## 3 Simulation, Results, and Discussion
### Bended Structure
#### 3.2.2 Effect of the Test Tube Radius  
In addition to its quick and easy handling, the test tube's parallel position configuration enabled us to investigate more possible structure cases according to the tube radius, for optimization purposes. However, the normal configuration [41] allowed only a single radius case (r = 0.75 mm), since the tube was inserted through a hole drilled in the substrate. Figure 9 presents a CST simulation validated by Ansys HFSS for a test tube of radius r = 0.75 mm. The two software S\({}_{21}\) response results at resonance were similar for different concentrations, with a 50 MHz offset (Figure 9a,b). A sensor sensitivity of 1.7 kHz and a quality factor of 88.35% were achieved using CST. These results were close to those obtained at HFSS 1.5 kHz and 62.25%, respectively. For this case, the device operates at around 2.4 GHz. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bending Radius** & \begin{tabular}{c} **Resonant Frequency** \\ **0\% (MHz)** \\ \end{tabular} & \begin{tabular}{c} **Resonant Frequency** \\ **100\% (MHz)** \\ \end{tabular} & \
\begin{tabular}{c} **\Delta fr** \\ **(MHz)** \\ \end{tabular} &
\begin{tabular}{c} **Maximum Q Factor** \\ **Maximum Q Factor** \\ \end{tabular} \\ \hline R = 10 mm & 2295.6 & 2046.3 & 249.3 & 38.6 \\ R = 7.5 mm & 2225.6 & 1936.4 & 289.2 & 34 \\ R = 5 mm & 1990.7 & 1596.3 & 394.5 & 27.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Effect of bending radius on the sensitivity Q factor of the bent sensor. Figure 8: Designed sensor in the CST interface: (**a**) bended structure; (**b**) \(\mathbf{S_{21}}\) response of water–ethanol mixtures for different bending radii and concentrations. Similarly, as shown in Figure 10, the sensitivity increased almost 2.5-fold compared to the case with r = 0.75 mm, while the quality factor (which has a direct link with the imaginary component of the permittivity) decreased by 15%. The CST and HFSS results curves almost overlap. The resonant frequency of this case decreased, averaging 2.2 GHz. For r = 2.5 mm, an improvement in the performance of the proposed sensor was noticed. The frequency band decreased and reached an average value of 2 GHz at resonance, with stable sensitivity and a slight decrease in the quality factor. In addition, the CST- and HFSS-simulated S\({}_{21}\) results are quite close--almost superimposed (Figure 11). Figure 10: Simulated results: (**a**) S\({}_{21}\) response and (**b**) resonant frequency and Q factor for different mixture water concentrations, with r = 1.5 mm. Figure 9: Simulated results: (**a**) **S\({}_{21}\)** response and (**b**) resonant frequency and Q factor for different mixture water concentrations, with r = 0.75 mm. For r = 3.75 mm (Figure 12), the simulation results were closer, and almost overlapped at lower concentrations. On the other hand, they moved slightly further apart at other concentrations, and a remarkable increase in sensitivity compared to the previous cases was observed. In the same way, a slight decrease in the quality factor was observed. The resonant frequency decreased until it reached 1.8 GHz. In the same way, for r = 5 mm (Figure 13), the sensitivity was improved by more than 3 times relative to that of r = 0.75 mm, with a decrease in the quality factor by 30%. The S\({}_{21}\) HFSS validation results were close to those obtained by CST for different concentrations of water in the mixture. The resonant frequency reached values of around 1.4 GHz. Figure 11: Simulated results: (**a**) S\({}_{21}\) response and (**b**) resonant frequency and Q factor for different mixture water concentrations, with r = 2.5 mm. Figure 12: Simulated results: (**a**) S\({}_{21}\) response and (**b**) resonant frequency and Q factor for different mixture water concentrations, with r = 3.75 mm. According to Table 3, the accuracy and reliability of the proposed device was improved through five measurements for different tube radii.