624 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004

Acoustic Impedance Matching of PiezoelectricTransducers to the Air

Tomas E. Gomez Alvarez-Arenas

Abstract—The purpose of this work is threefold: to inves-tigate material requirements to produce impedance match-ing layers for air-coupled piezoelectric transducers, to iden-tify materials that meet these requirements, and to proposethe best solution to produce air-coupled piezoelectric trans-ducers for the low megahertz frequency range. Toward thisend, design criteria for the matching layers and possibleconfigurations are reviewed. Among the several factors thataffect the efficiency of the matching layer, the importance ofattenuation is pointed out. A standard characterization pro-cedure is applied to a wide collection of candidate materialsto produce matching layers. In particular, some types of fil-tration membranes are studied. From these results, the bestmaterials are identified, and the better matching configu-ration is proposed. Four pairs of air-coupled piezoelectrictransducers also are produced to illustrate the performanceof the proposed solution. The lowest two-way insertion lossfigure is 24 dB obtained at 0.45 MHz. This increases forhigher frequency transducers up to 42 dB at 1.8 MHz and50 at 2.25 MHz. Typical bandwidth is about 15–20%.

I. Introduction

Over the last decades, noncontact and air-coupled ul-trasonic techniques have experienced an enormous im-

petus. Materials characterization, nondestructive testing(NDT), and surface metrology are some of the areas inwhich these techniques are being applied. Good reviewsabout developments of air-coupled transducers and non-contact techniques for NDT and materials characteriza-tion are given in [1]–[4]. More recently, successful use ofair-coupled piezoelectric transducers has been reportedfor some particular applications [4]–[8]. However, design,fabrication, and applications of air-coupled piezoelectrictransducers still suffer either from the limitation in mate-rials availability for effective impedance matching or fromthe complexity of the proposed solution.

Air-coupled piezoelectric transducers require the use ofimpedance matching layers to partially mitigate the enor-mous impedance mismatch between air and piezoelectricelement. Several matching configurations have been pro-posed, examples are single quarter-wavelength (λ/4) lay-ers and variations of this configuration such as λ/8 [9] and(n+1) λ/4, [10] stacks of λ/4 layers, half-wavelength con-figurations (λ/2) [11], and a stack of very thin matchinglayers whose total acoustic thickness is λ/4 [12]. In any of

Manuscript received May 26, 2003; accepted January 6, 2004.Funding received from project 07N/0109/2002 from Comunidad deMadrid.

The author is with the Instituto de Acustica, CSIC, 28006 Madrid,Spain (e-mail: tgomez@ia.cetef.csic.es).

these configurations, a key aspect for the successful designof air-coupled transducers is the acoustic impedance of theouter layer. This is seriously limited by the availability ofconsistent materials having the required very low acous-tic impedance, very low attenuation, and thickness for thedesigned configuration and working frequency.

II. Design of Quarter Wavelength Matching

Layers

The huge impedance mismatch between air and piezo-electric ceramics has two main consequences for the designof air-coupled piezoelectric transducers: sensitivity is verylow (∼ −60 dB) and bandwidth is very narrow (∼ 5%) [13].Sensitivity can be improved by a single matching layer, butwidening the frequency bandwidth requires the use of twoor more matching layers [13].

There are two different procedures to determine theoptimum acoustic impedance of the λ/4 matching lay-ers. They lead to somewhat different results, and they arebriefly reviewed here. The first one is based on the opti-mization of the energy transfer through the two interfacesinvolved in the problem: piezoelectric element-matchinglayer and matching layer-air, in which the piezoelectric el-ement is considered an infinite layer. At a plane interfacebetween media A and B, having acoustic impedances ZA

and ZB, respectively, solution of reflection and transmis-sion problem for normal incidence is given by (1) [14]:

ut =2ZA

ZA + ZBui, ur =

ZB − ZA

ZB + ZAui, (1)

where u is the particle velocity, and subscripts i, r, and tdenotes incident, reflected, and transmitted waves, respec-tively.

The transmitted wave through a matching layer, from apiezoelectric element to air, is the sum of the contributionof each of the multiple reverberations within the matchinglayer. At the resonant frequency of a quarter-wavelengthmatching layer, all terms in this summation have the samephase when the wave leaves the matching layer; a geomet-rical series is obtained. The series that represent the ampli-tude of the transmitted wave and its summation are givenin (2).

t1t2

∞∑n=0

(r1r2)n =t1t2

1 − r1r2, r1r2 < 1, (2)

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

0885–3010/$20.00 c© 2004 IEEE

alvarez-arenas: review of design criteria for air-coupled transducers 625

to incident wave amplitude. From (1), they are given as:t1,2 = 2Zp,l

Zp,l+Zl,aand r1,2 = Zl,a−Zp,l

Zl,a+Zp,l. Subscripts 1 and 2

denote the two interfaces involved: piezoelectric ceramic-matching layer, and matching layer-air, respectively. Z isthe acoustic impedance, and the subscripts p, l, and a, de-note the piezoelectric ceramic, the matching layer, and theair, respectively.

