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 θ
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
Output vo
Supply
Voltage
vref + − R i
From magnitude
From phase

6. Capacitive Angular Velocity Sensor
Supply
Voltage
vref + − i
Current
Sensor

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

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

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
Charge
Source q
Equivalent
Capacitance C

10. Sensitivity 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

11. Piezoelectric Material Sensitivities
Charge Sensitivity
Sq (pC/N)
Voltage Sensitivity
Sv (mV.m/N)
Lead Zirconate Titanate (PZT)
Barium Titanate
Quartz
Rochelle Salt
110
140
2.5
275 10 6 50 90

12. 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

13. Frequency response curve of a piezoelectric accelerometer
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

14. Charge Amplifier Impedance matching Reduce speed of charge leakage RfCf A −
vo/K K + + q C Cc
Output vo −
Piezoelectric
Sensor
Cable
Charge
Amplifier
Impedance matching
Reduce speed of charge leakage