Abstract. The impedance matching layer is a vital part in contemporary ultrasonic detection systems. It serves to match the impedance of the piezoelectric transducer to that of the studied object, and to improve the frequency band. Among a few approaches, the inhomogeneous layer with continuously changing acoustic impedance has been known to combine considerable advantage with complicated physical and technical background. This has left its detailed analysis unaccomplished, and a number of related questions open. A simple theoretical model is propbsed, which allows to obtain qualitative knowledge of the behaviour of the frequency band with layer parameters. The model is used to study the conditions for optimum performance, particularly in particle/ polymer composite layers. The standard two-phase composite approach leads to unsatisfactory results. A solution on a three-phase structure with linearly shaped density and velocity profiles is discussed.

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