Many attempts have been made to design broad bandwidth transducers. Most of these have been concentrated on simple configurations such as a single piezoceramic disk with a small number of impedance matching layers on its front and/or back faces. For the complex-structured Tonpilz transducer, some methods described in the literature are not appropriate and simple trial-and-error attempts to choose matching layers are time consuming. Consequently, a systematic procedure based on the Mason equivalent circuit representation of the transducer and a nonlinear goal programming algorithm has been implemented. This procedure allows one to design both broadband and high-power transducers. The mathematical implementation of this procedure produces excellent results. Moreover, it could easily be adapted for other design objectives such as minimization of weight, cost, size, etc.
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Crombrugge et al. (1985) studied this question.