Models for Piezoelectric Transducers Used in Broadband Ultrasonic Applications
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Introduction Piezoelectric transducers are key elements of many broadband ultrasonic systems, either pulse-echo or through-transmission, used for imaging and detection purposes. In ultrasonic broadband applications such as medical imaging, or non-destructive testing, piezoelectric transducers should generate/receive ultrasonic signals with good efficiency over a large frequency range. This implies the use of piezoelectric transducers with high sensitivity, broad bandwidth and short-duration impulse responses. High sensitivity provides large signal amplitudes which determine a good dynamic range for the system and the short duration of the received ultrasonic signal provides a good axial resolution. The most important and common type of piezoelectric transducer elements used in ultrasonic broadband applications is a thin piezoelectric plate, with lateral dimensions much greater than the thickness, driven in a simple thickness extensional mode of vibration [1-2]. They usually operate in the frequency range 0.5-15 MHz. Different types of piezoelectric materials are used for the active transducer element. Ferroelectric ceramics, like lead zirconate titanate (PZT), lead metaniobate, etc., have a high piezoelectric coupling coefficient. Piezoelectric polymers like polyvinylidene difluoride (PVDF) and copolymers have useful low-acoustic impedances. Piezoelectric composites are mixtures of piezoceramics with nonpiezoelectric polymers. When designing a broadband piezoelectric transducer or when finding optimal transducer system configurations, it is useful to be able to predict the global response by means of theoretical calculations, bearing in mind that there is a large number of materials and configuration parameters involved in the global system [3, 4]. The aim of this chapter is to summarize A.A. Vives (ed.), Piezoelectric Transducers and Applications, doi: 10.1007/978-3-540-77508-9_4, © Springer-Verlag Berlin Heidelberg 2008
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José Luis San Emeterio and Antonio Ramos
the basic modeling approaches describing the electrical and ultrasonic characteristics of broadband multilayer transducers. In the active piezoelectric plates, the length and width to thickness ratios are sufficiently large so that one-dimensional models are good approximations to predict the properties of the transducer [5-10]. Modeling the transducer as a two-port network permits the use of the transfer matrix formalism of the circuit theory. In this chapter, a general methodology for the treatment of all the components of a transducer system, including acoustic matching layers and electric matching components, as a set of cascade networks [11-13], is also described. A computer program for design and optimization of transducer systems can be easily developed [11].
4.2 The Electromechanical Impedance Matrix Figure 4.1 shows a simple diagram of a broadband piezoelectric transducer. A piezoelectric layer of thickness t, with very thin electrodes of area A at its surfaces, is embedded between an attenuating backing material and the irradiated medium (l
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