The Operating Frequency of a Continuous Wave Transducer is Determined by

Transducer

Underwater Acoustics

William A. Kuperman , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

II.A Transducers

A transducer converts some sort of energy to sound (source) or converts sound energy (receiver) to an electrical signal. In underwater acoustics, piezoelectric and magnetostrictive transducers are commonly used; the former connects electric polarization to mechanical strain and the latter connects magnetization of a ferromagnetic material to mechanical strain. In addition there are: electrodynamic transducers in which sound pressure oscillations move a current-carrying coil through a magnetic field causing a back electromagnetic field, and electrostatic transducers in which charged electrodes moving in a sound field change the capacitance of the system. Explosion, airgun, electric discharge, and lasers are also used as wideband sources.

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ULTRASONICS

M.J.S. Lowe , in Encyclopedia of Vibration, 2001

Generation of Ultrasound

Transducers for the generation of ultrasound most commonly use piezoelectric materials to convert an electrical signal into the mechanical motion. Figure 1 shows a section through a typical ultrasonic NDT transducer, designed to excite longitudinal waves. An electrical signal is supplied as a voltage across the thickness of a piezoelectric disk which then vibrates. The first through-thickness vibration mode of the disk excites waves in the fluid or structure in front of the transducer. Thus, the center frequency of operation of the transducer can be controlled by the selection of the thickness of the disk. Damping material behind the disk absorbs the backward-traveling waves and also damps the resonance of the disk. The damping enables the transducer to produce waves which are short in time and so wide in frequency bandwidth. Transducers usually have a durable material, known as a wear plate, which is attached to the front of the piezoelectric disk for protection. The transducer may also act as a receiver, in which case it simply works in reverse: the incoming waves excite motion in the piezoelectric disk which then generates an electrical signal. The two most popular choices of the material for the piezoelectric disk are the ceramic lead zirco-nate titanate (PZT) and the polymer polyvinylidene fluoride (PVDF). Piezoelectric transducers may be used throughout the ultrasonic frequency range.

Figure 1. Section through a piezoelectric transducer.

Although piezoelectric transducers are the most common, there are some alternative types in use. Electromechanical transducers which use a moving coil, similar to a loudspeaker, can generate waves with large amplitudes, but their maximum frequency is limited to some tens of kHz. Electromagnetic EMAT transducers generate wave motion directly in a conducting material. An alternating current is passed through a coil which is in close proximity to the body and within a static magnetic field. Either or both of the phenomena of Lorenz forces and magnetostriction then introduce an alternating stress field in the body. Although the electromechanical coupling of these transducers is not strong, they have the advantage that they do not need direct contact with the body and so can be used for example on dirty surfaces. They are used mostly in the frequency range from some hundreds of kHz to a few MHz. Finally, lasers may be used to generate and detect ultrasound. Sound is generated using a relatively powerful source, either by inducing a cyclic thermoelastic strain (by locally heating the material), or by spalling small quantities of the material from the surface, thereby initiating a transient reaction force. Detection of displacements at the surface of a body requires only a low-power laser interferometer. Lasers have very wide bandwidths and have the advantage that the transduction is contactless.

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Life Cycle Tribology

P. Harper , ... U. Olofsson , in Tribology and Interface Engineering Series, 2005

3.2 Ultrasonic Transducers and Focusing

The transducer consists of a piezo-electric element in a waterproof housing. The transducer was a nominal 10 MHz, focused (the centre frequency was at 8.8 MHz), and 90% bandwidth. In this work it is necessary to focus the wave onto the oil film (normal contact transducers would result in spreading of the beam and reflection from regions surrounding the film). Focusing is achieved by means of a concave lens bonded to the piezoelement. The transducer has a focal distance of 75 mm in water and a corresponding focal area of diameter ~520pim. The piston ring has a thickness of 2 mm with a slight crowning. The ultrasonic spot size falls within a region of the ring face that is virtually flat. Reference [ 12] describes in more detail the focusing of ultrasonic waves and the resulting spatial resolution.

Figure 3 shows a schematic of the transducer location and focusing system. The transducer was mounted in a small water bath above the piston ring rig. A positioning fixture allows the accurate location of the transducer over the piston ring contact.

