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Abstract—The purpose of this work is threefold: to inves- tigate material requirements to produce impedance match- ing layers for air-coupled piezoelectric ...
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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004

Acoustic Impedance Matching of Piezoelectric Transducers to the Air ´ Tom´as E. G´ omez Alvarez-Arenas Abstract—The purpose of this work is threefold: to investigate material requirements to produce impedance matching layers for air-coupled piezoelectric transducers, to identify materials that meet these requirements, and to propose the best solution to produce air-coupled piezoelectric transducers for the low megahertz frequency range. Toward this end, design criteria for the matching layers and possible configurations are reviewed. Among the several factors that affect the efficiency of the matching layer, the importance of attenuation is pointed out. A standard characterization procedure is applied to a wide collection of candidate materials to produce matching layers. In particular, some types of filtration membranes are studied. From these results, the best materials are identified, and the better matching configuration is proposed. Four pairs of air-coupled piezoelectric transducers also are produced to illustrate the performance of the proposed solution. The lowest two-way insertion loss figure is 24 dB obtained at 0.45 MHz. This increases for higher frequency transducers up to 42 dB at 1.8 MHz and 50 at 2.25 MHz. Typical bandwidth is about 15–20%.

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I. Introduction ver the last decades, noncontact and air-coupled ultrasonic techniques have experienced an enormous impetus. Materials characterization, nondestructive testing (NDT), and surface metrology are some of the areas in which these techniques are being applied. Good reviews about developments of air-coupled transducers and noncontact techniques for NDT and materials characterization are given in [1]–[4]. More recently, successful use of air-coupled piezoelectric transducers has been reported for some particular applications [4]–[8]. However, design, fabrication, and applications of air-coupled piezoelectric transducers still suffer either from the limitation in materials availability for effective impedance matching or from the complexity of the proposed solution. Air-coupled piezoelectric transducers require the use of impedance matching layers to partially mitigate the enormous impedance mismatch between air and piezoelectric element. Several matching configurations have been proposed, examples are single quarter-wavelength (λ/4) layers and variations of this configuration such as λ/8 [9] and (n + 1) λ/4, [10] stacks of λ/4 layers, half-wavelength configurations (λ/2) [11], and a stack of very thin matching layers whose total acoustic thickness is λ/4 [12]. In any of

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Manuscript received May 26, 2003; accepted January 6, 2004. Funding received from project 07N/0109/2002 from Comunidad de Madrid. The author is with the Instituto de Ac´ ustica, CSIC, 28006 Madrid, Spain (e-mail: [email protected]).

these configurations, a key aspect for the successful design of air-coupled transducers is the acoustic impedance of the outer layer. This is seriously limited by the availability of consistent materials having the required very low acoustic impedance, very low attenuation, and thickness for the designed configuration and working frequency.

II. Design of Quarter Wavelength Matching Layers The huge impedance mismatch between air and piezoelectric ceramics has two main consequences for the design of air-coupled piezoelectric transducers: sensitivity is very low (∼ −60 dB) and bandwidth is very narrow (∼ 5%) [13]. Sensitivity can be improved by a single matching layer, but widening the frequency bandwidth requires the use of two or more matching layers [13]. There are two different procedures to determine the optimum acoustic impedance of the λ/4 matching layers. They lead to somewhat different results, and they are briefly reviewed here. The first one is based on the optimization of the energy transfer through the two interfaces involved in the problem: piezoelectric element-matching layer and matching layer-air, in which the piezoelectric element is considered an infinite layer. At a plane interface between media A and B, having acoustic impedances ZA and ZB , respectively, solution of reflection and transmission problem for normal incidence is given by (1) [14]: ut =

2ZA ZB − ZA ui , ur = ui , ZA + ZB ZB + ZA

(1)

where u is the particle velocity, and subscripts i, r, and t denotes incident, reflected, and transmitted waves, respectively. The transmitted wave through a matching layer, from a piezoelectric element to air, is the sum of the contribution of each of the multiple reverberations within the matching layer. At the resonant frequency of a quarter-wavelength matching layer, all terms in this summation have the same phase when the wave leaves the matching layer; a geometrical series is obtained. The series that represent the amplitude of the transmitted wave and its summation are given in (2). t1 t2

