## 4 Bending Analysis
### Effect of Bending on Reflection Coefficients S11  
The \(S\)-parameters of the designed antennas were critically analyzed to examine the effects of bending on impedance mismatch or the reflection coefficient \(S_{11}\) and the signal strength after bending. The impact of bending on the reflection coefficient of the flexible antennas operating at a different range of frequencies was examined by testing the three categories of (i) 2.2-2.5 GHz, (ii) 2.5-5.0 GHz, and (iii) greater than 5.0 GHz, where the antennas, designed on PET, PTFE, and PVC, were analyzed in the chamber for bending levels of 27 and 14 mm. The \(S\)-parameters depict the impact of the different levels of bending on the reflection coefficient in terms of signal strength and the impedance mismatch with the TL. A significant change in signal strength is caused by the bending or twisting of a flexible antenna because of the impedance mismatch with the TL or the creation of the surface waves. Although signal strength may improve after bending because of its impact on the directivity of the antenna, most of the time it actually decreases; see Figures 13-15.  
In Figure 13, when a radial curvature of 27 mm is applied over the flexible antennas operating at 2.45 GHz, compared with the flat status of the antennas, the Teflon-based antenna is highly impacted, with approx. 28% signal degradation, whereas the PET-based antenna is less impacted, with approx. 7.7% reduction in its signal strength. This degradation, although more extreme, is similar to that observed with the 14 mm bending process, where the Teflon-based antenna suffered a high 55% reduction in signal strength, and the PET-based antenna demonstrated the least degradation with 23%.  
For the experimental analysis of the flexible antennas operating at 4.25 GHz, however (Figure 14), the Teflon-based antenna suffered the least degradation. Compared with the flat status of the antennas, for the bending level of 27 mm, the Teflon substrate bore the least impact of only 14% of signal strength reduction, which simultaneously defines its impedance mismatch at 27 mm and confirms the analysis in [1]. The signal strength reduction for both the PET and PVC substrate antennas is almost similar at approx. 22%. Indeed, with the 14 mm bending, the PVC-based flexible antenna suffered an immense signal reduction of approx. 60%, whereas the Teflon substrate antenna possesses the least signal strength degradation of 25% lower than its flat status strength.  
In Figure 15, which compares the signal strengths in a flat condition for the flexible antennas operating at the higher 7.45 GHz frequency, the \(S\)-parameters illustrate that for the bending of the antennas to 27 mm, Teflon, as the substrate of the antenna, shows the least degradation with a low value of 12%. This contrasts with the PVC-based antenna, which is heavily impacted, with an approx. 50% signal reduction. However, when the bending curvature increases to 14 mm, the impact measurements are reversed, with the Teflon substrate antenna being impacted with a high 55% reduction in its signal strength. The experimental results demonstrate that, with around 9% reduction, the PVC-based antenna has the highest tolerance for the increased bending, with its comparatively low signal strength degradation and impedance mismatch being the least affected in this category. In this analysis, a PVC-based antenna was ascertained to be the most efficient for the frequency range greater than 5 GHz.