Capacitive Interface Electronics for Sensing and Actuation

Capacitive Interface Electronics for Sensing and Actuation

Bernhard E. Boser University of California, Berkeley [email protected]

B. E. Boser

Capacitive Interface Electronics

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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


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Applications

B. E. Boser


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Accelerometer flexture

anchor

x

a

2



1mG

 2π  10kHz 

2

1  2.5pm  Angstrom 40

N Unit Cells Fixed Plates

acceleration

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Gyroscope • Vibrate along drive axis with oscillator @ fdrive

• Detect vibration @ fdrive about sense axis with accelerometer xtyp  20 fm Classical radius of electron: 2.8 fm

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Capacitive Displacement Sensors Gap closing

Overlap

xo

x

x xo C  x   Co

xo xo  x

1 dC  x  1  Co dx xo

C  x   Co

xo  x xo

1 dC  x  1  Co dx xo

x 0

Cap closing actuator has higher sensitivity B. E. Boser


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Capacitive Displacement Sensors Gap closing

Overlap

x=20fm xo=20mm

x=20fm xo=2mm Co = 1pF

Co = 1pF

Co  10 zF  1020 F    

High sensitivity Limited travel range Nonlinear Pull-in B. E. Boser

Co  1 zF  1021 F    

Low sensitivity (large xo) Large travel range Linear (first order) No pull-in (first order)


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Alternative Geometries Gap Closing Design

Overlap Sensor Design

• •

• •

low sensitivity large travel range

Displacement

high sensitivity small travel range

Compromise

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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


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Capacitance to Voltage Conversion x N movable fingers

+Vs = 1V

Co = 1 pF C = 10 zF

L A

Cs1 = Co + C

A

Vx =Vs C/Co = 10 nV

Anchor A

t

x0+x

A

Cs2 = Co - C

x= 0 x> 0

-Vs = -1V

• • • sense capacitor Cs B. E. Boser

maximize C minimize Co maximize Vs

reference capacitor Cref Capacitive Interface Electronics

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Parasitics Parasitic Elements Cs1 Cs2

substrate

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shield

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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

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Modulation in 2-Chip Sensors

Modulation

Sense Voltage

Reject drift in bond-wire capacitance Ref: Lang et al, Cancelling low frequency errors in MEMS systems, 2009. B. E. Boser


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Mechanical Modulation

Ref: P. Lajevardi, V.P. Petkov, and B. Murmann, "A ΣΔ Interface for MEMS Accelerometers using Electrostatic SpringConstant Modulation for Cancellation of Bondwire Capacitance Drift," in Digest ISSCC 2012, pp. 196-197. B. E. Boser


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Capacitive Interface Circuits Continuous Time

• •

Output modulated High valued bias resistor

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Sampled Data

• •

No bias resistor, direct interface to ADC Noise folding


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Noise Folding

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“Boxcar” Sampling

• ~ 10dB noise / power reduction possible • sensitive to clock jitter & nonlinearity B. E. Boser


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 Feedback – Electrostatic force feedback – Stability – Sigma-delta conversion • Conclusions B. E. Boser


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Electrostatic Force Feedback Benefits: • Reduced sensitivity to transducer nonlinearity ain

+

S

A

Vout

• Increased bandwidth (gyroscopes)

F

Challenges: • Need accurate feedback force • Stability • Increased noise

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Scale Factor Openloop Vout

Feedback 1 dC 2 Vfb  mx 2 dx acceleration force

x dC Vs x Vs  2   2 r dx Co r xo

feedback force

x C

2 V 1 dC xˆ    fb 2 dx m

Vs

xcell

xˆ 

ADC

Do ADC output

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r2 xo scale factor

Do 

Vout Vs

• • •


Final measurement depends on absolute voltage Need precision reference for good scale factor accuracy Feedback is nonlinear 23

Stability Sense mode

typical high performance gyroscope frequency response

Challenges:

“Parasitic” modes

• 2nd order system • High Q  180o phase lag at resonance

• Higher order resonances • Additional loop delay (e.g. DAC) B. E. Boser


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Feedback Actuator Non-Collocated

Collocated

separate electrodes for sense and feedback

same electrodes for sense and feedback

Normalized Magnitude (dB)

Normalized Magnitude (dB)

Phase (°)

Phase (°)

Frequency (Hz)

Frequency (Hz)

Stabilize with lead compensator? B. E. Boser


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Sampled Data System Loop Gain

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Positive Feedback Magnitude (dB)

Phase (°)

DC gain < 0

Small But Enough Margin

Huge Positive Margins

stable

Frequency (kHz)

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Sigma-Delta A/D Conversion

xˆ

x

• Very low overhead: only comparator (and 1-bit DAC) • Sensor acts as loop filter • Or so it seems … B. E. Boser


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Input

Power

Broad-band Noise

Noise Frequency

ONLY Electronic Noise ONLY Quantization Noise Quantization + Electronic Noise

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Noise Filter with Feed-forward for Stability

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Lead Compensator

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• Feedback – Electrostatic force feedback – Stability – Sigma-delta conversion  Conclusions B. E. Boser


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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 B. E. Boser


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