Ultrasonic transducers

1.1 Introduction

Transducer is a device which converts energy of one form to that of another. With reference to ultrasonic transducer the ultrasonic energy is to be converted to electrical, mechanical, or other energy form. A reversible transducer transforms energy in both directions with equal efficiencies.

The transducers can be classified as follows:

1. Piezoelectric oscillators: Principle of piezoelectric effect is used and this is reversible. The possible frequency range is from 20 kHz to well over 10 GHz.

2. Magnetostrictive oscillators: Employs the phenomenon of magnetostriction, a reversible form of conversion. Can be made to operate at mega-hertz and even gigahertz frequencies.

3. Mechanical transducers: Includes whistles and sirens (mechanical oscillators) and radiometers, and are irreversible. Mainly used for high-power applications.

4. Electromagnetic transducers: Applied for high-intensity applications at low frequencies, in the audible range. They have been used for low-intensity work at frequencies of up to 50 kHz and, also as receivers at mega­hertz frequencies.

5. Electrostatic transducers: Used as generators at low intensities with an upper frequency limit of a few hundred kilo-hertz. Reversible in conversion and used as receivers at frequencies as high as 100 MHz.

6. Miscellaneous transducers: Includes thermal, chemical, and optical transducers.

Ultrasonic receivers are categorized into two

1. Receivers terminating acoustic beams: The cross-section of the receiver embraces the whole or a large proportion of that of the beam and its dimensions extend from several to a large number of wavelengths. The presence of the receiver materially affects the configuration of the acoustic field, to give rise to regular reflections of the beam.

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2. Receivers acting as probes: ultrasonic probe receivers are used for mapping out acoustic fields and for measurement of local intensities. the use of probe receivers is restricted to lower frequencies (e.g. in the kilo-hertz range)., as their dimensions need to be small enough, not to upset the characteristics of the field,( to be less than about one-tenth of a wavelength).

1.2 Piezoelectric transducers

1.2.1 General considerations

Piezoelectric transducers employ the piezoelectric effect, discovered by the Pierre and Jacques Curie in 1880. The effect occurs naturally in certain single crystals with polar axes, (e.g. quartz, tourmaline, lithium sulphate, cadmium sulphide, and zinc oxide.)

When mechanical stress is applied to the surfaces of piezoelectric crystals, coated with silver or gold, equal and opposite electric charges will be induced on them and a voltage will be observed. This is the direct piezoelectric effect, and the crystalline axis perpendicular to the coated faces is the relevant polar axis. When a voltage is applied across the electrodes to produce an electric field, a converse effect is observed, resulting in a mechanical strain.

These effects are associated with compressions and shears, in quartz, for example, the principal polar axes are called the X- and Y axes, there is three of each. The X-axes are oriented at angles of 120° apart, and with corresponding Y-axis perpendicular to it. The electrodes lie at right angles to an X-axis for X-cut quartz crystals, and are associated with compressions, and Y-cut quartz crystals with shears. The Z-axis, is known as the optic axis and lies perpendicular to the planes containing the X- and Y-axes. Optic is a non-polar axis for which the piezoelectric effect is not observed.

A piezoelectric transducer oscillates at the applied frequency with amplitude of the order of 10-6 times its thickness, on applying an alternating voltage across its electrodes,. If, the transducer is excited at one of its resonance frequencies the amplitude is considerably increased, e.g. to about 10-4 times the thickness at the fundamental frequency

Artificially induced piezoelectric transducers are of polycrystalline structure. They are made up of large numbers of minute crystallites bonded together, to the required shape and size. The final product is in the form of a ceramic. Prior to polarisation, these ceramic transducers do not require to be cut with reference to any particular axis, as they are isotropic. So it is possible to have a shape in any convenient form by adding small quantities of other materials, the transducer’s properties can be improved or adjusted.

The piezoelectric effect is measured by the d coefficient, which can be expressed in one or two ways.

(i) If the crystal is subjected to a mechanical stress, at the same time, the electrodes are short-circuited by a wire, charges induced by the stress will flow through the wire until the potential difference across the

crystal is reduced to zero. Considering, q is the value of the total charge flowing and F the force producing the stress, then d coefficient can be given as

d=q/f coulombs per Newton 3.1

(ii) When a voltage V is applied across the crystal, on which no load is applied e.g. vacuum, a displacement l is produced due to the resultant strain, then volts per metre 3.2

The electromechanical coupling coefficient is defined as

Both d and k vary with temperature and reduce to zero at the Curie temperature Tc.

