Download chapter7

Acoustic Sensors and
Actuators
Chapter 7
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
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.
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

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.
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
Concept of wavelength
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.
Transverse waves on a tight
string
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.
Acoustic waves - speed

The speed of an acoustic wave is directly related
to the change in volume and the resulting
change in pressure
c=
pV
V0
m/s
0 is the density of the undisturbed fluid,
V is the change in volume,
p is the change in pressure
V is the volume
Acoustic waves - speed

In gasses, this simplifies to the following
c=
p0
0
m/s
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
Speed of sound
Table 6.1. Speed of sound in some materials at given temperatures.
Material
Speed [m/s]
Temperature [ C]
Air
331
20
Fresh water
1,486
20
Sea water
1,520
20
Granite
6,000
Steel
5,200
20
Copper
3,600
20
Aluminum
6,320
Beryllium
12,900
Acoustic waves - theory

Assuming a harmonic longitudinal wave of
frequency f, it may be written in general terms
as:
p = P0sin(kx  t)
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
Acoustic waves - theory

The amplitude of the wave is:
P0 = k0 c 2 ym
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:
k = 2 = 
l c
Acoustic waves - theory

Waves carry energy.




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).



A shockwave (earthquake) can cause damage
A loud sound can hurt our ears.
Attenuation of a wave depends on the medium
Attenuation reduces the amplitude of the wave.
Attenuation of waves is exponential
Acoustic waves - theory


Attenuation constant is defined for each material
The amplitude of the wave, as it propagates,
changes as follows
p = P0 e x sin(kx  t)
Attenuation causes loss of energy as the wave propagates
Dissipates energy of the wave
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.
Reflection, transmission and
refraction
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 t which is equal to:
c
sin t = c2 sin i
1
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
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.
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 l/2 while maxima
occur atel/4 on either side of a node.
Standing waves
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.
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 = 0 c
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
Bell’s Microphone
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.
The carbon microphone
The carbon microphone
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.
The magnetic microphone
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
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 Faraday’s law: Given a
coil moving in the magnetic field, it produce an
emf :
d
V=  N
dt
Dynamic microphone
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.)
Capacitive microphones




Also called “condenser” microphones
Idea is trivially simple:
Allow sound to move a plate in a capacitor
Sense the change in capacitance
Capacitive microphones

The operation is based on the two basic
equations of the parallel plate capacitor
C = A ,
d
C=
Q
V

V=Qd
eA
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!
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.
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.
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
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
s 1.
The voltage across the two metallic plates, in
the absence of any outside stimulation
(sound) is:
1
V =  s ss
0 + s 1
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:
V =  ss+ss
0
1
This voltage, is the true output of the sensor, can be
related to the sound pressure as:

s =
p
p0s1 + 8 T/A
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
The electret microphone

Thus, the change in output voltage due
to sound waves is:
p
V =  s +s s
0
1 p0 s1 + 8T/A
This voltage can now be amplified as necessary.
The electret microphone

Electret microphones are very popular



But: their impedance is very high



simple and inexpensive
do not require a source (they are passive devices).
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.
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.
Electret microphones
Electret microphones
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.
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:
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
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.
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
P = d
d is the piezoelectric constant,
 the stress in the material.
C
m2
The piezoelectric effect - theory

Polarization is direction dependent in the crystal
and may be written as:
P = Pxx + Pyy + Pzz
x, y, z are the standard axes in the crystal.
The relation above now becomes.
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 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 = gP
e is strain (dimensionless), g is called the constant
coefficient ( is permittivity)
g=d

dij
or: gij = 
ij
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:
k 2 = dgE
or: kij2 = 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
Table 7.2. Piezoelectric coefficients and other propertiesin monocry stals
Crystal
Piezoe lectric
Permittivit y, ij
Coup li ng coefficient