Figure 3. Schematic diagram of the transducer location and focusing through a water bath and the cylinder wall

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X-Ray and Ultrasound Imaging

J.M. Thijssen , M. Mischi , in Comprehensive Biomedical Physics, 2014

2.13.2 Array Transducers

Array transducers are found in many types and configurations. The most important types are the phased array and the linear array transducers. In a phased array transducer ( Figure 1(a) ), all the elements are used quasi-simultaneously, that is, the elements are all active for the generation of one image line. Beam steering and focusing are obtained by systematically adapting the transmission delays in transmission and the reception delays in reception. In this way, sector-shaped images are produced. This principle, in analogy with sonar and radar array systems, was first introduced in the Netherlands. As early as 1968, Jan Somer, working at TNO, Utrecht, the Netherlands, reported about a medical US phased array equipment that he had developed and tested on a patient (Somer, 1968). He was aiming at diagnosis of brain disorders (Kamphuisen et al., 1972). Some years later, the same principle was 're-invented' by Von Ramm and Thurstone (1975), who tried out cardiological applications of phased arrays (Kisslo et al., 1976). This equipment was commercialized by Grumman, Inc., system RT-400.

Figure 1. Phased (a), linear (b), and curved (c) array transducer.

The linear array principle means that a number of array elements produce a US beam that is perpendicular to the transducer surface. This principle was used for the first time by Bom and Lancée at the Thorax Centre of the Erasmus University, Rotterdam, the Netherlands (Bom et al., 1971). This rudimentary 'cardiological' linear array consisted of only 20 separate elements, but it produced easily interpretable real time images of the beating heart. In modern linear array transducers, the number of elements is sufficiently high to use a sub-array of elements for each image line that is shifted along the whole array in steps equal to the element pitch. In this way, a rectangular image of, for example, 128 scan lines is produced. The sub-arrays can also be used for apodization, (dynamic-) focusing, beam steering, and image compounding ( Sections 2.13.4 and 2.13.5 ).

Linear array transducers are available in several configurations. The two main configurations are the rectangular linear array ( Figure 1(b) ) and the convex linear array ( Figure 1(c) ). Linear array transducers are used in many clinical applications where a wide superficial area is to be examined, for example, vascular imaging. The convex linear array produces sector-shaped images, where the apparent center of rotation is located above the contact line between the transducer and the skin of the patient. Convex arrays are generally used for abdominal echography.

Some endoscopic transducers, such as intravascular and transrectal transducers, consist of a cylindrical, that is, a 360° convex array of elements yielding a 360° rotational image. This idea was also worked out by Bom and colleagues in what they called a 32-element intracardiac catheter tip transducer (Bom et al., 1972). The same idea was more recently developed further for intravascular scanning. More specifically, the group of Rotterdam University developed a catheter with a motor-driven rotating shaft transducer that could be inserted in coronary arteries over a guidewire transducer ( Figure 2 , top). The idea of a cylindrical array intravascular US transducer for the diagnosis and treatment of coronary plaques (Bom et al., 1998) was further developed by industry into a disposable add-on to an intravascular scanning system ( Figure 2 , bottom).

Figure 2. Top: Mechanical intravascular US (IVUS) transducer. Bottom: Cylindrical array IVUS transducer.

All these configurations can be called 1D arrays as they operate in a single azimuth plane, the X  − Z plane. Since the thickness of the slice scanned by an array transducer is directly related to the height of the elements, it can be understood that the elevational (y-direction, orthogonal to the scanning slice) effective beam thickness is wider, that is, the spatial resolution is much lower, than in the azimuth scan plane. For this reason, most transducers are covered by a cylindrical lens ( Figures 3 and 4(a) ) so as to yield a fixed elevation focus at the depth of interest for the clinical application. Also, in some modern equipment, the transducer elements are cut into five sub-elements, which enables a variable focusing in the elevation direction in addition to fixed focusing by the cylindrical acoustic lens. This type of transducer, shown in Figure 4(b) , is called a 1.5D array (Daft et al., 1994; Tournois et al., 1995).

Figure 3. Linear array transducer with cylindrical lens yielding narrowing of elevational beam (slice thickness reduction).

Figure 4. (a) 1D linear array transducer. (b) 1.5D array transducer. (c) 2D array (matrix) transducer.

Redrawn from Szabo TL (2004) Diagnostic Ultrasound Imaging. Amsterdam, NL: Elsevier/Academic Press.