∞ 

(r1 r2 )n =

n=0

t1 t2 , r1 r2 < 1, 1 − r1 r2

(2)

where t represents the ratio of transmitted to incident wave amplitude, and r represents the ratio of reflected

c 2004 IEEE 0885–3010/$20.00 

´lvarez-arenas: review of design criteria for air-coupled transducers a

to incident wave amplitude. From (1), they are given as: 2Zp,l Z −Zp,l t1,2 = Zp,l +Z and r1,2 = Zl,a . Subscripts 1 and 2 l,a l,a +Zp,l denote the two interfaces involved: piezoelectric ceramicmatching layer, and matching layer-air, respectively. Z is the acoustic impedance, and the subscripts p, l, and a, denote the piezoelectric ceramic, the matching layer, and the air, respectively. Considering plane waves, the ratio of energy flux transmitted to the air to the energy flux incident on the matching layer (γt ) is given in (3):  γt =

t1 t2 1 − r1 r2

2

Za . Zp

(3)

For maximum transmitted energy, given the values of Zp , Za , the value of Zl is given as:  Zt = Za Zp . (4) The same result is obtained if the multiple reverberations inside the matching layer are ignored, and the amount of energy transmitted through each interface is maximized. However, considering multiple reverberations is of interest in order to account for the contribution of the attenuation. For an ideal quarter-wavelength matching layer [no attenuation and acoustic impedance given by (4)] working at its resonant frequency, there is no energy loss (γt = 1); and (4) can be generalized for a stack of “n” matching layers, the impedance of the jth layer is given as [15]:  n+1 (j) Zl = Zpn−j+1 Zaj . (5) The second procedure was proposed by Desilets et al. [16]. In this case, the finite thickness of the piezoelectric element is considered. A transmission line model (KLM) is used, and optimum bandwidth and maximum efficiency are imposed to determine both the number of λ/4 matching layers required and the acoustic impedance of each one. First, the number of matching layers is determined from Za , Zp , and the effective piezoelectric coupling coefficient of the ceramic (kt2 ). Then the impedance of each layer is determined. Two cases are analyzed in [16]: for a single λ/4 matching layer, acoustic impedance is given as Zl = 2/3 1/3 3/7 4/7 Za Zp ; for a double-matching layer: Zl = Za Zp , for 6/7 1/7 the first one, and Zl = Za Zp for the second one. A piezoelectric ceramic radiating to air is considered now (Zp ≈ 35 MRayl, Za ≈ 400 Rayl). Using the first approach, obtained impedances are 0.11 MRayl and 0.79 MRayl–0.02 MRayl for the single- and the doublematching layer configurations, respectively. For the second approach, regardless of the value of kt2 , more than two matching layers are required. However, and to make possible a direct comparison, impedance values provided by Desilets’s approach [16] also are calculated. The results are: 0.02 MRayl, and 0.26 MRayl–0.002 MRayl, for singleand double-matching layer schemes, respectively. Differences between both approaches are clear; in particular,

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lower acoustic impedance values for the matching layers are obtained by Desilets’s method [16]. However, both methods agree that very low impedance materials are required. As acoustic impedance is given by Z = ρc, this in turn imposes the condition of low density (ρ) and acoustic velocity (c) in the selection of matching layer materials. Such low-density solids are porous, for this kind of materials, the coefficient of acoustic attenuation is inherently high and increase with frequency. Low acoustic velocity leads to very thin λ/4 matching layers, especially for high frequencies. As a result, it is difficult to build piezoelectric transducers operating at frequencies higher than 0.5 MHz. Examples of candidate materials are silica aerogels. A 200 Kg/m3 aerogel presents an acoustic velocity about 300 m/s, and its acoustic impedance is 0.06 MRayl. To produce λ/4 matching layers at 1 MHz, the thickness of the layer must be 75 µm. Tuning the resonant frequency of the matching layer to the resonant frequency of the ceramic with an accuracy about 5% imposes a thickness tolerance of about a few microns. Unfortunately, such low-impedance values required are not always attainable in practice. Some materials have acoustic impedance in the range 1–0.1 MRayl (e.g., some kinds of paper, rubbers, and silicone rubber loaded with micro-spheres), and a few in the range 0.1–0.01 MRayl (e.g., some foams and some polymeric filtration membranes). But there is almost no material (apart from very light aerogels and a few open cell foams) under 0.01 MRayl. In addition, the practical use of such materials is questionable. This lack of materials imposes a practical limitation to the impedance of the outermost matching layer. In addition, single-matching layer scheme and narrow-band frequency response are concomitant. Therefore, whenever wider bandwidth (>5%) is required, the use of two or more matching layers is necessary. In these cases, it is not possible to adhere to the criteria for the acoustic impedance of the matching layers obtained before, because there is not any material that fulfills the impedance requirement for the outermost matching layer. An interesting solution is that proposed in [13] and [17]. It consists of a double-matching layer. The outer layer is made of the best available material (low impedance, low attenuation, and right thickness for the desired working frequency) and an additional intermediate matching layer, whose properties are determined to improve the bandwidth without significantly affecting the sensitivity. Moreover, not all materials with low acoustic impedance can be used to produce matching layers; most of them present a very high attenuation coefficient. So far, attenuation in the matching layer has attracted much less interest than it does the impedance, although attenuation is becoming the most restrictive. Actually, there is no criterion concerning the maximum acceptable attenuation in the matching layer. However, it is needed in order to select materials for this purpose. In general, the stronger influence of the attenuation in the matching layer is obtained for the single matchinglayer scheme. Therefore, this case is analyzed here and

