Optimization of Acoustic Matching Layers for Piezocomposite Transducers

Nicola Lamberti Dip. di Ingegneria dellhformazione ed Ingegneria Elettrica, UniversitA di Salerno, 84084 Fisciano (SA), Italy.

Francisco Montero de Espinosa Instituto de Acustica, C.S.I.C., Serrano 144,28006 Madrid, Spain.

Nicolas Perez, Hector Gomez, Carlos Negreira Instituto de Fisica, U. de la Republica, 11200 Montevideo, Uruguay.

Abstract - At present, lot of piezoelectric broad band ultrasonic transducers use as active material piezoe- lectric ceramic composites. In a typical transducer based on piezocomposites the active material is mounted on a soft backing and one matching layer is placed on the front, radiating face, with the aim to match the acoustic impedance of the medium and to enlarge the bandwidth. In this paper an optimization work is shown to demonstrate that a composite con- figuration can be used in the matching layer in order to improve the efficiency and the band of the trans- ducers. An approximated two-dimensional analytical model has been used to optimize the design of a com- posite-structured matching layer in the case of 2-2 composites, obtaining different results for the polymer and piezoceramic composite phases.

acoustic impedance of the matching material becomes too close and higher than the one of the piezocompo- site polymer phase, resulting, with some composite geometry, in a destruction of the composite concept.

Matching layer Polymer

/

I Backing Piezoceramjc

Fig. 1. Geometry of the analyzed 2-2 composite. INTRODUCTION

In the last years, most of the piezoelectric broad band ultrasonic transducers for both, medical and NDE purposes, use as active material piezoelectric ceramic composites. A lot of scientific and technological re- search has been devoted to the optimization of piezo- composite materials, in order to increase the trans- ducer band and efficiency [ 11. In a typical transducer based on piezocomposites the active material is mounted on a soft backing and one matching layer is placed on the front, radiating face of the transducer, with the aim to match the acoustic impedance of the medium and to enlarge the bandwidth. Sbndard trans- ducer one dimensional models - KLM, Mason, etc. - are used to optimize the design of the matching layer, supposing that the piezocomposite is a homoge- neous material. With these approaches the specific

In this paper we use an approximated two-dimen- sional analytical model, previously used to describe multielement array transducers [2], and multi fie- quency 2-2 composites [3], to optimize the design of a composite-structured matching layer in the case of 2-2 composites. The transducer structure is shown in Fig. 1. The model consider the piezoceramic element of the composite as a two-dimensional (in the x and y directions) resonator whose vibration can be de- scribed, in the frequency domain, by means of a 5 x 5 matrix. In this model we satisfy the stress and electri- cal boundary conditions only in an integral form, but these approximations do not substantially affect the results [4], [5]. The polymer strips are also considered as two-dimensional structures and their model is de- duced from that of the piezoelectric element simply canceling all the piezoelectric constants and by taking

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the strip capacitance into account [3]. The full com- posite can be seen as a cascade connection, in the x di- rection, of the piezoelectric 5-bipole alternated to the non-piezoelectric polymer 5-bipole. The connection between the ports of the multipoles represents the me- chanical contact between the elements. In order to build up the matrix of the overall composite, we used an algorithm which computes the resulting matrix of the cascade of the two elemental matrices. Iterating this algorithm to all the composite elements, we obtain the total matrix [2]. With this matrix we are able to compute the composite electrical input impedance and transfer functions.

MATCHING LAYER DESIGN

The 2-2 piezocomposite that we have used as active transducer element, is constituted by nine piezoelectric (PZT-4 by Vemitron) strips separated by eight poly- mer (Araldite H by Ciba & Geigy) strips. The com- posite hckness t and length L are respectively: t = 2 mm and L = 8.4 mm, while the widths are wp = 1 mm and w, = 0.7 mm for the piezoceramic and the polymer strips respectively. In order to stress the influence of the matching layer on the transducer performance we have not inserted the backing in the transducer design. As a first step we designed the matching layer by con- sidering the composite as a homogeneous material and by using the Souquet criterion [6]:

where zm is the specific acoustic impedance of the matching layer, while z, and ZL are specific acoustic impedance of the composite and the load (zL = 1.5 Mrayls - water). The impedance of the composite was computed taking fo = 800 kHz as resonance fre- quency - propagation velocity v, = 3200 m/s -, and by making the mean weighted of the PZT-4 and Araldite densities:

