B. E. Boser. 1. Capacitive Interface Electronics for Sensing and Actuation.
Bernhard E. Boser. University of California, Berkeley
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
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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 1020 F
High sensitivity Limited travel range Nonlinear Pull-in B. E. Boser
Co 1 zF 1021 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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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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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
• • •
Capacitive Interface Electronics
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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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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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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