The frequency response of a transducer depends on its Q factor. If the characteristic impedances of transducer and medium are R1 and R2, then Q can be represented as where K is a dimensionless constant.

Ceramic transducers have higher d coefficients and electromagnetic coupling coefficients compared to the quartz crystals. But quartz crystals are highly stable.

1.2.2. Coupling of Piezo electric transducers

A suitable liquid must be provided to avoid an air gap , for efficient coupling of ultrasound between the transducer and a solid. To generate longitudinal waves at normal temperatures, a film of oil is usually enough, but, at low temperatures a high-vacuum grease is used to prevent loss of continuity of characteristic impedance. While working with high temperatures, a couplant which does not evaporate, should be chosen.

.For transverse wave propagation, it is necessary to use adhesive such as epoxy resin, so as to ensure the couplant has enough strength to withstand the application of the shear stresses without collapsing. Canada balsam or even nail varnish , on some occasions will provide good coupling for shear waves, depending on the temperatures.

1.2.3 Ultrahigh frequency (u.h.f.) piezoelectric transducers

An early method of generating u.h.f. ultrasonics was to place one end of a single-crystal quartz rod inside an electromagnetic cavity resonator Ci (see Figure ). The surface was excited at the required frequency, and waves were propa­gated along the rod. Initially the method was applied only for producing ultrasound in single-crystal quartz , due to difficulty of coupling other materials to the free end of the rod. Another electromagnetic cavity resonator C2 at the other end of the rod acted as a receiver. In later stages the free ends of the rod and solid specimen was coated with thin film of indium.

1.2.4 Piezoelectric sandwich transducers

To generate waves at the frequencies ranging from 40 kHz down to 20 kHz.frequency, for High-intensity applications ,with a piezoelectric ceramic, the thickness should exceed 100 mm.

A ceramic block of this thickness is both expensive and is highly absorbent. Due to this, absorbed acoustical energy being converted into heat, results in a rapid increase of temperature and the Curie temperature is soon reached, with a consequent disappearance of the piezoelectric effect. To avoid this sandwiching of the piezoelectric transducers can be applied.

A sandwich transducer consists of a comparatively thin piezoelectric plate located between two thicker metal plates.They have high compressive strengths and by compressing the sandwich permanently using high tensile bolt damage can be prevented. (see Figure 3.7); the transducer is said to be mechanically biased.

1.2.5 Surface wave piezoelectric transducers

Surface waves can be generated by using mode conversion with a longitudinal wave transducer as the primary source, but it is also possible to propagate them directly. Surface waves are produced by placing an ordinary longitudinal wave transducer in contact with the edge of the material and inclined at an angle of 45° (Fig 3.4) and are received in same fashion. Another method of generating and receiving surface waves is by coating two electrodes on the surface of a piezoelectric material and applying the exciting voltage at the required frequency across them (see Figure 3.5). This technique was used for delay line applications

1.2.6 Operation of piezoelectric transducers

A quartz crystal mounted at its nodes, is an ideal one for propagating continuous waves over a narrow frequency band. Electrical connections must be made to the electrodes and additional damping caused by them should be kept minimal. Nodal mounting is not advisable for very thin transducers and where contact with a solid medium has to be maintained. For cases like these, the transducer is held in position by means of a light spring against a solid surface. Then the solid surface provides one electrical contact with the transducer electrode and the other is provided by the spring. To have maximum efficiency, the impedances of the exciting and receiving electri­cal circuits should be correctly matched to the electrical impedance of the transducer.

