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One-Dimensional Electromechanical Equivalent Circuit for Piezoelectric Array Elements

  • Abdelmajid BybiEmail author
  • Hilal Drissi
  • Mohammed Garoum
  • Anne-Christine Hladky-Hennion
Conference paper
Part of the Advances in Science, Technology & Innovation book series (ASTI)

Abstract

In this chapter, we report a simple one-dimensional electromechanical method to model piezoelectric transducer array elements well known by slender bar elements. The method is inspired from Mason’s simplified model, which is tested in the case of a piezoelectric plate and extended to a rectangular slender bar. The research work investigates the effects of the material parameters on the electroacoustic performances, i.e., on the electrical impedance and the displacement. First, it compares the performances of a piezoelectric plate obtained experimentally and those calculated from the equivalent circuit. Two approaches are tested: the first method consists of the determination of the circuit components from the manufacturer parameters and the second one deduces them from the measured electrical impedance. The second approach is then tested in the case of a piezoelectric rectangular slender bar similar to those constituting the medical imaging transducer arrays. In this case, the electrical impedance and the displacement obtained are very close to the measured ones, especially around the resonance frequency. The same approach will be used to study a complete transducer array, i.e., taking into account all the elements, the filling material, the matching layers, and the backing. This constitutes the objective of our future work.

Keywords

Piezoelectric transducer arrays Electromechanical equivalent circuits Mason’s model Piezoelectric slender bar 

