E. Boser 14

Differential Interface

Single-Ended Pseudo-Differential


Interference common-mode signal

B. E. Boser 15

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

B. E. Boser 19

Noise Folding


B. E. Boser 20

“Boxcar” Sampling


• ~ 10dB noise / power reduction possible

• sensitive to clock jitter & nonlinearity

B. E. Boser 21

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


B. E. Boser 32

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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