For pulsed wave operation it is essential that the pulses are kept sufficiently short to prevent their overlapping. No stationary waves are to be produced in the medium. To produce very short pulses and where a narrow frequency band is not needed, transducer material, such as a ceramic is used. The transducer is backed by a block of a material having a very high acoustic absorption coefficient and of sufficiently large electrical conductivity to provide contact with that transducer surface. A mixture of tungsten powder and Aroldite is used for this purpose. A high direct voltage (typically from 300 V to 600 V) of instantaneous duration is applied periodically to the transducer electrodes at the required pulse repetition frequency. At each electrical impulse, the transducer experiences a high initial strain after which it oscillates over about two or three cycles, the amplitude decreasing rapidly.. Thus, for a transducer operating at a frequency of 6 MHz to produce pulses each of three wavelengths, the pulse duration is about only 0.5μ for propagation into most metals. The relation between pulse-length (PL) in seconds and the frequency bandwidth can be given as:

PL= 1.3/ Frequency Bandwidth 3.4

1.3 Magnetostrictive transducers

Magnetostrictive transducers are made of ferromagnetic materials, which can easily be magnetised and displays magnetostriction or the Joule effect. When a bar or rod of one of these materials is placed in a magnetic field, it suffers a change in length, either an increase or decrease, depending on the nature of the material and the strength of the field, immaterial of the sign of strain. Hence, when the direction of magnetic field is reversed, there is no change in the sense of the strain. Figure 3.11 shows the relationship between mechanical strain and the magnitude of the field strength for a few ferromagnetic materials. The graph imples, the variation is not a linear one, in general. Nickel is found to be the most satisfactory material for magnetostrictive transducers, having an electromechanical coupling coefficient of 31 per cent and a Curie temperature of 358°C. Permendur, an alloy, has a higher Curie point (about 900°C) and low electromechanical coupling coefficient.

Though ferrites (non metals) has an advantage of being poor conductors and not being heated by eddy currents, and exhibit magnetostrictive effect are not often used as transducers due to their poor mechanical properties.

There is a converse magnetostrictive effect, in which a mechanical stress applied to a ferromagnetic rod lying in a magnetic field gives rise to a change in the magnetic flux density. This is known as the Villari effect.

Magnetostrictive transducers are in the forms of rods surrounded by coil windings (see Figure 3.7). An alternating magnetic field of the same frequency is induced by an alternating current through the coil ; giving rise to longitudinal oscillations of the rod.

These oscillations take place at a twice the frequency of the field and take on the form of unsmooth, rectified alternating current, resulting in unwanted frequencies. As in the case of ceramic transducers. This disadvantage is avoided by polarisation, as in ceramic transducers. It is not possible to obtain a high polarising field by permanent magnetisation, and a steady direct field of suitable magnitude is provided by passing a direct current through another coil wound round the transducer. So, the oscilla­tions occur about some other point instead of taking place about the origin of the curve. If the amplitude of the applied alternating field is low for changes to take place along the linear portion of the curve, and, is less than the value of the polarising field, then sinusoidal oscillations occur at the applied frequency.

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The resonance frequency inversely proportional with the length of the transducer rod. The frequency is increased by decreasing the length, but, simultaneously , there is a intensity is lowered for a rod of given cross-sectional dimensions , which results from the reduction in size of the vibrating mass. So, at frequencies more than 100 kHz ,the output from this type of transducer becomes vanishingly small.

The considerable leakage of magnetic flux is observed , which is a disadvantage of using rod-shaped oscillators . Transducers designed to form closed magnetic circuits are used for high-intensity applications The window-type transducer is clamped nodally, and the vibrations produced are longitudinal. In ring-type transducer, vibrations are in a radial manner, and hence ultrasonic energy is focused at the centre resulting in high acoustic intensity.

Absorption of ultrasound by induction of Eddy currents and Hystersis results in increased amount of eating. Though there are a number of ferromagnetic materials with low hysteresis losses, their magnetostrictive properties are poor. The losses due to eddy current can be reduced by using laminated stacks consisting of alternating sheets of the metal and of some insulating material such as mica. Since the rise in temperature may result in loss of magnetostrictive properties, it is necessary to cool the transducer during its operation.

