The main purpose of the paper is to contribute at presenting an analytical and a numerical modeling which would be relevant for interpreting the couplings between a circular membrane, a peripheral cavity having the same external radius as the membrane, and a thin air gap (with a geometrical discontinuity between them), and then to characterize small scale electrostatic receivers and to propose procedures that could be suitable for fitting adjustable parameters to achieve optimal behavior in terms of sensitivity and bandwidth expected. Therefore, comparison between these theoretical methods and characterization of several shapes is dealt with, which show that the models would be appropriate to address the design of such transducers.
A miniaturized electrostatic receiver design, having a central cylindrical backing electrode of small radius surrounded by a flat annular cavity behind the circular membrane, can lead to both a higher sensitivity and a larger frequency bandwidth compared to the ones achieved with other designs, while bringing a geometrical simplicity which is advantageous from the point of view of microfabrication. An appropriate computational method, relying on a specific 2-D axisymmetrical simulation using an adaptive mesh and accounting for both viscous and thermal boundary layer effects, provides results against which analytical results can be tested. An analytical approach, which leads to solutions based on the eigenmode expansion of the membrane displacement, the acoustic pressure field depending on the radial coordinate in the central fluid gap but being assumed quasi-uniform in the annular cavity, is much faster in terms of running time and appears to be sufficiently accurate to achieve final optimization of this kind of devices.
Investigating accurately the acoustic behaviour of small fluid-filled cavities and ducts and their association is a problem of persistent importance, because nowadays both experimental investigations and theoretical modelling must provide results of increasingly higher precision. The motivation here is provided mainly by the acoustic measurement tools used for both the calibration of microphones and the artificial ear (IEC 60318-1). Both improved analytical models of small acoustic components (small tubes and slits), which account for the effects of the viscous and thermal boundary layers accurately in the frequency range of interest (20 Hz to 20 kHz), and experimental characterization of their input impedances (with a relative uncertainty of the order of magnitude of 10−2) have been proposed recently (Rodrigues et al 2008 J. Sound Vib. 315 890–910). Existing analytical procedures for coupled components suffer from strong approximations at the interfaces between narrow tubes and slits or other elements as well as the open space. A dedicated numerical model can be used in order to investigate accurately the acoustic field at these interfaces. The numerical model presented in the paper relies on a suitable linear exact formulation, based upon two coupled equations involving particle velocity and temperature variation (Joly 2010 Acta Acust. United Acust. 96 102–14) and utilizes an adaptive anisotropic meshing technique to model correctly the strong variations which occur around the geometrical discontinuities and inside the boundary layers. Application to a 2D axisymmetrical device (annular slit ending in an aperture in an infinite screen) is considered to present the ability of the method. Acoustic pressure, temperature variation and particle velocity distributions inside and around the end of the slit are depicted, and the input acoustic admittance of the slit obtained numerically is compared with both experimental and analytical results available.
Swept-sines provide a tool for fast and high-resolution measurement of evoked otoacoustic emissions. During the measurement, a response to swept-sine(s) is recorded by a probe placed in the ear canal. Otoacoustic emissions can then be extracted by various techniques, e.g., Fourier analysis, the heterodyne method, and the least-square-fitting (LSF) technique. This paper employs a technique originally proposed with exponential swept-sines, which allows for direct emission extraction from the measured intermodulation impulse response. It is shown here that the technique can be used to extract distortion-product otoacoustic emissions (DPOAEs) evoked with two simultaneous swept-sines. For proper extraction of the DPOAE phase, the technique employs previously proposed adjusted formulas for exponential swept-sines generating so-called synchronized swept-sines (SSSs). Here, the SSS technique is verified using responses derived from a numerical solution of a cochlear model and responses measured in human subjects. Although computationally much less demanding, the technique yields comparable results to those obtained by the LSF technique, which has been shown in the literature to be the most noise-robust among the emission extraction methods.
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