This idea was extended toward a two-dimensional (2D) array ( Figure 4(c) ) by von Ramm, Smith, and colleagues (Sheikh et al., 1991; von Ramm and Smith, 1991) to be able to scan a 3D volume instead of a 2D plane. Since the number of elements was much higher than the number of channels available for transmit and receive, a subset of active elements was chosen (sparse array).

Industrial developments followed after this feasibility study and improved 3D imaging by moving part of the primary electronics toward the transducer, thereby enabling the use of all the elements, although not simultaneously. Philips Medical Systems (now Philips Healthcare) was the primary company following this approach, which resulted in a 2D array of approximately 3000 elements ( Figure 5 ).

Figure 5. Left: A 2D array transducer based on the principle of 3D raster scanning; right: principle of raster scanning yielding a 3D acquisition.

For some applications, in order to reduce the complexity of a 2D array system and yet perform 4D imaging (dynamic 3D), electromechanical solutions are still preferred where a 1D array is made rotate and span a volume by scanning a number of sequential planes.

The 2D array enables fan beam, or multibeam transmission and multibeam (n  −   4) reception. In this way, a whole 3D volume can be scanned rather quickly at a volume rate of 4–40   HZ, depending on the depth range and the scanning angle. The number of azimuth scan planes for a single volume is in the order of 32–64. For cardiological applications, this rate is not sufficient to scan the fast-moving heart structures without distortion, and an ECG-triggered set of narrow sub-volumes (n  =   4–7 heart beats) is acquired during breath hold and processed into a full volume after digital storage of the data.

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Ultrasonic Instruments and Devices I

Emmanuel P. Papadakis PH.D. , in Physical Acoustics, 1999

2 Angle Beams

Most transducers are built with longitudinal wave active elements. These radiate normal to their wear plate surfaces into the workpieces. To generate shear waves at an angle to the surface for flaw detection, angle blocks are used between the transducers and the workpiece. The transducer is clamped with couplant and mechanical fasteners to the angle block, and the angle block uses added couplant to touch the workpiece. When a longitudinal wave impinges upon a boundary at an angle other than normal incidence, the boundary conditions require a longitudinal solution and a shear solution in the second medium ( Mason, 1958). Only the shear solution in the workpiece is desired, to avoid ambiguity.

To achieve this by design, the ultrasonic longitudinal wave velocity in the angle block is chosen to be lower than the longitudinal velocity in the workpiece. Under these conditions, the block can be manufactured with an angle that gives total internal reflection to the longitudinal wave and a propagating solution for the shear wave at some desired angle, such as 70° or 45° from the normal. The combination of transducers and angle blocks yield angle beam transducers that are widely used in detecting flaws in engineering materials. The beam of ultrasound from one such angle beam transducer is shown in Figure 27. The method used was a photoelastic method in Lucite® using strobed light synchronized with but delayed from the ultrasonic pulse. A variety of commercial transducers are shown in Figures 28 and 29.

Fig. 27. The radiation beam of pulses from an angle beam transducer radiating into Lucite® as illuminated by a synchronous pulsed photoelastic method.

(R. C. Wyatt, Central Electricity Generating Board, U.K. Used by permission.)

Fig. 28. Several commercial transducers of various configurations.

(Panametrics, Inc. Used by permission.)

Fig. 29. Several commercial transducers of various configurations.

(Panametrics, Inc. Used by permission.)

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Ultrasonic Instruments and Devices I

Albert Goldstein , Raymond L. Powis , in Physical Acoustics, 1999

a Matching

The transducer has maximum broadband sensitivity when properly matched electrically to its driving and reception circuits and acoustically to the patient. A shunt inductance coil (see Figure 17) used to cancel the reactive component of the element impedance provides simple electrical matching (Thurston, 1960). When the coil and element reactive impedances cancel at the element center frequency, the impedance of the element is better matched to the typical 50Ω circuit impedance than the untuned case (Hunt et al., 1983). Complex broadband matching networks, which provide a wider frequency response with minimum distortion, have also been used (Augustine and Anderson, 1979).

