Acoustic Sensors and Actuators

Acoustic Sensors and Actuators

Acoustic Sensors and Actuators

Chapter 7Chapter 7

Introduction Introduction

Acoustics - “Sound” and its effects Frequencies - 0 to over 1 GHz Audio: 20Hz to 20 kHz Ultrasound: 20 kHz and up Infrasound: 0 to 20 Hz. Sound: Longitudinal pressure waves

Acoustics - “Sound” and its effects Frequencies - 0 to over 1 GHz Audio: 20Hz to 20 kHz Ultrasound: 20 kHz and up Infrasound: 0 to 20 Hz. Sound: Longitudinal pressure waves

Introduction Introduction As a means of sensing and actuation, sound

waves have developed in a number of directions. Use of sound waves in the audible range for

sensing of sound (microphones, hydrophones, pressure sensors)

Actuation using speakers. Sonar – the generation and detection of acoustics

(including infra and ultrasound) in the ocean Testing of material, material processing and in

medicine.

As a means of sensing and actuation, sound waves have developed in a number of directions.

Use of sound waves in the audible range for sensing of sound (microphones, hydrophones, pressure sensors)

Actuation using speakers. Sonar – the generation and detection of acoustics

(including infra and ultrasound) in the ocean Testing of material, material processing and in

medicine.

Acoustic waves Acoustic waves

Sound waves are longitudinal elastic waves. The pressure wave as it propagates, changes

the pressure along the direction of its propagation.

Example: acoustic waves, impinging on our eardrums will push or pull on the eardrum to affect hearing.

Any wave, including acoustic waves have three fundamental properties:

Frequency, wavelength and speed of propagation

Sound waves are longitudinal elastic waves. The pressure wave as it propagates, changes

the pressure along the direction of its propagation.

Example: acoustic waves, impinging on our eardrums will push or pull on the eardrum to affect hearing.

Any wave, including acoustic waves have three fundamental properties:

Frequency, wavelength and speed of propagation


The frequency, f, of a wave is the number of variations of the wave per second.

Normally defined for harmonic waves and is understood to be the number of cycles of the harmonic (sinusoidal for example) wave.

For example, if we were to count the number of crests in an ocean wave passing through a fixed point in one second, the result would be the frequency of the wave.

The frequency, f, of a wave is the number of variations of the wave per second.

Normally defined for harmonic waves and is understood to be the number of cycles of the harmonic (sinusoidal for example) wave.

For example, if we were to count the number of crests in an ocean wave passing through a fixed point in one second, the result would be the frequency of the wave.


Wavelength, is the distance a wave propagates in one cycle.

In the example of the ocean wave the wavelength is the distance between two crests (or two valleys)

Velocity, c, of the wave is the speed with which the front of the wave propagates and, as indicated above, is frequency dependent.

These three quantities are related as: = c/f

Wavelength, is the distance a wave propagates in one cycle.

In the example of the ocean wave the wavelength is the distance between two crests (or two valleys)

Velocity, c, of the wave is the speed with which the front of the wave propagates and, as indicated above, is frequency dependent.

These three quantities are related as: = c/f

Concept of wavelengthConcept of wavelength


Waves can be transverse waves, longitudinal waves or a combination of the two.

Transverse waves are those waves which cause a change in amplitude in directions transverse to the direction of propagation of the wave.

Example: a tight string vibrates perpendicular to the length of the string. The wave itself propagates along the string.

The wave propagates away from the source, in all directions.

Waves can be transverse waves, longitudinal waves or a combination of the two.

Transverse waves are those waves which cause a change in amplitude in directions transverse to the direction of propagation of the wave.

Example: a tight string vibrates perpendicular to the length of the string. The wave itself propagates along the string.

The wave propagates away from the source, in all directions.

Transverse waves on a tight string

Transverse waves on a tight string


Generation of longitudinal waves:

Example: piston in a tube Example: diaphragm in air Effect: changes in volume

cause changes in pressure. These propagate - give rise to the wave.

Generation of longitudinal waves:

Example: piston in a tube Example: diaphragm in air Effect: changes in volume

cause changes in pressure. These propagate - give rise to the wave.

Acoustic waves - speedAcoustic waves - speed

The speed of an acoustic wave is directly related to the change in volume and the resulting change in pressure

The speed of an acoustic wave is directly related to the change in volume and the resulting change in pressure

c =

Δ pV

Δ V ρ0

m / s

ρ0 is the density of the undisturbed fluid, ΔV is the change in volume, Δp is the change in pressure V is the volume

Acoustic waves - speedAcoustic waves - speed

In gasses, this simplifies to the following In gasses, this simplifies to the following

ρ0 is the density of the undisturbed fluid, is the ratio of specific heats for the gas, p0 is the undisturbed gas pressure

Thus, the speed of acoustic waves is material, pressure and temperature dependent

c =

p0

ρ0

m / s

Speed of soundSpeed of sound

Table 6.1. Speed of sound in some materials at given temperatures.Material Speed [m/s] Temperature [° ]CAir 331 20

Fresh water 1,486 20 Sea water 1,520 20

Granite 6,000Steel 5,200 20Copper 3,600 20Aluminum 6,320Beryllium 12,900

Table 6.1. Speed of sound in some materials at given temperatures.Material Speed [m/s] Temperature [° ]CAir 331 20

Fresh water 1,486 20 Sea water 1,520 20

Granite 6,000Steel 5,200 20Copper 3,600 20Aluminum 6,320Beryllium 12,900

Acoustic waves - theoryAcoustic waves - theory

Assuming a harmonic longitudinal wave of frequency f, it may be written in general terms as:

Assuming a harmonic longitudinal wave of frequency f, it may be written in general terms as:

p is pressure in the medium, P0 the pressure amplitude of the wave k is a constant. The wave propagates in the x direction 2f is the angular frequency

p = P0

sin ( kx − t )


The amplitude of the wave is: The amplitude of the wave is:

ym is the maximum displacement of a particle during compression or expansion in the wave. The constant k is called the wave number or the phase constant and is given as:

P0

= k ρ0

c2

ym

k =

2

=

c


Waves carry energy. A shockwave (earthquake) can cause damage A loud sound can hurt our ears.

A wave is said to be a propagating wave if it carries energy from one point to another.

The wave can propagate in an unbounded medium with or without attenuation (losses). Attenuation of a wave depends on the medium Attenuation reduces the amplitude of the wave.

Attenuation of waves is exponential

Waves carry energy. A shockwave (earthquake) can cause damage A loud sound can hurt our ears.

A wave is said to be a propagating wave if it carries energy from one point to another.

The wave can propagate in an unbounded medium with or without attenuation (losses). Attenuation of a wave depends on the medium Attenuation reduces the amplitude of the wave.

Attenuation of waves is exponential


Attenuation constant is defined for each material The amplitude of the wave, as it propagates,

changes as follows

Attenuation constant is defined for each material The amplitude of the wave, as it propagates,

changes as follows

p = P0

e− α x

sin ( kx − t )

Attenuation causes loss of energy as the wave propagates Dissipates energy of the wave

Acoustic waves - theoryAcoustic waves - theory When a propagating wave encounters a

discontinuity in the unbounded space (an object such as a wall, a change in air pressure, etc) part of the wave is reflected and part of it is transmitted into the discontinuity.

Reflection and a transmission occur at any discontinuity

These reflected and transmitted waves may propagate in directions other than the original wave.

Transmission causes refraction of the wave.

When a propagating wave encounters a discontinuity in the unbounded space (an object such as a wall, a change in air pressure, etc) part of the wave is reflected and part of it is transmitted into the discontinuity.

Reflection and a transmission occur at any discontinuity

These reflected and transmitted waves may propagate in directions other than the original wave.

Transmission causes refraction of the wave.

Reflection, transmission and refraction

Reflection, transmission and refraction


The reflected wave is reflected at an angle equal to the angle of incidence (r=i)

The transmitted wave propagates in the material at an angle t which is equal to:

The reflected wave is reflected at an angle equal to the angle of incidence (r=i)

The transmitted wave propagates in the material at an angle t which is equal to:

sin t

=

c2

c1

sin i

c2 is the speed of propagation of the wave in the medium into which the wave transmits c1 the speed in the medium from which the wave originates


The reflected waves propagate in the same medium as the propagating wave

Interfere with the propagating wave. Their amplitude can add (constructive interference)

or subtract (destructive interference). The net effect is that the total wave can have

amplitudes smaller or larger than the original wave. This phenomenon leads to the idea of a standing

wave.

