## 3 Flexible Substrate Antenna Design
### Property Examination  
After the selection of the conductive and substrate materials, the next step is to analyze the properties of the selected materials. The propagation and loss properties of the dielectric substrate need to be known for the prospective material before it is implemented as the substrate of the antenna. For this purpose, the properties of the conductive material and the polymers--PET, PTFE Teflon, and PVC sheets--are listed in Table 2. Results indicate that the PTFE Teflon sheet with a thickness of 100 \(\upmu\)m has the highest density, temperature CTE, and shrinking capability, at 150\({}^{\circ}\) C, and the lowest dielectric strength, dissipation factor, and moisture absorption capability. This establishes Teflon as a good choice for a moisture- and thermal-resistant polymer material. The next substrate, PET with a thickness of 70 \(\upmu\)m, possesses good physical and electrical properties, such as high tensile and dielectric strength and low dissipation factor, making it suitable for highly deformational applications.  
Flexible PVC is a low-cost material with high strength, and is formed by the addition of compatible plasticizers to PVC to lower the crystallinity of the material. It has very good resistance to ultraviolet (UV) radiation and is non-reactant to various organic materials, such as crude oil at high temperatures. Comparatively, it has the worst physical properties, such as the lesser ability to withstand high pressure and deformability. Hence, these three polymer substrates, in terms of their ability to withstand high bending, can be placed in the order of PET, then PTFE, and PVC in the lowest position. Classification in terms of thermal properties would resort this order to PVC, then PET, and then PTFE, with Teflon at the lowest position. The implications of certain curvatures on these materials may result in additional impacts that influence the use of one of these polymers as the selected substrate for the antennas. As previously discussed in the first part of this article, the bending of the antenna with a flexible polymer substrate has the greatest impact on its resonant frequency, \(S\)-parameters, and radiation efficiency. Figure 4 shows the actual PET, Teflon, and PVC polymer sheets used as the substrates in fabricating our proposed flexible antenna design. After the properties of the polymer substrates and the conductive and substrate material are tested, the next step is to develop the antenna's shape and design.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Substrate**} & \multirow{3}{*}{**Model/ Thickness**} & \multirow{3}{*}{**Density**} & \multirow{3}{*}{**Transile Strength**} & \multirow{3}{*}{**Tensile Strength**} & \multirow{3}{*}{**Modulus**} & \multirow{3}{*}{**Dielectric Constants**} & \multirow{3}{*}{**Dielectric Constant**} & \multirow{3}{*}{**Dielectric Constant**} & \multirow{3}{*}{**Dielectric Constant**} & \multirow{3}{*}{**Dielectric Constant**} & \multirow{3}{*}{**CTE-15 \({}^{\circ}\)C} & \multirow{3}{*}{**Moisture Absorption (\%)**} & \multirow{3}{*}{**Shrinkage (\%)**} \\  & & & & & & & & & & & & \\  & & & & & & & & & & & \\  & & & & & & & & & & & \\ \hline \multirow{3}{*}{**PET**} & Melinex & 401 & & & & & & & & & & \\  & Polyester & 70 \(\upmu\)m & & & & & & & & & \\ \hline \multirow{3}{*}{**PTE**} & Teflon & Teflon & & & & & & & & & & \\  & 100 \(\upmu\)m & 2.1 & 3.9 & 65 & 2.70 & 285 & 0.0002 & to & to & to \\  & & & & & & & & & & & \\  & & & & & & & & & & & \\  & & & & & & & & & & & \\ \hline \multirow{3}{*}{**PVC**} & Flexible & PVC-O & 1.4 & 2.2 & 217 & 3.70 & 635 & 0.04 & to & to & to \\  & & 110 \(\upmu\)m & & & & & & & & 7 & 1 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Properties of flexible polymers: PET, PTFE, PVC.