65.1 Transducer

Transducer Materials • Scanning with Array Transducers • Linear-Array Transducer Performance • Designing a Phased-Array Transducer • Summary

65.3 Blood Flow Measurement Using Ultrasound

Fundamental Concepts • Velocity Estimation Techniques • New Directions

65.2 Ultrasonic Imaging

Fundamentals • Application and Example Calculations • Economics

Richard L. Goldberg

University of North Carolina

Stephen W. Smith

Duke University

Jack G. Mottley

University of Rochester

K. Whittaker Ferrara

Riverside Research Institute




Richard L. Goldberg and Stephen W. Smith

An ultrasound transducer generates acoustic waves by converting magnetic, thermal, and electrical energy into mechanical energy. The most efficient technique for medical ultrasound uses the piezoelectric effect, which was first demonstrated in 1880 by Jacques and Pierre Curie [Curie and Curie, 1880]. They applied a stress to a quartz crystal and detected an electrical potential across opposite faces of the material. The Curies also discovered the inverse piezoelectric effect by applying an electric field across the crystal to induce a mechanical deformation. In this manner, a piezoelectric transducer converts an oscillating electric signal into an acoustic wave, and vice versa.

Many significant advances in ultrasound imaging have resulted from innovation in transducer tech­nology. One such instance was the development of linear-array transducers. Previously, ultrasound systems had made an image by manually moving the transducer across the region of interest. Even the faster scanners had required several seconds to generate an ultrasound image, and as a result, only static targets could be scanned. On the other hand, if the acoustic beam could be scanned rapidly, clinicians could visualize moving targets such as a beating heart. In addition, real-time imaging would provide instantaneous feedback to the clinician of the transducer position and system settings.

To implement real-time imaging, researchers developed new types of transducers that rapidly steer the acoustic beam. Piston-shaped transducers were designed to wobble or rotate about a fixed axis to mechanically steer the beam through a sector-shaped region. Linear sequential arrays were designed to electronically focus the beam in a rectangular image region. Linear phased-array transducers were designed to electronically steer and focus the beam at high speed in a sector image format.

This section describes the application of piezoelectric ceramics to transducer arrays for medical ultrasound. Background is presented on transducer materials and beam steering with phased arrays. Array performance is described, and the design of an idealized array is presented.

TABLE 65.1 Maerial Properties of Linear-Array Elements Made of PZT-5H









Speed of sound




Acoustic impedance




Relative dielectric constant




Electromechanical coupling coefficient




Mechanical loss tangent

Tan 8m



Electrical loss tangent

Tan 8C



Transducer Materials

Ferroelectric materials strongly exhibit the piezoelectric effect, and they are ideal materials for medical ultrasound. For many years, the ferroelectric ceramic lead-zirconate-titanate (PZT) has been the standard transducer material for medical ultrasound, in part because of its high electromechanical conversion efficiency and low intrinsic losses. The properties of PZT can be adjusted by modifying the ratio of zirconium to titanium and introducing small amounts of other substances, such as lanthanum [Berlin­court, 1971]. Table 65.1 sHows the material properties of linear-array elements made from PZT-5H.

PZT has a high dielectric constant compared with many piezoelectric materials, resulting is favorable electrical characteristics. The ceramic is mechanically strong, and it can be machined to various shapes and sizes. PZT can operate at temperatures up to 100°C or higher, and it is stable over long periods of time.

The disadvantages of PZT include its high acoustic impedance (Z = 30 MRayls) compared with body tissue (Z = 1.5 MRayls) and the presence of lateral modes in array elements. One or more acoustic matching layers can largely compensate for the acoustic impedance mismatch. The effect of lateral modes can be diminished by choosing the appropriate element dimensions or by subdicing the elements.

