## 3 Results
### Tunable Sensor
The gas being detected had a very low concentration (10,000 ppm), which only negligibly altered the effective permittivity of the surrounding environment and therefore could not adversely affect the WPT system. Actual gas detection was only possible due to the sensitive interdigital structure of the resonator, which was only minimally coupled to the power supply (nf separation in the loop). Then, a horn antenna was added to the wireless system, as illustrated in Figure 10. The horn antenna listed in Table 5 operates as a dual transmitting/receiving antenna for the RFID reader and was used to communicate with the sensor tag. Figure 11 presents the measurement setup in an anechoic chamber. \begin{table}
\begin{tabular}{c c c c} \hline \hline \# & \(P_{\text{g}}\) (dBm) & \(P_{\text{A}}\) (dBm) & \(V_{\text{r}}\) (V) \\ \hline
1 & \(-40\) & \(10.9\) & \(0.35\) \\
2 & \(-35\) & \(15.8\) & \(0.65\) \\
3 & \(-30\) & \(20.9\) & \(1.40\) \\
4 & \(-25\) & \(26.0\) & \(2.60\) \\
5 & \(-20\) & \(31.0\) & \(3.80\) \\
6 & \(-15\) & \(36.0\) & \(7.30\) \\
7 & \(-10\) & \(41.0\) & \(7.50\) \\
8 & \(-5\) & \(45.1\) & \(7.60\) \\
9 & \(0\) & \(47.1\) & \(7.70\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measured input power and the corresponding rectifier voltage. Figure 10: Schematic diagram of the entire system. Figure 12 depicts the measured RCS response of the tag in an anechoic chamber in which a monostatic measurement with the Rohde & Schwarz ZVA40 network analyzer was performed. The operation of the tag was based on an evaluation of the reflection coefficient of the double-ridged horn antenna DRH20 [40], in front of which the tag was placed at a distance of 20 cm. The far field for the diagonal of the horn aperture of 0.1 m in size was around 0.2 m at 3.2 GHz, so the condition for the assessment of RCS was fulfilled. The RCS response of the tag was calculated using relations given in [41] as:  
\[\sigma^{tag}=20\log\biggl{|}\frac{S_{11}{}^{tag}-S_{11}{}^{iso}}{S_{11}{}^{ ref}-S_{11}{}^{iso}}\biggr{|}\sigma^{ref}, \tag{4}\]  
where S\({}_{11}{}^{tag}\) is the reflection coefficient when the measured tag was used as a scatterer. In turn, S\({}_{11}{}^{ref}\) symbolizes the reflection coefficient when a reference metallic plate was used as a scatterer. Next, S\({}_{11}{}^{iso}\) represents the reflection coefficient of the antenna itself when no scatterer was installed and comprises residual reflection from the experiment environment. Finally, \(\sigma^{tag}\) is the RCS of the measured tag while \(\sigma^{ref}\) is the RCS of the reference scatterer, which was a rectangular metal plate with dimensions of a \(\times\) b = 45 \(\times\) 30 mm\({}^{2}\) (similar to those of the measured tag) and a thickness of 0.3 mm. The analytical formula for the reference scatterer RCS was given in [42] as:  
\[\sigma^{ref}=4\pi\frac{a^{2}b^{2}}{\lambda^{2}}, \tag{5}\]  
where \(\lambda\) is the signal wavelength in free space. The monostatic measurement arrangement made it possible to avoid angle-dependent formulas for reference scatterers and to eliminate the influence of the mutual coupling between the transmitting and receiving antennas in the bistatic measurement. A frequency sweep of the vector network analyzer was performed over a frequency range of 1.5 GHz (2.5 to 4 GHz) in order to detect the RCS resonant peaks that served to distinguish tag peaks. However, resonant peaks represented the frequency shift in the RCS response of the tag, which depended on the energy input given by the generator consequently from the voltage across the varactor diode while supposing that the transmission loop of the WPT was placed at a distance of 10 mm. Figure 11: Measurement setup in an anechoic chamber: (**a**) front view of RFID tag and measuring antenna; (**b**) back view of RFID tag and WPT loop.