Early static imaging transducers used a heavily damped backing layer to attain a wide transducer bandwidth to produce short echoes. However, because a great deal of acoustic energy was absorbed in the backing layer, these transducers were inefficient and had low sensitivity. Improvements in transducer efficiency and sensitivity came from better acoustic matching of the element to the patient. This acoustic matching was accomplished by using λ/4 layers of intermediate impedance materials (between the Z_T = 34 MRayls of the ceramic and the Z_M = 1.5 MRayls of the patient). Even though the λ/4 matching condition can only be attained at the crystal center frequency, the crystal loading caused by the matching layers produces wider bandwidth and more efficient transducers (Kossoff, 1966). Still more efficient transducers can be made from air-backed crystals with several front λ/4 layers by using the transmission line properties of thin crystals (Desilets et al., 1978). For minimum transducer insertion loss, the matching layers should be made of low-loss materials and the glue bond thickness should preferably be less than one twentieth of a wavelength to have a negligible effect (Hunt et al., 1983).

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Electro-mechano-acoustical circuits

Leo L. Beranek , Tim J. Mellow , in Acoustics: Sound Fields and Transducers, 2012

Part VIII Transducers

A transducer is defined as a device for converting energy from one form to another. Of importance in this text is the electromechanical transducer for converting electrical energy into mechanical energy, and vice versa. There are many types of such transducers. In acoustics we are concerned with microphones, earphones, loudspeakers, and vibration pickups and vibration producers which are generally linear passive reversible networks.

The type of electromechanical transducer chosen for each of these instruments depends upon such factors as the desired electrical and mechanical impedances, durability, and cost. It will not be possible here to discuss all means for electromechanical transduction. Instead we shall limit the discussion to electromagnetic and electrostatic types. Also, we shall deal with mechano-acoustic transducers for converting mechanical energy into acoustic energy.

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Gravitational Wave Detectors

Rosa Poggiani , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

IV.B.2 Electronic Noise

Any transducer modulates a source of electrical energy, acting in some way on an electrical circuit and producing either a voltage, current, or frequency output. A transducer can be modeled as a two-port device described by a 2  ×   2 impedance matrix Z _ij . It has two inputs, force and velocity, and two outputs, current and voltage. The parameters Z ₁₂ (forward transconductance) and Z ₂₁ (reverse transconductance) are the transducer sensitivity and the back-action effect on the bar. In fact, any transducer can operate in reverse mode and a current noise at its output can apply a fluctuating force on the bar. Moreover, an amplifier is in series to the transducer to amplify the signal. The noise sources due to the transducer and amplifier are described using the voltage and current noise V(ω) and I(ω) at the entrance of the amplifier. The spectral density of the back-action noise is

(23) ${\text{S}}_{\text{ba}}(\omega )=\frac{{|{\text{Z}}_{12}|}^2}{2\text{M}}\text{I}(\omega ){\text{t}}_{\text{m}}.$

The spectral density of the series noise is

(24) ${\text{S}}_{\text{sn}}(\omega )=\frac{2\text{M}}{{|{\text{Z}}_{12}|}^2}\frac{\text{V}(\omega )}{{\text{t}}_{\text{m}}}.$

While the thermal noise and the back-action noise are proportional to t _m, the series noise is proportional to t ⁻¹ _m; there is an optimal measurement time.

The total noise budget must be compared to the standard quantum limit. Using the spread σ_p  ∼ Mω_rσ _x in the uncertainty principle, it is possible to deduce the minimum detectable strain:

(25) ${\text{h}}_{\text{min}}\sim \frac{1}{\text{L}}\sqrt{\frac{ħ}{\text{M}{\omega }_{\text{r}}}}.$

For a typical bar with a mass of 1 ton and a length of 3   m, resonant at 1   kHz, h _min  ∼   10⁻²¹, on the order of the relevant astrophysical signals. Having fixed the frequency of interest, there is not too much room to improve the limit since the sound velocity is not varying very much from material to material; thus the size of the bar is fixed as well.

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Sensors for Control

Clarence W. de Silva , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

VI.C Self-Induction Sensors

There are transducers based on the principle of self-induction. Unlike mutual-induction transducers, only a single coil is employed. This coil is activated by an AC supply voltage v _ref . The current produces a magnetic flux, which is linked with the coil. The level of flux linkage (or self-inductance) can be varied by moving a ferromagnetic object within the magnetic field. This changes the reluctance of the flux path and the inductance in the coil. This change is a measure of the displacement of the ferromagnetic object. The change in inductance is measured using an inductance measuring circuit (e.g., an inductance bridge). Note that self-induction transducers are usually variable-reluctance devices.