Other piezoelectric materials are used for various applications. Composites are made from PZT interspersed in an epoxy matrix [Smith, 1992]. Lateral modes are reduced in a composite because of its inhomogeneous structure. By combining the PZT and epoxy in different ratios and spatial distributions, one can tailor the composite’s properties for different applications. Polyvinylidene difluoride (PVDF) is a ferroelectric polymer that has been used effectively in high-frequency transducers [Sherar and Foster, 1989]. The copolymer of PVDF with trifluoroethylene has an improved electromechanical conversion efficiency. Relaxor ferroelectric materials, such as lead-magnesium-niobate (PMN), become piezoelectric when a large direct-current (dc) bias voltage is applied [Takeuchi et al., 1990]. They have a very large dielectric constant (e > 20,000g„), resulting in higher transducer capacitance and a lower electrical impedance.

Scanning with Array Transducers

Array transducers use the same principles as acoustic lenses to focus an acoustic beam. In both cases, variable delays are applied across the transducer aperture. With a sequential or phased array, however, the delays are electronically controlled and can be changed instantaneously to focus the beam in different regions. Linear arrays were first developed for radar, sonar, and radio astronomy [Allen, 1964; Bobber, 1970], and they were implemented in a medical ultrasound system by Somer in 1968 [Somer, 1968].

Linear-array transducers have increased versatility over piston transducers. Electronic scanning involves no moving parts, and the focal point can be changed dynamically to any location in the scanning plane. The system can generate a wide variety of scan formats, and it can process the received echoes for other applications, such as dynamic receive focusing [von Ramm and Thurstone, 1976], correction for phase aberrations [Flax and O’Donnell, 1988; Trahey et al., 1990], and synthetic aperture imaging [Nock and Trahey, 1992].



FIGURE 65.1 Focusing and steering an acoustic beam using a phased array. A 6-element linear array is shown (a) in the transmit mode and (b) in the receive mode. Dynamic focusing in receive allows the scanner focus to track the range of returning echoes.

The disadvantages of linear arrays are due to the increased complexity and higher cost of the trans­ducers and scanners. For high-quality ultrasound images, many identical array elements are required (currently 128 and rising). The array elements are typically less than a millimeter on one side, and each has a separate connection to its own transmitter and receiver electronics.

The widespread use of array transducers for many applications indicates that the advantages often outweigh the disadvantages. In addition, improvement in transducer fabrication techniques and inte­grated circuit technology have led to more advanced array transducers and scanners.

Focusing and Steering with Phased Arrays

This subsection describes how a phased-array transducer can focus and steer an acoustic beam along a specific direction. An ultrasound image is formed by repeating this process over 100 times to interrogate a two – (2D) or three-dimensional (3D) region of the medium.

Figure 65.1a illustrates a simple example of a six-element linear array focusing the transmitted beam. One can assume that each array element is a point source that radiates a spherically shaped wavefront into the medium. Since the top element is farthest from the focus in this example, it is excited first. The remaining elements are excited at the appropriate time intervals so that the acoustic signals from all the elements reach the focal point at the same time. According to Huygens’ principle, the net acoustic signal is the sum of the signals that have arrived from each source. At the focal point, the contributions from every element add in phase to produce a peak in the acoustic signal. Elsewhere, at least some of the contributions add out of phase, reducing the signal relative to the peak.

For receiving an ultrasound echo, the phased array works in reverse. Fig. 65.1b sHows an echo origi­nating from focus 1. The echo is incident on each array element at a different time interval. The received signals are electronically delayed so that the delayed signals add in phase for an echo originating at the focal point. For echoes originating elsewhere, at least some of the delayed signals will add out of phase, reducing the receive signal relative to the peak at the focus.

In the receive mode, the focal point can be dynamically adjusted so that it coincides with the range of returning echoes. After transmission of an acoustic pulse, the initial echoes return from targets near the transducer. Therefore, the scanner focuses the phased array on these targets, located at focus 1 in Fig. 65.1b. AS echoes return from more distant targets, the scanner focuses at a greater depth (focus 2 in the figure). Focal zones are established with adequate depth of field so that the targets are always in focus in receive. This process is called dynamic receive focusing and was first implemented by von Ramm and Thurstone in 1976 [von Ramm and Thurstone, 1976].

Array-Element Configurations

An ultrasound image is formed by repeating the preceding process many times to scan a 2D or 3D region of tissue. For a 2D image, the scanning plane is the azimuth dimension; the elevation dimension is perpendicular to the azimuth scanning plane. The shape of the region scanned is determined by the array-element configuration, described in the paragraph below.

