Circuit model for thermoviscous propagation in annular waveguides

Area of Science:

• Acoustics
• Electrical Engineering
• Wave Propagation

Background:

• Thermoviscous acoustic wave propagation in waveguides is crucial for device design.
• Annular cross-sections present unique challenges for acoustic modeling.
• Existing models may lack accuracy or efficiency for complex geometries.

Purpose of the Study:

• To develop an accurate and efficient circuit model for thermoviscous acoustic wave propagation in annular waveguides.
• To validate the model against established simulation methods.
• To facilitate the analysis and engineering of devices with annular cross-sections.

Main Methods:

• Derivation of a circuit model from the low reduced frequency (LRF) wave propagation model in rectangular layers.
• Approximation of complex LRF solutions for annular waveguides.
• Formulation of a compact T-network model using standard circuit elements.
• Validation using finite element method (FEM) simulations of input acoustic impedance.

Main Results:

• The circuit model accurately captures annular waveguide behavior within a specific frequency bandwidth.
• Model accuracy is maintained with the lumped-element approximation.
• Cascading multiple circuit models extends bandwidth without sacrificing accuracy.
• The model provides a simplified analytical description suitable for circuit simulation.

Conclusions:

• The developed circuit model offers an efficient and accurate method for analyzing acoustic wave propagation in annular waveguides.
• The T-network model can be readily implemented in circuit simulators.
• This facilitates the design and analysis of micro-electro-mechanical systems (MEMS) and microphones with annular components.