Acoustic Sensors and Actuators

1
Acoustic Sensors and Actuators

• Chapter 7

2
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

3
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.

4
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

5
Acoustic waves

• 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.

6
Acoustic waves

• Wavelength, l, 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 l c/f

7
Concept of wavelength
8
Acoustic waves

• 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.

9
Transverse waves on a tight string
10
Acoustic waves

• 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.

11
Acoustic waves - speed

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

?0 is the density of the undisturbed fluid, ?V
is the change in volume, ?p is the change in
pressure V is the volume
12
Acoustic waves - speed

• In gasses, this simplifies to the following

?0 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
13
Speed of sound
14
Acoustic waves - theory

• 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 ????f is the
angular frequency
15
Acoustic waves - theory

• 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

16
Acoustic waves - theory

• 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

17
Acoustic waves - theory

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

Attenuation causes loss of energy as the wave
propagates Dissipates energy of the wave
18
Acoustic 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.

19
Reflection, transmission and refraction
20
Acoustic waves - theory

• 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 qt which is equal to

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
21
Acoustic waves - theory

• 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.

22
Acoustic waves - theory

• 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.

23
Standing waves
24
Standing 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.

25
Acoustic waves - theory

• 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 r0c

26
Microphones

• 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

27
Bells Microphone
28
The 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.

29
The carbon microphone
30
The carbon microphone
31
The 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.

32
The magnetic microphone
33
The magnetic microphone

• 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

34
Moving 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 Faradays law Given a coil
  moving in the magnetic field, it produce an emf

35
Dynamic microphone
36
Moving 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.)

37
Capacitive microphones

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

38
Capacitive microphones

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

The output voltage proportional to the distance d
between the plates A source of charge must be
available. Sources of charge are not easy to
come by except from external sources -
Impractical!
39
The 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.

40
The electret microphone

• 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.

41
The electret microphone

• The electret microphone is a capacitive
  microphone
• Made of two conducting plates with a layer of an
  electret material under the upper plate

42
The electret microphone

• 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

43
The electret microphone

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

This voltage, is the true output of the sensor,
can be related to the sound pressure as
A is the area of the membrane, T the tension, ?
is the specific heat ratio, p0 is ambient
pressure and ?p the change in pressure due to
sound
44
The electret microphone

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

This voltage can now be amplified as necessary.
45
The electret microphone

• 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.

46
The electret microphone

• 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.

47
Electret microphones
48
Electret microphones
49
The 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.

50
The piezoelectric effect

• 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

51
The piezoelectric effect

• 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

52
The piezoelectric effect

• 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.

53
The 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

d is the piezoelectric constant, ? the stress in
the material.
54
The piezoelectric effect - theory

• 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.
dij are the piezoelectric coefficients along the
orthogonal axes of the crystal.
55
The piezoelectric effect - theory

• 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 is strain (dimensionless), g is called the
constant coefficient (e is permittivity)
56
The piezoelectric effect - theory

• 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

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.
57
Crystals - piezoelectric properties
58
Ceramics - piezoelectric properties
59
Polymers - piezoelectric properties
60
Piezoelectric 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

Voltage developed across it is
d thickness A area
61
Piezoelectric 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

62
Piezoelectric microphone

• Applying a force (due to sound pressure) on the
  surface (Figure 7.16).
• Given this structure, and a change in pressure
  ?p, the change in voltage expected is

A linear relation is therefore available to sense
the sound pressure
63
Piezoelectric microphone
64
Piezoelectric microphone

• 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.

65
Piezoelectric 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.

66
Other 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 Faradays law (N1) 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.

67
The film microphone
68
Acoustic 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.

69
Acoustic actuators

• The basic structure of a loudspeaker
• The force is given by the Lorenz force, NBIL.
• Magnetic field supplies by permanent magnets

70
A titanium diaphragm speaker
71
Loudspeakers

• 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.

72
Loudspeakers

• 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.

73
Loudspeakers

• 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

74
Loudspeakers

• 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

Rmr acoustic impedance (of air), Rml total
mechanical resistance seen by the diaphragm Xml
total mass reactance seen by the diaphragm
75
Loudspeakers

• 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.

76
Loudspeakers

• 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.

77
Frequency response of a speaker
78
Loudspeakers

• 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.

79
Loudspeakers

• 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.

80
Directional response
81
Small loudspeakers
82
Low frequency loudspeaker (top)
83
Low frequency loudspeaker (side)
84
Moving 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.

85
Moving coil earphone
86
Moving coil earphone
87
Moving armature actuator

• 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.

88
Moving armature actuator

• 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.

89
Magnetic buzzers
90
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

91
Piezoelectric earphone
92
Piezoelectric 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.

93
Piezoelectric buzzer
94
Piezoelectric buzzers

• 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).

95
Piezoelectric buzzers
96
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.

97
24 kHz, UT transmitter and receiver
98
Ultrasonic sensors and actuators

• 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

99
40 kHz ultrasonic sensor
100
40 kHz ultrasonic transmitter/receiver for ranging
101
Ultrasonic 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.

102
Ultrasonic 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.

103
Piezoelectric resonator

• Equivalent circuit of a piezoelectric material.
• This circuit has two resonances a parallel
  resonance and a series resonance (called
  antiresonance)

104
Piezoelectric resonator

• The resonant frequencies are given as

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
105
Piezoelectric resonator

• 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
106
Ultrasonic 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.

107
Ultrasonic 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.)

108
Ultrasonic sensor - construction
109
Ultrasonic sensors - sample
110
Specification sheet
111
Pulse-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.

112
Pulse-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.

113
Fault location by ultrasound
114
Sensing 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.

115
Sensing 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

c speed of sound vf fluid speed
116
Magnetostrictive 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

117
EMATs

• 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 (lt100kHz) and have low efficiencies.

118
Structure of EMATs
119
Piezoelectric 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

120
Piezoelectric 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.

121
Linear piezoelectric actuator
122
Stacked 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.

123
Stacked piezoelectric actuator
124
Saw 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

125
Saw devices

• 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!

126
SAW 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.

127
Surface waves in a solid
128
Saw devices

• 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.

129
SAW generator
130
SAW devices

• 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
  1.875?m width for each strip and 1.875?m 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).

131
SAW devices

• 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

132
SAW 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.

133
SAW Resonator
134
SAW Resonator

• 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.

135
SAW Resonator

• 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)

136
SAW resonators for communication
137
SAW delay line
138
SAW Resonator

• 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.

139
SAW Resonator

• 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

140
SAW sensor
141
SAW sensor
142
SAW Resonator

• 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

? is the coefficient of linear expansion ? the
temperature coefficient of sound velocity.
143
SAW Resonator

• 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

This is linear and a SAW sensor has a sensitivity
of about 10????C.
144
SAW Resonator

• 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.