Linear Sequential Arrays. Sequential liner arrays have as many as 512 elements in current commercial scanners. A subaperture of up to 128 elements is selected to operate at a given time. As shown in Fig. 65.2a, the scanning lines are directed perpendicular to the face of the transducer; the acoustic beam is focused but not steered. The advantage of this scheme is that the array elements have high sensitivity when the beam is directed straight ahead. The disadvantage is that the field of view is limited to the rectangular region directly in front of the transducer. Linear-array transducers have a large footprint to obtain an adequate field of view.

Curvilinear Arrays. Curvilinear or convex arrays have a different shape than sequential linear arrays, but they operate in the same manner. In both cases, the scan lines are directed perpendicular to the transducer face. A curvilinear array, however, scans a wider field of view because of its convex shape, as shown in Fig. 65.2 b.

Linear Phased Arrays. The more advanced linear phased arrays have 128 elements. All the elements are used to transmit and receive each line of data. As shown in Fig. 65.2c, tHe scanner steers the ultrasound beam through a sector-shaped region in the azimuth plane. Phased arrays scan a region that is significantly wider than the footprint of the transducer, making them suitable for scanning through restricted acoustic windows. As a result, these transducers are ideal for cardiac imaging, where the transducer must scan through a small window to avoid the obstructions of the ribs (bone) and lungs (air).

1.5D Arrays. The so-called 1.5D array is similar to a 2D array in construction but a 1D array in operation. The 1.5D array contains elements along both the azimuth and elevation dimensions. Features such dynamic focusing and phase correction can be implemented in both dimensions to improve image quality. Since a 1.5D array contains a limited number of elements in elevation (e. g., 3 to 9 elements), steering is not possible in that direction. Figure 65.2d illustrates a B-scan made with a 1.5D phased array. Linear sequential scanning is also possible with 1.5D arrays.

2D Phased Arrays. A 2D phased-array has a large number of elements in both the azimuth and elevation dimensions. Therefore, 2D arrays can focus and steer the acoustic beam in both dimensions. Using parallel receive processing [Shattuck et al., 1984], a 2D array can scan a pyramidal region in real time to produce a volumetric image, as shown in Fig. 65.2e [Von Ramm and Smith, 1990].

Linear-Array Transducer Performance

Designing an ultrasound transducer array involves many compromises. Ideally, a transducer has high sensitivity or SNR, good spatial resolution, and no artifacts. The individual array elements should have wide angular response in the steering dimensions, low cross-coupling, and an electrical impedance matched to the transmitter.


FIGURE 65.2 Array-element configurations and the region scanned by the acoustic beam. (a) A sequential linear array scans a rectangular region; (b) a curvilinear array scans a sector-shaped region; (c) a linear phased array scans a sector-shaped region; (d) a 1.5D array scans a sector-shaped region; (e) a 2D array scans a pyramidal-shaped region.

Figure 65.3a illustrates the connections to the transducer assembly. The transmitter and receiver circuits are located in the ultrasound scanner and are connected to the array elements through 1 to 2 m of coaxial cable. Electrical matching networks can be added to tune out the capacitance of the coaxial cable and/or the transducer element and increase the signal-to-noise ratio (SNR).

A more detailed picture of six-transducer elements is shown in Fig. 65.3b. Electrical leads connect to the ground and signal electrodes of the piezoelectric material. Acoustically, the array elements are loaded on the front side by one or two quarter-wave matching layers and the tissue medium. The matching layers may be made from glass or epoxy. A backing material, such as epoxy, loads the back side of the array elements. The faceplate protects the transducer assembly and also may act as an acoustic lens. Faceplates are often made from silicone or polyurethane.

The following subsections describe several important characteristics of an array transducer. Figure 65.3c shows a six-element array and its dimensions. The element thickness, width, and length are labeled as t, a, and b, respectively. The interelement spacing is d, and the total aperture size is D in


FIGURE 65.3 (a) The connections between the ultrasound scanner and the transducer assembly for two elements

Of an array. (b) A more detailed picture of the transducer assembly for six elements of an array. (c) Coordinate system and labeling used to describe an array transducer.

