# Textile-Based Flexible Coils for Wireless Inductive Power Transmission
## 4 Fabrication
### Conductive Track Layer
The sheet resistance (\(\Omega/\square\)) of the realized conductive layer can be calculated from Equation (3) using the R\({}_{\mathrm{DC}}\) measured and the length of the conductive track, \(l_{track}\), from the CAD software used to produce the printing screens is 2417 mm. The manufacturer of the conductive paste recommends a cured layer thickness, \(t_{cRX}\), of 18 \(\upmu\)m to achieve optimal sheet resistance. The thickness of a printed conductive layer is greater than the recommended value in this paper because the minimum DC resistance was desired. Consequently, a mathematical theoretical sheet resistance is calculated as \(R_{sheetCal}=R_{sheetRec}\times t_{cRec}/t_{c}\), where \(t_{c}\) is the average thickness of the conductive layer measured using the non-contact method. These theoretical sheet resistances, \(R_{sheetCal}\), can be compared with the practical sheet resistance \(R_{sheet}\) to verify that the sheet resistance on the samples was as expected. The thicknesses, theoretical sheet resistance, practical sheet resistance, and DC resistance of the conductive layer are listed in Table 1, each cured sub-layer has two printed deposits. The results are based on the measurements of five different samples. In Table 1, the thicknesses of the overall layer, which are comprised of eight sub-layers, are approximately 5% less than twice the thickness of layers with four sub-layers. This means that the thickness of upper sub-layers is less than the lower sub-layers due to the reduced separation between substrate and screen mesh when the upper sub-layers are printed. As more sub-layers of conductive track are printed the thickness of the entire conductive layer is increases and the standard deviation is reduced, and consequently the surface roughness and deviation of the DC resistance are also reduced. By comparing the theoretical sheet resistance, it can be observed that the practical value was higher than expected on all samples, due to the mix of different resistivities between the conductive binder and silver particles. Measured values of DC resistances of printed coils with four different numbers of conductive sub-layers are shown in Figure 6. They are compared with the theoretical calculation of DC resistance the conductors with given thickness have, the values of thickness and resistances are calculated based on 10 measurements of three different samples of each number of sub-layers. By adding up to eight conductive sub-layers, a conductive layer of approximately 224 \(\upmu\)m thickness was printed to achieve a nominally 1 \(\Omega\) DC resistance. The relationship between DC resistance and the thickness of the conductive layer is a continuous function from the minimal thickness to the maximal. The practical DC resistance is within \(-15\%\) to +10% of the theoretical calculation because of the variation of the thickness of printed layer in different areas due to the process used. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Quantity** & **Value for 4 Sub-Layers** & **Value for 8 Sub-Layers** \\ \hline \(t_{c}\) & Thickness of conductive layer & 116 \(\upmu\)m \(\pm\) 13\% & 224 \(\upmu\)m \(\pm\) 11\% \\ \(R_{\mathrm{DC}}\) & Measured DC resistance & 2.10 \(\Omega\) \(\pm\) 25\% & 1.05 \(\Omega\)\(\pm\) 5\% \\ \(R_{\mathrm{DC}}\) & Theoretical DC resistance & 2 \(\Omega\) & 1 \(\Omega\) \\ \(R_{sheet}\) & Measured sheet resistance & 3.91 m\(\Omega/\square\) & 1.97 m\(\Omega/\square\) \\ \(R_{sheetCal}\) & Calculated sheet resistance & 3.10 m\(\Omega/\square\) & 1.61 m\(\Omega/\square\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thickness and resistance characteristics of printed coils.