References

  1. Arnau, A. (2008). Piezoeletric transducers and appllications. Springer Science & Business Media.Google Scholar
  2. Bybi, A. (2012). Contribution à l’étude et à la correction de la diaphonie dans les réseaux de transducteurs piézoélectriques pour l’imagerie médicale. Dissertation, Université de Valenciennes et du Hainaut Cambrésis.Google Scholar
  3. Cobbold, R. S. C. (2006). Foundations of biomedical ultrasound. Oxford University Press.Google Scholar
  4. Erhart, J., Půlpán, P., & Pustka, M. (2016). Piezoelectric ceramic resonators. Springer.Google Scholar
  5. Ferrari, V., Marioli, D., & Taroni, A. (2001). Theory, modeling and characterization of PZT-on-alumina resonant piezo-layers as acousticwave mass sensors. Sensors and Actuators, A: Physical, 92(1–3), 182–190.  https://doi.org/10.1016/S0924-4247(01)00561-1.CrossRefGoogle Scholar
  6. Friedrich, W., Kaarmann, H., & Lerch, R. (1990). Finite element modeling of acoustic radiation from piezoelectric phased antennas. In IEEE ultrasonics symposium, Honolulu, HI (pp. 763–767).Google Scholar
  7. Grewe, M. G., Gururaja, T. R., Shrout, T. R., & Newnham, R. E. (1990). Acoustic properties of particle/polymer composites for ultrasonic transducer backing applications. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 37(6), 506–514.  https://doi.org/10.1109/58.63106.CrossRefGoogle Scholar
  8. Hernandez, C., Bernard, Y., & Razek, A. (2010). Validation du modèle d’un transducteur de langevin piezoélectrique par schéma électrique equivalent. In 5ème colloque sur les Matériaux en Gérnie Electrique, Montpellier.Google Scholar
  9. Huang, J., Que, P. W., & Jin, J. H. (2004). A parametric study of beam steering for ultrasonic linear phased array transducer. Russian Journal of Nondestructive Testing, 40(4), 254–259.  https://doi.org/10.1023/B:RUNT.0000043674.60035.0e.CrossRefGoogle Scholar
  10. Hutchens, C. G., & Morris, S. A. (1985). A two-dimensional equivalent circuit for the tall thin piezoelectric bar. In IEEE ultrasonics symposium (pp. 671–676). San Fransisco.Google Scholar
  11. Kim, M., Kim, J., & Cao, W. (2006). Electromechanical coupling coefficient of an ultrasonic array element. Journal of Applied Physics, 99(7), 074102-1-6.  https://doi.org/10.1063/1.2180487.CrossRefGoogle Scholar
  12. Maréchal, P., Levassort, F., Tran-Huu-Hue, L. P., & Lethiecq, M. (2007). Lens-focused transducer modeling using an extended KLM model. Ultrasonics, 46(2), 155–167.  https://doi.org/10.1016/j.ultras.2007.01.006.CrossRefGoogle Scholar
  13. Pérez, N., Buiochi, F., Brizzotti Andrade, M. A., & Adamowski, J. C. (2016). Numerical characterization of piezoceramics using resonance curves. Materials, 9(2), 1–30.  https://doi.org/10.3390/ma9020071.CrossRefGoogle Scholar
  14. Queirós, R., Girão, P. S., & Serra, A. C. (2005). Single-mode piezoelectric ultrasonic transducer equivalent circuit parameter calculations and optimization using experimental data. In IMEKO TC4 symposium (pp. 468–470).Google Scholar
  15. Royer, D., & Dieulesaint, E. (1999). Elastic waves in solids II: Generation, acousto-optic interaction, applications. Springer Science & Business Media.Google Scholar
  16. Sato, J., Kawabuchi, M., & Fukumoto, A. (1979). Dependance of electromechanical coupling coefficient on the width-to-thickness ratio plank-shaped piezoelectric transducers used for electronically scanned ultrasound diagnostic system. Journal of the Acoustic Society of America, 66, 1609–1611.  https://doi.org/10.1121/1.383657.CrossRefGoogle Scholar
  17. Savakus, H. P., Klicker, K. A., & Newnham, R. E. (1981). PZT-epoxy piezoelectric transducers: A simplified fabrication procedure. Materials Research Bulletin, 16(6), 677–680.  https://doi.org/10.1016/0025-5408(81)90267-1.CrossRefGoogle Scholar
  18. Sherrit, S., Leary, S. P., Dolgin, B., & Bar-Cohen, Y. (1999). Comparison of the Mason and KLM equivalent circuits for piezoelectric resonators in the thickness mode. In IEEE ultrasonics symposium, Lake Tahoe (pp. 921–926).Google Scholar
  19. Wilson, O. B. (1988). Introduction to theory and design of sonar transducers. Los Altos: Peninsula Publication.Google Scholar
  20. Wooh, S. C., & Shi, Y. (1999). A simulation study of the beam steering characteristics for linear phased arrays. Journal of Nondestructive Evaluation, 18(2), 39–57.  https://doi.org/10.1023/A:1022645204774.CrossRefGoogle Scholar
  21. Zhang, J. Y. (2011). Réseaux de transducteurs haute fréquence (100–300 MHz) à déphasage réalisés à partir des technologies MEMS. Dissertation, Université de Valenciennes et du Hainaut Cambrésis.Google Scholar
  22. Zhang, J. Y., Xu, W. J., Carlier, J., Ji, X. M., Nongaillard, B., Queste, S., et al. (2012). Modelling and simulation of high-frequency (100 MHz) ultrasonic linear arrays based on single crystal LiNbO3. Ultrasonics, 52(1), 47–53.  https://doi.org/10.1016/j.ultras.2011.06.009.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Abdelmajid Bybi
    • 1
    Email author
  • Hilal Drissi
    • 2
  • Mohammed Garoum
    • 1
  • Anne-Christine Hladky-Hennion
    • 3
  1. 1.Ecole Supérieure de Technologie de Salé, Materials Energy Acoustics Team (MEAT)Mohammed V University in RabatSaléMorocco
  2. 2.Ecole Supérieure de Technologie de Salé, Laboratoire d’Analyse des systèmes Traitement d’Information et du Management Intégré (LASTIMI)Mohammed V University in RabatSaléMorocco
  3. 3.Département ISENIEMN, UMR, CNRS 8520Lille CedexFrance

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