Coupled Multi-Parameter Optimization of a Differential Resonant Photoacoustic Cell with Impedance-Matched Pickup for Trace Acetylene Detection

The performance of a resonant photoacoustic (PA) cell depends on coupled geometric and acoustic parameters acting through the acoustic field, thermoviscous boundary losses, and the microphone load. Building on established analytical, numerical, and equivalent-circuit rules for PA-cell design, this work develops a system-specific co-optimization of a dual-tube longitudinal resonator for trace acetylene (C2H2) detection. Three aspects are integrated. First, beam–tube coupling and the buffer–tube length ratio are considered together; balancing antinode pressure, resonance frequency, and quality factor Q gives a tube radius of 3.25 mm and a buffer length equal to half the tube length, with a simulated three-dimensional photoacoustic conversion amplification of 1.6. Second, coupling through the shared buffers splits the first longitudinal mode into a 1597 Hz anti-phase mode and a 1621 Hz in-phase mode. The sensor is operated at the anti-phase mode, where differential extraction gives approximately twice the single-tube simulated amplitude while rejecting spatially coherent common-mode noise. Third, a transmission-line analysis identifies the low shunt impedance introduced by a conventional ducted microphone cavity and motivates a direct-insertion pickup. The fabricated cell has a C2H2 sensitivity of 24.6 mV/ppm (R2=0.9984). At 300 s, the minimum Allan deviation is 9.4 ppb and the corresponding 3σ limit of detection is 28.2 ppb. A mixed-gas interference test performed with the same cell gives a C2H2 relative error of 4.09%.