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used to determine an upper bound for the maximum acceptable value of the attenuation coefficient in the matching layer. Similar to the way (3) was obtained, it is straightforward to introduce the influence of the attenuation; at resonance condition we obtain that the sum of the contributions of all the internal reverberations to the transmission through the matching layer is now given by: t1 t2

∞ 

(r1 r2 )n e−(2n+1)αl =

n=0

t1 t2 e−αl , 1 − r1 r2 e−2αl

(6)

where α is the attenuation coefficient in the matching layer, and l is the thickness. Ratio of transmitted to incident energy flux from the piezoelectric element through the matching layer into the load (air) then is given by:  γt =

t1 t2 e−αl 1 − r1 r2 e−2αl

2

Za . Zp

(7)

Energy loss in the matching layer is: Loss(dB) = 10 log(γt ).

(8)

In other words, the contribution of the attenuation in the matching layer to the one-way insertion loss of the transducer is obtained regardless of the other components of the transducer (e.g., piezoelectric element, backing, electrical matching, electrical excitation). This is of interest from a material-selection point of view. To illustrate the importance of attenuation in the matching layer, its difference in comparison to waterimmersion transducers and to provide a rough estimate of the maximum acceptable attenuation coefficient, it is necessary to present some practical examples. We analyze in detail the influence of the attenuation for the cases of two different loads: water (Za ≈ 1.5 MRayl) and air (Za ≈ 400 Rayl), in both cases Zp = 30 MRayl. Actual thickness of the matching layer for air-coupled is different from the thickness of the matching layer for water immersion, although it is always λ/4. In order to get comparable results instead of the attenuation coefficient, α, we use the attenuation per wavelength γ = αλ. Considered values for both cases are: γ = 0, 6 × 10−3 , 0.012, 0.024, 0.048, 0.096, and 0.192 Np. At 1 MHz, typical thickness of a λ/4 matching layer is about 0.1 mm and 1 mm for aircoupled and water immersion, respectively. Consequently, attenuation values given before are approximately in the range 0–480 Np/m for an air-coupled matching layer and 0–48 Np/m for a water-immersion matching layer. Fig. 1 shows the energy loss in the matching layer, according to (8), for water immersion [Fig. 1(a)] and aircoupled [Fig. 1(b)] matching layers, respectively. For water immersion, the optimum impedance value is 6.4 MRayl. The performance presents a little dependency on the attenuation, and its contribution to the total one-way insertion loss of the transducer is very small. For air-coupled piezoelectric transducers, optimum impedance value is located about 0.12 MRayl, and attenuation has a strong influence. The reason for such a different behavior lies in

Fig. 1. Contribution of the attenuation coefficient and the acoustic impedance of the matching layer to the one-way insertion loss. Attenuation coefficient per wavelength (γ) in Np is on each curve. (a) Water coupled, (b) air-coupled.

