Electrical power factor for a single crystal tonpilz versus a plate with matching layers

Abstract

For underwater transducers mounted on small platforms, reactive electrical power can constitute a main restriction on the usable frequency range. The frequency range in which the amount of reactive power is acceptable can be increased by increasing the electromechanical coupling coefficient of the active material. However, to avoid large electrical power factor ripple, the transducer design must also have a low mechanical quality factor, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{m}$</tex> . A ferroelectric single crystal can have electromechanical coupling coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k=0.9$</tex> . The optimum <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{m}$</tex> is then as low as 0.6, which is challenging to achieve. We investigated this challenge for a tonpilz design, by calculating <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{m}$</tex> for different combinations of head masses and tonpilz stiffnesses, and by calculating the stiffness to density ratio required in the head material to avoid flexural resonances. The effective coupling coefficient of a real transducer is reduced compared to the material coupling coefficient, and in many applications some power factor ripple can be accepted. Both factors relax the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{m}$</tex> requirement. We calculated the power factor of a tonpilz design with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k=0.82$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{m}=1.9$</tex> , and showed that the power factor ripple is smaller than 0.2 in a frequency band that is 150 % wide relative to the resonance frequency. The frequency independent matching inherent in the tonpilz gives this design an advantage regarding power factor ripple, and this can weigh up for a large <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q_{m}$</tex> . We showed this by comparing the tonpilz to an air-backed composite plate. Like the tonpilz, the composite plate had <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k=0.82$</tex> , but it was matched to water by two conventional acoustic matching layers. Compared to the tonpilz, the composite design had a larger distance between the −3dB points of the acoustic power. Beyond these points, the acoustic power was however falling off more rapidly, resulting in an electrical power factor ripple of nearly 0.5.