The reflected waves propagate in the same medium as the propagating wave

Interfere with the propagating wave. Their amplitude can add (constructive interference)

or subtract (destructive interference). The net effect is that the total wave can have

amplitudes smaller or larger than the original wave. This phenomenon leads to the idea of a standing

wave.


Interference will cause some locations in space to have lower amplitudes (or zero) while others will have amplitudes larger than the incident wave.

This is called a standing wave because the locations of zero amplitudes (called nodes) are fixed in space as are the locations of maxima.

Figure 7.5 shows this and also the fact that the nodes of the standing wave are at distances of /2 while maxima occur ate /4 on either side of a node.

Interference will cause some locations in space to have lower amplitudes (or zero) while others will have amplitudes larger than the incident wave.

This is called a standing wave because the locations of zero amplitudes (called nodes) are fixed in space as are the locations of maxima.

Figure 7.5 shows this and also the fact that the nodes of the standing wave are at distances of /2 while maxima occur ate /4 on either side of a node.

Standing wavesStanding waves

Standing wavesStanding waves

Example of standing waves: vibrating tight strings reflections occur at the

locations the strings are attached.

This vibration at various wavelengths, and its interaction with the air around accounts for the music we perceive when a violin plays.

Example of standing waves: vibrating tight strings reflections occur at the

locations the strings are attached.

This vibration at various wavelengths, and its interaction with the air around accounts for the music we perceive when a violin plays.


Scattering is reflection of the waves in all directions due to anything in the path of the waves.

Dispersion is the propagation of various frequency components are different frequency causing distortion in the received sound wave.

Wave impedance or acoustic impedance is the product of density and velocity:

Z = ρ0c

Scattering is reflection of the waves in all directions due to anything in the path of the waves.

Dispersion is the propagation of various frequency components are different frequency causing distortion in the received sound wave.

Wave impedance or acoustic impedance is the product of density and velocity:

Z = ρ0c

MicrophonesMicrophones

Microphones are sound sensors (really - transient pressure sensors)

Speakers are sound actuators The first microphones and speakers (or

earphones) were devised and patented for use in telephones.

Alexander Graham Bell patented the first variable resistance microphone in 1876

Microphones are sound sensors (really - transient pressure sensors)

Speakers are sound actuators The first microphones and speakers (or

earphones) were devised and patented for use in telephones.

Alexander Graham Bell patented the first variable resistance microphone in 1876

Bell’s MicrophoneBell’s Microphone

The carbon microphoneThe carbon microphone

First practical microphone was invented by Edison The solution was replaced with carbon or graphite

particles –the carbon microphone. In continuous use in telephones ever since Rather poor performance (noise, limited frequency

response, dependence on position and distortions) An “amplifying” device (can modulate large currents)

and hence its use in telephones. It is still being used, to drive an earpiece directly

without the need for an amplifier.

First practical microphone was invented by Edison The solution was replaced with carbon or graphite

particles –the carbon microphone. In continuous use in telephones ever since Rather poor performance (noise, limited frequency

response, dependence on position and distortions) An “amplifying” device (can modulate large currents)

and hence its use in telephones. It is still being used, to drive an earpiece directly

without the need for an amplifier.

The carbon microphoneThe carbon microphone

The magnetic microphoneThe magnetic microphone

Better known as the moving iron microphone, together with its cousin, the moving iron gramophone pickup have largely disappeared and have been replaced by better devices.

Its structure is quite common in sensors (we have seen a similar device used as a pressure sensor in chapter 6 the variable reluctance pressure sensor).

The basic structure is shown in Figure 7.10.

Better known as the moving iron microphone, together with its cousin, the moving iron gramophone pickup have largely disappeared and have been replaced by better devices.

Its structure is quite common in sensors (we have seen a similar device used as a pressure sensor in chapter 6 the variable reluctance pressure sensor).

The basic structure is shown in Figure 7.10.


Operation: the armature (a piece of iron that moves due to the action of sound or a needle in the case of a pickup) decreases the gap towards one of the poles of the iron core.

This changes the reluctance in the magnetic circuit.

If the coil is supplied with a constant voltage, the current in it depends on the reluctance of the circuit.

Hence the current in the coil sound level

Operation: the armature (a piece of iron that moves due to the action of sound or a needle in the case of a pickup) decreases the gap towards one of the poles of the iron core.

This changes the reluctance in the magnetic circuit.

If the coil is supplied with a constant voltage, the current in it depends on the reluctance of the circuit.

Hence the current in the coil sound level

Moving coil microphoneMoving coil microphone

Known as the dynamic microphone. The first microphone that could reproduce the

whole range of the human voice Has survived into our own times even though

newer, simpler devices have been developed and will be discussed shortly.

Operation is based on Faraday’s law: Given a coil moving in the magnetic field, it produce an emf :

Known as the dynamic microphone. The first microphone that could reproduce the

whole range of the human voice Has survived into our own times even though

newer, simpler devices have been developed and will be discussed shortly.

Operation is based on Faraday’s law: Given a coil moving in the magnetic field, it produce an emf :

V = − Nd Φ

dt

Dynamic microphoneDynamic microphone

Moving coil microphoneMoving coil microphone

Fundamentally the same as a common loudspeaker

Any small loudspeaker can serve as a dynamic microphone

The dynamic microphone, just like the moving iron microphone is a dual device capable of serving as a loudspeaker or earphone (other than size, power, etc.)

Fundamentally the same as a common loudspeaker

Any small loudspeaker can serve as a dynamic microphone

The dynamic microphone, just like the moving iron microphone is a dual device capable of serving as a loudspeaker or earphone (other than size, power, etc.)

Capacitive microphonesCapacitive microphones

Also called “condenser” microphones Idea is trivially simple: Allow sound to move a plate in a capacitor Sense the change in capacitance

Also called “condenser” microphones Idea is trivially simple: Allow sound to move a plate in a capacitor Sense the change in capacitance

Capacitive microphonesCapacitive microphones

The operation is based on the two basic equations of the parallel plate capacitor

The operation is based on the two basic equations of the parallel plate capacitor

C = ε A

d

, C =

Q

V

→ V = Qd

eA

The output voltage proportional to the distance d between the platesA source of charge must be available.

Sources of charge are not easy to come by except from external sources - Impractical!

The electret microphoneThe electret microphone

Solution: the capacitive electret microphone Electret: a permanent electric field material just

like the permanent magnet but for the electric field If a special material is exposed to an external

magnetic field, a polarization of the atoms inside the material occurs.

When the external electric field is removed, the internal polarization vector is retained and this polarization vector sets up a permanent external electric field.

Solution: the capacitive electret microphone Electret: a permanent electric field material just

like the permanent magnet but for the electric field If a special material is exposed to an external

magnetic field, a polarization of the atoms inside the material occurs.

When the external electric field is removed, the internal polarization vector is retained and this polarization vector sets up a permanent external electric field.


Electrets are made by applying the electric field while the material is heated to increase the atom energy and allow easier polarization.

As the material cools the polarized charges remain in this state.

Materials used for this purpose are Teflon FEP (Fluorinated Ethylene Propylene), Barium Titanite (BaTi) Calcium-Titanite-Oxide (CaTiO3) and many others.

Some materials can be made into electrets by simply bombarding the material, in its final shape by an electron beam.

Electrets are made by applying the electric field while the material is heated to increase the atom energy and allow easier polarization.

As the material cools the polarized charges remain in this state.

Materials used for this purpose are Teflon FEP (Fluorinated Ethylene Propylene), Barium Titanite (BaTi) Calcium-Titanite-Oxide (CaTiO3) and many others.

Some materials can be made into electrets by simply bombarding the material, in its final shape by an electron beam.


The electret microphone is a capacitive microphone Made of two conducting plates with a layer of an

electret material under the upper plate

The electret microphone is a capacitive microphone Made of two conducting plates with a layer of an

electret material under the upper plate


The electret here is made of a thin film to allow the flexibility and motion necessary.

The electret generates a surface charge density ± on the upper plane and lower metal backplane.

