1. Ultrasound Transducers
Saudi Board of Radiology: Physics Refresher Course
Ultrasound Transducers
Kostas Chantziantoniou, MSc2, DABR
Head, Imaging Physics Section
King Faisal Specialist Hospital & Research Centre
Biomedical Physics Department
Riyadh, Kingdom of Saudi Arabia

2. Ultrasound Pulse Production and Reception
A transducer is a device that can convert one form of energy into another. Ultrasound
transducers are used to convert an electrical signal into ultrasonic energy that can be
transmitted into tissue, and to convert ultrasonic energy reflected back from the tissue
into an electrical signal.
The general composition of an ultrasound transducer is shown below:
the most important component is a thin
piezoelectric (crystal) element located near the
face of the transducer
the front and back face of the element is coated
with a thin conducting film to ensure good
contact with the two electrodes
the outside electrode is grounded to protect the
patient from electrical shock
an insulated cover is used to make the device
watertight
an acoustic insulator made of cork or rubber is
used to prevent the passing of sound into the
housing (i.e.: reduces transducer vibrations)
the inside electrode is against a thick backing block that absorbs sound waves
transmitted back into the transducer

3. Matching Layer
A matching layer of material is placed on the front surface of the transducer to improve
the efficiency of energy transmission into the patient. The material used has an
impedance in between that of the transducer and tissue; and it has a thickness one forth
the wavelength of sound in the transducer crystal material (quarter wave matching).
Piezoelectric Crystal
Certain material (or crystals) are such that the application of an electrical field causes a change in their physical dimensions. The reverse effect, where an external pressure causes a change in the crystal’s physical dimensions and thus induces a voltage between electrodes, is called the piezoelectric effect. Piezoelectric means pressure
electricity.
some naturally occurring materials posses piezoelectric properties (eg: quartz) but
most crystals used in diagnostic ultrasound are man-made ceramics like lead
zirconate titanate (PZT)
the advantage is using ceramics is that they can be formed into different shapes
piezoelectric crystals can be designed to vibrate in either the thickness or radial mode,
but in medical imaging it is the thickness mode that is used
the piezoelectric effect of a transducer element is destroyed if heated above its Curie
temperature limit (328C for PZT and 573C for quartz)
transducer crystals do not conduct electricity

4. Creating a sound wave from an electrical pulse
When a positive voltage (A) is applied across the surface of the crystal, it creates an electric field across the crystal surface which cause the molecules (dipoles) in the crystal to realign and thus changing the shape (width) of the crystal. A B C
Voltage Pulse
Positive
Time
Negative
When the voltage polarity is changed from positive to negative, there is a point in time
when the electric field across the crystal is zero (at voltage equal to zero) and the crystal
relaxes (B). When the voltage polarity is reversed (i.e.: negative) the crystal realigns
once again and changes its width once again (C).

5. The net effect the alternating voltage pulse has on the crystal is to make it oscillate back
and forth about its width. This change in shape of the crystal increases and decreases
the pressure in front of the transducer, thus producing ultrasound waves.
Ultrasound wave direction
Rarefaction region created when crystal
surface is contracting (less pressure on surface)
wavefront diagram
Compression region created when crystal
surface is expanding (more pressure on surface)
Ultrasound wave direction

6. Creating an electrical signal from a sound wave
When the compression region (A) of the ultrasound wave is incident on the front surface of the crystal, it induces a high pressure region on the surface which in turn compresses the crystal. This cause the molecules in the crystal to re-align and induce an electric field across the crystal which generates an electrical voltage signal that is proportional to the intensity of the compression region. A B
Rarefaction region relaxes crystal surface
(less pressure on surface)
wavefront diagram
Compression region compresses crystal
surface (more pressure on surface)
When the rarefaction region (B) of the ultrasound wave is incident on the front
surface of the crystal, it induces a low pressure region on the surface which in turn
relaxes the crystal.

7. The net effect the ultrasonic wave has on the crystal is to make it oscillate back
and forth about its width. This change in shape of the crystal induces a voltage signal
that also varies in time and in amplitude.
NOTE
A transducer can function both as a transmitter and a receiver of ultrasound energy, but
it can not transmit and receive at the same time.
Transmitter Mode
Receiver Mode

8. Transducer Characteristics
Transducer Thickness
A transducer can be made to emit sound of any frequency by driving it (in continuous
mode) with an alternating voltage of that frequency. However, a transducer vibrates
most violently and produces the largest output (pressure amplitude) of sound when
 = • t
where the  is wavelength of sound and t is the thickness of the piezoelectric crystal.
The frequency of the emitted sound waves is then given by
frequency = v = v
 • t
where v is the speed of sound in the piezoelectric crystal.
operating frequency  crystal thickness 

