A theoretical model of an electrostatic ultrasonic transducer incorporating resonating conduits

Alan Walker, Anthony Mulholland

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This article considers a theoretical model of an electrostatic transducer with resonating conduits con-nected to the cavities in the backplate. A 1D (in space) model is proposed so that the inverse problem of
optimizing the design parameters of the device for a desired output is not computationally prohibitive.
The mathematical model is described based on matching the acoustic impedances at each interface of the
device. The resulting ordinary differential equation is solved to give the frequency domain response of
the system and the pressure output at the membrane. Derivation of the electrical impedance, transmission
voltage response and reception force response is also provided. The model is implemented to compare a
standard device (no conduits coming from the cavity) with a device with one conduit coming from the
cavity. The model output is collated with experimental data and then used to analyse the maximum pres-
sure output for various cavity and conduit dimensions. The results show a significant dependence of the
device performance on the cavity and conduit dimensions. The incorporation of fluid-filled conduits onto
the cavities in the backplate significantly increases the pressure output as well as the transmission and
reception sensitivities. The results show that a practical transducer design could be achieved by suitable
choices of device geometry and the physical properties of the materials employed
Original languageEnglish
Pages (from-to)796-810
Number of pages15
JournalIMA Journal of Applied Mathematics
Volume75
Issue number5
DOIs
Publication statusPublished - 2010
Externally publishedYes

Fingerprint

Ultrasonic transducers
Transducer
Electrostatics
Theoretical Model
Cavity
Acoustic impedance
Output
Transducers
Impedance
Inverse problems
Ordinary differential equations
Parameter Design
Physical property
Physical properties
Frequency Domain
Mathematical models
Membranes
Inverse Problem
Acoustics
Ordinary differential equation

Cite this

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abstract = "This article considers a theoretical model of an electrostatic transducer with resonating conduits con-nected to the cavities in the backplate. A 1D (in space) model is proposed so that the inverse problem ofoptimizing the design parameters of the device for a desired output is not computationally prohibitive.The mathematical model is described based on matching the acoustic impedances at each interface of thedevice. The resulting ordinary differential equation is solved to give the frequency domain response ofthe system and the pressure output at the membrane. Derivation of the electrical impedance, transmissionvoltage response and reception force response is also provided. The model is implemented to compare astandard device (no conduits coming from the cavity) with a device with one conduit coming from thecavity. The model output is collated with experimental data and then used to analyse the maximum pres-sure output for various cavity and conduit dimensions. The results show a significant dependence of thedevice performance on the cavity and conduit dimensions. The incorporation of fluid-filled conduits ontothe cavities in the backplate significantly increases the pressure output as well as the transmission andreception sensitivities. The results show that a practical transducer design could be achieved by suitablechoices of device geometry and the physical properties of the materials employed",
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A theoretical model of an electrostatic ultrasonic transducer incorporating resonating conduits. / Walker, Alan; Mulholland, Anthony.

In: IMA Journal of Applied Mathematics, Vol. 75, No. 5, 2010, p. 796-810.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A theoretical model of an electrostatic ultrasonic transducer incorporating resonating conduits

AU - Walker, Alan

AU - Mulholland, Anthony

N1 - Unable to verify journal is peer-reviewed

PY - 2010

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AB - This article considers a theoretical model of an electrostatic transducer with resonating conduits con-nected to the cavities in the backplate. A 1D (in space) model is proposed so that the inverse problem ofoptimizing the design parameters of the device for a desired output is not computationally prohibitive.The mathematical model is described based on matching the acoustic impedances at each interface of thedevice. The resulting ordinary differential equation is solved to give the frequency domain response ofthe system and the pressure output at the membrane. Derivation of the electrical impedance, transmissionvoltage response and reception force response is also provided. The model is implemented to compare astandard device (no conduits coming from the cavity) with a device with one conduit coming from thecavity. The model output is collated with experimental data and then used to analyse the maximum pres-sure output for various cavity and conduit dimensions. The results show a significant dependence of thedevice performance on the cavity and conduit dimensions. The incorporation of fluid-filled conduits ontothe cavities in the backplate significantly increases the pressure output as well as the transmission andreception sensitivities. The results show that a practical transducer design could be achieved by suitablechoices of device geometry and the physical properties of the materials employed

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