Generates an electric field intensity in the gap s1. The voltage across the two metallic plates, in the

absence of any outside stimulation (sound) is:

The electret here is made of a thin film to allow the flexibility and motion necessary.

The electret generates a surface charge density ± on the upper plane and lower metal backplane.

Generates an electric field intensity in the gap s1. The voltage across the two metallic plates, in the

absence of any outside stimulation (sound) is:

V =

s s1

ε0

s + ε s1


If sound is applied to the diaphragm, the electret will move down a distance Δs and a change in voltage occurs as:

If sound is applied to the diaphragm, the electret will move down a distance Δs and a change in voltage occurs as:

Δ V = s Δ s

ε0

s + ε s1

This voltage, is the true output of the sensor, can be related to the sound pressure as:

Δ s =

Δ p

γ p0

s1

+ 8 π T / A

A is the area of the membrane, T the tension, is the specific heat ratio, p0 is ambient pressure and Δp the change in pressure due to sound


Thus, the change in output voltage due to sound waves is:

Thus, the change in output voltage due to sound waves is:

This voltage can now be amplified as necessary.

Δ V = s

ε0

s + ε s1

Δ p

γ p0

s1

+ 8 π T / A


Electret microphones are very popular simple and inexpensive do not require a source (they are passive devices).

But: their impedance is very high special circuits for connection to instruments. Typically an FET pre-amplifier is required to match the

high impedance of the microphone to the lower input impedance of the amplifier.

The membrane is typically made of a thin film of electret material on which a metal layer is deposited to form the movable plate.

Electret microphones are very popular simple and inexpensive do not require a source (they are passive devices).

But: their impedance is very high special circuits for connection to instruments. Typically an FET pre-amplifier is required to match the

high impedance of the microphone to the lower input impedance of the amplifier.

The membrane is typically made of a thin film of electret material on which a metal layer is deposited to form the movable plate.


In many ways, the electret microphone is almost ideal. The frequency response can be totally flat from zero to a

few Mhz. Very low distortions and excellent sensitivities (a few

mV/bar). They are usually very small (some no more than 3 mm in

diameter and about 3mm long) They can be found everywhere, from recording devices

to cell phones. A sample of electret microphones is shown in Figure

7.14.

In many ways, the electret microphone is almost ideal. The frequency response can be totally flat from zero to a

few Mhz. Very low distortions and excellent sensitivities (a few

mV/bar). They are usually very small (some no more than 3 mm in

diameter and about 3mm long) They can be found everywhere, from recording devices

to cell phones. A sample of electret microphones is shown in Figure

7.14.

Electret microphonesElectret microphones

The piezoelectric effectThe piezoelectric effect

Piezoelectric effect is the generation of electric charge in crystalline materials upon application of mechanical stress.

The opposite effect is equally useful: application of charge across the crystal causes mechanical deformation in the material.

The piezoelectric effect occurs naturally in materials such as quartz ( SiO2 - a silicon oxide)

Has been used for many decades in so called crystal oscillators.

Piezoelectric effect is the generation of electric charge in crystalline materials upon application of mechanical stress.

The opposite effect is equally useful: application of charge across the crystal causes mechanical deformation in the material.

The piezoelectric effect occurs naturally in materials such as quartz ( SiO2 - a silicon oxide)

Has been used for many decades in so called crystal oscillators.


It is also a property of some ceramics and polymers We have already met the piezoresistive materials of

chapter 5 (PZT is the best known) and the polymer piezoresistive materials PVF and PVDF.

The piezoelectric effect has been known since 1880 First used in 1917 to detect and generate sound waves

in water for the purpose of detecting submarines (sonar). The piezoelectric effect can be explained in a simple

model by deformation of crystals:

It is also a property of some ceramics and polymers We have already met the piezoresistive materials of

chapter 5 (PZT is the best known) and the polymer piezoresistive materials PVF and PVDF.

The piezoelectric effect has been known since 1880 First used in 1917 to detect and generate sound waves

in water for the purpose of detecting submarines (sonar). The piezoelectric effect can be explained in a simple

model by deformation of crystals:


Deformation in one direction (B) displaces the molecular structure so that a net charge occurs as shown (in Quartz crystal - SiO2)

Deformation in a perpendicular axis (B) forms an opposite polarity charge

Deformation in one direction (B) displaces the molecular structure so that a net charge occurs as shown (in Quartz crystal - SiO2)

Deformation in a perpendicular axis (B) forms an opposite polarity charge


The charges can be collected on electrodes deposited on the crystal

Measurement of the charge is then a measure of the displacement or deformation.

The model uses the quartz crystal (SiO2) but other materials behave in a similar manner.

Also, the behavior of the crystal depends on how the crystal is cut and different cuts are used for different applications.

The charges can be collected on electrodes deposited on the crystal

Measurement of the charge is then a measure of the displacement or deformation.

The model uses the quartz crystal (SiO2) but other materials behave in a similar manner.

Also, the behavior of the crystal depends on how the crystal is cut and different cuts are used for different applications.

The piezoelectric effect - theoryThe piezoelectric effect - theory

The polarization vector in a medium (polarization is the electric dipole moment of atoms per unit volume of the material) is related to stress through the following simple relation

The polarization vector in a medium (polarization is the electric dipole moment of atoms per unit volume of the material) is related to stress through the following simple relation

P = d C

m2

d is the piezoelectric constant, the stress in the material.


Polarization is direction dependent in the crystal and may be written as:

Polarization is direction dependent in the crystal and may be written as:

x, y, z are the standard axes in the crystal. The relation above now becomes.

P = Pxx

+ Pyy

+ Pzz

Pxx

= d11

xx

+ d12

yy

+ d13

zz

Pyy

= d21

xx

+ d22

yy

+ d23

zz

Pzz

= d31

xx

+ d32

yy

+ d33

zz

dij are the piezoelectric coefficients along the orthogonal axes of the crystal.


The coefficient depends on how the crystal is cut. To simplify discussion we will assume that d is

single valued The inverse effect is written as:

The coefficient depends on how the crystal is cut. To simplify discussion we will assume that d is

single valued The inverse effect is written as:

e = gP

e is strain (dimensionless), g is called the constant coefficient (ε is permittivity)

g = d

ε

or : gij

=

dij

εij


The piezoelectric coefficients are related to the electrical anisotropy of materials (permittivity).

A third coefficient is called the electromechanical coupling coefficient and is a measure of the efficiency of the electromechanical conversion:

The piezoelectric coefficients are related to the electrical anisotropy of materials (permittivity).

A third coefficient is called the electromechanical coupling coefficient and is a measure of the efficiency of the electromechanical conversion:

k

2

= dgE or : kij

2

= dij

gij

Eij

E is the Young modulus.

The electromechanical coupling coefficient is simply the ratio between the electric and mechanical energies per unit volume in the material.

Crystals - piezoelectric properties

Crystals - piezoelectric properties

Table 7.2. Piezoelectric coefficients and other propertiesin monocrystalsCrystal Piezoelectric

coefficient dij, x10−12

[C/N]

Permittivit ,y εij Coupling coefficientkmax

Quartz (SiO2) 11=2d .31, 14=0.7d ε11=4.5, ε33=4.63 0.1ZnS 14=3d .18 ε11=8.37 0.1CdS 15=d -14, 33=10d .3,

31=d -5.2ε11=9.35, ε33=10.3 0.2

ZnO 15=d -12, 33=12d ,31=d -4.7

ε11=8.2 0.3

KD P ( 2KH P 4O ) 14=1d .3, 36=21d ε11=42, ε33=21 0.07AD P ( 4NH H2 4PO ) 14=d -1.5, 36d =48 ε11=56, ε33=15.4 0.1BaTi 3O 15=400d , 33=100d ,

31=d -35ε11=3000, ε33=180 0.6

LiN 3bO 31=d -1.3, 33d =18,22=20d , 15=70d

ε11=84, ε33=29 0.68

LiT 3aO 31=d -3, 33=7d ,22=7d .5, 15=26d

ε11=53, ε33=44 0.47

Table 7.2. Piezoelectric coefficients and other propertiesin monocrystalsCrystal Piezoelectric

coefficient dij, x10−12

[C/N]

Permittivit ,y εij Coupling coefficientkmax

Quartz (SiO2) 11=2d .31, 14=0.7d ε11=4.5, ε33=4.63 0.1ZnS 14=3d .18 ε11=8.37 0.1CdS 15=d -14, 33=10d .3,