Considering plane waves, the ratio of energy flux trans-mitted to the air to the energy flux incident on the match-ing layer (γt) is given in (3):

γt =(

t1t21 − r1r2

)2Za

Zp. (3)

For maximum transmitted energy, given the values ofZp, Za, the value of Zl is given as:

Zt =√

ZaZp. (4)

The same result is obtained if the multiple reverber-ations inside the matching layer are ignored, and theamount of energy transmitted through each interface ismaximized. However, considering multiple reverberationsis of interest in order to account for the contribution ofthe attenuation. For an ideal quarter-wavelength match-ing layer [no attenuation and acoustic impedance given by(4)] working at its resonant frequency, there is no energyloss (γt = 1); and (4) can be generalized for a stack of “n”matching layers, the impedance of the jth layer is givenas [15]:

Z(j)l = n+1

√Zn−j+1

p Zja. (5)

The second procedure was proposed by Desilets et al.[16]. In this case, the finite thickness of the piezoelectricelement is considered. A transmission line model (KLM)is used, and optimum bandwidth and maximum efficiencyare imposed to determine both the number of λ/4 match-ing layers required and the acoustic impedance of each one.First, the number of matching layers is determined fromZa, Zp, and the effective piezoelectric coupling coefficientof the ceramic (k2

t ). Then the impedance of each layer isdetermined. Two cases are analyzed in [16]: for a singleλ/4 matching layer, acoustic impedance is given as Zl =Z

2/3a Z

1/3p ; for a double-matching layer: Zl = Z

3/7a Z

4/7p , for

the first one, and Zl = Z6/7a Z

1/7p for the second one.

A piezoelectric ceramic radiating to air is considerednow (Zp ≈ 35 MRayl, Za ≈ 400 Rayl). Using thefirst approach, obtained impedances are 0.11 MRayl and0.79 MRayl–0.02 MRayl for the single- and the double-matching layer configurations, respectively. For the sec-ond approach, regardless of the value of k2

t , more thantwo matching layers are required. However, and to makepossible a direct comparison, impedance values providedby Desilets’s approach [16] also are calculated. The resultsare: 0.02 MRayl, and 0.26 MRayl–0.002 MRayl, for single-and double-matching layer schemes, respectively. Differ-ences between both approaches are clear; in particular,

lower acoustic impedance values for the matching layersare obtained by Desilets’s method [16].

However, both methods agree that very low impedancematerials are required. As acoustic impedance is given byZ = ρc, this in turn imposes the condition of low density(ρ) and acoustic velocity (c) in the selection of match-ing layer materials. Such low-density solids are porous, forthis kind of materials, the coefficient of acoustic attenua-tion is inherently high and increase with frequency. Lowacoustic velocity leads to very thin λ/4 matching layers,especially for high frequencies. As a result, it is difficultto build piezoelectric transducers operating at frequencieshigher than 0.5 MHz. Examples of candidate materials aresilica aerogels. A 200 Kg/m3 aerogel presents an acous-tic velocity about 300 m/s, and its acoustic impedance is0.06 MRayl. To produce λ/4 matching layers at 1 MHz,the thickness of the layer must be 75 µm. Tuning the res-onant frequency of the matching layer to the resonant fre-quency of the ceramic with an accuracy about 5% imposesa thickness tolerance of about a few microns.

Unfortunately, such low-impedance values required arenot always attainable in practice. Some materials haveacoustic impedance in the range 1–0.1 MRayl (e.g., somekinds of paper, rubbers, and silicone rubber loaded withmicro-spheres), and a few in the range 0.1–0.01 MRayl(e.g., some foams and some polymeric filtration mem-branes). But there is almost no material (apart from verylight aerogels and a few open cell foams) under 0.01 MRayl.In addition, the practical use of such materials is ques-tionable. This lack of materials imposes a practical limita-tion to the impedance of the outermost matching layer. Inaddition, single-matching layer scheme and narrow-bandfrequency response are concomitant. Therefore, wheneverwider bandwidth (>5%) is required, the use of two or morematching layers is necessary. In these cases, it is not pos-sible to adhere to the criteria for the acoustic impedanceof the matching layers obtained before, because there isnot any material that fulfills the impedance requirementfor the outermost matching layer. An interesting solu-tion is that proposed in [13] and [17]. It consists of adouble-matching layer. The outer layer is made of the bestavailable material (low impedance, low attenuation, andright thickness for the desired working frequency) and anadditional intermediate matching layer, whose propertiesare determined to improve the bandwidth without signifi-cantly affecting the sensitivity.

