13.9 Ultrasonic transducers
Ultrasonic devices are used in many
fields of measurement, particularly for measuring fluid flow rates, liquid
levels and translational displacements. Details of such applications can be
found in later chapters. Uses of ultrasound in imaging systems will also be
briefly described at the end of this section, although the coverage in this case
will be brief since such applications are rather outside the scope of this
text.
Ultrasound is a band of frequencies
in the range above 20 kHz, that is, above the sonic range that humans can
usually hear. Measurement devices that use ultrasound consist of one device
that transmits an ultrasound wave and another device that receives the wave.
Changes in the measured variable are determined either by measuring the change
in time taken for the ultrasound wave to travel between the transmitter and
receiver, or, alternatively, by measuring the change in phase or frequency of
the transmitted wave.
The most common form of ultrasonic
element is a piezoelectric crystal contained in a casing, as illustrated in
Figure 13.10. Such elements can operate interchangeably as either a transmitter
or receiver. These are available with operating frequencies that vary between
20 kHz and 15 MHz. The principles of operation, by which an alternating voltage
generates an ultrasonic wave and vice versa, have already been covered in the
section above on piezoelectric transducers.
For completeness, mention should also
be made of capacitive ultrasonic elements. These consist of a thin, dielectric
membrane between two conducting layers. The membrane is stretched across a back
plate and a bias voltage is applied. When a varying voltage is applied to the
element, it behaves as an ultrasonic transmitter and an ultra[1]sound wave is
produced. The system also works in the reverse direction as an ultrasonic
receiver. Elements with resonant frequencies in the range between 30 kHz and 3
MHz can be obtained (Rafiq, 1991).
13.9.1 Transmission speed
The transmission speed of ultrasound
varies according to the medium through which it travels. Transmission speeds
for some common media are given in Table 13.1.
When transmitted through air, the
speed of ultrasound is affected by environmental factors such as temperature,
humidity and air turbulence. Of these, temperature has the largest effect. The
velocity of sound through air varies with temperature according to:
V = 331.6 +
0.6T m/s (13.2)
where T is the temperature in °C.
Thus, even for a relatively small temperature change of 20 degrees from 0°C to
20°C, the velocity changes from 331.6 m/s to 343.6 m/s.
Humidity changes have a much smaller
effect. If the relative humidity increases by 20%, the corresponding increase
in the transmission velocity of ultrasound is 0.07% (corresponding to an
increase from 331.6 m/s to 331.8 m/s at 0°C).
Changes in air pressure itself have
negligible effect on the velocity of ultrasound. Similarly, air turbulence
normally has no effect (though note that air turbulence may deflect ultrasound
waves away from their original direction of travel). However, if turbulence
involves currents of air at different temperatures, then random changes in
ultrasound velocity occur according to equation (13.2).
13.9.2 Direction of travel of
ultrasound waves
Air currents can alter the direction
of travel of ultrasound waves. An air current moving with a velocity of 10 km/h
has been shown experimentally to deflect an ultrasound wave by 8 mm over a
distance of 1 m.
13.9.3 Directionality of ultrasound
waves
Although it has perhaps been implied
above that ultrasound waves travel in a narrow line away from the transmitter,
this is not in fact what happens in practice. The ultra[1]sound
element actually emits a spherical wave of energy whose magnitude in any
direction is a function of the angle made with respect to the direction that is
normal to the face of the ultrasonic element. The peak emission always occurs
along a line that is normal to the transmitting face of the ultrasonic element,
and this is loosely referred to as the ‘direction of travel’ in the earlier
paragraphs. At any angle other than the ‘normal’ one, the magnitude of
transmitted energy is less than the peak value. Figure 13.11 shows the
characteristics of the emission for a range of ultrasonic elements. This is
shown in terms of the attenuation of the transmission magnitude (measured in
dB) as the angle with respect to the ‘normal’ direction increases. For many
purposes, it
is useful to treat the transmission
as a conical volume of energy, with the edges of the cone defined as the
transmission angle where the amplitude of the energy in the transmission is - 6
dB compared with the peak value (i.e. where the amplitude of the energy is half
that in the normal direction). Using this definition, a 40 kHz ultrasonic
element has a transmission cone of ±50° and a 400 kHz element has a
transmission cone of ±3°.
13.9.4 Relationship between
wavelength, frequency and directionality of ultrasound waves
The frequency and wavelength of
ultrasound waves are related according to:
where
This shows that the relationship
between
It is clear from Table 13.2 that the
directionality (cone angle of transmission) reduces as the nominal frequency of
the ultrasound transmitter increases. However, the cone angle also depends on
factors other than the nominal frequency, particularly on the shape of the
transmitting horn in the element, and different models of ultrasonic element
with the same nominal frequency can have substantially different cone angles.
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