Azimuth. The acoustic wavelength in the load medium, usually human tissue, is designated as X, while the wavelength in the transducer material is Xt.

Examples are given below for a 128-element linear array operating at 5 MHz. The array is made of PZT-5H with element dimensions of 0.1 x 5 x 0.3 mm. The interelement spacing is d = 0.15 mm in


Z rai

подпись: z raiFIGURE 65.3 (continued)

Azimuth, and the total aperture is D = 128-0.15 mm = 19.3 mm. See Table 65.1 fOr the piezoelectric material characteristics. The elements have an epoxy backing of Z = 3.25 MRayls. For simplicity, the example array does not contain a X/4 matching layer.

Axial Resolution

Axial resolution determines the ability to distinguish between targets aligned in the axial direction (the

Direction of acoustic propagation). In pulse-echo imaging, the echoes off of two targets separated by r/2 have a path length difference of r. If the acoustic pulse length is r, then echoes off the two targets are just distinguishable. As a result, the axial resolution is often defined as one-half the pulse length [Christensen,

. A transducer with a high resonant frequency and a broad bandwidth has a short acoustic pulse and good axial resolution.

Radiation Pattern

The radiation pattern of a transducer determines the insonified region of tissue. For good lateral reso­lution and sensitivity, the acoustic energy should be concentrated in a small region. The radiation pattern for a narrow-band or continuous-wave (CW) transducer is described by the Rayleigh-Sommerfeld dif­fraction formula [Goodman, 1986]. For a pulse-echo imaging system, this diffraction formula is not exact due to the broadband acoustic waves used. Nevertheless, the Rayleigh-Sommerfeld formula is a reasonable first-order approximation to the actual radiation pattern.

The following analysis considers only the azimuth scanning dimension. Near the focal point or in the far field, the Fraunhofer approximation reduces the diffraction formula to a Fourier transform formula. For a circular or rectangular aperture, the far field is at a range of



Figure 65.3c shows the coordinate system used to label the array aperture and its radiation pattern. The array aperture is described by

подпись: figure 65.3c shows the coordinate system used to label the array aperture and its radiation pattern. the array aperture is described by


подпись: (65.2)

Where the rect(x) function is a rectangular pulse of width x, and the comb(x) function is a delta function repeated at intervals of x. The diffraction pattern is evaluated in the x0 plane at a distance z from the

подпись: where the rect(x) function is a rectangular pulse of width x, and the comb(x) function is a delta function repeated at intervals of x. the diffraction pattern is evaluated in the x0 plane at a distance z from the(65.1)


FIGURE 65.4 Radiation pattern of Eq. (65.3) for a 16-element array with a = X, d = 2X, and D = 32X. The angular response, the first term of Eq. (65.3), is also shown as a dashed line.

Transducer, and 0x is the angle of the point x0 from the normal axis. With the Fraunhofer approximation, the normalized diffraction pattern is given by

N n. D a sin □ x □ D d sin □ x □ D D sin □ x □

PXUPXLPsinc g n x gttomb (65.3)

In azimuth, where the Fourier transform of Eq. (65.2) has been evaluated at the spatial frequency

F □ i □ (65.4)

X □; □

Figure 65.4 Shows a graph of Eq. (65.3) for a 16-element array with a = X, d = 2X, and D = 32X. In the graph, the significance of each term is easily distinguished. The first term determines the angular response weighting, the second term determines the location of grating lobes off-axis, and the third term determines the shape of the main lobe and the grating lobes. The significance of lateral resolution, angular response, and grating lobes is seen from the CW diffraction pattern.

Lateral resolution determines the ability to distinguish between targets in the azimuth and elevation dimensions. According to the Rayleigh criterion [Goodman, 1986], the lateral resolution can be defined by the first null in the main lobe, which is determined from the third term of Eq. (65.3).

□ sin-1 — (65.5)


In the azimuth dimension. A larger aperture results in a more narrow main lobe and better resolution.