the impedance mismatch between the piezoelectric element and the load. In the case of air, this mismatch is very high. Most of the energy is reflected back at the solid/air interface, and a great number of multiple reflections within the matching layer are required to build up the transmitted signal. On the contrary, for water-immersion transducers, this impedance mismatch is much lower. Most of the energy is transmitted at once through the matching layer, and multiple internal reflections within it have a minor effect. The criterion concerning the maximum, acceptable, acoustic attenuation coefficient in the matching layer will depend on the particular application the transducer is intended for. In particular, for γ > 0.14 Np contribution of attenuation in the matching layer to the total one-way insertion loss of the air-coupled transducer is higher than 15 dB. This seems to be the maximum acceptable figure for most of the applications involved in NDT and materials characterization. For γ = 0.14 Np, acoustic impedance of the matching layer can be changed from 0.04 MRayl to

´lvarez-arenas: review of design criteria for air-coupled transducers a

0.3 MRayl without significantly reducing transducer sensitivity (−15 ± 1 dB). In other words, the higher the attenuation, the more relaxed is the constraint concerning the acoustic impedance. An important point is the dependency of the attenuation coefficient with the frequency. If this is a linear dependency (constant-Q materials), the attenuation per wavelength (γ) is constant; therefore, the contribution of the attenuation in the matching layer to the total insertion loss of the transducer is independent of the frequency. On the contrary, if attenuation per wavelength increases with the frequency, there is an upper frequency limit for the suitable operation of that material as matching layer. For most porous solids, experimentally observed variation of the attenuation with the frequency is well described by a power law in which exponent may vary between 0.5 and 4, depending on the mechanisms that contribute to the attenuation (viscous flow, thermal dissipation, internal friction, viscoelasticity, or scattering) [18], [19]. Therefore, when a material has the right impedance to be used as a matching layer for air-coupled transducers, it is necessary to determine both attenuation and variation of the attenuation with the frequency to determine the optimum frequency range in which this particular material is to be used. So far, three criteria concerning materials properties for impedance matching of air-coupled piezoelectric transducers has been introduced. Attenuation per wavelength (γ) must be as low as possible (70%), to achieve the required acoustic impedance values; nominal pore size in the submicron scale, to reduce scattering losses; and use of cellular and/or particulate microstructures as they exhibit the lowest attenuation figures, while avoiding the use of fibrous filters (like filtration papers) for they exhibit higher attenuation coefficients [4], [18], [22], [23]. Air-coupled through transmission spectroscopy at normal incidence for the frequency range 0.5–5 MHz was used in this work to determine λ/2 resonant frequency, acoustic impedance, and attenuation coefficient of the filtration membranes [4]. For the frequency range up to 2.5 MHz, air-coupled piezoelectric transducers were used. In addition, for the frequency range 2.5–5 MHz, a pair of water-immersion transducers, center frequency 4 MHz, were used. In spite of the reduced sensitivity of these transducers operating in air, it is possible to have a clear signal transmitted through the samples because materials

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004 TABLE I Materials and Acoustic Properties Measured from the λ/2 Thickness Resonance.

Material

Pore size (µm)

Vinylic/acrylic copolymer1 Polyethersulfone1 Polyethersulfone1 Polyethersulfone1 Polyethersulfone1 Nylon1 Nylon1 PVDF1 Polypropylene1 Polypropylene1 Acrylic copolymer1 Acrylic copolymer1 Polyethersulfone/copolymer1 Mixed cellulose esters2 Mixed cellulose esters2 Mixed cellulose esters2 Mixed cellulose esters2 Mixed cellulose esters2 Mixed cellulose esters2 Mixed cellulose esters2 Mixed cellulose esters2 Mixed cellulose esters2 PVDF (hydrophobic)2 PVDF (hydrophilic)2 PVDF2 PTFE2 Cellulose nitrate3 Cellulose nitrate3 Cellulose nitrate3 Cellulose nitrate3

0.80 0.80 0.45 0.20 0.10 0.45 0.20 0.45 0.45 0.20 0.30 1.20 0.45 5.00 3.00 1.20 0.80 0.65 0.45 0.22 0.10 0.025 0.22 0.22 0.10 0.50 0.65 0.30 0.20 0.10

λ/2 resonant frequency (MHz)

γ at λ/2 (Np)

0.60 1.03 1.30 1.50 2.40 2.00 3.20 1.92 1.40 1.82 No thickness No thickness 1.82 0.70 0.86 0.80 0.75 1.00 1.00 1.30 2.40 4.00 No thickness No thickness 4.3 0.30 1.03 1.60 1.94 2.00