Moreover, not all materials with low acoustic impedancecan be used to produce matching layers; most of thempresent a very high attenuation coefficient. So far, atten-uation in the matching layer has attracted much less in-terest than it does the impedance, although attenuationis becoming the most restrictive. Actually, there is no cri-terion concerning the maximum acceptable attenuation inthe matching layer. However, it is needed in order to selectmaterials for this purpose.

In general, the stronger influence of the attenuation inthe matching layer is obtained for the single matching-layer scheme. Therefore, this case is analyzed here and

626 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004

used to determine an upper bound for the maximum ac-ceptable value of the attenuation coefficient in the match-ing layer. Similar to the way (3) was obtained, it is straight-forward to introduce the influence of the attenuation; atresonance condition we obtain that the sum of the contri-butions of all the internal reverberations to the transmis-sion through the matching layer is now given by:

t1t2

∞∑n=0

(r1r2)ne−(2n+1)αl =t1t2e

−αl

1 − r1r2e−2αl, (6)

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

γt =(

t1t2e−αl

1 − r1r2e−2αl

)2Za

Zp. (7)

Energy loss in the matching layer is:

Loss(dB) = 10 log(γt). (8)

In other words, the contribution of the attenuation inthe matching layer to the one-way insertion loss of thetransducer is obtained regardless of the other componentsof the transducer (e.g., piezoelectric element, backing, elec-trical matching, electrical excitation). This is of interestfrom a material-selection point of view.

To illustrate the importance of attenuation in thematching layer, its difference in comparison to water-immersion transducers and to provide a rough estimateof the maximum acceptable attenuation coefficient, it isnecessary to present some practical examples. We ana-lyze in detail the influence of the attenuation for the casesof two different loads: water (Za ≈ 1.5 MRayl) and air(Za ≈ 400 Rayl), in both cases Zp = 30 MRayl. Actualthickness of the matching layer for air-coupled is differentfrom the thickness of the matching layer for water immer-sion, although it is always λ/4. In order to get compa-rable results instead of the attenuation coefficient, α, weuse the attenuation per wavelength γ = αλ. Consideredvalues 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 ofa λ/4 matching layer is about 0.1 mm and 1 mm for air-coupled and water immersion, respectively. Consequently,attenuation values given before are approximately in therange 0–480 Np/m for an air-coupled matching layer and0–48 Np/m for a water-immersion matching layer.

Fig. 1 shows the energy loss in the matching layer, ac-cording to (8), for water immersion [Fig. 1(a)] and air-coupled [Fig. 1(b)] matching layers, respectively. For wa-ter immersion, the optimum impedance value is 6.4 MRayl.The performance presents a little dependency on the at-tenuation, and its contribution to the total one-way inser-tion loss of the transducer is very small. For air-coupledpiezoelectric transducers, optimum impedance value is lo-cated about 0.12 MRayl, and attenuation has a strong in-fluence. The reason for such a different behavior lies in

Fig. 1. Contribution of the attenuation coefficient and the acous-tic 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 ele-ment and the load. In the case of air, this mismatch is veryhigh. Most of the energy is reflected back at the solid/airinterface, and a great number of multiple reflections withinthe matching layer are required to build up the transmittedsignal. On the contrary, for water-immersion transducers,this impedance mismatch is much lower. Most of the en-ergy is transmitted at once through the matching layer,and multiple internal reflections within it have a minoreffect.

The criterion concerning the maximum, acceptable,acoustic attenuation coefficient in the matching layer willdepend on the particular application the transducer is in-tended for. In particular, for γ > 0.14 Np contributionof attenuation in the matching layer to the total one-wayinsertion loss of the air-coupled transducer is higher than15 dB. This seems to be the maximum acceptable figurefor most of the applications involved in NDT and materi-als characterization. For γ = 0.14 Np, acoustic impedanceof the matching layer can be changed from 0.04 MRayl to

alvarez-arenas: review of design criteria for air-coupled transducers 627

0.3 MRayl without significantly reducing transducer sensi-tivity (−15 ± 1 dB). In other words, the higher the atten-uation, the more relaxed is the constraint concerning theacoustic impedance.

