# Front-End Amplifiers for Tuning Forks in Quartz Enhanced PhotoAcoustic Spectroscopy
## 1 Introduction  
Optical sensors are well established for real-time, in situ and non-invasive trace gas detection [1]. They are widely exploited in different fields, such as breath analysis [2], environmental monitoring [3], industrial control [4] and explosive detection [5]. Among sensors based on optical techniques, quartz-enhanced photoacoustic spectroscopy (QEPAS) sensors have proved their capability to detect low gas concentrations, down to a part-per-trillion in volume [6]. In QEPAS, a laser beam is focused between the prongs of a quartz tuning fork (QTF) [7; 8]. If the laser wavelength is resonant with a radiative transition, modulated-intensity light absorption causes the generation of weak acoustic waves via non-radiative relaxation processes. The acoustic wave is then detected by the QTF if the laser modulation frequency matches a QTF resonance frequency. Due to the quartz piezoelectric property,the prongs mechanical strain induced by the acoustic wave on the QTF generates a displacement of charges. Gold electrodes deposited on the QTF surface collect the charges and allow the electrical signal to be acquired [9]. The lowest gas concentration detectable by the sensor is strictly related to the signal-to-noise ratio (SNR). Therefore, the front-end electronics must be designed in order to collect the QTF signal as well as to keep the noise as low as possible. With this aim, several architectures can be studied for enhancing the SNR. The QTF piezo-electric signal can be considered either as a current or as a voltage signal. Thus, the QTF can be represented both as a current source and as a voltage source, each requiring an appropriate way to collect the generated signal. When represented as a current source, the front-end electronics for the QTF is implemented as a transimpedance amplifier, which is the most common configuration for sensitive elements generating current signals when externally stimulated [10; 11; 12]. In transimpedance amplifiers, the current signal is converted into a voltage signal by an operational amplifier, in which a feedback loop resistor defines the current-to-voltage conversion coefficient (i.e., transimpedance). The higher the value of the feedback loop resistor, the higher the gain and the noise of the amplifier, whereas the bandwidth decreases. In such a single-ended configuration, the resistor thermal noise directly affects the current signal generated by the QTF [13]. Transimpedance amplifiers have been widely employed for studying the performance of QEPAS sensors [14; 15; 16] and QTFs [17; 18]. However, a different approach can also be used. The quartz charge constant, i.e., the electric charges developed per applied stress, is 4.6 pC/N, while the voltage constant, which represents the electric field produced in the quartz per applied stress, results 118 V\(\cdot\)m/N [19; 20; 21; 22]. These parameters characterize the piezoelectric properties of quartz and suggest that the QTF could have a low charge sensitivity but a high voltage sensitivity, and that the front-end electronics to be used is a voltage amplifier.  
In [23], a preliminary study on the performances of a transimpedance and a voltage amplifier employed as the QTF front-end electronics was performed by exciting the sensitive element with a speaker. In this work, we propose four different amplifier architectures to collect and amplify the QTF signal when employed in a standard mid-IR QEPAS sensor. A quantum cascade laser (QCL) was used as the excitation source for the QEPAS sensor to detect water vapor in standard air. For all amplifier architectures, the SNR has been calculated as the ratio between the peak values of the normalized QEPAS signal (corresponding to the maximum of the water absorption features) and the standard deviation of the normalized QEPAS signal acquired far from the absorption features.