Design of a parallel Helmholtz resonator structure as a hazardous greenhouse gases sensor using the transfer matrix method

Respiratory system problems are often exacerbated by the inhalation of hazardous airborne gases, making early and accurate gas detection critical for health and environmental safety. This study addresses this issue by proposing a novel, high-performance acoustic gas sensor based on a parallel Helmholtz resonator system integrated with a waveguide defect. The core objective is to enhance gas detection sensitivity through an efficient, low-cost design. Analytical modeling using the transfer matrix method and Sylvester's theorem reveals that altering the geometry of an air-filled unit cell enables precise control over low-frequency acoustic wave filtering. Introducing a defect in the system creates a localized resonant mode within the acoustic band gap, which is tunable by modifying defect length and cross-section. Replacing the air in the resonator with different gas samples demonstrates the sensor's capability, as a strong linear relationship is observed between sound speed and resonance frequency. This ensures consistent detection sensitivity across various gases. The sensor achieves a sensitivity of 0.88 Hz s m^-1, a figure of merit of 8.8 × 10⁶ s m^-1, an exceptionally high-quality factor of 3.0 × 10⁹, and a detection limit as low as 5.7 × 10^-9 y m/s. These findings confirm the sensor's potential for accurate, efficient gas detection relevant to respiratory health, offering significant advantages over conventional, more complex systems.