A broad angular response is desired to maintain sensitivity while steering off-axis. The first term of Eq. (65.3) determines the one-way angular response. The element is usually surrounded by a soft baffle,

Such as air, resulting in an additional cosine factor in the radiation pattern [Selfridge et al., 1980]. Assuming transmit/receive reciprocity, the pulse-echo angular response for a single element is


(a/ □ Sin □ X )

подпись: (a/ □ sin □ x )

Ttos2 □

подпись: ttos2 □(65.6)

In the azimuth dimension. As the aperture size becomes smaller, the element more closely resembles a point source, and the angular response becomes more broad. Another useful indicator is the -6-dB angular response, defined as the full-width half-maximum of the angular response graph.

Grating lobes are produced at a location where the path length difference to adjacent array elements is a multiple of a wavelength (the main lobe is located where the path length difference is zero). The acoustic contributions from the elements constructively interfere, producing off-axis peaks. The term grating lobe was originally used to describe the optical peaks produced by a diffraction grating. In ultrasound, grating lobes are undesirable because they represent acoustic energy steered away from the main lobe. From the Comb function in Eq. (65.3), the grating lobes are located at



подпись: (65.7)□ sin-1 — i □ 1,2,3, □ X d

In azimuth.

If d is a wavelength, then grating lobes are centered at ±90 degrees from the steering direction in that dimension. Grating lobes at such large angles are less significant because the array elements have poor angular response in those regions. If the main lobe is steered at a large angle, however, the grating lobes are brought toward the front of the array. In this case, the angular response weighting produces a relatively weak main lobe and a relatively strong grating lobe. To eliminate grating lobes at all steering angles, the interelement spacing is set to X/2 or less [Steinberg, 1967].

Figure 65.5 sHows the theoretical radiation pattern of the 128-element example. For this graph, the angular response weighting of Eq. (65.6) was substituted into Eq. (65.3). The lateral resolution, as defined by Eq. (65.7), 0x = 0.9 degrees at the focal point. The -6-dB angular response is ±40 degrees from Eq. (65.6).

Electrical Impedance

The electric impedance of an element relative to the electrical loads has a significant impact on transducer signal-to-noise ratio (SNR). At frequencies away from resonance, the transducer has electrical charac­teristics of a capacitor. The construction of the transducer is a parallel-plate capacitor with clamped capacitance of





Where eS is the clamped dielectric constant.

Near resonance, equivalent circuits help to explain the impedance behavior of a transducer. The simplified circuit of Fig. 65.6a is valid for transducers operating at series resonance without losses and with low acoustic impedance loads [Kino, 1987]. The mechanical resistance Rm represents the acoustic loads as seen from the electrical terminals:


4k2GCo Zc


FIGURE 65.5. Radiation pattern of the example array element with a = 0.1 mm, d – 0.15 mm, D = 19.2 mm, and X = 0.3 mm. The angular response of Eq. (65.6) was substituted into Eq. (65.3) for this graph.


FIGURE 65.6 Simplified equivalent circuits for a piezoelectric transducer: (a) near-series resonance and (b) near­parallel resonance.

Where k is the electromechanical coupling coefficient of the piezoelectric material, ZC is the acoustic impedance of the piezoelectric material, Z1 is the acoustic impedance of the transducer backing, and Z2 is the acoustic impedance of the load medium (body tissue). The power dissipated through Rm corre­sponds to the acoustic output power from the transducer.

The mechanical inductance Lm and mechanical capacitance Cm are analogous to the inductance and capacitance of a mass-spring system. At the series resonant frequency of

F □ r(65.10)


M m

The impedances of these components add to zero, resulting in a local impedance minimum.


FIGURE 65.7 Complex electrical impedance of the example array element. Series resonance is located at 5.0 MHz, and parallel resonance is located at 6.7 MHz.

The equivalent circuit of Fig. 65.6a cAn be redrawn in the form shown in Fig. 65.6b. In this circuit, C0 is the same as before, but the mechanical impedances have values of Lm’, Cm’, and Ra. The resistive component Ra is



□□ C0 Z1 □ Z2

R □

4 k2




The inductor and capacitor combine to form an open circuit at the parallel resonant frequency of

F □ (65.12)

W Lm Cc

The parallel resonance, which is at a slightly higher frequency than the series resonance, is indicated by a local impedance maximum.

