## 3 Results
### Theoretical Model
#### 3.3.4 Application to the Detection of Propane Gas  
According to Figures 2a and 3, the sensor's resistance changed as a function of time. Therefore, if our goal was to apply it in a new propane gas detector, the sensor had to operate at a specific point in the dynamic response, which we called the \"operating point\". Now, if the sensor's response time was selected at three seconds, the operating point had the coordinates (\(\approx\)1151.9 [s] \(\approx\) 1,518,215 [K\(\Omega\)]) (see Figure 6). Then, we designed the electronic circuit from that operating point. Figure 7a shows the electronic diagram of the propane gas detector. The detector was based on a Wheatstone bridge, an instrumentation amplifier with two operational amplifiers, a comparator circuit, and a voltage source of \(\pm\)12 Volts. Its operating temperature was 250 \({}^{\circ}\)C, it detected concentrations of 1000 ppm, and its response time was three seconds. Its working principle consisted of calibration and detection stages [39]. In the calibration stage, the chemical sensor (the ZnAl2O4) was placed in an air atmosphere, its terminals were connected to one arm of the Wheatstone bridge, and the variable resistance \(R_{C}\) was changed until the bridge calibration was achieved, such that the voltage difference (output voltage of the Wheatstone Bridge) was \(V_{B}-V_{A}=0\). \(V_{A}\) and \(V_{B}\) were compared with the instrumentation amplifier, and their difference was multiplied by the gain. The output voltage was defined through:  
\[V_{o}=(V_{B}-V_{A})\bigg{(}1+K+\frac{R_{2}+R_{4}}{R_{g}}\bigg{)}, \tag{31}\]  
where \(R_{g}\) is the amplifier gain, \(R_{1},R_{2},R_{3},R_{4}\), are precision resistors, and \(K=\frac{R_{4}}{R_{3}}=\frac{R_{2}}{R_{1}}\). When \(V_{B}-V_{A}=0\) was satisfied, the voltage \(V_{o}\) was zero. This voltage may be due to the fact that the comparator circuit had negative saturation and therefore, the diode did not conduct, eliminating any negative signal. Therefore, the alarm signal had a value of zero, \(V_{Alarm}=0\). That is, the device would not detect the presence of propane gas in the atmosphere. In the detection stage, when the sensor surface came into contact with propane gas, the sensor had a surface current and suffered a resistance variation. Consequently,  
Figure 6: Graphical representation of the operating point and sensor’s response time (3 s). the Wheatstone test was unbalanced, and the voltage \(V_{A}\) was less than the voltage \(V_{B}\). Subsequently, the instrumentation amplifier compared both voltages and amplified 10 times, the difference:  
\[V_{o}=10(V_{B}-V_{A})\to V_{o}>0, \tag{32}\]  
with \(R_{1}=R_{2}=R_{3}=R_{4}=1000\)\(\Omega\), \(K=10\), and \(R_{g}=250\)\(\Omega\) (see Equation (31) and Figure 7). Since the voltage \(V_{o}\) was greater than zero, the comparator had positive saturation. Therefore, the alarm signal was equal to the positive saturation voltage of the operational amplifier minus the voltage drop of the rectifier diode (\(V_{d}=0.7\) V), \(V_{Alarm}=V_{sat}\approx 11.3\)\(V\). Therefore, the device detected the presence of propane gas in the monitored atmosphere. Figure 7 shows the propane gas detector's design obtained with proteus(r) software. The detector was 10 cm \(\times\) 10 cm, and its main features were low construction cost, high working temperatures, short response time, high sensitivity, easy repair, and a chemical sensor based on the oxide ZnAl\({}_{2}\)O\({}_{4}\). Figure 7: Propane gas detector: (**a**) electronic diagram, (**b**) printed circuit and electronic components’ distribution, and (**c**) 3D view. In particular, we performed a comparison of our results obtained from the dynamic response and the designed device of the ZnAl\({}_{2}\)O\({}_{4}\) with other semiconducting oxides that have been investigated as potential gas sensors. For example, in references [1; 9; 27] they report changes in electrical resistance as a function of time, concentration of propane atmospheres and sensitivity humidity on the ZnAl\({}_{2}\)O\({}_{4}\) and ZnO.