31=d -5.2ε11=9.35, ε33=10.3 0.2

ZnO 15=d -12, 33=12d ,31=d -4.7

ε11=8.2 0.3

KD P ( 2KH P 4O ) 14=1d .3, 36=21d ε11=42, ε33=21 0.07AD P ( 4NH H2 4PO ) 14=d -1.5, 36d =48 ε11=56, ε33=15.4 0.1BaTi 3O 15=400d , 33=100d ,

31=d -35ε11=3000, ε33=180 0.6

LiN 3bO 31=d -1.3, 33d =18,22=20d , 15=70d

ε11=84, ε33=29 0.68

LiT 3aO 31=d -3, 33=7d ,22=7d .5, 15=26d

ε11=53, ε33=44 0.47

Ceramics - piezoelectric properties

Ceramics - piezoelectric properties

Table 7.3. Piezoelectric coefficients and other properties in ceramicsCeramic Piezoelectric coefficient

dij, x10−12 [C/N]Permittivit ,yε

Couplingcoefficientkmax

BaTi 3O (a t120°C) 15=260d , 31=d -45,33=d -100

1400 0.2

BaTi 3+5O %CaTi 3O (a t105°C) 31=43d , 33=77d 1200 0.25

P (bZr0.53Ti0.47) 3+O (0.5-3)%L 2 2a Oor B 2i O2 or T 2 5 a O (at 290°C)

15=380d , 31=119d ,33=282d

1400 0.47

( 0Pb .6Ba0.4) 2 6 Nb O (a t300°C) 31=67d , 33=167d 1800 0.28( 0.5K Na0.5) 3 NbO (at 240°C) 31=49d , 33=160d 420 0.45

Table 7.3. Piezoelectric coefficients and other properties in ceramicsCeramic Piezoelectric coefficient



BaTi 3O (a t120°C) 15=260d , 31=d -45,33=d -100

1400 0.2

BaTi 3+5O %CaTi 3O (a t105°C) 31=43d , 33=77d 1200 0.25

P (bZr0.53Ti0.47) 3+O (0.5-3)%L 2 2a Oor B 2i O2 or T 2 5 a O (at 290°C)

15=380d , 31=119d ,33=282d

1400 0.47

( 0Pb .6Ba0.4) 2 6 Nb O (a t300°C) 31=67d , 33=167d 1800 0.28( 0.5K Na0.5) 3 NbO (at 240°C) 31=49d , 33=160d 420 0.45

Polymers - piezoelectric properties

Polymers - piezoelectric properties

Table 7.4. Piezoelectric coefficients and other properties in polymersPolymer Piezoelectric coefficient



PVDF 31=23d , 33=d -33 106−113 0.14Copolymer 31=11d , 33=d -38 65−75 0.28

Table 7.4. Piezoelectric coefficients and other properties in polymersPolymer Piezoelectric coefficient



PVDF 31=23d , 33=d -33 106−113 0.14Copolymer 31=11d , 33=d -38 65−75 0.28

Piezoelectric devicesPiezoelectric devices

A piezoelectric device is built as a simple capacitor, (capacitance C)

Assuming force is applied on the x-axis in this figure, the charge generated by force is:

A piezoelectric device is built as a simple capacitor, (capacitance C)

Assuming force is applied on the x-axis in this figure, the charge generated by force is:

Qx

= d11

Fx

Voltage developed across it is:

V =

Qx

C

=

d11

Fx

C

=

d11

Fx

d

ε A

d = thicknessA = area

Piezoelectric devicesPiezoelectric devices

The thicker the device the larger the voltage. A smaller area has the same effect. Output is directly proportional to force (or pressure which

is force/area). Most common piezoelectric materials for sensors

PZT (lead-zirconite-titanium-oxide) Polymer films such as PVDF (PolyVinyliDeneFluoride). Barium Titanate (BiTiO3) in crystal or ceramic form Crystalline quartz are used for some applications. Thin films of ZnO on semiconductors

The thicker the device the larger the voltage. A smaller area has the same effect. Output is directly proportional to force (or pressure which

is force/area). Most common piezoelectric materials for sensors

PZT (lead-zirconite-titanium-oxide) Polymer films such as PVDF (PolyVinyliDeneFluoride). Barium Titanate (BiTiO3) in crystal or ceramic form Crystalline quartz are used for some applications. Thin films of ZnO on semiconductors

Piezoelectric microphonePiezoelectric microphone

Applying a force (due to sound pressure) on the surface (Figure 7.16).

Given this structure, and a change in pressure Δp, the change in voltage expected is:

Applying a force (due to sound pressure) on the surface (Figure 7.16).

Given this structure, and a change in pressure Δp, the change in voltage expected is:

Δ V =

d11

Δ pA d

ε A

=

d11

d

ε

Δ p

A linear relation is therefore available to sense the sound pressure


These devices can operate at very high frequencies

Often use in ultrasonic sensors Piezoelectric microphone can be used as

piezoelectric actuators in which it is just as efficient.

This complete duality is unique to piezoelectric transducers and, to a smaller extent, to magnetostrictive transducers.

Usually, the same device can be used in either mode.

These devices can operate at very high frequencies

Often use in ultrasonic sensors Piezoelectric microphone can be used as

piezoelectric actuators in which it is just as efficient.

This complete duality is unique to piezoelectric transducers and, to a smaller extent, to magnetostrictive transducers.

Usually, the same device can be used in either mode.

Piezoelectric microphonePiezoelectric microphone Typical construction consists of films (PVDF or copolymers)

with metal coatings for electrodes either as a round, square or almost any other shape shape.

One particularly useful form is a tube-like electrode usually used in hydrophones.

These elements can be connected in series to coved a larger area such as is sometimes required in hydrophones.

The piezoelectric microphone has exceptional qualities and a flat frequency response.

Used in many applications chief among them as pickup in musical instruments and detection of low intensity sounds such as the flow of blood in veins.

Other applications: voice activated devices, hydrophones.

Typical construction consists of films (PVDF or copolymers) with metal coatings for electrodes either as a round, square or almost any other shape shape.

One particularly useful form is a tube-like electrode usually used in hydrophones.

These elements can be connected in series to coved a larger area such as is sometimes required in hydrophones.

The piezoelectric microphone has exceptional qualities and a flat frequency response.

Used in many applications chief among them as pickup in musical instruments and detection of low intensity sounds such as the flow of blood in veins.

Other applications: voice activated devices, hydrophones.

Other microphonesOther microphones

The ribbon microphone. A variation of the moving coil microphone. A thin metallic foil (aluminum) between poles of a magnet. As the ribbon moves, an emf is induced across it based

on Faraday’s law (N=1) in this case. The current produced by this emf is the output. Wide, flat frequency responses Susceptible to background noise and vibration. Sometimes used for studio reproduction. Impedance of these microphones is very low, typically

less tha 1 and must be properly interfaced.

The ribbon microphone. A variation of the moving coil microphone. A thin metallic foil (aluminum) between poles of a magnet. As the ribbon moves, an emf is induced across it based

on Faraday’s law (N=1) in this case. The current produced by this emf is the output. Wide, flat frequency responses Susceptible to background noise and vibration. Sometimes used for studio reproduction. Impedance of these microphones is very low, typically

less tha 1 and must be properly interfaced.

The film microphoneThe film microphone

Acoustic actuatorsAcoustic actuators

Among these we shall discuss two: The classical loudspeaker used in audio

work. Piezoelectric actuators for the purpose

of sound generation will be introduced. Audible devices referred to as buzzers Mechanical actuation will be discussed

separately later in this chapter.

Among these we shall discuss two: The classical loudspeaker used in audio

work. Piezoelectric actuators for the purpose

of sound generation will be introduced. Audible devices referred to as buzzers Mechanical actuation will be discussed

separately later in this chapter.

Acoustic actuatorsAcoustic actuators

The basic structure of a loudspeaker

The force is given by the Lorenz force, NBIL.

Magnetic field supplies by permanent magnets

The basic structure of a loudspeaker

The force is given by the Lorenz force, NBIL.