coeffi cient dij, x10
kmax
[C/N]
Qua rtz (SiO2)
d11=2.31, d14=0.7
11=4.5, 33=4.63
0.1
ZnS
d14=3.18
11=8.37
0.1
CdS
d15=-14, d33=10 .3,
11=9.35, 33=10.3
0.2
d31=-5.2
ZnO
d15=-12, d33=12 ,
11=8.2
0.3
d31=-4.7
KDP (KH2PO4)
d14=1.3, d36=21
11=42, 33=21
0.07
ADP (NH4H2PO4)
d14=-1.5, d36=48
11=56, 33=15.4
0.1
BaTiO3
d15=400 , d33=100 ,
11=3000 , 33=180
0.6
d31=-35
LiNbO3
d31=-1.3, d33=18,
11=84, 33=29
0.68
d22=20 , d15=70
LiTaO3
d31=-3, d33=7,
11=53, 33=44
0.47
d22=7.5, d15=26
Ceramics - piezoelectric
properties
Table 7.3. Piezoelectric coefficients and other properties in ceramics
Cerami c
Piezoe lectric coefficie nt Permittivit y,

dij, x10  [C/N]

BaTiO3+5%CaTiO3 (at 105C)
d15=260 , d31=-45,
d33=-100
d31=43 , d33=77
Coup li ng
coeffi cient
kmax
0.2

0.25
Pb(Zr0.53Ti0.47)O3+(0.5-3)%La2O2
or Bi2O2 or Ta2O5 (at 290C)
(Pb0.6Ba0.4)Nb2O6 (at 300C)
(K0.5Na0.5)NbO3 (at 240C)
d15=380 , d31=119 ,
d33=282
d31=67 , d33=167
d31=49 , d33=160

0.47


0.28
0.45
BaTiO3 (at 120C)
Polymers - piezoelectric
properties
Table 7.4. Piezoelectric coefficients and other properties in polymers
Polymer
Piezoe lectric coefficie nt
Permittivit y,


dij, x10 [C/N]
PVDF
Copolymer
d31=23 , d33=-33
d31=11 , d33=-38


Coupli ng
coeffi cient
kmax
0.14
0.28
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:
Qx = d11 Fx
Voltage developed across it is:
Qx d11 Fx d11 Fx d
V=
=
=
C
C
A
d = thickness
A = area
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
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:
V =
d11 pA d d11 d
=  p
A
A linear relation is therefore available to sense the sound
pressure
Piezoelectric microphone
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.
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.
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 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 microphone
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.
Acoustic actuators



The basic structure of
a loudspeaker
The force is given by
the Lorenz force,
NBIL.
Magnetic field
supplies by
permanent magnets
A titanium diaphragm speaker
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.
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.
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
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:
Pr =
2I 2 B 2 (2 rN)2 Rmr
2
2
Rml
+ Xml
Rmr = acoustic impedance (of air),
Rml = total mechanical resistance seen by the diaphragm
Xml = total mass reactance seen by the diaphragm
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.
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.




Frequency response of a
speaker
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.





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.
Directional response
Small loudspeakers
Low frequency loudspeaker
(top)
Low frequency loudspeaker
(side)
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.
Moving coil earphone
Moving coil earphone
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.
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.
Magnetic 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 earphone
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.
Piezoelectric buzzer
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).
Piezoelectric buzzers
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.
24 kHz, UT transmitter and
receiver
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
40 kHz ultrasonic sensor
40 kHz ultrasonic
transmitter/receiver for ranging
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.
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.
Piezoelectric resonator


Equivalent circuit of a
piezoelectric material.
This circuit has two
resonances – a parallel
resonance and a series
resonance (called
antiresonance)
Piezoelectric resonator

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
Piezoelectric resonator

The relation between the two frequencies is:
fp = fs 1 + m
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
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.
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.)
Ultrasonic sensor - construction
Ultrasonic sensors - sample
Specification sheet
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.
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.
Fault location by ultrasound
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.

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:
T=
D
c + vf cos
c speed of sound
vf fluid speed
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
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
(<100kHz) and have low efficiencies.
Structure of EMATs
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
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.
Linear piezoelectric actuator
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.
Stacked piezoelectric actuator
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
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: l=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 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.
Surface waves in a solid
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.
SAW generator
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l/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).
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
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.
SAW Resonator
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.
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)
SAW resonators for
communication
SAW delay line
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.
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
SAW sensor
SAW sensor
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:
L = L0 1 +  T  T0 ,
c = c0 1 +  T  T0
 is the coefficient of linear expansion
 the temperature coefficient of sound velocity.
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:
f =    T
f
This is linear and a SAW sensor has a sensitivity of about
10C.
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.