An important point is the dependency of the attenua-tion coefficient with the frequency. If this is a linear depen-dency (constant-Q materials), the attenuation per wave-length (γ) is constant; therefore, the contribution of theattenuation in the matching layer to the total insertionloss of the transducer is independent of the frequency. Onthe contrary, if attenuation per wavelength increases withthe frequency, there is an upper frequency limit for thesuitable operation of that material as matching layer. Formost porous solids, experimentally observed variation ofthe attenuation with the frequency is well described by apower law in which exponent may vary between 0.5 and 4,depending on the mechanisms that contribute to the atten-uation (viscous flow, thermal dissipation, internal friction,viscoelasticity, or scattering) [18], [19]. Therefore, when amaterial has the right impedance to be used as a matchinglayer for air-coupled transducers, it is necessary to deter-mine both attenuation and variation of the attenuationwith the frequency to determine the optimum frequencyrange in which this particular material is to be used.

So far, three criteria concerning materials propertiesfor impedance matching of air-coupled piezoelectric trans-ducers has been introduced. Attenuation per wavelength(γ) must be as low as possible (<0.14 Np could be agood upper bound for most NDT applications). Acous-tic impedance of the outer matching layer must be in therange from 0.04 MRayl to 0.3 MRayl (for γ ≈ 0.14 Np).Material must exhibit a linear (or less) dependency of at-tenuation coefficient with frequency to make possible theuse of such material without frequency limitations. In addi-tion, it is necessary that a quarter-wavelength layer couldbe made out of that material. This means that it mustbe possible to produce a plane layer of uniform thickness,to produce a layer with the right thickness (resonant fre-quency), and to attach it efficiently to the transducer sur-face without either damaging the material or corrupting itsproperties. Unfortunately, this is not always possible, par-tially because these materials are either extremely fragile,difficult to machine, or both.

Examples of unsuited porous materials are numer-ous: (e.g., sintered aluminium powder compacts (SAP)[20], balsa wood [21], paper materials [22], and porousPMMA [23]). Except for SAPs, they all have an acous-tic impedance close to the ideal value. It also is possi-ble to obtain thin and plane layers of these materials,but attenuation per wavelength values are extremely high(γ ≈ 0.8 Np for paper materials, and γ ≈ 0.17 − 5 Np forporous PMMA). Silica aerogel has the lowest attenuationcoefficient (γ ≈ 0.06 Np) ever reported for a material withan acoustic impedance close to 0.1 MRayl [18], [24], and[25]. In addition, attenuation coefficient has an almost lin-ear dependency with the frequency; but it is extremely dif-ficult to produce a thin, uniform layer of this material andto attach it to the transducer surface. Some low-frequency,

air-coupled piezoelectric transducers (70 kHz) were pro-duced using aerogel matching layers [26]; but, so far at-tempts to produce air-coupled, piezoelectric transducersover 1 MHz, did not succeed [27]. Silicone rubber loadedwith micro-spheres also has been used, but it presents adiscrete tradeoff between low impedance and low attenua-tion (0.3 MRayl and γ ≈ 0.6 Np) [28].

A very interesting approach is the use of porous mem-branes. Yano et al. [28] first suggested use of porousmembranes; they used a polyolefin membrane (acousticimpedance 0.24 MRayl, λ/4 resonant frequency 1 MHz,and γ at 1 MHz: 0.276 Np). However, the best results wereobtained by Kelly et al. [11], Hayward and Gachagan [29],and Kelly et al. [30], who were the first to use membranefilters. In this case, a cellulose nitrate membrane filterwas used as an outer matching layer (acoustic impedance0.12 MRayl, λ/4 resonant frequency 0.71 MHz, and γ at1 MHz 0.25 Np). Use of membrane filters is promising be-cause there is a wide commercial offer of different materi-als, and grades; they all are highly porous, easy to handle,and have flat and parallel faces with a typical thickness be-tween 20 and 200 µm. A recent work [4] shows that acous-tic impedance of a wide collection of membrane filters arein the range 0.08–0.63 MRayl, attenuation per wavelengthmeasured at λ/2 resonance is within 0.1–0.6 Np, and λ/4resonance lies within the range 0.3–2 MHz. That is, someof them meet the requirements proposed for air-coupledimpedance matching layers. Moreover, membrane filters,such as paper materials, present a highly anisotropy andelastic constants in the thickness direction and are muchlower than elastic constants in the membrane plane. Due tothis particular property, it is possible to obtain a materialthat exhibits very low acoustic impedance in the normaldirection; but it is quite consistent and flexible.

