Variable Capacitance Transducers

• The Capacitance of a two plate capacitor is given by

CkA

x

A – Overlapping Area

x – Gap width

k – Dielectric constant

rk 0 0 rPermitivity 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

DC Outputvo

CapacitanceBridge

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

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

• Sensitivity isK

CS

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

x

KC

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

2x

K

x

CS

Outputvo

SupplyVoltage

vref

+

−

Cref

C = K/x

+

−A

+

−

Op amp

CapacitanceBridge

xK

Cvv refref

o

k

vo

Fixed Plate

Levelh

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

CapacitanceBridge

Outputvo

SupplyVoltage

vref

+

−

R +

−

i

Displacement Measurement

id

dtCv

v v

Roref o

x

KC

v

v RKj xo

ref

1

1

xRK

M

1 12

From magnitude From phase

x RK tan

SupplyVoltage

vref

+

−

i CurrentSensor

+

−

Capacitive Angular Velocity Sensor

id

dtCv v

dC

dtref ref

C

d

dt

i

Kvref

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

+

AC Excitation

vref

CompensatorZ1

SensorZ2

Bridge Completion

Z3 Z4

BridgeOutput

vo

v

v v

Z

v v

Zref o

1 2

0

v

Z Z Z Z

Z Zvo ref

4 3 2 1

4 31

/ /

/

Z

Z

Z

Z2

1

4

3

vv

Z Z ZZo

ref1 4 31 /

Capacitance Bridge Circuit

v v

Z

v

Zref

3 4

00

For a balanced circuit Bridge output due to sensor change

ChargeSource

q

EquivalentCapacitance

C

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

CjZ

1

• 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

Sq

Fq

SA

q

pq 1

Sd

v

pv 1

q C v

vq kSS

Material Charge Sensitivity Sq (pC/N)

Voltage SensitivitySv (mV.m/N)

Lead Zirconate Titanate (PZT)Barium Titanate

QuartzRochelle Salt

1101402.5275

106

5090

Piezoelectric Material Sensitivities

Piezoelectric Accelerometer

Outputvo

Direction ofSensitivity

(Input)

Spring

Inertia Mass

PiezoelectricElement

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

Acc

eler

omet

er

Sig

nal (

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

Charge Amplifier

Outputvo

Cf

vo/K +

−A

+

−Charge

Amplifier

Rf

CcC

PiezoelectricSensor

Cable

q

K

• Impedance matching

• Reduce speed of charge leakage

0o o o o oc f o

f

v v v v v Kq C C C v

K K K R

R Cdv

dtv R

dq

dtf fo

o f

v s

q s

R s

R C so f

f f

1

v j

q j

R j

R C jo f

f f

1

c f fR C