By using velocity transformer, an increased intensity, distributed over a smaller area, can also be obtained with both rod and window types of transducers. This consists of a tapered coupling rod and provides an increase in the value of the particle velocity at the end remote from the transducer. For maximum efficiency, the transformer is designed to resonate by making it one wavelength long and supporting it at a nodal point, i.e. at a distance of a quarter-wavelength from the transducer. The diagram illustrates the application of the velocity transformer to the construction of the ultrasonic drill

Magnetostrictive oscillators being reversible can be used as receivers. An example of a magnetostrictive probe receiver consists of a nickel rod held vertically in a fluid in which ultrasound is radiated in an upward direction. The rod is con­tained in a plastic tube so that only the free end is exposed to the waves which are then transmitted along its length. A current is induced by the Villari effect in the pick-up coil placed near the upper end of the rod. Another coil carrying a direct current provides the polarising field. The formation of stationary waves is prevented by placing an absorbent material at the top of the rod.

Nickel film transducers are used for producing and receiving ultrasound of very high frequencies ranging from 100 MHz to 100 GHz in solids. A thin film of nickel, of thickness corresponding to one half-wavelength at the resonant frequency, is deposited on the end-surface of the specimen into which sound is to be passed. The rod is located with its plated end inside a microwave electromagnetic cavity resonator, excited at the required frequency. The receiver may consist of a similar film coated on the opposite surface of the specimen and also located in a cavity resonator. Instead a single nickel film can act as both source and receiver, using reflection method. No coupling material is required and no special technique is necessary for coating the nickel film.

1.4. Mechanical Transducers

Mechanical ultrasonic generators are used for high-intensity propagation in liquids and gases at frequencies of up to about 25 kHz .They exist mainly in the forms of whistles and sirens. They are powerful and less expensive than piezoelectric and magnetostrictive transducers, but with limited scope of applications.

Ultrasonic whistles are of two types, the cavity resonator, used mainly for gases, and the wedge resonator, employed for both gases and liquids. .

1.4.1. Cavity Resonators

Galton whistle (see Figure 3.12) consists of a cylinder terminated by the end-surface of a piston which can be adjusted to provide resonance at the required frequency The fluid, flows through an annular slit at high speed and strikes the rim of the tube where vortices appear and produce edge-tones. The frequency of the edge-tones depends on the velocity of the fluid which can be adjusted until the cavity resonates. For air, at a frequency of 20 kHz, fundamental resonance takes place for a cavity length of approximately 4 mm.

The second type of cavity resonator is the Hartmann generator, similar in design to the Galton whistle, except that the annular slit is replaced by a conical nozzle (see Figure 3.13). The fluid is forced through the nozzle and emerges at a supersonic velocity to produce shock waves, which cause the cavity to be excited at a high intensity. Resonance is achieved by adjusting the fluid velocity.

1.4.2. Wedge Resonator

The wedge resonator consists of a rectangular plate with wedge-shaped edges, mounted on nodal supports and placed in a fluid jet stream.(Figure 3.14). The wedge is set up into flexural vibrations having an intensity comparable with that attained by the Hartmann generator. Operating frequencies are of the order of 20 kHz.

Sirens also are used for generating high-energy ultrasound in fluids. The siren consists of a rotor disc with a number of identical holes spaced evenly around the circumference of a circle slightly smaller than the disc. The rotor turns concentrically in front of a similar disc (the stator), which is kept at rest whilst fluid jets are directed through the holes. The frequency of the emitted ultrasound is equal to the frequency of interruption of the jet flow, as the holes move relatively to one another, and is calculated as the product of the number of holes in the rotor and the speed of revolution. The tone emitted by the siren is not a pure one but this is unimportant for the applications for which it is used. One advantage of this instrument is that by altering the speed of rotation the frequency can be varied in a continuous manner.

The use of mechanical receivers has been restricted to measurements of intensities in liquids and gases. The two principal types of mechanical receivers are the Rayleigh disc and the radiometer.

The Rayleigh disc consists of a thin circular disc suspended vertically in the ultrasonic field by means of a torsion fibre. Initially the disc is positioned, with its plane surfaces parallel with the direction of propagation. In the presence of ultrasound, the sound waves exert a couple on the disc, which rotates until brought to rest in a steady position as a result of an opposing couple exerted by the suspension. The angle of rotation required to reach the state of equilibrium depends on the the acoustic intensity.

A radiometer is a device which measures directly the pressure of radiation, a quantity which is proportional to the acoustic intensity. The simplest form of radiometer is a tiny solid sphere suspended in the sound field. It is deflected horizontally in the direction of propagation when the ultrasound is present. The device is calibrated by subjecting it to known fluid pressures and then measuring the result­ing displacements.