Figure 65.7 sHows a simulated plot of magnitude and phase versus frequency for the example array element described at the beginning of this subsection. The series resonance frequency is immediately identified at 5.0 MHz with an impedance minimum of Z = 350 Q. Parallel resonance occurs at 6.7 MHz with an impedance maximum of Z = 4000 Q. Note the capacitive behavior (approximately -90-degree phase) at frequencies far from resonance.

Designing a Phased-Array Transducer

In this subsection the design of an idealized phased-array transducer is considered in terms of the performance characteristics described above. Criteria are described for selecting array dimensions, acous­tic backing and matching layers, and electrical matching networks.

Choosing Array Dimensions

The array element thickness is determined by the parallel resonant frequency. For X/2 resonance, the thickness is

T □□■ □ (65.13)

2 2 fp

Where ct is the longitudinal speed of sound in the transducer material.

There are three constraints for choosing the element width and length: (1) a nearly square cross-section should be avoided so that lateral vibrations are not coupled to the thickness vibration; as a rule of thumb [Kino and DeSilets, 1979],

A/t □ 0.6 or a/t □ 10 (65.14)

(2) a small width and length are also desirable for a wide angular response weighting function; and (3) an

Interelement spacing of X/2 or less is necessary to eliminate grating lobes.

Fortunately, these requirements are consistent for PZT array elements. For all forms of PZT, ct > 2c, where c is the speed of sound in body tissue (an average of 1540 m/s). At a given frequency, then Xt > 2X. Also, Eq. (65.13) states that Xt = 2t at a frequency of fp. By combining these equations, t > X for PZT array elements operating at a frequency of fp. If d = X/2, then a < X/2 because of the finite kerf width that separates the elements. Given this observation, then a < t/2. This is consistent with Eq. (65.14) to reduce lateral modes.

An element having d = X/2 also has adequate angular response. For illustrative purposes, one can assume a zero kerf width so that a = X/2. In this case, the -6-dB angular response is 0x = ±35 degrees according to Eq. (65.6).

The array dimensions determine the transducer’s lateral resolution. In the azimuth dimension, if d = X/2, then the transducer aperture is D = nX/2, where n is the number of elements in a fully sampled array. From Eq. (65.5), the lateral resolution in azimuth is


X □ sin-1 — (65.15)


Therefore, the lateral resolution is independent of frequency in a fully sampled array with d = X/2 . For this configuration, the lateral resolution is improved by increasing the number of elements.

Acoustic Backing and Matching Layers

The backing and matching layers affect the transducer bandwidth and sensitivity. While a lossy, matched backing improves bandwidth, it also dissipates acoustic energy that could otherwise be transmitted into the tissue medium. Therefore, a low-impedance acoustic backing is preferred because it reflects the acoustic pulses toward the front side of the transducer. In this case, adequate bandwidth is maintained by acoustically matching the transducer to the tissue medium using matching layers.

Matching layers are designed with a thickness of X/4 at the center frequency and an acoustic impedance between those of the transducer ZT and the load medium ZL. The ideal acoustic impedances can be determined from several different models [Hunt et al., 1983]. Using the KLM equivalent circuit model [Desilets et al., 1978], the ideal acoustic impedance is

Zj □ ^ZtZ2l (65.16)

For a single matching layer. For matching PZT-5H array elements (ZT = 30 MRayls) to a water load (ZL = 1.5 MRayls), a matching layer of Z1 = 4.1 MRayls should be chosen. If two matching layers are used, they should have acoustic impedances of


FIGURE 65.8 A transducer of real impedance Rt being excited by a transmitter with source impedance R0 and source voltage Vjn.

Z2 □ ^ZTZbL (65.17b)

In this case, Z1 = 8.3 MRayls and Z2 = 2.3 MRayls for matching PZT-5H to a water load.

When constructing a transducer, a practical matching layer material is not always available, with the ideal acoustic impedance [Eq. (65.16) or (65.17)]. Adequate bandwidth is obtained by using materials that have an impedance close to the ideal value. With a single matching layer, for example, conductive epoxy can be used with Z = 5.1 MRayls.

