Abstract
An analytical model is presented that describes the acoustical impedance of cylindrical tubes and concentrically connected systems of such tubes valid up to the ultrasonic application. This allows the evaluation of microsized geometries encountered in acoustical microdevices, such as housing enclosures and sound port Helmholtz resonators. Each tube is treated as an acoustic transmission line (TL). Connected tubes are described using a coupling impedance, which accounts for viscous and inertial effects due to duct size changes. The acoustic TL model is directly derived from Navier-Stokes and energy equation, including frequency dependent boundary layer effects of the viscous and thermal dissipation. The results for various evaluated enclosure and resonator geometries are in good agreement with finite element method (FEM) simulation in both audio and ultrasonic frequency range and are compared to dedicated lumped element models referenced in literature. The presented model provides benefits in three ways: it is faster than FEM simulation and allows an implementation into analytical models and circuit simulation tools. Finally, it allows geometries with characteristic dimensions close to and above the wavelength to be treated with high precision in contrast to lumped element models.
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