# Multiparameter Analysis of the Ultrasonic Transducer Transfer Function Using a Genetic Algorithm
###### Abstract  
The transfer function is an important parameter describing ultrasonic transducers which are designed to operate in various media. The typically high impedance of piezoelectric transducers is matched to a particular loading medium (gas, liquid, biological medium) by using multicomponent matching layers, which have specific impedances and thicknesses in accordance with the generally known matching criteria: Chebyshev, DeSilets or Souquet. When properly selected, the materials used for the matching layers allow the most optimal parameters to be obtained for both transmitting and the receiving ultrasonic energy. However, studies rarely focus on the possibility of shaping the obtained transfer function, which is also a parameter that is important in some applications of transducers intended for pulse operation, especially in liquid media (e.g., in hydroacoustics) or in biological media (e.g., in ultrasound imaging). The values and shapes of such a function are influenced by factors which are identical to the parameters describing the matching layers. This article presents the possibilities and advantages of using a genetic algorithm to shape the characteristics of the transfer functions that have a particular importance in the search for an optimal (typically the greatest) bandwidth of a transducer intended for operation in a particular medium. type: _Applied_  
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transducer, which allows the maximum amplitude of the reflected pulse to be obtained. The DeSilets criterion [3] is based on analyzing the matching of the impedances in order to allow an optimal pulse shape. It is worth noting that the layer impedances calculated for the above-mentioned criteria differ significantly. With the use of the Chebyshev, DeSilets and Souquet criteria, matching layers are selected on the basis of only acoustic impedance values for individual materials. The choice of a particular criterion depends on the type of transducer application and on its operating conditions. Publications [4; 5] describe how the value of the transfer function is affected by both the acoustic impedance of multicomponent matching layers and the thicknesses of individual layers. In particular, the influence of acoustic impedance on the shape of the transfer function has been analyzed in the above-mentioned works, which indicate limited possibilities of selecting appropriate materials for a transducer intended for operation in air. The possibility of shaping the transfer function by changing the thicknesses of the matching layers was also presented. The results of these analyses have shown how significantly the selection of individual materials and their thicknesses affects the shape of the transfer function. Acoustic attenuation of the materials which comprise the matching layers can also be an important factor in the transducer design. Publication [6] analyzes the influence of the attenuation properties of the material forming the matching layer on the losses in the energy transmitted by the transducer. The presented results indicate that the attenuation of the matching layer has a significant influence, especially in the case of air. When selecting a material for the matching layer, its attenuation may have a greater significance than the impedance value. Publication [7] analyzes the possibility for an optimal selection of matching layers for ultrasonic transducers from the perspective of the value of the transmission coefficient. The research focused on identifying the influence of the acoustic impedance and acoustic attenuation coefficient for transducers operated in air and water. Publications [8; 9] provide examples of how genetic algorithms are used in the selection of matching layers for air-operated transducers. This article presents how a genetic algorithm can be applied in a multiparameter analysis of the possibility to shape the transfer function of ultrasonic transducers intended for operation in various media.