10. Why should the transducer thickness be equal to 1/2 of the desired wavelength?
Back surface
Front surface A B C D
Backing
Block    
Patient
Thickness (t)
When the piezoelectric element is driven by a alternating voltage the crystal
vibrates (i.e.: the width of the crystal moves back and forth). The front face of the crystal emits sound both in the forward and backward directions as does the back surface.
wave front (A) will get absorbed by the transducer’s backing material
wave front (D) will enter into the patient
the wave front (C) is reflected at the back face of the disk, and by the time it joins
wave front (D), it has traveled an extra distance 2t. If this distance equals a
wavelength the wave fronts (D) and (C) reinforce for they are in phase, and
constructive interference or resonance occurs.
if wave fronts (D) and (C) are not in phase, then there will be some destructive
interference
same reasoning applies to wave front (B)

11. Constructive Interference
(waves A & B add to form a
new wave of amplitude A + B)
Destructive Interference
(waves A & B add to form a new
wave of amplitude A + B = 0)
If wave B is wave front (C) and wave F is wave front (D) then we see that when transducer thickness is one half the wavelength, both wave fronts are in phase and constructive interference (ie: their individual amplitudes add) occurs.

12. changing the thickness of the crystal changes the frequency but not the ultrasound
amplitude (determined by applied voltage waveform) or speed (determined by
piezoelectric crystal)
high frequency transducers are thin and low frequency transducers are thicker
to change the frequency one has to change the transducer

13. Resonant Frequency
The frequency at which the transducer is the most efficient as a transmitter of sound
is also the frequency at which it is most sensitive as a receiver of sound. This
frequency is called the natural or resonant frequency of the transducer.
the thickness and the material (i.e.: speed of sound in the crystal) of the piezoelectric
crystal determines the resonant frequency of the transducer
transducers crystals are normally manufactured so that their thickness (t) is equal to
one-half of the wavelength () of the ultrasound produced by the transducer
Bandwidth
The range of frequencies in the emitted ultrasound wave is called the bandwidth and is defined to be the full width of the frequency distribution at half maximum (FWHM).
Resonant Frequency
bandwidth  SPL 

14. Continuous voltage waveform Pulsed voltage waveform
Frequency distribution of emitted ultrasound wave
Continuous waveform
can be represented by
a single sine wave (one
frequency), thus frequency
distribution is very
narrow
Pulsed waveform
can be represented by
the sum of many sine
waves each of different
frequency, thus frequency
distribution is wide

15. Q-factor
The Q-factor of a transducer system describes the shape of the frequency distribution
(response curve) and is defined as
Q-factor = f0
(f2 - f1)
Bandwidth = (f2 - f1)
where f0 is the resonance frequency, f1 is the frequency below resonance at which
intensity is reduced by half and f2 is the frequency above resonance at which
intensity is reduced by half
high Q transducers produce relatively
pure frequency spectrums and low Q
transducers produce a wider range of
frequencies
short pulses correspond to reduce Q
values and vice versa
bandwidth  Q-factor 

16. Pulse Ultrasound Mode
Because a transducer can be a transmitter and a receiver of ultrasonic energy, it clearly stands to reason that a continuous voltage waveform can not be used. If such a waveform was used, the transducer would always function as a transmitter. Since the internally generated sound waves are stronger than the returning echoes, the returning signal is lost in the noise of the system. To over come this problem, most transducers are used in a pulse mode where the voltage waveform consists of many pulses each separated by a fixed distance and time. The transducer functions as a transmitter during pulse excitation and as a receiver during the time interval between pulses.
Voltage waveform
Ultrasound pulses produced by transducer
NOTE
most transducers are designed to have short pulses (improved resolution) with low
Q values (broad bandwidth - desirable in order to receive echoes of many different
frequencies)

17. Blocks of damping material, usually tungsten/rubber in a epoxy resin, are placed behind
transducers to reduce (or dampen) the vibrations and to shorten pulses.
the exponential decay of the pressure wave over time is called damping
if damping is heavy the transducer has a short ring down time and is said to have a
low Q value
a transducers with lighter damping is said to have a high Q value

18. Pulse Repetition Frequency (PRF)
PRF is the number of pulses occurring in 1 second
Pulse Repetition Period (PRP)
PRP is the time from the beginning of one pulse to the beginning of the next pulse

19. Spatial Pulse Length (SPL)
SPL is the length of space over which a single pulse occurs, and is defined as
SPL = n • 
where n is the number of cycles in the pulse and  is the wavelength.
NOTE
An important parameter when considering axial resolution

20. Pulse Duration (PD)
PD is the time it takes for a single pulse to occur and is defined as
PD = n • T
where n is the number of cycles in the pulse and T is the period.
Duty Factor (DF)
DF is the fraction of time that ultrasound generation (in the form of pulses) is ON, and
is defined as:
DF = PD
PRP