P p W p +Pi Wi pc = w p +wi

With pp = 7500 kg/m3 (PZT-4 mass density) andp, = 1170 kg/m3 (Araldite mass density), we obtain for the

composite pc = 4894 kg/m3. The composite specific acoustic impedance is therefore z, = 15.7 Mrayls, and by applying the Souquet formula (1) we obtain z, = 4.1 Mrayls. As far as the matching layer thickness is concerned, it was computed in a way that tm = h/4 at the vibration frequency &, and supposing a propaga- tion velocity in the matching layer v,,, = 2000 m / s ; the obtained result is t,,, = 0.625 mm. In order to verify the transducer performance with the matching layer we compute the Transmission Transfer Function (TTF) of a single piezoelectric element as the ratio between the force exerted by the element on the load and the applied voltage, and compared the result with that obtained without matching layer. Fig. 2 shows t h s comparison. As expected, the curve obtained when the matching layer is present has a wider band and a lower efficiency. In the figure the result ob- tained with t, = 0.615 mm is also shown; this differ- ent thickness let us to obtain a flatter response and therefore it is chosen as optimum result. The specific acoustic impedance of the matching layer is greater than that of the polymer one (zl = 3.15 Mrayl) and therefore a mismatch is expected for this composite phase. In order to investigate this situation, we com- puted the TTF of a polymer element with the match- ing layer and compared it with that computed without matching layer. The results are shown in Fig. 3. As it can be seen, with the matching layer a larger band- width is obtained, but the result is poorer than that obtained for the piezoelectric element. In order to im- prove the transducer performance we match the pie- zocomposite to the load by means of a composite matching layer, i.e. a matching layer composed by strips with the same thickness, but different specific acoustic impedance. The acoustic impedance of the plate in front of the piezoceramic and polymer ele- ments are computed by separately applying the Souquet criterion to the two composite phases:

The obtained results with zp = 34 Mrayl are: zmP = 5.4 Mrayl and z,, = 2.4 Mrayl. The emission of the pie- zoelectric element computed in this case is compared

1106 - 2000 IEEE ULTRASONICS SYMPOSIUM

-nomat ........ 0.625 - -0.615

-10 -

0.4 05 0 6 0 7 0.8 0.9 1.0 1.1 1.2

fW1

-nomat ........ 4.1

..... ........ / \\ \- ~

~,+,-

Fig. 2. Comparison between the normalized responses of the single piezoceramic element without matching layer (no mat) and with a layer with thickness t,,, = 0.625 mm, and t,,, = 0.615 nun.

0 I 1 I I I

-10

-20

B Y E -30

-40

-so I I I I I I I I J 0.4 05 0.6 0.7 0 8 0 9 1.0 1.1 I 2

fWl

Fig. 3. Comparison between the normalized responses of the single polymer element without match- ing layer (no mat) and with a layer which spe- cific acoustic impedance is z,,, = 4.1 Mrayls.

in Fig. 4 with the result obtained with z,,, = 4.1 Mrayl. As it can be seen the best result is obtained when the same layer is used for the two phases. Fig. 5 shows the same comparison for the emission of the polymer element. In this case the results obtained with the con- tinuos matching layer and the composite matching layer are comparable. Finally, in order to improve the responses both of the piezoceramic and polymer ele- ments we computed the responses with a composite layer with z,,,,, = 4.1 Mrayl and z, = 2.4 Mrayl. The result obtained for the piezoceramic is the same of the

continuos layer one, while in Fig. 5 we report the one obtained for the polymer. As far as the flatness of band is considered, this last is the better result. The obtained results show that a composite matching layer can improve the transducer response. The specific acoustical impedance of the phase in front of the pie- zoceramic elements can be computed by using the Souquets expression (l), i.e., by considering the im- pedance of the composite. The impedance of the phase in front of the polymer can be still computed by means of the Souquets expression, but by considering the impedance of the polymer itself (4). Further, the response of the piezoceramic element is not influenced by the polymer matching layer phase, while the re- sponse of the polymer depends on both the matching layer phases. Another problem is to realize the com- posite matching layer with a uniform thickness (= h4) and two different materials, that means two different propagation velocities; in the computed results we supposed that the velocities in the two matching layer phases are the same. The classical solution to realize matching layers is to use a polymer loaded with some powder, varying the respective proportion in order to obtain the desired acoustic impedance. The propaga- tion velocity of the obtained material accordingly varies. In literature there are some papers in which are reported the material mechanical properties in func- tion of the components proportion; for example, in [7] it can be seen that by using a tungsten-vinyl compos- ite with 92% in vinyl, an impedance of 4.1 Mrayl and a velocity 1650 m / s are obtained. By using a polyu- rethane polymer (Grace 70010) powdered with alu- mina, (10% of alumina), an impedance of 2.4 Mrayl and a velocity 1700 m / s are obtained. This results shows the possibility to realize a matching layer with two phases of different acoustic impedance, but with the same propagation velocity.

