Slide 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
Slide 2: DC Output
vo Capacitance
Bridge Rotating Plate A Fixed Plate Rotation Capacitive Rotation Sensor One plate rotates and the other is stationary
Common area is proportional to the angle θ The relationship is linear and K is the sensor constant
Sensitivity is
Slide 3: Moving Plate
(e.g., Diaphragm) Position
x vo Fixed Plate 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 Output
vo Supply
Voltage
vref + − Cref C = K/x + − A + − Op amp Capacitance
Bridge
Slide 4: k vo Fixed Plate Level
h Liquid 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
Slide 5: Displacement Measurement From magnitude From phase
Slide 6: Capacitive Angular Velocity Sensor
Slide 7: 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
Slide 8: + AC
Excitation vref Compensator
Z1 Sensor
Z2 Bridge Completion Z3 Z4 Bridge
Output
vo v Capacitance Bridge Circuit For a balanced circuit Bridge output due to sensor change
Slide 9: 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
Slide 10: Output impedance of a piezoelectric sensor is very high
It varies with the frequency ~MΩ 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
Slide 11: Piezoelectric Material Sensitivities
Slide 12: Piezoelectric Accelerometer Output
vo Direction of
Sensitivity
(Input) Spring Inertia Mass Piezoelectric
Element 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
Slide 13: Accelerometer Signal (dB) Frequency (Hz) 5,000 20,000 Useful Range 1 Resonance 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
Slide 14: Charge Amplifier Output
vo Cf vo/K + − A + − Charge
Amplifier Rf Cc C Piezoelectric
Sensor Cable q K Impedance matching
Reduce speed of charge leakage