## 3 Design Procedure and Simulation Results
At 13.56 MHz with a maximum misaligned distance of 10 mm, the PTE is 30.2% whereas at 40.68 MHz with a maximum misaligned distance of 10 mm, the PTE is 49.2%. 2. _Angular Misalignment_: In order to validate the effects of angular misalignment on the PTE, the implantable coil is rotated through angles 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) relative to the external coil. At 13.56 MHz, when \(\alpha\) = 15\({}^{\circ}\), the PTE is 52.3% and with the increase of angular misalignment the PTE declines sharply, and the PTE is 29.4% at \(\alpha\) = 60\({}^{\circ}\). At 40.68 MHz, when \(\alpha\) = 15\({}^{\circ}\), the PTE is 65.1% and at \(\alpha\) = 60\({}^{\circ}\), the PTE is 42.1%. 3. _Combination of Lateral and Angular misalignment_: Here, the PTE is tested for misalignment angles 0\({}^{\circ}\) to 60\({}^{\circ}\) along with laterally displaced positions 1 mm to 10 mm. At 60\({}^{\circ}\) angular rotation and 10 mm lateral displacement, the PTE at 13.56 MHz and 40.68 MHz are 39.1% and 57.6% respectively. The overall PTE under perfect alignment, lateral and/or angular misalignments are shown in Figure 5c,d. The proposed geometry of the coils are shown in Figure 6.  
_Step 5_: _SAR at Tissue Medium_: The SAR is a number that measures the rate at which energy is absorbed by the human body when exposed to electromagnetic radiations. According to FCC, a SAR level of less than 1.6 W/kg is considered safe and therefore it is important to make sure that the frequency absorbed by human tissue does not exceed this level. The SAR is defined by [10; 29]  
\[SAR=\sigma|E|^{2}/\rho\]  
where \(\sigma\) is the tissue conductivity, \(E\) is the intensity of electric field, and \(\rho\) is the human tissue density. The SAR cannot be measured experimentally and therefore the SAR of the system is simulated at 13.56 MHz and 40.68 MHz using HFSS. The implantable coil is usually placed in less than 10 mm of depth in human tissue. So, to analyze the design in this realistic environment, the human tissue model is formed using three consecutive layers of 1 mm skin, 2 mm fat and 7 mm muscle. Table 3 shows the dielectric properties of the layers to be used for constructing the model. At 13.56 MHz, the PTE and SAR are 48.2% and 0.91 W/kg respectively, whereas at 40.68 MHz, the PTE and SAR are 55.7% and 5.0 W/kg respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coils** & **PCB Parameter** & \(f_{0}\) **= 13.56 MHz** & \(f_{0}\) **= 40.68 MHz** \\ \hline \multirow{6}{*}{\(L_{1}\)} & \(r_{intL_{1}}(\text{mm})\) & 25.5 & 35.95 \\  & \(r_{outL_{1}}(\text{mm})\) & 27.5 & 38.05 \\  & \(W_{L_{1}}(\text{mm})\) & 2 & 2.1 \\  & \(H_{L_{1}}(\text{mm})\) & 0.07 & 0.07 \\  & \(N_{L_{1}}\) & 1 & 1 \\ \hline \multirow{6}{*}{\(L_{2}\)} & \(r_{intL_{2}}(\text{mm})\) & 4.75 & 5.07 \\  & \(r_{outL_{2}}(\text{mm})\) & 22.45 & 23.42 \\ \cline{1-1}  & \(W_{L_{2}}(\text{mm})\) & 1.5 & 0.85 \\ \cline{1-1}  & \(H_{L_{2}}(\text{mm})\) & 0.07 & 0.07 \\ \cline{1-1}  & \(S_{L_{2}}(\text{mm})\) & 1.2 & 0.9 \\ \cline{1-1}  & \(N_{L_{2}}\) & 6 & 10 \\ \hline \multirow{6}{*}{\(L_{3}\)} & \(r_{intL_{3}}(\text{mm})\) & 0.45 & 0.45 \\ \cline{1-1}  & \(r_{outL_{3}}(\text{mm})\) & 9.95 & 9.95 \\ \cline{1-1}  & \(W_{L_{3}}(\text{mm})\) & 0.3 & 0.8 \\ \cline{1-1}  & \(H_{L_{3}}(\text{mm})\) & 0.07 & 0.07 \\ \cline{1-1}  & \(S_{L_{3}}(\text{mm})\) & 0.62 & 0.65 \\ \cline{1-1}  & \(N_{L_{3}}\) & 10 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimized geometries for proposed coil designs. Though at 40.68 MHz the PTE is high, the SAR had crossed 1.6 W/kg, the limit designated by the FCC and hence, it is unsafe and causes tissue damage. Figure 7a,b shows the change in PTE with respect to the distance between the coils at 13.56 MHz and 40.68 MHz respectively. For an input power of 1 W, the simulated SAR value at 13.56 MHz and 40.68 MHz are shown in Figure 7c,d respectively.