III. Experimental Results

A wide set of filtration membranes are studied and arelisted in Table I. Three criteria were used to select thesemembranes. High porosity (>70%), to achieve the requiredacoustic impedance values; nominal pore size in the sub-micron scale, to reduce scattering losses; and use of cel-lular and/or particulate microstructures as they exhibitthe lowest attenuation figures, while avoiding the use of fi-brous filters (like filtration papers) for they exhibit higherattenuation coefficients [4], [18], [22], [23].

Air-coupled through transmission spectroscopy at nor-mal incidence for the frequency range 0.5–5 MHz wasused in this work to determine λ/2 resonant frequency,acoustic impedance, and attenuation coefficient of the fil-tration membranes [4]. For the frequency range up to2.5 MHz, air-coupled piezoelectric transducers were used.In addition, for the frequency range 2.5–5 MHz, a pairof water-immersion transducers, center frequency 4 MHz,were used. In spite of the reduced sensitivity of these trans-ducers operating in air, it is possible to have a clear sig-nal transmitted through the samples because materials

628 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004

TABLE IMaterials and Acoustic Properties Measured from the λ/2 Thickness Resonance.

Pore size λ/2 resonant γ at λ/2 ImpedanceMaterial (µm) frequency (MHz) (Np) (MRayl)

Vinylic/acrylic copolymer1 0.80 0.60 0.287 0.074Polyethersulfone1 0.80 1.03 0.150 0.100Polyethersulfone1 0.45 1.30 0.130 0.131Polyethersulfone1 0.20 1.50 0.111 0.244Polyethersulfone1 0.10 2.40 0.073 0.254

Nylon1 0.45 2.00 0.137 0.162Nylon1 0.20 3.20 0.151 0.313PVDF1 0.45 1.92 0.322 0.228

Polypropylene1 0.45 1.40 0.530 0.074Polypropylene1 0.20 1.82 0.439 0.081

Acrylic copolymer1 0.30 No thickness resonances observed.Acrylic copolymer1 1.20 No thickness resonances observed.

Polyethersulfone/copolymer1 0.45 1.82 0.250 0.203Mixed cellulose esters2 5.00 0.70 0.249 0.095Mixed cellulose esters2 3.00 0.86 0.198 0.094Mixed cellulose esters2 1.20 0.80 0.249 0.109Mixed cellulose esters2 0.80 0.75 0.212 0.083Mixed cellulose esters2 0.65 1.00 0.250 0.095Mixed cellulose esters2 0.45 1.00 0.216 0.098Mixed cellulose esters2 0.22 1.30 0.202 0.150Mixed cellulose esters2 0.10 2.40 0.190 0.256Mixed cellulose esters2 0.025 4.00 0.159 0.557PVDF (hydrophobic)2 0.22 No thickness resonances observed.PVDF (hydrophilic)2 0.22 No thickness resonances observed.

PVDF2 0.10 4.3 0.140 0.638PTFE2 0.50 0.30 0.600 0.017

Cellulose nitrate3 0.65 1.03 0.246 0.084Cellulose nitrate3 0.30 1.60 0.209 0.165Cellulose nitrate3 0.20 1.94 0.206 0.211Cellulose nitrate3 0.10 2.00 0.221 0.243

1Pall Corporation, Pall Gelman Laboratory, product catalog, Ann Arbor, MI 48103-9019, http://www.pall.com.2Millipore, Billerica, MA 01821, http://www.millipore.com.3Whatman International, Ltd. Whatman House, Kent ME16 0LS, U.K.,http://www.whatman.com.

under investigation are very thin and have low acousticimpedance and relatively low attenuation. To improve thesignal-to-noise ratio, an emitter transducer was driven bya high-voltage square pulse (up to 400 V) tuneable to thetransducer center frequency; the received signal in the re-ceiver transducer was amplified (P/R 5077, PanametricsInc., Waltham, MA) and displayed in an oscilloscope (TDS5052, Tektronix Inc., Beaverton, OR) where spectral anal-ysis was performed.

A sample is located, at normal incidence, between twotransducers. Transmission coefficient versus frequency ismeasured for the frequency range in which the first thick-ness resonance of the sample is located. Further details aregiven in [4]. Density and thickness of the membrane are in-dependently measured. Velocity (v) is obtained from thefrequency location of the thickness resonance (fr):

v(n) =f

(n)r

2ln, n = 1, 2, 3, . . . , (9)

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

α = α +lnR2

2l,

where, α =frπ

vQand R =

(Zmemb − Zair)2

(Zmemb + Zair)2 . (10)

Measured first order resonant frequency(f

(1)r

)and cal-

culated attenuation and impedance, at this frequency, foreach membrane are collected in Table I. Observed varia-tion of the acoustic properties for membranes of the samematerial and grade but from different batches is about 2%.Thickness variations between different membranes (samematerial and grade) are about 5–10%; hence, changes inthe location of the resonant frequency of each membranetype are also about 10%. In a few cases, no thickness reso-nances are observed; this could be explained by a very highattenuation in the sample, nonhomogeneous properties, ora frequency location of the resonance out of the analyzedrange.

