The effectiveness of a Sierpinski carpet-inspired transducer

Sara Koubayssi, Alan Walker, Paul Roach

Research output: Contribution to journalArticle

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Abstract

Piezoelectric ultrasonic transducers have the ability to act both as a receiver and a transmitter of ultrasound. Standard designs have a regular structure and therefore operate effectively over narrow bandwidths due to their single length scale. Naturally occurring transducers benefit from a wide range of length scales giving rise to increased bandwidths. It is therefore of interest to investigate structures which incorporate a range of length scales, such as fractals. This paper applies an adaptation of the Green function renormalization method to analyze the propagation of an ultrasonic wave in a series of pre-fractal structures. The structure being investigated here is the Sierpinski carpet. Novel expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities as a function of the operating frequency are presented. Comparisons of metrics between three new designs alongside the standard design (Euclidean structure) and the previously investigated Sierpinski gasket device are performed. The results indicate a significant improvement in the reception sensitivity of the device, and improved bandwidth in both the receiving and transmitting responses.
Original languageEnglish
Article number1750050
Number of pages15
JournalFractals
Volume25
Issue number5
DOIs
Publication statusPublished - 1 Sep 2017

Fingerprint

Sierpinski Carpet
Transducer
Transducers
Length Scale
Bandwidth
Fractals
Ultrasonic transducers
Acoustic impedance
Piezoelectric transducers
Ultrasonic waves
Green's function
Sierpinski Gasket
Ultrasonic Wave
Fractal Structure
Transmitters
Ultrasound
Ultrasonics
Renormalization
Range of data
Transmitter

Keywords

  • ultrasound
  • Sierpinski Carpet
  • Sierpinski Gasket
  • Ultrasonic Transducer
  • Green Function Renormalization

Cite this

Koubayssi, Sara ; Walker, Alan ; Roach, Paul. / The effectiveness of a Sierpinski carpet-inspired transducer. In: Fractals. 2017 ; Vol. 25, No. 5.
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The effectiveness of a Sierpinski carpet-inspired transducer. / Koubayssi, Sara; Walker, Alan; Roach, Paul.

In: Fractals, Vol. 25, No. 5, 1750050, 01.09.2017.

Research output: Contribution to journalArticle

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AB - Piezoelectric ultrasonic transducers have the ability to act both as a receiver and a transmitter of ultrasound. Standard designs have a regular structure and therefore operate effectively over narrow bandwidths due to their single length scale. Naturally occurring transducers benefit from a wide range of length scales giving rise to increased bandwidths. It is therefore of interest to investigate structures which incorporate a range of length scales, such as fractals. This paper applies an adaptation of the Green function renormalization method to analyze the propagation of an ultrasonic wave in a series of pre-fractal structures. The structure being investigated here is the Sierpinski carpet. Novel expressions for the non-dimensionalized electrical impedance and the transmission and reception sensitivities as a function of the operating frequency are presented. Comparisons of metrics between three new designs alongside the standard design (Euclidean structure) and the previously investigated Sierpinski gasket device are performed. The results indicate a significant improvement in the reception sensitivity of the device, and improved bandwidth in both the receiving and transmitting responses.

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