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Acoustic Wave Sensors and Responses

D.S. BallantineJr., ... E.T. Zellers , in Acoustic Wave Sensors, 1997

3.2.2 INTERDIGITAL TRANSDUCER FREQUENCY RESPONSE

Each transducer finger may be considered to be a discrete source for the generation of surface waves in a piezoelectric medium because the piezoelectrically generated stress varies with position near each transducer finger. A simple transfer function relates the continuous wave (CW) voltage V ₁ applied to a finger and the electrical potential associated with the waves radiated in each direction [43]:

(3.39) ${\varphi }^{\pm }={\mu }_s{V}_1,$

where μ _s is a substrate-dependent constant, ϕ⁺ is associated with the rightward propagating SAW, while ϕ⁻ is a leftward propagating SAW. The parameter μ _s may be considered frequency independent: the frequency response of the transducer arises mainly from interference between finger contributions, and is relatively insensitive to the frequency response of the individual elements. This approximation is typically made in analyzing wave scattering from an array of elements: the "element factor" is typically considered frequency-independent compared with the "array factor."

When an array of fingers is excited, as occurs with an interdigital transducer (IDT), the wave potential for a rightward propagating wave ϕ⁺ evaluated at position z is a vector sum of the contributions from each finger:

(3.40) ${\varphi }^{+}\left(z\right)={\mu }_s{\displaystyle \sum _{n=0}^{N_{f-1}}{V}_n{e}^{jk\left(z-z_n\right)}},$

where z _n is the position of the n ^th finger excited with voltage V _n ;N _f is the total number of fingers.Equation 3.40 has the form of a discrete Fourier transform [45] of the sequence V _n . Consequently, the frequency response of the device is proportional to the Fourier transform of the sequence of transducer finger contributions. Schemes have been devised to vary the individual finger contributions in order to achieve a desired frequency response. The interested reader is referred to excellent books on SAW filter design by Datta [43], Morgan [44], and Ristic [46].

If N _f identical fingers are spaced periodically with period d and excited with alternating voltages V _n = (-1) ⁿ V _o ,Equation 3.40 becomes

(3.41) ${\varphi }^{+}\left(0\right)={\mu }_s{V}_0{\displaystyle \sum _{n=0}^{N_{f-1}}{\left(-1\right)}^n{e}^{-jnkd/2}.}$

The sum in Equation 3.41 is a geometric series whose elements become unity, and add constructively, when kd/2 =mπ, where m is an odd integer. This condition defines the relationship between SAW wavelength, λ, and transducer periodicity,d, for coherent addition, as shown in Figure 3.19. The IDT excites odd harmonics at odd multiples of the synchronous frequency:f _m =mf ₁.

Figure 3.19. Relationship between transducer periodicity and coherently excited waves.

Moving away from the synchronous frequency, the addition of components from individual fingers becomes incoherent, giving rise to the frequency response

(3.42) $\left|{\varphi }^{+}\left(f\right)\right|=\left|\frac{\sin \left(X\right)}{X}\right|$

in which

(3.43) $X=\frac{N_p\pi \left(f-f_0\right)}{f_0}$

where f _o is the transducer's synchronous frequency and N _p is the number of IDT periods:N _p =N _f /2. The wave potential as a function of the detuning parameter X, described by Equation 3.23, is shown in Figure 3.20 (page 78). Note that when X is a multiple of π, ϕ⁺ is zero — a result of complete cancellation between finger contributions. Consequently, the frequency interval B between the first nulls on either side of the synchronous frequency is

Figure 3.20. The calculated transducer response, sin(X)/X, vs the "detuning parameter,"X.

(Reprinted with permission. See Ref. [46a].)

(3.44) $B=\frac{2}{N_p}.$

Thus, the transducer bandwidth B is inversely proportional to the number of IDT fingers. As will be described in Chapter 4, a narrow bandwidth is desirable for oscillator applications in order to avoid spurious oscillations and to improve stability.

The frequency response measured between a pair of transducers having λ _o = 32 μm and N _p = 50 finger pairs is shown in Figure 3.21 (page 79). The amplitude, shown on a log (decibel) scale, shows the characteristic sin(X)/X behavior. The delay line phase shift φ is

Figure 3.21. The frequency response measured between a pair of interdigital transducers.

(Reprinted with permission. See Ref. [46a].)

(3.45) $\phi \left(f\right)=kL=\frac{2\pi fL}{v_0},$

where L is the path length (center-to-center distance) between transducers. Differentiation of Equation 3.45 shows that the phase slope dφ/df is proportional to L/λ, the transducer separation in wavelengths.

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