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1 Capacitive Interface Electronics for Sensing and Actuation Bernhard E. Boser University of California, Berkeley 1

2 Outline Capacitive Sensors Applications Displacement sensors Readout electronics Sensor interface Circuit topologies Electronic noise Feedback Electrostatic force feedback Stability Sigma-delta conversion Conclusions 2

3 Applications 3

4 Accelerometer flexture x a 1mG 2 2 2π 10kHz anchor 2. 5pm 1 Angstrom 40 Fixed Plates N Unit Cells acceleration 4

5 Gyroscope Vibrate along drive axis with f drive Detect f drive about sense axis with accelerometer xtyp 20 fm Classical radius of electron: 2.8 fm 5

6 Capacitive Displacement Sensors Gap closing Overlap x o x x x o x C x o C o x x o 1 dc x 1 C dx x o o x 0 C x C o x x x o o 1 dc x 1 C dx x o o Cap closing actuator has higher sensitivity 6

7 Capacitive Displacement Sensors Gap closing Overlap x=20fm x o =20mm x=20fm x o =2mm C o = 1pF C o = 1pF 20 C 10 zf 10 F o High sensitivity Limited travel range Nonlinear Pull-in 21 C 1 zf 10 F o Low sensitivity (large x o ) Large travel range Linear (first order) No pull-in (first order) 7

8 Displacement Alternative Geometries Gap Closing Design high sensitivity small travel range Overlap Sensor Design low sensitivity large travel range Compromise 8

9 Outline Capacitive Sensors Applications Displacement sensors Readout electronics Sensor interface Circuit topologies Electronic noise Feedback Electrostatic force feedback Stability Sigma-delta conversion Conclusions 9

10 Capacitance to Voltage Conversion x N movable fingers +V s = 1V C o = 1 pf C = 10 zf A A t L x 0 +x A Anchor A x = 0 C s1 = C o + C V x =V s C/C o = 10 nv C s2 = C o - C x > 0 -V s = -1V maximize C minimize C o maximize V s sense capacitor C s reference capacitor C ref 10

11 Parasitics Parasitic Elements C s1 C s2 substrate shield 11

12 Capacitive Transducer Interface 12

13 Interference 13

14 Differential Interface Single-Ended Pseudo-Differential Interference common-mode signal 14

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 15

16 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,

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

18 Capacitive Interface Circuits Continuous Time Sampled Data Output modulated High valued bias resistor No bias resistor, direct interface to ADC Noise folding 18

19 Noise Folding 19

20 Boxcar Sampling ~ 10dB noise / power reduction possible sensitive to clock jitter & nonlinearity 20

21 Outline Capacitive Sensors Applications Displacement sensors Readout electronics Sensor interface Circuit topologies Electronic noise Feedback Electrostatic force feedback Stability Sigma-delta conversion Conclusions 21

22 Electrostatic Force Feedback Benefits: a in + - S A V out Reduced sensitivity to transducer nonlinearity Increased bandwidth (gyroscopes) F Challenges: Need accurate feedback force Stability Increased noise 22

23 Scale Factor Openloop Feedback V out x dc V x V dx C x s 2 2 r o r x s o 1 2 dc V dx 2 fb feedback force mx acceleration force C V s xcell ADC xˆ D x 2 o r o ADC output scale factor D o V V out s xˆ 2 1 dc V fb 2 dx m Final measurement depends on absolute voltage Need precision reference for good scale factor accuracy Feedback is nonlinear 23

24 Stability Sense mode typical high performance gyroscope frequency response Challenges: Parasitic modes 2 nd order system High Q 180 o phase lag at resonance Higher order resonances Additional loop delay (e.g. DAC) 24

25 Feedback Actuator Non-Collocated separate electrodes for sense and feedback Collocated same electrodes for sense and feedback Normalized Magnitude (db) Normalized Magnitude (db) Phase ( ) Phase ( ) Frequency (Hz) Frequency (Hz) Stabilize with lead compensator? 25

26 Sampled Data System Loop Gain 26

27 Positive Feedback Magnitude (db) DC gain < 0 Phase ( ) Small But Enough Margin Huge Positive Margins stable Frequency (khz) 27

28 Sigma-Delta A/D Conversion x ˆx Very low overhead: only comparator (and 1-bit DAC) Sensor acts as loop filter Or so it seems 28

29 Input Power Broad-band Noise Noise Frequency ONLY Electronic Noise ONLY Quantization Noise Quantization + Electronic Noise 29

30 Noise Filter with Feed-forward for Stability 30

31 Lead Compensator 31

32 Outline Capacitive Sensors Applications Displacement sensors Readout electronics Sensor interface Circuit topologies Electronic noise Feedback Electrostatic force feedback Stability Sigma-delta conversion Conclusions 32

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: 2 nd order system, parasitic resonances Sigma-delta ADC: noise enhancement 33

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