It is important to underline the fact that this work con-siders only the use of commercial membrane filters. Asmentioned above, this is quite convenient for the special

alvarez-arenas: review of design criteria for air-coupled transducers 629

TABLE IIWorking Frequencies and Selected Materials for λ/4

Matching Layers.

λ/4 resonantfrequency (±10%) Grade

(MHz) Material (pore size µm)

0.30 Vinylic/acrylic copolymer 0.800.40 Cellulose ester 1.200.50 Polyethersulfone 0.800.65 Polyethersulfone 0.450.75 Polyethersulfone 0.201.00 Nylon 0.451.20 Polyethersulfone 0.101.60 Nylon 0.202.00 Cellulose ester 0.0252.15 PVDF 0.10

properties of these materials and the high-quality stan-dards that the filtration industry imposes on its products.However, major limitation of filtration membranes as λ/4matching layers is that thickness of the membrane cannotbe changed. This means that each membrane (commer-cial type for a material and grade) could be used as λ/4matching layer at one and fixed frequency. However, as itis proposed in this work, once the right material is deter-mined, different resonant frequencies are obtained by usingdifferent membrane grades.

From data shown in Table I, best materials arepolyethersulfone and nylon membranes because they ex-hibit the lowest attenuation coefficient (γ < 0.152 Np),and proper values of the acoustic impedance (0.1–0.313 MRayl). For polyethersulfone membranes, a changeof pore size from 0.8 µm to 0.1 µm, shifts the resonant fre-quency (λ/2) from 1.03 MHz to 2.4 MHz. Therefore, tun-ing the matching layer to the working frequency of a giventransducer can be achieved by selecting the proper mem-brane grade. The smaller the pore size, the higher the res-onant frequency in the membrane and the lower the atten-uation, on the contrary, acoustic impedance also increases.For lower frequencies, possible choices are vinylic/acryliccopolymer and cellulose membranes. For higher frequen-cies, some mixed cellulose esters and PVDF membranesare to be used. It is worthwhile to point out that [4] demon-strates there is an empirical relation between membranegrade and ultrasonic velocity in the material. If membranegrade and filtration properties given by manufacturers forsuch grade are known, it is possible to predict the velocityin that membrane, and therefore, the frequency locationof the thickness resonances. Unfortunately, so far there isno effective way to predict attenuation coefficient in themembrane filters.

Table II summarizes the selected membranes forimpedance matching in the frequency range 0.3–3 MHz. Astypical bandwidth of air-coupled, piezoelectric transducersusing λ/4 matching layers is about 20%, at least one mem-brane for each frequency interval of approximately 20%width is proposed in Table II. For these materials, vari-

ation of the attenuation coefficient with the frequency isinvestigated. Toward this end, it is necessary to measuretwo or more orders of the thickness resonance. Calculatedattenuation at these frequencies are fitted (in the senseof square minima) to a power law that has been demon-strated to be a good empirical approach for the attenuationin many porous materials:

α = α0fβ or γ = γ0f

β−1 where γ0 = α0v,(11)

where f is the frequency, α is the attenuation coefficient,γ is the attenuation per wavelength, and v is the acousticvelocity. From this power law an estimation of the atten-uation coefficient at λ/4 and the frequency dependency ofthe attenuation per wavelength are obtained.

As an example, measured transfer function modulus fortwo polyethersulfone, two cellulose nitrate, and two ny-lon membranes are shown in Fig. 2. First and higher or-der (up to five in some cases) thickness resonances areobserved. At each resonance order, velocity and attenua-tion are calculated from (9) and (10). Measured acousticattenuation coefficient in cellulose esters, vinylic/acryliccopolymer, polyethersulfone, cellulose nitrate, and nylonmembranes are presented in Fig. 3.