22. Ultrasound Beam Characteristics
In order to understand the beam characteristics of ultrasound we have to revisit our
view of wave front (compression region) generation. A piezoelectric crystal surface
actually behaves more like a series of vibrating points and not as the piston-like
surface that we have implied previously.
simplified
model
more accurate
model
the compression waves are not uniform (at least not close to the crystal surface)
each vibrating point produces multiple concentric rings or waves that eventually form
a continuous front as they reinforce each other along a line parallel to the surface of
the crystal
the distance at which the waves become synchronous depends on their wavelength,
the shorter the wavelength the close the front forms to the surface of the transducer

25. Fresnel Zone (Near Field)
The length of the Fresnel zone is given by: d2
4 • 
where d is the diameter of the transducer and  is the wavelength.
the Fresnel zone increases with transducer size and frequency (lower wavelength)
ultrasound imaging normally uses the Fresnel zone but not the Fraunhofer zone in
which resolution is poor
beam intensity falls off because of attenuation

27. Fraunhofer Zone (Far Field)q
The angle of divergence of the Fraunhofer zone is given by:
sin(q) =  d
where d is the diameter of the transducer and  is the wavelength.
beam intensity falls of due to attenuation and beam divergence
angle of divergence increases with decreasing transducer diameter and frequency
no useful imaging can be made in this region

28. Side Lobes
Side lobes are small beams of greatly reduced intensity that are emitted at angles to
the primary beam and they often cause image artifacts.
the origin of these lobes are due from radial vibrations from the edges of the
transducer

29. Grating Lobes
Grating lobes result when ultrasound energy is emitted far off-axis by multi-element
arrays, and are a consequence of the non-continuous transducer surface of the discrete elements.
this misdirected energy of relatively low amplitude results in the appearance of
highly, off-axis objects in the main beam

30. Axial (Linear, Range, Longitudinal, Depth) Resolution
Axial resolution is the ability to separate two objects lying along the axis of the beam
and is determined by the spatial pulse length (SPL).
Case: SPL < X
Case: SPL = 2X
Objects a and b separate by distance X
Objects resolvable
Objects not resolvable
limiting resolution = SPL = n• where n is the number of cycles and
 is the wavelength

31. because axial resolution is depended to the SPL then it is also depended on pulse
frequency and duration (PD)
with a typical wavelength of 0.3 mm and three cycles per pulse, the axial resolution
is approximately 0.5 mm
axial resolution deteriorates with increasing pulse length, decreasing frequency and
increasing wavelength
the use of damping transducers (low Q) produces short pulses that improves axial
resolution
frequency  axial resolution  (improved)
cycle/pulse  axial resolution 
SPL  axial resolution  (worsened)

32. Lateral (Azimuthal) Resolution
Lateral resolution is the ability to separate two adjacent objects and is determined by
the width of the beam and line density.
Object separation narrower than beam width
Object separation wider than beam width
lateral resolution is equal to beam width in the scan plane
lateral resolution is best in the Fresnel zone where ultrasound waves are parallel
lateral resolution is generally a few millimeters
beam width  lateral resolution  (improved)

33. Elevation Resolution (Slice Thickness)
Elevation resolution is the dimensions of the ultrasound beam perpendicular to the
image plane and depends on the transducer element height in much the same way that the lateral resolution is dependent on the transducer element width.

34. Focused Transducers
High frequency beams have two advantages over low-frequency beams:
(1) axial resolution is superior; and
(2) the Fresnel zone is longer
It would seem logical to use high frequencies for all imaging. High frequencies however, have a major drawback related to penetration. Tissue absorption increases
with increasing frequency, so a relatively low frequency beam is required to penetrate thick parts.
It would then seem logical to use low frequency transducers and to increase the size of the transducer to keep the beam coherent for sufficient depth to reach the point of interest (longer Fresnel zone). Although larger transducers improve coherence they deteriorate lateral resolution. The dilemma is at least partially resolved with the use focused transducers.
NOTE
focused transducers reduce beam width which improves lateral resolution
they also concentrate beam intensity thereby increasing penetration and echo
intensity thus improving image quality

35. the focal zone is the region over which the beam is focused
the focal length is the distance from the transducer to the centre of the focal zone
the depth of focus is the distance over which the beam is in a reasonable focus
a small diameter transducer has a shorter focal zone and spreads more rapidly in
the far zone
most diagnostic transducers are focused, which is achieved using a either a curved
piezoelectric crystal, an acoustic lens or electronics (phased arrays)

36. A focused transducer produces a narrower beam at the focal zone and, therefore, has
better lateral resolution than an unfocused transducer of the same size.

37. In reality we have:
It is important to realize, that even for flat, unfocused transducer elements, there is
some beam narrowing or “focusing”.

38. Curved Piezoelectric
Crystal
Acoustic Lens
Electronic Focusing
(Phased Array)