The torsion balance radiometer is designed for waves travelling in a horizontal direction and the common balance type for vertically directed waves(Fig 3.15 a and Fig 3.15b)

1.5 Electromagentic Transducers

A lightweight electromagnetic transducers have been used for low-intensity ultrasonic measure­ments in poorly conducting solids and liquids. But the method requires constant application of a steady magnetic field m which is a major disadvantage

1.5.1. Giacomini’s method:

A bar of poorly conducting solid is coated with a thin conducting strip of negligible mass over opposite halves of the upper and lower surfaces and the end-face. It is supported horizontally at the nodal positions by electrically conducting wires, and the coated end is subjected to a horizontal magnetic field at right angles to the axis. When an alternating current is passed through the conducting strip, the bar vibrates longitudinally, in accordance with Fleming’s left-hand rule of electromagnetism.

Because electromagnetic transducers are reversible, vibrations in the bar are picked up by the conducting strip which, in the presence of a steady magnetic field, will have induced in it an alternating e.m.f. in accordance with Fleming’s right-hand rule of electromagnetism. This e.m.f. is related to the acoustic intensity. Thus the device can be used as both a transmitter and a receiver of ultrasound.

1.5.2. Filipczynski’s Method:

An aluminium film in the form of a continuous and winding narrow strip is evaporated on to a perspex block to provide a coil of negligible mass. The block is then immersed in the liquid and located inside a gap between the pole-pieces of a permanent magnet which supplies a steady magnetic field of high intensity. Ultrasonic waves pass from the liquid into the block, giving rise to oscillations of the aluminium coil which induce in it an e.m.f. related to the intensity in the block.

1.6 Electrostatic transducers

An electrostatic transducer consists essentially of two parallel plates of a conducting material placed close to one another to form an electrical capacitor. One plate is fixed and the other is free to vibrate in a direction at right angles to the surface of the plates. A high resistance is placed in series with the capacitor and steady charges on the plates maintained by a direct potential difference of several hundred volts (Fig 3.18).

For operation as a transmitter, a signal at the desired frequency, is fed to the plates , output voltage of amplitude not exceeding the direct potential difference. The periodic variation of the charges induces vibrations of the movable plate.

For use as a receiver, the movable plate is placed in position to receive the sound waves and its consequent vibrations give rise to periodic variations of the electrical capacitance of the transducer, producing an alternating current which flows through the high resistance; the resulting alternating voltage proportional the intensity of the received sound.

The electrostatic transducer in the form of the condenser microphone has long been used at audible frequencies. Diaphragm being light , inertial effects are negligible and the sensitivity remains constant over a wide frequency range. It can be used for gases and liquids as both a receiver and a trans­mitter at frequencies of up to about 300 kHz.

1.7 Miscellaneous Transducer

Other methods of generating and receiving ultrasound involve the uses of thermal, chemical, and optical devices. The chemical changes observed in materials irradiated with ultrasound, is used as a means of detec­tion. It is also possible to generate ultrasonic waves in a transparent medium by the crossing of two laser beams originating from a common source.

There are a number of applications which make use of thermal transducers. One thermal type of transmitter is the spark-gap generator, which radiates ultrasound as a result of periodic tempera­ture changes taking place when a high alternating voltage of a given frequency is discharged across a gap in a circuit.

The hot-wire microphone, is a receiving thermal transducer,consisting of a thin wire, made from platinum and heated to just below redness. When sound waves strike the wire, it cools down by an amount directly dependent on the intensity. This is indicated by a decrease in its electrical resistance. The hot-wire microphone has been used successfully for gases at frequencies of up to 600 kHz.

Ultrasonic intensities can also be measured from the rise in tempera­ture within the beam, as shown in Figure 3.19. The heat produced by the ultrasound is absorbed by the liquid in the thermally insulated flask. Expansion of the liquid results in a rise in the level of the liquid in the graduated capillary tube, calibrated by supplying a measured amount of heat from the heating coil. The waves transmitted through the liquid are finally absorbed by the glass wool placed at the end of the vessel. Acoustic powers of from 50 mW to 30 W can be measured to an accuracy of better than 10 per cent with this device.