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Sensors

Sensors. Resistive, Capacitive Strain gauges, piezoresistivity Simple XL, pressure sensor ADXL50 Noise. V x. R 0. R 0. V +. V -. R(x). R 0. Resistive sensors. R(x) = R 0 (1+ a x) E.g. TCR, gauge factor Generate thermal noise Wheatstone bridge minimizes sensitivity to

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Sensors

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  1. Sensors • Resistive, Capacitive • Strain gauges, piezoresistivity • Simple XL, pressure sensor • ADXL50 • Noise

  2. Vx R0 R0 V+ V- R(x) R0 Resistive sensors • R(x) = R0(1+ax) • E.g. TCR, gauge factor • Generate thermal noise • Wheatstone bridge minimizes sensitivity to • Nominal resistance value • Power supply variation • Other inputs • R(x) = R0(1+ax) (1+by)

  3. Area (A) Separation (d) Capacitive sensors • Typically used to measure displacement • C ~= e0 A/d • Can be used in Wheatstone bridge (with AC excitation) • Sensitive to environmental coupling • Typically want amplifier very close • Typically need to shield other varying conductors • Definitely don’t want charge-trapping dielectrics nearby • No intrinsic noise

  4. F F Strain Sensors • Shape change • dL/L = e • da/a = -ne (Poisson’s ratio) • R(a,b,L) = r L/A • R(e) = R0(1+(1+2n) e ) • R(e) = R0(1+G e ) • Piezoresistive • r(e) = r0(1+ GPe ) • R(e) = R0(1+(GP+G) e ) • GP ~ -20, 30 (poly), ~100 (SCS) • Piezoelectric • Strain generates charge, charge generates strain

  5. Simple piezoresistive pressure sensor

  6. Simple piezoresistive accelerometer

  7. Simple capacitive accelerometer • Cap wafer may be micromachined silicon, pyrex, … • Serves as over-range protection, and damping • Typically would have a bottom cap as well. C(x)=C(x(a)) Cap wafer

  8. Simple capacitive pressure sensor C(x)=C(x(P))

  9. ADXL50 Accelerometer • +-50g • Polysilicon MEMS & BiCMOS • 3x3mm die

  10. ADXL50 Sensing Mechanism • Balanced differential capacitor output • Under acceleration, capacitor plates move changing capacitance and hence output voltage • On-chip feedback circuit drives on-chip force-feedback to re-center capacitor plates.

  11. Analog Devices Polysilicon MEMS

  12. ADXL50 – block diagram

  13. Digital Output MEMS Gyroscope Chip Proof Mass SenseCircuit Rotation induces Coriolis acceleration Electrostatic Drive Circuit J. Seeger, X. Jiang, and B. Boser

  14. 1mm Drive 0.01Å Sense MEMS Gyroscope Chip J. Seeger, X. Jiang, and B. Boser

  15. Thermal Noise • Fundamental limitation to sensor performance due to thermal noise • “White” noise, Johnson noise, Brownian motion all the same • Not the same as flicker, popcorn, 1/f noise • Equipartition theorem (energy perspective) • every energy storage mode will have ½ kBT of energy • Nyquist (power perspective): • Every dissipator will contribute PN = 4 kBT B • B = bandwidth of interest in Hz

  16. Equipartition • ½ kBT = 4x10-21 J @ room temperature (300K) • ½ C V2 = ½ kBT • C=1pF  Vn = 60uV (RMS value) • ½ k x2 = ½ kBT • K = 1N/m  xn = 0.06nm • ½ m v2 = ½ kBT • m = 10-9 kg (~100um cube)  vn = 2x10-6 m/s

  17. Nyquist • PN = 4 kBT B • In a resistor • PN = VN2/R = 4 kBT B • VN = sqrt(4 kBT R B) • = sqrt (4 kBT R) sqrt(B) • If R = 1kZ then • VN = 4nV/sqrt(Hz) sqrt(B)

  18. N m LNA ADC V Sensor and interface electronics Analog to Digital Converter Low noise amplifier measurand transducer Filter

  19. Summary • Resistive and capacitive sensors most common • Sensing, amplification, filtering, feedback on the same chip ~$2 • Minimum detectable signal limited by thermal noise

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