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IMA Journal of Applied Mathematics Advance Access originally published online on September 15, 2008
IMA Journal of Applied Mathematics 2008 73(6):936-949; doi:10.1093/imamat/hxn030
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Enhancing the performance of piezoelectric ultrasound transducers by the use of multiple matching layers

Anthony J. Mulholland{dagger}

Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, UK

Nishal Ramadas, Richard L. O'Leary, Agnes C. S. Parr and Gordon Hayward

The Centre for Ultrasonic Engineering, Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, UK

Alexandre Troge and Richard A. Pethrick

Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow G1 1XL, UK

{dagger} Email: ajm{at}maths.strath.ac.uk

Received on July 2, 2007; Revision received June 17, 2008. Accepted on July 28, 2008

A linear system model is developed for a composite piezoelectric transducer with multiple matching layers. The large number of degrees of freedom in this model and the sensitivity of the device performance to these parameters make the inverse problem, of choosing these parameters to optimize the device's performance, an extremely difficult task. However, by accepting a small number of assumptions on the nature of the propagating waves in the device a Chebyshev polynomial approach is used to reduce the degrees of freedom and arrive at an algorithm for a device design. A typical device is investigated using this approach and it is shown that a threefold improvement in the device performance can be achieved over the standard single-matching-layer design. The modelling also indicated that great care has to be taken in bonding the matching layers together to ensure the homogeneity of the bonds. A transducer with four matching layers was subsequently manufactured and the experimental results show a significant improvement in the device performance, in agreement with the model predictions.

Keywords: ultrasonic transducers; multiple matching layers; Chebyshev.


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