0.287 0.150 0.130 0.111 0.073 0.137 0.151 0.322 0.530 0.439 resonances resonances 0.250 0.249 0.198 0.249 0.212 0.250 0.216 0.202 0.190 0.159 resonances resonances 0.140 0.600 0.246 0.209 0.206 0.221

Impedance (MRayl) 0.074 0.100 0.131 0.244 0.254 0.162 0.313 0.228 0.074 0.081 observed. observed. 0.203 0.095 0.094 0.109 0.083 0.095 0.098 0.150 0.256 0.557 observed. observed. 0.638 0.017 0.084 0.165 0.211 0.243

1 Pall

Corporation, Pall Gelman Laboratory, product catalog, Ann Arbor, MI 481039019, http://www.pall.com. 2 Millipore, Billerica, MA 01821, http://www.millipore.com. 3 Whatman International, Ltd. Whatman House, Kent ME16 0LS, U.K., http://www.whatman.com.

under investigation are very thin and have low acoustic impedance and relatively low attenuation. To improve the signal-to-noise ratio, an emitter transducer was driven by a high-voltage square pulse (up to 400 V) tuneable to the transducer center frequency; the received signal in the receiver transducer was amplified (P/R 5077, Panametrics Inc., Waltham, MA) and displayed in an oscilloscope (TDS 5052, Tektronix Inc., Beaverton, OR) where spectral analysis was performed. A sample is located, at normal incidence, between two transducers. Transmission coefficient versus frequency is measured for the frequency range in which the first thickness resonance of the sample is located. Further details are given in [4]. Density and thickness of the membrane are independently measured. Velocity (v) is obtained from the frequency location of the thickness resonance (fr ): (n)

v (n) =

fr n, n = 1, 2, 3, . . . , 2l

(9)

where n is the order of the resonance. Attenuation is obtained from the width of the resonance peak (Q-factor):

lnR2 , 2l 2 fr π (Zmemb − Zair ) (10) where, α ˜= and R = 2. vQ (Zmemb + Zair )   (1) Measured first order resonant frequency fr and calculated attenuation and impedance, at this frequency, for each membrane are collected in Table I. Observed variation of the acoustic properties for membranes of the same material and grade but from different batches is about 2%. Thickness variations between different membranes (same material and grade) are about 5–10%; hence, changes in the location of the resonant frequency of each membrane type are also about 10%. In a few cases, no thickness resonances are observed; this could be explained by a very high attenuation in the sample, nonhomogeneous properties, or a frequency location of the resonance out of the analyzed range. It is important to underline the fact that this work considers only the use of commercial membrane filters. As mentioned above, this is quite convenient for the special α=α ˜+

´lvarez-arenas: review of design criteria for air-coupled transducers a TABLE II Working Frequencies and Selected Materials for λ/4 Matching Layers. λ/4 resonant frequency (±10%) (MHz)

Material

Grade (pore size µm)

0.30 0.40 0.50 0.65 0.75 1.00 1.20 1.60 2.00 2.15

Vinylic/acrylic copolymer Cellulose ester Polyethersulfone Polyethersulfone Polyethersulfone Nylon Polyethersulfone Nylon Cellulose ester PVDF

0.80 1.20 0.80 0.45 0.20 0.45 0.10 0.20 0.025 0.10

properties of these materials and the high-quality standards that the filtration industry imposes on its products. However, major limitation of filtration membranes as λ/4 matching layers is that thickness of the membrane cannot be changed. This means that each membrane (commercial type for a material and grade) could be used as λ/4 matching layer at one and fixed frequency. However, as it is proposed in this work, once the right material is determined, different resonant frequencies are obtained by using different membrane grades. From data shown in Table I, best materials are polyethersulfone and nylon membranes because they exhibit the lowest attenuation coefficient (γ < 0.152 Np), and proper values of the acoustic impedance (0.1– 0.313 MRayl). For polyethersulfone membranes, a change of pore size from 0.8 µm to 0.1 µm, shifts the resonant frequency (λ/2) from 1.03 MHz to 2.4 MHz. Therefore, tuning the matching layer to the working frequency of a given transducer can be achieved by selecting the proper membrane grade. The smaller the pore size, the higher the resonant frequency in the membrane and the lower the attenuation, on the contrary, acoustic impedance also increases. For lower frequencies, possible choices are vinylic/acrylic copolymer and cellulose membranes. For higher frequencies, some mixed cellulose esters and PVDF membranes are to be used. It is worthwhile to point out that [4] demonstrates there is an empirical relation between membrane grade and ultrasonic velocity in the material. If membrane grade and filtration properties given by manufacturers for such grade are known, it is possible to predict the velocity in that membrane, and therefore, the frequency location of the thickness resonances. Unfortunately, so far there is no effective way to predict attenuation coefficient in the membrane filters. Table II summarizes the selected membranes for impedance matching in the frequency range 0.3–3 MHz. As typical bandwidth of air-coupled, piezoelectric transducers using λ/4 matching layers is about 20%, at least one membrane for each frequency interval of approximately 20% width is proposed in Table II. For these materials, vari-