Electrical Impedance Matching

Signal-to-noise ratio and bandwidth are also improved when electrical impedance of an array element is matched to that of the transmit circuitry. Consider the simplified circuit iN Fig. 65.8 wIth a transmitter

Of impedance R0 and a transducer of real impedance Rt. The power output is proportional to the power

Dissipated in Rt, as expressed as

TOC o "1-5" h z V2 R

Pt □^ where Vrt □ (65.18)

Out Rt out R □ Rt in

The power available from the transmitter is

Into a matched load. From the two previous equations, the power efficiency is

4RRt (65.20)

P„ "


For a fixed-source impedance, the maximum efficiency is obtained by taking the derivative of Eq. (65.20) with respect to Rt and setting it to zero. Maximum efficiency occurs when the source imped­ance is matched to the transducer impedance, R0 = Rt.


FIGURE 65.9 (a) Conventional single-layer ceramic; (b) five-layer ceramic of the same overall dimensions. The layers

Are electrically in parallel and acoustically in series. The arrows indicate the piezoelectric poling directions of each layer.

подпись: figure 65.9 (a) conventional single-layer ceramic; (b) five-layer ceramic of the same overall dimensions. the layers
are electrically in parallel and acoustically in series. the arrows indicate the piezoelectric poling directions of each layer.

(a) (b)

подпись: (a) (b)In practice, the transducer has a complex impedance of Rm in parallel with C0 (see Fig. 65.6), Which is excited by a transmitter with a real impedance of 50 Q. The transducer has a maximum efficiency
when the imaginary component is tuned out and the real component is 50 Q. This can be accomplished with electrical matching networks.

The capacitance C0 is tuned out in the frequency range near ro0 using an inductor of

L 0 1 (65.21)

0 n C

U0 C0

For an inductor in shunt, or

L □— T— (65.22)

N2C □ 1/R2Cn

0 0 / m 0

For an inductor in series. The example array elements described in the preceding subsection have C0 = 22 pF and Rm = 340 Q at series resonance of 5.0 MHz. Therefore, tuning inductors of L0 = 46 |iH or L1 = 2.4 |xH should be used.

A shunt inductor also raises the impedance of the transducer, as seen from the scanner, while a series inductor lowers the terminal impedance [Hunt et al., 1983]. For more significant changes in terminal impedance, transformers are used.

A transformer of turns ratio 1:N multiplies the terminal impedance by 1/N2. In the transmit mode, N can be adjusted so that the terminal impedance matches the transmitter impedance. In the receive mode, the open-circuit sensitivity varies as 1/N because of the step-down transformer. The lower terminal impedance of the array element, however, provides increased ability to drive an electrical load.

More complicated circuits can be used for better electrical matching across a wide bandwidth [Hunt et al., 1983]. These circuits can be either passive, as above, or active. Inductors also can be used in the scanner to tune out the capacitance of the coaxial cable that loads the transducer on receive.

Another alternative for electrical matching is to use multilayer piezoelectric ceramics [Goldberg and Smith, 1994]. Figure 65.9 Shows an example of a single layer and a five-layer array element with the same overall dimensions of a, b, and t. Since the layers are connected electrically in parallel, the clamped capacitance of a multilayer ceramic (MLC) element is

Where Csingle is the capacitance of the single-layer element (Eq. 65.8). As a result, the MLC impedance is reduced by a factor of N2. Acoustically, the layers of the MLC are in series so the X/2 resonant thickness is t, the stack thickness.

To a first order, an N-layer ceramic has identical performance compared with a 1:N transformer, but the impedance is transformed within the ceramic. MLCs also can be fabricated in large quantities more easily than hand-wound transformers. While MLCs do not tune out the reactive impedance, they make it easier to tune a low capacitance array element. By lowering the terminal impedance of an array element, MLCs significantly improve transducer SNR.


The piezoelectric transducer is an important component in the ultrasound imaging system. The trans­ducer often consists of a liner array that can electronically focus an acoustic beam. Depending on the configuration of array elements, the region scanned may be sector shaped or rectangular in two dimen­sions or pyramidal shaped in three dimensions.

