Theoretical Analysis and Experimental Verification of Top Orthogonal to Bottom Arrays of Conducting Strips on Piezoelectric Slab
Abstract
The purpose of this work is to present a theoretical analysis of top orthogonal to bottom arrays of conducting electrodes of infinitesimal thickness (conducting strips) residing on the opposite surfaces of piezoelectric slab. The components of electric field are expanded into double periodic Bloch series with corresponding amplitudes represented by Legendre polynomials, in the proposed semi-analytical model of the considered two-dimensional (2D) array of strips. The boundary and edge conditions are satisfied directly by field representation, as a result. The method results in a small system of linear equations for unknown expansion coefficients to be solved numerically. A simple numerical example is given to illustrate the method. Also a test transducer was designed and a pilot experiment was carried out to illustrate the acoustic-wave generating capabilities of the proposed arrangement of top orthogonal to bottom arrays of conducting strips.Keywords:
boundary value problem, Fourier series, Bloch series, partial differential equations, piezoelectric transducerReferences
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3. Biryukov S., Polevoi V. (1996), The electrostatic problem for SAW interdigital transducers in external electric field – part I: a general solution for a limited number of electrodes, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 43(6): 1150–1159, https://doi.org/10.1109/58.542059
4. Bløtekjær K., Ingebrigtsen K.A., Skeie H. (1973), A method for analyzing waves in structures consisting of metal strips on dispersive media, IEEE Transactions on Electron Devices, 20(12): 1133–1138, https://doi.org/10.1109/T-ED.1973.17806
5. Chen R., Cabrera-Munoz N.E., Lam K.H., Hsu H., Zheng F., Zhou Q., Shung K.K. (2014), PMN-PT single-crystal high-frequency kerfless phased-array, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 61(6): 1033–1041, https://doi.org/10.1109/TUFFC.2014.2999
6. Daniau W., Kumar A.K.S., Paruch P., Marre D., Triscone J.-M., Ballandras S. (2004), A novel piezoelectric interdigital transducer for the excitation of high frequency surface acoustic waves, IEEE Ultrasonics Symposium, 2004, Vol. 1, pp. 441–444., https://doi.org/10.1109/ULTSYM.2004.1417757
7. Danicki E. (1996), Strips electrostatics – spectral approach, 1996 IEEE Ultrasonics Symposium. Proceedings, Vol. 1, pp. 193–196, https://doi.org/10.1109/ULTSYM.1996.583957
8. Danicki E., Nowicki A., Tasinkevych Y. (2013), Interdigitated interdigital transducer for surface elastometry of soft damping tissue, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 60(6): 1260–1262, https://doi.org/10.1109/TUFFC.2013.2690
9. Danicki E.J. (2010), Electrostatics of crossed arrays of strips, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 57(7): 1701–1705, https://doi.org/10.1109/TUFFC.2010.1601
10. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G. (1953), Higher transcendental functions, Vol. 1, New York: McGraw-Hill, http://apps.nrbook.com/bateman/Vol1.pdf
11. Fissi L.E., Jaouad A., Vandormael D., Francis L.A. (2015), Fabrication of new Interdigital transducers for surface acoustic wave device, Physics Procedia, 70: 936–940, https://doi.org/10.1016/j.phpro.2015.08.194
12. Morgan D.P. (1999), Quasi-static analysis of floating-electrode unidirectional SAW transducers (FEUDTs), 1999 IEEE Ultrasonics Symposium. Proceedings. International Symposium (Cat. No.99CH37027), Vol. 1 , pp. 107–111, https://doi.org/10.1109/ULTSYM.1999.849366
13. Na J.K., Blackshire J.L., Kuhr S. (2008), Design, fabrication, and characterization of single-element interdigital transducers for NDT applications, Sensors and Actuators A: Physical, 148(2) 359–365, https://doi.org/10.1016/j.sna.2008.08.018
14. Nguyen V.H., Richert S., Park H., Böker A., Schnakenberg U. (2017), Single interdigital transducer as surface acoustic wave impedance sensor, Procedia Technology, 27: 70–71, https://doi.org/10.1016/j.protcy.2017.04.032
15. Peach R.C. (1981), A general approach to the electrostatic problem of the SAW interdigital transducer, IEEE Transactions on Sonics and Ultrasonics, 28(2): 96–104, https://doi.org/10.1109/T-SU.1981.31227
16. Schau H.C. (1991), Edge-connected, crossed-electrode array for two-dimensional projection and beam forming, IEEE Transactions on Signal Processing, 39(2): 289–297, https://doi.org/10.1109/78.80811
17. Senveli S.U., Tigli O. (2015), A novel surface acoustic wave sensor for microparticle sensing and quantification, IEEE Sensors Journal, 15(10): 5748–5754, https://doi.org/10.1109/JSEN.2015.2446491
18. Seo C.H., Yen J. T. (2009), A 256×256 256x256 2-D array transducer with row-column addressing for 3-D rectilinear imaging, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 56(4): 837–847, https://doi.org/10.1109/TUFFC.2009.1107
19. Tasinkevych Y., Danicki E. (2011), Wave generation and scattering by periodic baffle system in application to beam-forming analysis, Wave Motion, 48(2) 130–145, https://doi.org/10.1016/j.wavemoti.2010.10.002
20. Wang W., Oh H., Lee K., Yoon S., Yang S. (2009), Enhanced sensitivity of novel surface acoustic wave microelectromechanical system-interdigital transducer gyroscope, Japanese Journal of Applied Physics, 48(6): 06FK09, https://doi.org/10.1143/jjap.48.06fk09
21. White R.M., Voltmer F.M. (1965), Direct piezoelectric coupling to surface elastic waves, Applied Physics Letters, 7(12): 314–316, https://doi.org/10.1063/1.1754276
22. Yen J.T., Seo C.H., Awad S.I., Jeong J.S. (2009), A dual-slab transducer array for 3-D rectilinear imaging, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 56(1): 204–212, https://doi.org/10.1109/TUFFC.2009.1020