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ation of the attenuation coefficient with the frequency is investigated. Toward this end, it is necessary to measure two or more orders of the thickness resonance. Calculated attenuation at these frequencies are fitted (in the sense of square minima) to a power law that has been demonstrated to be a good empirical approach for the attenuation in many porous materials: α = α0 f β or γ = γ0 f β−1 where γ0 = α0 v, (11) where f is the frequency, α is the attenuation coefficient, γ is the attenuation per wavelength, and v is the acoustic velocity. From this power law an estimation of the attenuation coefficient at λ/4 and the frequency dependency of the attenuation per wavelength are obtained. As an example, measured transfer function modulus for two polyethersulfone, two cellulose nitrate, and two nylon membranes are shown in Fig. 2. First and higher order (up to five in some cases) thickness resonances are observed. At each resonance order, velocity and attenuation are calculated from (9) and (10). Measured acoustic attenuation coefficient in cellulose esters, vinylic/acrylic copolymer, polyethersulfone, cellulose nitrate, and nylon membranes are presented in Fig. 3. Attenuation per wavelength increases with frequency for mixed cellulose esters [Fig. 3(a)]. In addition, the smaller the pore size, the smaller the attenuation. Attenuation in a 0.025 µm membrane is low enough for our purpose, and attenuation of 5, 0.8, and 0.45 µm membranes is higher than the proposed upper bound. Attenuation in vinylic/acrylic copolymers [Fig. 3(b)] increases strongly with frequency. Therefore, this material is to be used only at frequencies lower than 0.35 MHz. Polyethersulfone [Fig. 3(b)] presents the lowest attenuation. It increases with frequency; and the smaller the pore size the lower the attenuation. Cellulose nitrate membranes [Fig. 3(c)] are constant-Q materials; hence, there is no high-frequency limit for the use of this material as impedance matching layers, unfortunately, the absolute value is a little high (γ ≈ 0.2 − 0.22 Np) for the intended application. Nylon membranes [Fig. 3(c)] present very low attenuation values, and the increasing rate of attenuation with frequency is lower for nylon than for polyethersulfones. Table III summarizes the details of the frequency power law (11) and attenuation at λ/4 for membranes shown in Table II.

IV. Practical Realization of Some Air-Coupled Transducers For completeness, four pairs of identical transducers, center frequency at 0.4, 0.6, 1.0, and 2.0 MHz with no backing were produced. The PZT-5A piezoceramic, 25mm diameter was used. For the outer matching-layer polyethersulfone (0.8 µm), polyethersulfone (0.45 µm), nylon (0.45 µm), and cellulose ester (0.025 µm) were used, respectively. Better results could be obtained using specific configurations for transmitter and receiver and/or us-

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Fig. 2. Experimentally measured transfer function modulus versus frequency for several membrane filters of different materials and grades. a) cellulose nitrate, b) polyethersulfone, c) nylon.

