Inhomogeneous Materials With Gradiently Varying Acoustic Prop- Erties And Its Application To Impedance Matching

Acoustic impedance matching has always been an important part of the ultrasonic transducer technology, aimed at improving the performance of the transducer. Since the fifties of last century, transducer impedance matching has been intensively studied, and many theories were putted forward among which are the methods of Mason equivalent circuit and KLM equivalent circuit still widely used in transducer designs. The design of matching layers has been developed from single layer to double layers and multi-layers. The matching of single layer follows the quarter wavelength matching theory, while those of the double layers or multi-layers, which broaden the bandwidth, are due to the mechanism of coupling resonance with the thickness of each layer being around a quarter wavelength. By far the double layers design is the most common scheme for high-end transducer designs.In this article, (1) we derive the impedance transfer equation of inhomogeneous materials which can be used to calculate the transmission spectrum. In combination with the equivalent circuit method, the impedance transfer equation can also be used to predict the performance of transducers with matching layers of gradiently varying properties. The result shows:(2) by using matching layers which has an impedance gradiently varying from the impedance of the incident medium to the impedance of the emergent medium, high frequency part of sound can fully transmit while the low-frequency part being prohibited under a cutoff frequency which increases as the thick-ness decreases. (3) The acoustic performance of the matching layers depends on the geometrical and physical parameters and their variation. The low cutoff frequency and the flat spectrum can not be both achieved, but good matching performance still can be achieved with optimized impedance distribution designs.(4) We also studied the multi-layers matching which is the discretization of continuous matching layer with gradient materials. The result shows the performance of multi-layers matching is similar to the matching with gradient materials. (5) Composite materials and variable cross-section tube equivalent method are used to realize the gradient material and their matching per-formance has been shown in accordance with the gradient matching theory. (6) The solution of transformation acoustics is also tried to solve the problem of impedance matching. The theory of transformation acoustics is based on the conformal transfor-mation of acoustic wave equation by which the sound could fully transmit in the whole frequency band theoretically without any resonance mechanism, and the waveform can be intact through two different mediums. In this paper, we design a scheme to realize the impedance matching. The simulation result shows a flat frequency response relative to the quarter wavelength matching.In this article, the study of the inhomogeneous materials with gradiently varying acoustic properties provides a new theoretical foundation for designing matching layers of high-end ultrasonic transducer...