The transducer performance large determines the resolution and the signal-to-noise ratio of the resulting ultrasound image. The design of an array involves many compromises in choosing operating frequency and array-element dimensions. Electrical matching networks and quarter-wave matching layers may be added to improve transducer performance.

Further improvements in transducer performance may result from several areas of research. Newer materials, such as composites, are gaining widespread use in medical ultrasound. In addition, 1.5D arrays or 2D arrays may be employed to control the acoustic beam in both azimuth and elevation. Problems in fabrication and electrical impedance matching must be overcome to implement these arrays in an ultrasound system.

Defining Terms

Acoustic impedance: In an analogy to transmission line impedance, the acoustic impedance is the ratio

Of pressure to particle velocity in a medium; more commonly, it is defined as Z = pc, where p = density and c = speed of sound in a medium [the units are kg/(m2-sec) or Rayls].

Angular response: The radiation pattern versus angle for a single element of an array.

Axial resolution: The ability to distinguish between targets aligned in the axial direction (the direction

Of acoustic propagation).

Azimuth dimension: The lateral dimension that is along the scanning plane for an array transducer.

Electrical matching networks: Active or passive networks designed to tune out reactive components

Of the transducer and/or match the transducer impedance to the source and receiver impedance.

Elevation dimension: The lateral dimension that is perpendicular to the scanning plane for an array


Grating lobes: Undesirable artifacts in the radiation pattern of a transducer; they are produced at a

Location where the path length difference to adjacent array elements is a multiple of a wavelength.

Lateral modes: Transducer vibrations that occur in the lateral dimensions when the transducer is

Excited in the thickness dimension.

Lateral resolution: The ability to distinguish between targets in the azimuth and elevation dimensions

(perpendicular to the axial dimension).

Quarter-wave matching layers: One or more layers of material placed between the transducer and the

Load medium (water or human tissue); they effectively match the acoustic impedance of the transducer to the load medium to improve the transducer bandwidth and signal-to-noise ratio.


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Goldberg RL, Smith SW. 1994. Multi-layer piezoelectric ceramics for two-dimensional array transducers. IEEE Trans Ultrason Ferroelec Freq Contr.

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Kino GS, DeSilets CS. 1979. Design of slotted transducer arrays with matched backings. Ultrason Imag 1:189.

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Shattuck DP, Weinshenker MD, Smith SW, von Ramm OT. 1984. Explososcan: A parallel processing technique for high speed ultrasound imaging with linear phased arrays. J Acoust Soc Am 75:1273.

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Smith WA. 1992. New opportunities in ultrasonic transducers emerging from innovations in piezoelectric materials. In FL Lizzi (ed), New Developments in Ultrasonic Transducers and Transducer Systems, 3-26. New York, SPIE.

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Further Information

A good overview of linear array design and performance is contained in von O. T. Ramm and S. W. Smith

(1983), Beam steering with linear arrays, IEEE Trans Biomed Eng 30:438. The same issue contains a more

General article on transducer design and performance: J. W. Hunt, M. Arditi, and F. S. Foster (1983),

Ultrasound transducers for pulse-echo medical imaging, IEEE Trans Biomed Eng 30:453.

The journal IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control frequently contains articles on medical ultrasound transducers. For subscription information, contact IEEE Service Center, 445 Hoes Lane, P. O. Box 1331, Piscataway, NJ 08855-1331, phone (800) 678-IEEE.

Another good source is the proceedings of the IEEE Ultrasonics Symposium, published each year. Also, the proceedings from New Developments in Ultrasonics Transducers and Transducer Systems, edited by F. L. Lizzi, was published by SPIE, Vol. 1733, in 1992.

[1] The weight average molecular weight, Mw, is defined by the equation,

[2]CR is defined as the ration of the total number of bits used to represent the digital signal before and after compression.

[3]In practical DPCM implementation, instead of x(n – k), quantized past samples of the signal are used in the linear predictor [2].

[4]Exposure is expressed in Roentgens (R) (which is not an SI unit) or in Coulombs of ionization collected per kilogram of air.


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