Fig. 3. Attenuation per wavelength versus frequency for some membrane filters. Symbols: experimental measurements. Solid line: power law fitting.

ing 1-3 piezocomposites. But the purpose at this point is to demonstrate in a general way the actual performance of the selected materials as quarter-wavelength matching layers.

epoxy resin). The major effect of this layer of glue is to introduce some extra attenuation. Sensitivity or two-way insertion loss is calculated by [31]:   VR IL = 20 log10 , (12) VI

To improve the frequency bandwidth and to relax the frequency tuning requirements, the approach proposed in [13] and [17] is used here; that is, an intermediate λ/4 matching layer is put in between the piezoelectric ceramic and the membrane filter. In this case, this matching layer is made of epoxy resin. To avoid corrupting the acoustic properties of the membrane, it is glued to the epoxy layer using a very thin film (10–20 µm) of highly viscous glue (whose acoustic properties are very similar to those of the

where VR is the electrical voltage generated by the receiving transducer into a 1-MΩ load, and VI is the voltage produced by the electrical source across a similar load. Results are shown in Fig. 4. Curves labelled 1, 2, 3, and 4 correspond to transducers at 0.4, 0.6, 1.0, and 2.0 MHz, respectively. In all cases, the characteristic frequency band response with three peaks is observed. This is due to the presence of two matching layers and no backing. The intermediate epoxy matching layer split the resonance peak

´lvarez-arenas: review of design criteria for air-coupled transducers a

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TABLE III Dependency of Attenuation Versus Frequency and Estimated Attenuation per Wavelength at λ/4 for Materials in Table II.

Material (grade µm)

λ/4 resonant frequency (MHz)

Vinylic/acrylic copolymer (0.80) Cellulose ester (1.20) Polyethersulfone (0.80) Polyethersulfone (0.45) Polyethersulfone (0.20) Nylon (0.45) Polyethersulfone (0.1) Nylon (0.1) Cellulose ester (0.025) PVDF (0.1)

0.30 0.40 0.50 0.65 0.75 1.00 1.20 1.6 2.00 2.15

γ at λ/4 (Np)

γ0 (Np/MHzβ−1 )

β−1

0.27 0.38 0.28 0.20 0.21 0.052 0.11 0.15 0.40 0.098 0.12 0.47 0.069 0.08 0.52 0.20 0.2 0.14 0.044 0.04 0.62 No higher order resonances observed. 0.141 No higher order resonances observed. 0.131 No higher order resonances observed.

1 Estimated

from value at λ/2 and frequency dependency of other membranes of the same material but different grade.

Fig. 4. Sensitivity versus frequency for the four pairs of produced aircoupled piezoelectric transducers matched to the air by a filtration membrane. “P” labels the peaks in the band due to the intermediate epoxy layer; “M” labels the peak due to the membrane filter layer.

of the piezoceramic into two peaks. These peaks have the label “P” in Fig. 4. Material for the outer matching layer is selected so that its λ/4 resonant frequency is located between the two “P” peaks. This contribution is labelled “M” in Fig. 4. Membranes used, as stated above, are as follows. Curve 1, polyethersulfone (0.8 µm); curve 2, polyethersulfone (0.45 µm); curve 3, nylon (0.45 µm); and curve 4, cellulose ester (0.025 µm). The location of the “M” peaks in Fig. 4 agrees with the estimated location of the λ/4 frequency (Table II), allowing a 10% tolerance in the thickness of the membrane as mentioned above. The lowest two-way insertion loss figure is −24 dB obtained at 0.45 MHz; this increases for higher frequency transducers up to −42 dB at 1.8 MHz, and −50 dB at 2.25 MHz. These data are slightly higher than those predicted from (8). Estimation of the −6 dB bandwidth is about 15%– 20%, although it can be further increased at the expense of sensitivity. For comparison purposes, Table IV summarizes the

properties of some other air-coupled piezoelectric transducers developed over the last 20 years. These cases are selected either for the novelty of the technique used, for the proven performance, or for the working frequency range. Data from this work also are included to allow a direct comparison. Performance of the proposed solution is comparable to, or better than, that obtained previously. There are two additional advantages of this method. First, it can be applied to produce air-coupled piezoelectric transducers for the frequency range 0.3–2.5 MHz just changing the membrane material or membrane grade. On the contrary, some of the techniques presented in Table IV have been tested only at a one particular frequency. Second, this technique is easier, faster, and cheaper than previous attempts because it makes use of a standard transducer manufacturing process and commercial materials widely available. V. Conclusions An investigation to estimate material requirements with special emphasis on the role of attenuation to produce matching layers for air-coupled piezoelectric transducers has been carried out. Previous studies of the acoustical properties of filtration membranes demonstrate that some of these materials exhibit very good properties to be used as quarterwavelength matching layers for air-coupled piezoelectric transducers for the frequency range 0.3–3 MHz. This frequency range is of special interest for applications related to materials characterization, NDT, and surface analysis. A wide set of different filtration membranes (materials and grades) that could be used as impedance matching layers for air-coupled piezoelectric transducers has been selected. Criteria used for this selection are high porosity, pore size in the submicron scale, and cellular microstructure. A systematic determination of their acoustic properties has been carried out. In particular, variation of the attenuation coefficient with frequency has been measured for these materials, for the first time.

