Modeling NDT piezoelectric ultrasonic transmitters J.L. San Emeterio a, * , A. Ramos a , P.T. Sanz a , A. Ru  ız a,b , A. Azbaid a a Instituto de Ac ustica. CSIC., Calle Serrano 144. 28006 Madrid, Spain b ICIMAF, Calle 15, no. 551, C.P. 10400, La Habana, Cuba Abstract Ultrasonic NDT applications are frequently based on the spike excitation of piezoelectric transducers by means of efficient pulsers which usually include a power switching device (e.g. SCR or MOS-FET) and some rectifier components. In this paper we present an approximate frequency domain electro-acoustic model for pulsed piezoelectric ultrasonic transmitters which, by inte- grating partial models of the different stages (driving electronics, tuning/matching networks and broadband piezoelectric trans- ducer), allows the computation of the emission transfer function and output force temporal waveform. An approximate frequency domain model is used for the evaluation of the electrical driving pulse from the spike generator. Tuning circuits, interconnecting cable and mechanical impedance matching layers are modeled by means of transmission lines and the classical quadripole approach. The KLM model is used for the piezoelectric transducer. In addition, a PSPICE scheme is used for an alternative simulation of the broadband driving spike, including the accurate evaluation of non-linear driving effects. Several examples illustrate the capabilities of the specifically developed software. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Piezoelectric transducers; NDT pulsers; Ultrasonic transmitters; Modeling 1. Introduction Classical analysis of the broadband response of piezo- electric transducers rely on the use of three-port matrix or circuit models, such as Mason or KLM, that provide an impulse response to be convolved with an ideal driving waveform (assuming electrical sources with lin- ear and resistive characteristics). Nevertheless, efficient pulsers for NDT applications are frequently based on the spike excitation of piezoelectric transducers. This type of pulsers usually includes a power switching device (e.g. SCR or MOS-FET) and some rectifier components [1–3]. The pulse waveform that actually arrives at the piezoelectric transducer electrodes, in the real high- voltage NDT context, is the result of different linear and non-linear interactions among the power switching, a capacitive discharge (including selective damping and tuning components) and the complex input impedance of the piezoelectric transducer under real loading con- ditions. Fig. 1 shows a block diagram for a piezoelectric ultrasonic transmitter, including the excitation elec- tronics, electrical tuning/damping networks at the elec- trical terminals of the transducer, the broadband piezoelectric transducer and the irradiated medium. Fig. 2 shows a more detailed circuital configuration for the high-voltage section (ramp generator and pulse shaper), and Fig. 3 a simplified version for the spike generation circuits which will be used to simulate the response of the high-voltage driving. The broadband piezoelectric transducer can be represented by an exact one-dimen- sional circuit model such as KLM [4] equivalent circuit. Mechanical impedance matching layers can be modeled by means of specific transmission lines [5]. Different emission transfer functions can be defined relating the transmitted force to the driving voltage ei- ther at the transducer terminals or at the generator. Their inverse Fourier transform provides the time domain impulse response. The transmission matrix (T- matrix or ‘‘ABCD’’-matrix) formalism of circuit analy- sis [6,7] is used to evaluate the emission transfer function when only linear networks are involved. Section 2 pre- sents an approximate procedure to evaluate the electri- cal driving pulse at the transducer terminals in the case of spike generators. The output force temporal * Corresponding author. Tel.: +34-91-5618806; fax: +34-91- 4117651. E-mail address: jluis@ia.cetef.csic.es (J.L. San Emeterio). 0041-624X/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.01.021 Ultrasonics 42 (2004) 277–281 www.elsevier.com/locate/ultras