Analog Sensors for Motion Measurement

1
Variable Capacitance Transducers

• The Capacitance of a two plate capacitor is given
  by

A Overlapping Area x Gap width k
Dielectric constant
Permitivity of vacuum
Relative permitivity

• A change in any one of these parameters may be
  used for sensing
• Examples - Transverse displacement, rotation, and
  fluid level
• A capacitance bridge can be used to measure the
  change in the capacitance
• Other methods include measuring a change in
  charge
• Charge charge amplifier
• Voltage high impedance device in parallel
• Current low impedance device in series
• Or inductance capacitance oscillator circuit

2
Capacitive Rotation Sensor

• One plate rotates and the other is stationary
• Common area is proportional to the angle

• The relationship is linear and K is the sensor
  constant
• Sensitivity is

Capacitance Bridge
DC Output vo
Fixed Plate
Rotation
A

?
Rotating Plate
3
Capacitive Displacement Sensor

• One plate is attached to the moving object and
  the other is kept stationary
• Capacitance is and
  sensitivity is

• This relationship is nonlinear but can be
  linearized by using an op amp circuit

C K/x
Capacitance Bridge
vo
Cref
A
-
Supply Voltage vref



Fixed Plate
Output vo
Op amp
Position x
-
Moving Plate (e.g., Diaphragm)
-
4
Displacement Measurement by changing Dielectric

• Displacement can be measured by attaching the
  moving object to a solid dielectric element
  placed in between the plates
• Liquid level as shown below can be measured as
  the dielectric medium between the plates changes
  with the liquid level

Capacitance Bridge
vo
Fixed Plate
Liquid
Level h
k
5
Displacement Measurement
From phase
From magnitude
6
Capacitive Angular Velocity Sensor
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Capacitive Sensor Applications

• Mechanical loading effects are negligible
• Variations in dielectric properties due to
  humidity, temperature, pressure, and impurities
  can cause errors
• Capacitance bridge can compensate for these
  effects
• Sensitivity 1pF per mm

8
Capacitance Bridge Circuit
Compensator Z1
Sensor Z2
AC Excitation
Bridge Output vo
v
?
vref

Z3
Z4
Bridge Completion
For a balanced circuit
Bridge output due to sensor change
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Piezoelectric Sensors

• Substances such as BaTiO3 (barium titanate),SiO2
  (quartz in crystalline), and lead zirconate
  titanate can generate an electric charge when
  subjected to stress (strain)
• Applications include
• Pressure and strain measuring devices
• Touch screens
• Accelerometers
• Torque/Force sensors
• Piezoelectric materials deform when a voltage is
  applied. Applications include
• Piezoelectric valves
• Microactuators and MEMS

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• Output impedance of a piezoelectric sensor is
  very high
• It varies with the frequency MO at 100Hz

Sensitivity

• Charge sensitivity For a surface
  area A (pressure applied stress)
• Voltage sensitivity change in voltage due to
  unit increment in pressure per unit thickness (d
  is the thickness)
• k is the dielectric constant of the crystal
  capacitor

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Piezoelectric Material Sensitivities
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Piezoelectric Accelerometer
Spring
Direction of Sensitivity (Input)
Inertia Mass
Piezoelectric Element
Output vo
Electrodes

• Inertia force caused by the acceleration produces
  a voltage
• Light weight, high frequency response (1MHz)
• High output impedance small voltages 1mV
• High spring stiffness natural frequency or
  resonant frequency is high (20kHz)
• Useful frequency range 5kHz

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Resonance
Accelerometer Signal (dB)
Useful Range
1
5,000
20,000
Frequency (Hz)
Frequency response curve of a piezoelectric
accelerometer

• Typical accelerometer sensitivities 10 pC/g
  (pico Coulomb per gravity) or 5mV/g
• Sensitivity depends on the piezoelectric
  properties and the way the inertia force is
  applied
• Large mass would result in a large force and a
  large output signal but
• Load the measurand
• Lower the resonant frequency

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Charge Amplifier
Rf
Cf
A
-
?vo/K

K

q
Output vo
C
Cc
-
Charge Amplifier
Piezoelectric Sensor
Cable

• Impedance matching
• Reduce speed of charge leakage

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