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004 TABLE IV Performance and Characteristics of Some Air-Coupled Piezoelectric Transducers.

Reference

Material

Technique

Two-way insertion loss (dB)

[32] [28]

RTV silicone Porous membrane Silicone loaded with micro-spheres Silicone loaded with micro-spheres 1-3 micromachined Kapton Silicone rubber + membrane filter

λ/4 (1 layer) λ/4 (1 layer) λ/4 (2 layers)

52 at 32 at 1 MHz 48 at 1 MHz

N.A.1 10 35

λ/4 (2 layers)

42 at 0.9 MHz

45

λ/4 (2 layers)

18 (one-way) at 0.86 MHz 32.9 at 580 kHz

6 (3 dB)

38 at 250 kHz 44 at 0.5 MHz 52 at 1 MHz 58 at 2 MHz 62 at 3 MHz 24 at 0.4 MHz 29 at 0.7 MHz 33 at 1 MHz 42 at 1.8 MHz (50 at 2.25 MHz)

N.A.

[17] [9] [29] [12]

Non λ/4 layers

This work

1 N.A.

λ/4 (2 layers)

Epoxy resin + filtration membranes

λ/4 (2 layers)

6 dB Bandwidth (%)

N.A.

17 20 20 8 9

= not available.

Best properties are observed for polyethersulfone and nylon membranes. Changing membrane grade is the way the membrane is tuned to the desired resonant frequency. For some special cases, mixed cellulose esters and PVDF membranes also can be used. All the membrane filters used in this work are commercial. The results obtained here set the basis for the development of specific membranes for this particular application. The most interesting modification of actual membrane filters concerns the thickness, which (together with the velocity in the membrane) determine resonant frequency. Future work also will focus on the theoretical study of attenuation in these materials. Four pairs of air-coupled piezoelectric transducers also were produced to test the efficiency of the proposed materials (center frequency at 0.4, 0.6, 1.0, and 2.0 MHz). The lowest two-way intersection loss figure is −24 dB obtained at 0.45 MHz; this increases for higher frequency transducers up to −42 dB at 1.8 MHz and −50 dB at 2.25 MHz. These results are compared to those obtained by other authors using other techniques. Sensitivity and bandwidth of the transducers developed here are comparable to or better than those results; in addition, significant advantages of the proposed solution are that the materials required are widely available and that the complexity of the transducer manufacturing process is significantly reduced. Acknowledgments The author acknowledges the assistance of Luis Quevedo (Pall Espa˜ na S.A.) and Francisco Iglesias (Merck Farma y Qu´ımica) for membrane selection and for providing samples. Also helpful discussions with Anna Roig

(Institut de Ciencia de Materials de Barcelona) concerning data and discussions about membrane microstructure.

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´ Tom´ as E. G´ omez Alvarez-Arenas was born in Madrid, Spain, in 1966. He received the M.S. and Ph.D. degrees in physics in 1989 and 1994, respectively, from the Universidad Complutense of Madrid, Spain. He joined the Spanish Research Council (CSIC), Madrid, Spain, in 1989 where he worked in several Spanish and European research projects and contracts about ultrasonic nondestructive testing, materials characterization, and piezoelectric composites. In 1995 he received a grant from the Spanish Ministry of Education and Science to work at the Centre for Ultrasonic Engineering, University of Strathclyde, Glasgow, Scotland, in the fields of air-coupled piezoelectric transducers and numerical modeling of acoustic wave propagation in random composites. In 1998 he received a research contract from the Spanish Science and Education Ministry to return to the CSIC to study ultrasonic wave propagation in suspensions and membrane processes. He is chief of the Ultrasonic: Signals, Systems and Technologies Department of the Instituto de Ac´ ustica (CSIC), Madrid. Actual research interests include: ultrasonic materials characterization, acoustic propagation in porous materials, ultrasonic NDT, air-coupled piezoelectric transducers, and Lamb waves propagation and generation.