CONCLUSIONS

In the paper an optimization work is shown to demon- strate that composite configurations can be also ap- plied to the matching layer in order to improve the ef- ficiency and the band of transducers based on piezo- ceramic composites. An approximated two-dimen- sional analytical model has been used to optimize the design of a composite-structured matching layer in the case of 2-2 composites, obtaining different results

2000 IEEE ULTRASONICS SYMPOSIUM - 1107

5 -

-30 1 I 1 I 0 4 05 0 6 0 7 0.8 0.9 1.0 I I 1.2

fW1

- 5.4, 2 4 . . . . . . . 4 1 -

Fig. 4. Comparison between the normalized responses of the single piezoelectric element with a com- posite matching layer (Zmp = 5.4 Mrayl, z,,,; = 2.4 Mrayl) and with a continuos layer with z, = 4.1 Mrayls.

0 1 I I I , r I -10 1 5 4. 2.4 4 1 . . . . . . . ..

-50 1 I I 0.4 0.5 0 6 0.7 0.8 0.9 1.0 1.1 1.2

fWl

Fig. 5. Comparison between the normalized responses of the single polymer element with a composite matching layer with Zmp = 5.4 Mrayl and Zmi = 2.4 Mrayl; with a composite matching layer with zmP = 4.1 Mrayl and z,; = 2.4 Mrayl, and with a continuos layer with z,,, = 4.1 Mrayls.

for the polymer and piezoceramic composite phases. The acoustical impedance of the matching layer phase in front of the piezoceramic elements can be computed by using the well-known Souquets formula and by considering the mean impedance of the composite; the impedance in front of the polymer can be computed by means of the same expression and by considering the impedance of the polymer itself. Further, the response

of the piezoceramic element is not influenced by the polymer matching layer phase, whle the response of the polymer depends on the two matching materials. This last result is probably due to the fact that the model used for the optimization does not take the shear stresses into account. The design method will be refined by FEM methods and verified by experiments when the technology used to fabricate the transducers will let us to do it.

REFERENCES

W. A. Smith, The role of piezocomposites in ultrasonic transducers, IEEE Ultrasonics Conj Proc., pp. 755-766, 1989.

N. Lamberti, V. Genovese, M. Pappalardo, A two-dimensional model of the multielement pie- zoelectric transducer, IEEE Ultrasonics Con$ Proc., pp. 785-789, 1990.

N. Lamberti, F. R. Montero de Espinosa, A. Iula, R. Carotenuto: Two-Dimensional Mod- eling of Multifrequency Piezocomposites; Ul- trasonics, Vol. 37, Is. 8, pp. 577-583, Jan. 2000.

N. Lamberti and M. Pappalardo, A General Approximated Two-Dimensional Model for Pie- zoelectric Array Elements, IEEE Trans. on U1- trason., Ferroelec. Frequency Contr. vol. 42, no. 2, pp. 243-252, Mar. 1995.

N. Lamberti, F. R. Montero de Espinosa, A. Iula, R. Carotenuto: Characterization of Pie- zoelectric Ceramics by Means of a Two Dimen- sional Model; IEEE Trans. on Ultrason., Fer- roelec. Frequency Contr. , in print. J. Souquet, P. Defranould and J. Desbois, Design of Low-Loss, Wide-Band Ultrasonic Transducer for Noninvasive Medical Applica- tions, IEEE Trans. on Sonics and Ultrasonics, vol. SU-26, no. 3, pp. 75-81, March 1979.

S.Lees, R. Gilmore, and P.Kranz, Acoustic properties of tungsten-vinyl compo~ites~ IEEE Trans. on Sonics and Ultrasonics, vol. SU-20, no. 1, pp. 1-2, 1973.

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