Attenuation per wavelength increases with frequencyfor mixed cellulose esters [Fig. 3(a)]. In addition, thesmaller the pore size, the smaller the attenuation. Attenu-ation in a 0.025 µm membrane is low enough for our pur-pose, and attenuation of 5, 0.8, and 0.45 µm membranesis higher than the proposed upper bound. Attenuation invinylic/acrylic copolymers [Fig. 3(b)] increases stronglywith frequency. Therefore, this material is to be usedonly at frequencies lower than 0.35 MHz. Polyethersulfone[Fig. 3(b)] presents the lowest attenuation. It increaseswith frequency; and the smaller the pore size the lowerthe attenuation. Cellulose nitrate membranes [Fig. 3(c)]are constant-Q materials; hence, there is no high-frequencylimit for the use of this material as impedance matchinglayers, unfortunately, the absolute value is a little high(γ ≈ 0.2 − 0.22 Np) for the intended application. Nylonmembranes [Fig. 3(c)] present very low attenuation values,and the increasing rate of attenuation with frequency islower for nylon than for polyethersulfones. Table III sum-marizes the details of the frequency power law (11) andattenuation 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 nobacking were produced. The PZT-5A piezoceramic, 25-mm diameter was used. For the outer matching-layerpolyethersulfone (0.8 µm), polyethersulfone (0.45 µm), ny-lon (0.45 µm), and cellulose ester (0.025 µm) were used,respectively. Better results could be obtained using spe-cific configurations for transmitter and receiver and/or us-

630 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004

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

ing 1-3 piezocomposites. But the purpose at this point isto demonstrate in a general way the actual performanceof the selected materials as quarter-wavelength matchinglayers.

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

Fig. 3. Attenuation per wavelength versus frequency for some mem-brane filters. Symbols: experimental measurements. Solid line: powerlaw fitting.

epoxy resin). The major effect of this layer of glue is tointroduce some extra attenuation. Sensitivity or two-wayinsertion loss is calculated by [31]:

IL = 20 log10

(VR

VI

), (12)

where VR is the electrical voltage generated by the receiv-ing transducer into a 1-MΩ load, and VI is the voltageproduced by the electrical source across a similar load.

Results are shown in Fig. 4. Curves labelled 1, 2, 3, and4 correspond to transducers at 0.4, 0.6, 1.0, and 2.0 MHz,respectively. In all cases, the characteristic frequency bandresponse with three peaks is observed. This is due to thepresence of two matching layers and no backing. The in-termediate epoxy matching layer split the resonance peak

alvarez-arenas: review of design criteria for air-coupled transducers 631

TABLE IIIDependency of Attenuation Versus Frequency and Estimated Attenuation per Wavelength at λ/4 for Materials in

Table II.

λ/4 resonantMaterial frequency

(grade µm) (MHz) γ at λ/4 (Np) γ0(Np/MHzβ−1) β − 1

Vinylic/acrylic copolymer (0.80) 0.30 0.27 0.38 0.28Cellulose ester (1.20) 0.40 0.20 0.21 0.052

Polyethersulfone (0.80) 0.50 0.11 0.15 0.40Polyethersulfone (0.45) 0.65 0.098 0.12 0.47Polyethersulfone (0.20) 0.75 0.069 0.08 0.52

Nylon (0.45) 1.00 0.20 0.2 0.14Polyethersulfone (0.1) 1.20 0.044 0.04 0.62

Nylon (0.1) 1.6 0.141 No higher order resonances observed.Cellulose ester (0.025) 2.00 0.131 No higher order resonances observed.

PVDF (0.1) 2.15 No higher order resonances observed.

1Estimated from value at λ/2 and frequency dependency of other membranes of the same material butdifferent grade.

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

of the piezoceramic into two peaks. These peaks have thelabel “P” in Fig. 4. Material for the outer matching layeris selected so that its λ/4 resonant frequency is located be-tween 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, polyether-sulfone (0.45 µm); curve 3, nylon (0.45 µm); and curve4, cellulose ester (0.025 µm). The location of the “M”peaks in Fig. 4 agrees with the estimated location of theλ/4 frequency (Table II), allowing a 10% tolerance in thethickness of the membrane as mentioned above. The low-est two-way insertion loss figure is −24 dB obtained at0.45 MHz; this increases for higher frequency transduc-ers 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 expenseof sensitivity.

For comparison purposes, Table IV summarizes the

properties of some other air-coupled piezoelectric trans-ducers developed over the last 20 years. These cases areselected either for the novelty of the technique used, for theproven performance, or for the working frequency range.Data from this work also are included to allow a directcomparison. Performance of the proposed solution is com-parable to, or better than, that obtained previously. Thereare two additional advantages of this method. First, it canbe applied to produce air-coupled piezoelectric transduc-ers for the frequency range 0.3–2.5 MHz just changing themembrane material or membrane grade. On the contrary,some of the techniques presented in Table IV have beentested only at a one particular frequency. Second, this tech-nique is easier, faster, and cheaper than previous attemptsbecause it makes use of a standard transducer manufac-turing process and commercial materials widely available.

V. Conclusions

An investigation to estimate material requirements withspecial emphasis on the role of attenuation to producematching layers for air-coupled piezoelectric transducershas been carried out.