Magnetic field supplies by permanent magnets

A titanium diaphragm speakerA titanium diaphragm speaker

LoudspeakersLoudspeakers

Magnets are made as strong as possible Gap as narrow as possible to ensure maximum

force for a given current. Coils are varnish insulated copper wires Wound tightly in a vertical spiral, Supported by a backing of paper, mylar or

fiberglass, The diaphragm or paper cone supplies the

restoring force and keeps the coil centered.

Magnets are made as strong as possible Gap as narrow as possible to ensure maximum

force for a given current. Coils are varnish insulated copper wires Wound tightly in a vertical spiral, Supported by a backing of paper, mylar or

fiberglass, The diaphragm or paper cone supplies the

restoring force and keeps the coil centered.


The cone is usually made of paper (in very small speakers they may be made of mylar or some plastics)

Suspended on the rim of the speaker which, in turn is made as stiff as possible to avoid vibrations.

Loudspeakers’ operation is essentially one of motion of the coil in response to variations of current through it which, in turn, change the pressure in front (and behind) the cone thus generating a longitudinal wave in air.

The cone is usually made of paper (in very small speakers they may be made of mylar or some plastics)

Suspended on the rim of the speaker which, in turn is made as stiff as possible to avoid vibrations.

Loudspeakers’ operation is essentially one of motion of the coil in response to variations of current through it which, in turn, change the pressure in front (and behind) the cone thus generating a longitudinal wave in air.


The same principle can be used to generate waves in fluids or even in solids.

The power rating of a speaker is usually defined as the power in the coil, (voltage across the coil multiplied by current in the coil)

This power can be rms or peak or peak-to-peak It is not the radiated power by the cone. It is the power dissipated by the coil. The radiated power is a portion of the total power

supplied to the speaker

The same principle can be used to generate waves in fluids or even in solids.

The power rating of a speaker is usually defined as the power in the coil, (voltage across the coil multiplied by current in the coil)

This power can be rms or peak or peak-to-peak It is not the radiated power by the cone. It is the power dissipated by the coil. The radiated power is a portion of the total power

supplied to the speaker


The radiated power depends both on the electrical and mechanical properties of the speaker. Assuming an unimpeded diaphragm connected to a coil of radius r and N turns in a magnetic field B, the radiated acoustic power is:

The radiated power depends both on the electrical and mechanical properties of the speaker. Assuming an unimpeded diaphragm connected to a coil of radius r and N turns in a magnetic field B, the radiated acoustic power is:

Pr

=

2 I

2

B

2

(2 rN )2

Rmr

Rml

2

+ Xml

2

Rmr = acoustic impedance (of air), Rml = total mechanical resistance seen by the diaphragm Xml = total mass reactance seen by the diaphragm


This only gives a rough idea of the power radiated

It does indicate that power is proportional to current, magnetic flux density and size (both physical and number of turns) of the coil.

There are other issues that have to be taken into account including reflections

Speakers are characterized by additional properties such as dynamic range, maximum displacement of the diaphragm and distortions.

This only gives a rough idea of the power radiated

It does indicate that power is proportional to current, magnetic flux density and size (both physical and number of turns) of the coil.

There are other issues that have to be taken into account including reflections

Speakers are characterized by additional properties such as dynamic range, maximum displacement of the diaphragm and distortions.


Two other properties are of paramount importance. Frequency response of the speaker, Directional response (also called the radiation pattern or

coverage pattern). The frequency response shows the response of the speaker

over the useful span of the device. Usually shown between 20Hz and 20kHz Also to be noted are peaks or resonances at 1.5 kHz and

then smaller resonances at 3, 4 and 13 kHz. These are usually associated with the mechanical structure of the speaker.

Two other properties are of paramount importance. Frequency response of the speaker, Directional response (also called the radiation pattern or

coverage pattern). The frequency response shows the response of the speaker

over the useful span of the device. Usually shown between 20Hz and 20kHz Also to be noted are peaks or resonances at 1.5 kHz and

then smaller resonances at 3, 4 and 13 kHz. These are usually associated with the mechanical structure of the speaker.

Frequency response of a speaker

Frequency response of a speaker


Response: between 20Hz and 20kHz, Bandwidth - 35Hz to 12 kHz. Note peaks or resonances at 1.5 kHz and then smaller

resonances at 3, 4 and 13 kHz. Usually associated with the mechanical structure of the

speaker. This is a general purpose speaker Others have responses at lower frequencies (woofers) or

higher (tweeters), Usually associated with the physical size of the

speakers.

Response: between 20Hz and 20kHz, Bandwidth - 35Hz to 12 kHz. Note peaks or resonances at 1.5 kHz and then smaller

resonances at 3, 4 and 13 kHz. Usually associated with the mechanical structure of the

speaker. This is a general purpose speaker Others have responses at lower frequencies (woofers) or

higher (tweeters), Usually associated with the physical size of the

speakers.


Directional response indicates the relative power density in different directions in space.

Figure 7.21 shows such a plot at selected frequencies.

Indicates where in space one can expect larger or lower power densities and the general coverage.

Note that the power density behind the speaker is lower than in front of it as expected.

Directional response indicates the relative power density in different directions in space.

Figure 7.21 shows such a plot at selected frequencies.

Indicates where in space one can expect larger or lower power densities and the general coverage.

Note that the power density behind the speaker is lower than in front of it as expected.

Directional responseDirectional response

Small loudspeakersSmall loudspeakers

Low frequency loudspeaker (top)

Low frequency loudspeaker (top)

Low frequency loudspeaker (side)

Low frequency loudspeaker (side)

Moving armature actuatorMoving armature actuator

Move the armature while keeping the coil fixed. The moving armature actuator (Figure 7.24) Has been used in the past in headphones In use today as earpieces in land telephones Its main use is in magnetic warning devices called

buzzers. Come in two basic varieties. One is simply a coil and a

membrane suspended as in Figure 7.24. Current in the coil attracts the membrane and variations

in current move it closer to the coil depending on the magnitude of the current.

Move the armature while keeping the coil fixed. The moving armature actuator (Figure 7.24) Has been used in the past in headphones In use today as earpieces in land telephones Its main use is in magnetic warning devices called

buzzers. Come in two basic varieties. One is simply a coil and a

membrane suspended as in Figure 7.24. Current in the coil attracts the membrane and variations

in current move it closer to the coil depending on the magnitude of the current.

Moving coil earphoneMoving coil earphone


A permanent magnet may also be present as shown to bias the device.

The device acts as a small loudspeaker but of a fairly inferior quality.

The coil is fairly large (many turns) and its impedance is fairly high

It can be connected directly in a circuit and driven by a carbon microphone without the need of an amplifier.

However for all other sound reproduction system it is not acceptable.

A permanent magnet may also be present as shown to bias the device.

The device acts as a small loudspeaker but of a fairly inferior quality.

The coil is fairly large (many turns) and its impedance is fairly high

It can be connected directly in a circuit and driven by a carbon microphone without the need of an amplifier.

However for all other sound reproduction system it is not acceptable.


Second form: In this form sound reproduction is not important but rather the membrane is made to vibrate at a fixed frequency, say 1 kHz to provide an audible warning.

This can be done by driving the basic circuit in Figure 7.24 by a square wave, usually directly from the output of a microprocessor or through a suitable oscillator (either electrical or, sometimes mechanical).

In some devices the circuitry necessary for oscillation is internal to the device and the only external connections are to power.

Currently buzzers are made in many sizes from a few mm to a few cm in diameter and at various powers.

Second form: In this form sound reproduction is not important but rather the membrane is made to vibrate at a fixed frequency, say 1 kHz to provide an audible warning.

This can be done by driving the basic circuit in Figure 7.24 by a square wave, usually directly from the output of a microprocessor or through a suitable oscillator (either electrical or, sometimes mechanical).

In some devices the circuitry necessary for oscillation is internal to the device and the only external connections are to power.

Currently buzzers are made in many sizes from a few mm to a few cm in diameter and at various powers.

Magnetic buzzersMagnetic buzzers

Piezoelectric earphones and buzzers

Piezoelectric earphones and buzzers

Piezoelectric earpiece: A piezoelectric disk is physically bonded to a

diaphragm (Figure 7.16) Connection to a voltage source will cause a

mechanical motion in the disk. When an ac source due to sound is applied, motion

of the disk reproduces the sound. An earphone of this type is shown in Figure 7.25

together with its piezoelectric element. Properties - same as the piezoelectric microphone

Piezoelectric earpiece: A piezoelectric disk is physically bonded to a

diaphragm (Figure 7.16) Connection to a voltage source will cause a

mechanical motion in the disk. When an ac source due to sound is applied, motion

of the disk reproduces the sound. An earphone of this type is shown in Figure 7.25

together with its piezoelectric element. Properties - same as the piezoelectric microphone

Piezoelectric earphonePiezoelectric earphone

Piezoelectric buzzersPiezoelectric buzzers

The earpiece can be used as a buzzer by driving it with an ac source.

