## 2 Reconfigurable RFID Sensor for Detecting Solvent Vapors/Gas
### Sensor  
There have been many efforts in recent years to develop LC sensors for different applications, including gas detection. The present research focused on LC-type passive sensors because they are simple structures with favorable electrical characteristics. The proposed sensor was based on a printed LC resonator with a dielectric layer sensitive to gas. The resonator was realized by a U-folded dipole (UD) terminated by a glide-symmetrical interdigital capacitor (IC-UD) [31]. The resonator was designed on the Kapton substrate Dupont Pyralux AP 8515R with a dielectric constant of 3, a thickness of 25 \(\upmu\)m, and a loss tangent of 0.002. The standard commercially applied PCB etching technology was used to fabricate the sensor test sample. The copper metallic layer's thickness was 18 \(\upmu\)m. To sensitize the resonator to the presence of acetone vapors, a sensitive phthalocyanine layer was applied and placed on the top of the UD resonator area for experimental validation and around the resonator for simulation. Finally, the resonator was placed inside a rectangular metallic loop in order to raise the overall RCS level of the tag. The advantages of the IC-UD such as its small electrical size, high sensitivity, and high quality factor were demonstrated in [14], in which the effect of the number of fingers of the IC and the position of the IC-UD inside the loop also were investigated. The resulting structure and the dimensions of the sensor tag are presented in Figure 1 and Table 1, respectively. The figure shows that the metallic loop was cut by an interdigital capacitor, the purpose of which is discussed in the next section. The expression of the interdigital capacitance, as given in [32], is:  
\[C=(\varepsilon_{r}+1)l_{ID}[(N-3)A_{1}+A_{2}]\ (\mathrm{pF}), \tag{1}\]  
where \(\varepsilon_{r}\) is the relative dielectric constant of the substrate, \(l_{ID}\) is the length of the interdigital capacitor finger, and \(N\) is the number of fingers. Next, \(A_{1}\) and \(A_{2}\) are the interior and exterior capacitances per unit length of the fingers, respectively. They can be approximately expressed as:  
\[A_{1}=4.409 tanh\left[0.55\left(\frac{h}{w_{ID}}\right)^{0.45}\right]\times 10^ {-6}\left(\frac{\mathrm{pF}}{\mathrm{\mu m}}\right), \tag{2}\]  
\[A_{2}=9.92 tanh\left[0.52\left(\frac{h}{w_{ID}}\right)^{0.5}\right]\times 10^ {-6}\left(\frac{\mathrm{pF}}{\mathrm{\mu m}}\right), \tag{3}\]  
where \(h\) is the height of the substrate material and \(w_{ID}\) is the width of the fingers. Figure 2 presents the RCS of the passive sensor tag when it was exposed to a plane wave. Two simulations; i.e., with and without the sensitive layer, were performed in computer simulation technology (CST) software. The IC-UD coupled to the loop provided a relatively high RCS level (\(-30\) dBm) at 3.2 GHz. This helped to detect the tag response at the desired distance range. A sensitive layer with a thickness of 100 \(\mathrm{\upmu m}\) and a relative dielectric constant of 3 was applied and simulated--the thickness of the sensitive layer for simulation purposes was chosen to be much higher than its real value. In fact, a very thin layer requires a high mesh resolution, which drastically increases the computation time. The simulation result shown in Figure 2 revealed that a small frequency shift \(\Delta t\) (from 3.2 to 2.75 GHz) was obtained due to the presence of the sensitive layer. The effect of its thickness on the frequency shift will be experimentally verified in Section 3. In the experiments, the real sensitive layer's thickness was set to 6 and 12 \(\mathrm{\upmu m}\).