## 4 Results  
The performance of QEPAS sensors depends on the gas pressure. High QTF quality factors and efficient sounds generation are required for QEPAS operation. When reducing the pressures (<200 Torr), the QTF quality factor increases while the number of molecules diminishes, negatively affecting the sound generation efficiency. Thereby an optimal gas pressure maximizing the QEPAS signal, as tradeoff between two opposite trends, has to be identified. A certified 1% C\({}_{2}\)H\({}_{6}\):N\({}_{2}\) gas mixture was used to investigate the QEPAS signal as a function of the pressure, for both spectrophotones. The current amplitude modulation depends on the gas pressure since the full width half maximum (FWHM) of the absorption line suffers from the pressure broadening. Similarly, the resonance frequency of the spectrophone is pressure-dependent: when prongs vibrate in a viscous fluid. This effect can be modeled as an increase of the prong's effective mass, which corresponds to a linear decrease of the resonance frequency while the pressure increases. Thus, for each spectrophone and for each pressure value the current amplitude modulation and the resonance frequency of the spectrophone were optimized. Ethane QEPAS peak values, occurring at an injection current of 112.5 mA and a TEC temperature of 16 \({}^{\circ}\)C, are reported in Figure 4 as a function of gas pressure for both spectrophotones. Data were normalized to the peak value corresponding to an optimum pressure in order to make the correlation between excitation frequency (represented by the different resonator) and gas pressure independent of extrinsic factors such as the employed preamplifier. This preliminary investigation allowed identification of the best operating condition of the two spectrophotones for ethene detection, namely pressure, waveform amplitude and frequency modulation of 300 Torr, 125 mV and 0.49 Hz for SP1 and 750 Torr, 150 mV and 6229.43 Hz for SP2. The performances of the sensors employing the two ADMs operating at their best conditions are compared in Figure 5, where the QEPAS spectral scans at the ethane peak are reported. Figure 3: Schematic of the QEPAS sensor for ethane detection. ADM: acoustic detection module. The experimental setup was conceived in order to easily swap the two ADMs while keeping fixed the rest of the apparatus. The light blue curves mimic the gas line. Figure 5 depicts the measured ethane QEPAS signals, resembling the opposite of the second derivative of the ethane absorption Lorentzian line-shape [41]. The peak is reached at \(\sim\)15 s time of acquisition, corresponding to a wavelength of 1684 nm (5937.3 cm\({}^{-1}\)). The peak signal measured with the ADM2 is 63.0 mV, 4.9 times higher than the 12.9 mV-peak signal measured by implementing ADM1. Using an averaging time of 100 ms, a 1-\(\sigma\) noise of 0.094 mV for ADM1 and 0.139 mV for ADM2 was measured. This gives signal-to-noise ratios and minimum detection limits (MDL) of: SNR1\(\sim\)136, MDL1 \(\sim\)73 ppm and SNR2\(\sim\)453, MDL2 \(\sim\)22 ppm, respectively for ADM1 and ADM2. The sensor long-term stability was then investigated. A 30 min long acquisition of consecutive QEPAS spectral scans of the ethane absorption line was performed employing each ADM at the best-found operating conditions. The peak signal value of each ramp, extracted by means of a MATLAB software, was plotted in Figure 6. Repeated scan-measurements were preferred to long-term acquisitions locked on a peak signal in order to neglect possible laser wavelength and optical power instabilities. The peak values recorded over the  
Figure 4: Normalized QEPAS peak signals at fixed ethane concentration (1% in nitrogen, certified) as a function of pressure measured for SP1 (black squares) and SP2 (red dots). Figure 5: Spectral scan of the ethane peak with QEPAS sensor employing SP1 (black curve) and SP2 (red curve). time are plotted in Figure 6. The ethane QEPAS sensor stability was investigated using both ADMs.