For incorporation in an electronic circuit, these devices often come either as a device with a third connection which, when appropriately driven forces the diaphragm to oscillate or has the necessary circuit to do so incorporated in the device.

Figure 7.26 shows a piezoelectric buzzer and, separately, its diaphragm shown from underneath.

The earpiece can be used as a buzzer by driving it with an ac source.

For incorporation in an electronic circuit, these devices often come either as a device with a third connection which, when appropriately driven forces the diaphragm to oscillate or has the necessary circuit to do so incorporated in the device.

Figure 7.26 shows a piezoelectric buzzer and, separately, its diaphragm shown from underneath.

Piezoelectric buzzerPiezoelectric buzzer


The piezoelectric element has two parts. The smaller piece, when properly driven, causes local

distortion in the diaphragm and the interaction of these distortions and those of the main element cause the device to oscillate at a set frequency which depends on sizes and shapes of the two piezoelectric elements.

These buzzers are very popular since they use little power and can operate down to about 1.5V,

Useful as directly driven devices in microprocessors. Can be used for audible feedback, a warning device (for

example for a moving robot or as a backup warning in trucks and heavy equipment).

The piezoelectric element has two parts. The smaller piece, when properly driven, causes local

distortion in the diaphragm and the interaction of these distortions and those of the main element cause the device to oscillate at a set frequency which depends on sizes and shapes of the two piezoelectric elements.

These buzzers are very popular since they use little power and can operate down to about 1.5V,

Useful as directly driven devices in microprocessors. Can be used for audible feedback, a warning device (for

example for a moving robot or as a backup warning in trucks and heavy equipment).

Ultrasonic sensors and actuators


In principle, identical to acoustic sensors and actuators

Somewhat different in construction Very different in terms of materials used and

range of frequencies. The ultrasonic range starts where the audible

range ends, Therefore ultrasonic sensor (i.e. microphone) or

actuator for the near ultrasound range should be quite similar to an acoustic sensor or actuator.

In principle, identical to acoustic sensors and actuators

Somewhat different in construction Very different in terms of materials used and

range of frequencies. The ultrasonic range starts where the audible

range ends, Therefore ultrasonic sensor (i.e. microphone) or

actuator for the near ultrasound range should be quite similar to an acoustic sensor or actuator.

24 kHz, UT transmitter and receiver

24 kHz, UT transmitter and receiver



Figure 7.31 shows an ultrasonic transmitter (left) and an ultrasonic receiver (right) operating in air at 24 kHz.

Same size and essentially the same construction. This is typical of piezoelectric devices in which the same

exact device can be used for both purposes Both use an identical piezoelectric disk The only difference is in the slight difference in the

construction of the cone. Figure 7.31 shows a closer view of another device, this

time operating at 40 kHz, also designed to operate in air in which the piezoelectric device is square, seen at the center below the brass supporting member

Figure 7.31 shows an ultrasonic transmitter (left) and an ultrasonic receiver (right) operating in air at 24 kHz.

Same size and essentially the same construction. This is typical of piezoelectric devices in which the same

exact device can be used for both purposes Both use an identical piezoelectric disk The only difference is in the slight difference in the

construction of the cone. Figure 7.31 shows a closer view of another device, this

time operating at 40 kHz, also designed to operate in air in which the piezoelectric device is square, seen at the center below the brass supporting member

40 kHz ultrasonic sensor40 kHz ultrasonic sensor

40 kHz ultrasonic transmitter/receiver for ranging

40 kHz ultrasonic transmitter/receiver for ranging

Ultrasonic sensorsUltrasonic sensors

Scope of ultrasonic sensing is very wide. Ultrasound is much better suited for use in solids

and liquids (higher velocities, lower attenuation) Support waves other than longitudinal which allow

additional flexibility ultrasonics shear waves, surface waves

Ultrasonic sensors exist at almost any frequency and exceeding 1 GHz (especially SAW devices).

Most sensors operate below 50 MHz.

Scope of ultrasonic sensing is very wide. Ultrasound is much better suited for use in solids

and liquids (higher velocities, lower attenuation) Support waves other than longitudinal which allow

additional flexibility ultrasonics shear waves, surface waves

Ultrasonic sensors exist at almost any frequency and exceeding 1 GHz (especially SAW devices).

Most sensors operate below 50 MHz.

Ultrasonic sensorsUltrasonic sensors

Most ultrasonic sensors and actuators are based on piezoelectric materials

Some are based on magnetostrictive materials A particularly important property of piezoelectric

materials that makes them indispensable in ultrasound is their ability to oscillate at a fixed, sharply defined frequency called the resonant frequency.

The resonant frequency of a piezoelectric crystal (or ceramic element) depends on the material itself, its effective mass, strain and physical dimensions and is also influenced by temperature, pressure and the like.

Most ultrasonic sensors and actuators are based on piezoelectric materials

Some are based on magnetostrictive materials A particularly important property of piezoelectric

materials that makes them indispensable in ultrasound is their ability to oscillate at a fixed, sharply defined frequency called the resonant frequency.

The resonant frequency of a piezoelectric crystal (or ceramic element) depends on the material itself, its effective mass, strain and physical dimensions and is also influenced by temperature, pressure and the like.

Piezoelectric resonatorPiezoelectric resonator

Equivalent circuit of a piezoelectric material.

This circuit has two resonances – a parallel resonance and a series resonance (called antiresonance)

Equivalent circuit of a piezoelectric material.

This circuit has two resonances – a parallel resonance and a series resonance (called antiresonance)


The resonant frequencies are given as: The resonant frequencies are given as:

fs

=

1

2 LC

fp

=

1

2 LC C0

/ C + C0

A single resonance is desirable Materials or shapes for which the two resonant frequencies are widely separated are used. Therefore a capacitance ratio is defined as:

m =

C

C0


The relation between the two frequencies is: The relation between the two frequencies is:

The larger the ratio m, the larger the separation between frequencies. The resistance R in the equivalent circuit acts as a damping (loss) factor. This is associated with the Quality factor of the piezoelectric material:

Q =

1

R

L

C

fp = fs 1 + m

Ultrasonic resonatorUltrasonic resonator

Resonance is important is two ways. At resonance the amplitude of mechanical

distortion is highest In receive mode, the signal generated is largest Means the sensor is most efficient at resonance.

The second reason is that the sensors operate at clear and sharp frequencies

Parameters of propagation including reflections and transmissions are clearly defined as are other properties such as wavelength.

Resonance is important is two ways. At resonance the amplitude of mechanical

distortion is highest In receive mode, the signal generated is largest Means the sensor is most efficient at resonance.

The second reason is that the sensors operate at clear and sharp frequencies

Parameters of propagation including reflections and transmissions are clearly defined as are other properties such as wavelength.

Ultrasonic sensorUltrasonic sensor

The construction of a piezoelectric sensor is shown in Figure 7.33. The piezoelectric element is rigidly attached to the front of the sensor

so that vibrations can be transmitted to and from the sensor. The lens shown in this case will focus the ultrasound beam to a focal

point Often just a thin flat sheet or the front, metal surface of the sensor or

it may be prismatic, conical or spherical as shown here. The damping chamber prevents ringing of the device The impedance matching circuit (not always present, sometimes it is

part of the driving supply) matches the source with the piezoelectric element.

Every sensor is specified for a resonant frequency and for environmental operation (solids, fluids, air, harsh environments, etc.)

The construction of a piezoelectric sensor is shown in Figure 7.33. The piezoelectric element is rigidly attached to the front of the sensor

so that vibrations can be transmitted to and from the sensor. The lens shown in this case will focus the ultrasound beam to a focal

point Often just a thin flat sheet or the front, metal surface of the sensor or

it may be prismatic, conical or spherical as shown here. The damping chamber prevents ringing of the device The impedance matching circuit (not always present, sometimes it is

part of the driving supply) matches the source with the piezoelectric element.