Previous studies of the acoustical properties of filtra-tion membranes demonstrate that some of these materi-als exhibit very good properties to be used as quarter-wavelength matching layers for air-coupled piezoelectrictransducers for the frequency range 0.3–3 MHz. This fre-quency range is of special interest for applications relatedto materials characterization, NDT, and surface analysis.A wide set of different filtration membranes (materials andgrades) that could be used as impedance matching layersfor air-coupled piezoelectric transducers has been selected.Criteria used for this selection are high porosity, pore sizein the submicron scale, and cellular microstructure. A sys-tematic determination of their acoustic properties has beencarried out. In particular, variation of the attenuation co-efficient with frequency has been measured for these ma-terials, for the first time.

632 ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 51, no. 5, may 2004

TABLE IVPerformance and Characteristics of Some Air-Coupled Piezoelectric Transducers.

Two-wayinsertion 6 dB

loss BandwidthReference Material Technique (dB) (%)

[32] RTV silicone λ/4 (1 layer) 52 at N.A.1

[28] Porous membrane λ/4 (1 layer) 32 at 1 MHz 10Silicone loaded with λ/4 (2 layers) 48 at 1 MHz 35

micro-spheres[17] Silicone loaded with λ/4 (2 layers) 42 at 0.9 MHz 45

micro-spheres[9] 1-3 micromachined λ/4 (2 layers) 18 (one-way) at 6 (3 dB)

Kapton 0.86 MHz[29] Silicone rubber + λ/4 (2 layers) 32.9 at 580 kHz N.A.

membrane filter[12] Non λ/4 layers 38 at 250 kHz N.A.

44 at 0.5 MHz52 at 1 MHz58 at 2 MHz62 at 3 MHz

This work Epoxy resin + λ/4 (2 layers) 24 at 0.4 MHz 17filtration membranes 29 at 0.7 MHz 20

33 at 1 MHz 2042 at 1.8 MHz 8

(50 at 2.25 MHz) 9

1N.A. = not available.

Best properties are observed for polyethersulfone andnylon membranes. Changing membrane grade is the waythe membrane is tuned to the desired resonant frequency.For some special cases, mixed cellulose esters and PVDFmembranes also can be used. All the membrane filters usedin this work are commercial. The results obtained here setthe basis for the development of specific membranes forthis particular application. The most interesting modifi-cation of actual membrane filters concerns the thickness,which (together with the velocity in the membrane) deter-mine resonant frequency. Future work also will focus onthe theoretical study of attenuation in these materials.

Four pairs of air-coupled piezoelectric transducers alsowere produced to test the efficiency of the proposed mate-rials (center frequency at 0.4, 0.6, 1.0, and 2.0 MHz). Thelowest two-way intersection loss figure is −24 dB obtainedat 0.45 MHz; this increases for higher frequency transduc-ers up to −42 dB at 1.8 MHz and −50 dB at 2.25 MHz.These results are compared to those obtained by other au-thors using other techniques. Sensitivity and bandwidth ofthe transducers developed here are comparable to or bet-ter than those results; in addition, significant advantagesof the proposed solution are that the materials required arewidely available and that the complexity of the transducermanufacturing process is significantly reduced.

Acknowledgments

The author acknowledges the assistance of LuisQuevedo (Pall Espana S.A.) and Francisco Iglesias (MerckFarma y Quımica) for membrane selection and for pro-viding samples. Also helpful discussions with Anna Roig

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

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Tomas E. Gomez Alvarez-Arenas wasborn in Madrid, Spain, in 1966. He receivedthe M.S. and Ph.D. degrees in physics in 1989and 1994, respectively, from the UniversidadComplutense of Madrid, Spain.

He joined the Spanish Research Council(CSIC), Madrid, Spain, in 1989 where heworked in several Spanish and European re-search projects and contracts about ultrasonicnondestructive testing, materials characteri-zation, and piezoelectric composites. In 1995he received a grant from the Spanish Ministry

of Education and Science to work at the Centre for Ultrasonic En-gineering, University of Strathclyde, Glasgow, Scotland, in the fieldsof air-coupled piezoelectric transducers and numerical modeling ofacoustic wave propagation in random composites. In 1998 he receiveda research contract from the Spanish Science and Education Min-istry to return to the CSIC to study ultrasonic wave propagation insuspensions and membrane processes. He is chief of the Ultrasonic:Signals, Systems and Technologies Department of the Instituto deAcustica (CSIC), Madrid. Actual research interests include: ultra-sonic materials characterization, acoustic propagation in porous ma-terials, ultrasonic NDT, air-coupled piezoelectric transducers, andLamb waves propagation and generation.