Every sensor is specified for a resonant frequency and for environmental operation (solids, fluids, air, harsh environments, etc.)

Ultrasonic sensor - constructionUltrasonic sensor - construction

Ultrasonic sensors - sampleUltrasonic sensors - sample

Specification sheetSpecification sheet

Pulse-echo operationPulse-echo operation

All ultrasonic sensors are dual – they can transmit or receive.

In many applications, like the example of range finding above, two sensors are used.

In others they are switched between transmit and receive modes.

This is the most common mode for operation in medical applications and in testing of materials.

Based on the fact that any discontinuity causes a reflection or causes scattering of the sound waves.

All ultrasonic sensors are dual – they can transmit or receive.

In many applications, like the example of range finding above, two sensors are used.

In others they are switched between transmit and receive modes.

This is the most common mode for operation in medical applications and in testing of materials.

Based on the fact that any discontinuity causes a reflection or causes scattering of the sound waves.

Pulse-echo operationPulse-echo operation

This reflection is an indication of the existence of the discontinuity Amplitude of the reflection is a function of the size of the

discontinuity. The exact location of the discontinuity can be found from the time it

takes the waves to propagate to and from the discontinuity. Figure 7.32 shows an example of finding the location/size of a

defect in a piece of metal. The front and back surfaces are seen, usually as large reflections

while the defect is usually smaller. Its location can be easily detected. The same idea can be used to create an image of a baby in the

womb and for position sensing in industry.

This reflection is an indication of the existence of the discontinuity Amplitude of the reflection is a function of the size of the

discontinuity. The exact location of the discontinuity can be found from the time it

takes the waves to propagate to and from the discontinuity. Figure 7.32 shows an example of finding the location/size of a

defect in a piece of metal. The front and back surfaces are seen, usually as large reflections

while the defect is usually smaller. Its location can be easily detected. The same idea can be used to create an image of a baby in the

womb and for position sensing in industry.

Fault location by ultrasoundFault location by ultrasound

Sensing fluid velocitySensing fluid velocity

There are three effects that can be used. 1. Sound velocity is relative to the fluid in which it

travels. (Our voice carries downwind faster (by the wind velocity) than in still air). This speed difference can be measured from the time it takes the sound to get from one point to another.

2. The second effect is based on the phase difference caused by this change in speed

3. Third is the doppler effect – the frequency of the wave propagating downwind is higher than the frequency in still air.

There are three effects that can be used. 1. Sound velocity is relative to the fluid in which it

travels. (Our voice carries downwind faster (by the wind velocity) than in still air). This speed difference can be measured from the time it takes the sound to get from one point to another.

2. The second effect is based on the phase difference caused by this change in speed

3. Third is the doppler effect – the frequency of the wave propagating downwind is higher than the frequency in still air.

Sensing fluid velocitySensing fluid velocity

An example of a fluid speed sensing using method 1. In this case, the distance and angle of the sensors is known and the transmit time, say downstream is:

An example of a fluid speed sensing using method 1. In this case, the distance and angle of the sensors is known and the transmit time, say downstream is:

T =

D

c + vf

cos

c speed of soundvf fluid speed

Magnetostrictive sensorsMagnetostrictive sensors

In air or in fluids, piezoelectric sensors are best. In solids there is an alternative - magnetostriction. These sensors are collectively called

magnetostrictive ultrasonic sensors Used at lower frequencies (about 100 kHz) to

generate higher intensity waves. All that is necessary is to attach a coil to the

material and drive it at the required frequency. The field generated in the material generates stress

which generates an ultrasonic wave

In air or in fluids, piezoelectric sensors are best. In solids there is an alternative - magnetostriction. These sensors are collectively called

magnetostrictive ultrasonic sensors Used at lower frequencies (about 100 kHz) to

generate higher intensity waves. All that is necessary is to attach a coil to the

material and drive it at the required frequency. The field generated in the material generates stress

which generates an ultrasonic wave

EMATsEMATs

An even simpler method is to generate an ac electromagnetic field inside the material in which sound waves are to be generated.

Because the induced electric currents, there is a force acting on these currents due to an external magnetic field generated by permanent magnets.

The interaction generates stresses and a sound wave. These sensors are called electromagnetic acoustic

sensors (EMAT – electromagnetic acoustic transducer). These sensors are quite common because of their

simplicity but they tend to operate at low frequencies (<100kHz) and have low efficiencies.

An even simpler method is to generate an ac electromagnetic field inside the material in which sound waves are to be generated.

Because the induced electric currents, there is a force acting on these currents due to an external magnetic field generated by permanent magnets.

The interaction generates stresses and a sound wave. These sensors are called electromagnetic acoustic

sensors (EMAT – electromagnetic acoustic transducer). These sensors are quite common because of their

simplicity but they tend to operate at low frequencies (<100kHz) and have low efficiencies.

Structure of EMATsStructure of EMATs

Piezoelectric actuatorsPiezoelectric actuators

One of the first actuator has been in use in analog clocks for decades.

Essentially a cantilever beam made of a piezoelectric crystal (quartz is common) that engages a geared wheel.

When a pulse is connected across the beam it bends (downwards) and moves the wheel one tooth at a time.

This actuation only requires minute motion. Its main importance - accuracy

One of the first actuator has been in use in analog clocks for decades.

Essentially a cantilever beam made of a piezoelectric crystal (quartz is common) that engages a geared wheel.

When a pulse is connected across the beam it bends (downwards) and moves the wheel one tooth at a time.

This actuation only requires minute motion. Its main importance - accuracy

Piezoelectric actuatorsPiezoelectric actuators

Other actuators have been designed which can move much larger distances and apply significant forces as well.

One such device is shown in Figure 7.38. It is 70x90mm in size and when a 600V is applied across

the piezoelectric element (grey patch) one end moves relative to the other (which must be fixed) about 8mm.

The rated force for this device is about 17kg force at rated voltage.

Some piezoelectric sensors and actuators can operate at lower voltages, large voltages are typical of piezoelectric actuators and is one serious limitation.

Other actuators have been designed which can move much larger distances and apply significant forces as well.

One such device is shown in Figure 7.38. It is 70x90mm in size and when a 600V is applied across

the piezoelectric element (grey patch) one end moves relative to the other (which must be fixed) about 8mm.

The rated force for this device is about 17kg force at rated voltage.

Some piezoelectric sensors and actuators can operate at lower voltages, large voltages are typical of piezoelectric actuators and is one serious limitation.

Linear piezoelectric actuatorLinear piezoelectric actuator

Stacked piezoelectric actuatorsStacked piezoelectric actuators

Individual elements, each with its own electrodes can be stacked to produce stacks of varying lengths.

In such devices, the displacement is anywhere between 0.1 to 0.25% of the stack length, but this is still a small displacement.

One of the advantages of these stacks is that the forces are even larger than those achievable by devices such as the one in Figure 7.38.

A small actuator, capable of a displacement of about 0.05mm and a force of about 40N is shown in Figure 7.39.

Individual elements, each with its own electrodes can be stacked to produce stacks of varying lengths.

In such devices, the displacement is anywhere between 0.1 to 0.25% of the stack length, but this is still a small displacement.

One of the advantages of these stacks is that the forces are even larger than those achievable by devices such as the one in Figure 7.38.

A small actuator, capable of a displacement of about 0.05mm and a force of about 40N is shown in Figure 7.39.

Stacked piezoelectric actuatorStacked piezoelectric actuator

Saw devicesSaw devices

Surface waves or Rayleigh waves. Surface waves propagate on the surface of an

elastic medium with little effect on the bulk of the medium

Have properties which are significantly different than longitudinal waves

The most striking difference is their much slower speed of propagation.

Propagation of surface waves is nondispersive

Surface waves or Rayleigh waves. Surface waves propagate on the surface of an

elastic medium with little effect on the bulk of the medium

Have properties which are significantly different than longitudinal waves

The most striking difference is their much slower speed of propagation.

Propagation of surface waves is nondispersive


The exact definition of Rayleigh wave is a wave that propagates at the interface between an elastic medium and vacuum or rarefied gas (air for example) with little penetration into the bulk of the medium.

A good analogy for surface waves are ocean waves. Under most conditions this would seem to be a

disadvantage but, looking at the wavelength alone as the ratio of velocity and frequency: =c/f,

The lower the velocity of the wave, the shorter the wavelength in that medium.

The smaller the physical size of a device!

The exact definition of Rayleigh wave is a wave that propagates at the interface between an elastic medium and vacuum or rarefied gas (air for example) with little penetration into the bulk of the medium.

A good analogy for surface waves are ocean waves. Under most conditions this would seem to be a

disadvantage but, looking at the wavelength alone as the ratio of velocity and frequency: =c/f,

The lower the velocity of the wave, the shorter the wavelength in that medium.

The smaller the physical size of a device!

SAW devicesSAW devices

Generation of surface waves: In a thick sample, one can set up a surface wave

by a process of wave conversion. A longitudinal wave device is used and energy

coupled through a wedge at an angle to the surface.

At the surface of the medium there will be both a shear wave and a surface wave (Figure 7.40).

This is an obvious solution but not necessarily the optimal.

Generation of surface waves: In a thick sample, one can set up a surface wave

by a process of wave conversion. A longitudinal wave device is used and energy

coupled through a wedge at an angle to the surface.

At the surface of the medium there will be both a shear wave and a surface wave (Figure 7.40).

This is an obvious solution but not necessarily the optimal.

Surface waves in a solidSurface waves in a solid


A more efficient method: apply metallic strips on the surface of a piezoelectric material in an interdigital fasion (comblike structure) as shown in Figure 7.41.

This establishes a periodic structure of metallic strips. When an oscillatory source is connected across the two sets of

electrodes, a periodic electric field is established in the piezoelectric material,

Because of this electric field, an equivalent, periodic stress pattern is established in the piezoelectric medium.

This generates a stress wave (sound wave) that now propagates away from the electrodes in both directions. The generation is most efficient when the period of the surface wave equals the inter-digital period.

A more efficient method: apply metallic strips on the surface of a piezoelectric material in an interdigital fasion (comblike structure) as shown in Figure 7.41.

This establishes a periodic structure of metallic strips. When an oscillatory source is connected across the two sets of

electrodes, a periodic electric field is established in the piezoelectric material,

Because of this electric field, an equivalent, periodic stress pattern is established in the piezoelectric medium.

This generates a stress wave (sound wave) that now propagates away from the electrodes in both directions. The generation is most efficient when the period of the surface wave equals the inter-digital period.

SAW generatorSAW generator


For example, in the structure in Figure 7.41, suppose the frequency of the source is 400 Mhz.

The speed of propagation in a piezoelectric is of the order of 3000 m/s.

This gives a wavelength of 7.5 m. Making each strip in the structure /4 gives 1.875m

width for each strip and 1.875m distance between neighboring strips.

This calculation shows that the dimensions required are very small (the same device, based on electromagnetic waves has a wavelength of 750mm).

For example, in the structure in Figure 7.41, suppose the frequency of the source is 400 Mhz.

The speed of propagation in a piezoelectric is of the order of 3000 m/s.

This gives a wavelength of 7.5 m. Making each strip in the structure /4 gives 1.875m

width for each strip and 1.875m distance between neighboring strips.

This calculation shows that the dimensions required are very small (the same device, based on electromagnetic waves has a wavelength of 750mm).


The comblike structure generates sound waves in the piezoelectric medium

A sound wave in the piezoelectric medium produces a signal in a comb-like structure.

The structure can be used both for generation and reception of surface waves which in turn means that the device can be used for sensing or actuation

The comblike structure generates sound waves in the piezoelectric medium

A sound wave in the piezoelectric medium produces a signal in a comb-like structure.

The structure can be used both for generation and reception of surface waves which in turn means that the device can be used for sensing or actuation

SAW ResonatorSAW Resonator

By far the most common use of surface acoustic waves (SAW) is in SAW resonators, filters and delay lines.

A SAW resonator is shown in Figure 7.42. The portion marked as In and Out are used as the input and output ports of the resonator (i.e. the outside connections of the resonator).

The parallel lines on each side are grooves etched in the quartz piezoelectric.

By far the most common use of surface acoustic waves (SAW) is in SAW resonators, filters and delay lines.

A SAW resonator is shown in Figure 7.42. The portion marked as In and Out are used as the input and output ports of the resonator (i.e. the outside connections of the resonator).

The parallel lines on each side are grooves etched in the quartz piezoelectric.


The input port establishes a surface wave The wave is reflected by the grooves on each

side. These reflection interfere with each other

establishing a resonance which depends on the grating of groves separation.

Only those signals that interfere constructively will establish a signal in the output port, the others cancel.

The input port establishes a surface wave The wave is reflected by the grooves on each

side. These reflection interfere with each other

establishing a resonance which depends on the grating of groves separation.

Only those signals that interfere constructively will establish a signal in the output port, the others cancel.


This device is popular as the element that defines the oscillator frequency in communication

A very small device can easily operate at low frequencies and can operate at frequencies above the limit of conventional oscillators.

The device in Figure 7.42 may also be viewed as a very narrow band filter and

This is in fact another of its uses. The basis of most sensors is a delay line (Figure)

This device is popular as the element that defines the oscillator frequency in communication

A very small device can easily operate at low frequencies and can operate at frequencies above the limit of conventional oscillators.

The device in Figure 7.42 may also be viewed as a very narrow band filter and

This is in fact another of its uses. The basis of most sensors is a delay line (Figure)

SAW resonators for communication

SAW resonators for communication

SAW delay lineSAW delay line


The device on the left generates a surface wave This is detected after a delay in the device on

the right. The delay depends on the distance between the

devices and, because the wavelength is usually small, the delay can be long.

Adding an amplifier in the feedback makes this an oscillator with frequency dependent on the delay.

The device on the left generates a surface wave This is detected after a delay in the device on

the right. The delay depends on the distance between the

devices and, because the wavelength is usually small, the delay can be long.

Adding an amplifier in the feedback makes this an oscillator with frequency dependent on the delay.


The basic SAW sensor is shown in Figure 7.45 It is based on a delay line in which the delay is influenced by

the stimulus. An essentially identical sensor is shown in Figure 7.46 which

has two identical delay lines and the output is differential. One line is used as the proper sensor, the second as a

reference to cancel common-mode effects such as temperature.

In most cases, the delay time is not measured but rather, a feedback amplifier (Figure 7.46) is connected (positive feedback) which causes the device to resonate at a frequency established by the time delay

The basic SAW sensor is shown in Figure 7.45 It is based on a delay line in which the delay is influenced by

the stimulus. An essentially identical sensor is shown in Figure 7.46 which

has two identical delay lines and the output is differential. One line is used as the proper sensor, the second as a

reference to cancel common-mode effects such as temperature.

In most cases, the delay time is not measured but rather, a feedback amplifier (Figure 7.46) is connected (positive feedback) which causes the device to resonate at a frequency established by the time delay

SAW sensorSAW sensor


The stimuli that can be measured are many. First, the speed of sound is temperature

dependent. Temperature changes both the physical length of the delay line and the sound speed as follows:

The stimuli that can be measured are many. First, the speed of sound is temperature

dependent. Temperature changes both the physical length of the delay line and the sound speed as follows:

α is the coefficient of linear expansion the temperature coefficient of sound velocity.

L = L0

1 + α T − T0

, c = c0

1 + T − T0


These two terms are contradicting in that both increase and hence the delay and oscillator frequency are a function of the difference between them.

The change in frequency with temperature is:

These two terms are contradicting in that both increase and hence the delay and oscillator frequency are a function of the difference between them.

The change in frequency with temperature is:Δ f

f

= δ − α Δ T

This is linear and a SAW sensor has a sensitivity of about 103 C.


In sensing pressure, the delay in propagation is due to stress in the piezoelectric as indicated above.

Measurement of displacement, force and acceleration are done by measuring the strain (pressure) produced in the sensor.

Many other stimuli can be measured including radiation (through the temperature rise), voltage (through the stress it produces through the electric field) and so on.

In sensing pressure, the delay in propagation is due to stress in the piezoelectric as indicated above.

Measurement of displacement, force and acceleration are done by measuring the strain (pressure) produced in the sensor.

Many other stimuli can be measured including radiation (through the temperature rise), voltage (through the stress it produces through the electric field) and so on.

Acoustic Sensors and Actuators

Documents

Transcript of Acoustic Sensors and Actuators