## 2 Main Blocks for Wirelessly-Powered Cage System
### Coil Design and Optimization
#### 2.1.1 Coil Optimization for Conventional Two-/Three-/Four-Coil Inductive Links
Depending on the application, the coil separation between \(L_{2}\) and \(L_{3}\) (\(z_{23}\)), the nominal load resistance (\(R_{\text{L}}\)), and the source resistance (\(R_{\text{s}}\)) are also determined. In the two-coil optimization procedure, \(k_{23}Q_{2}Q_{3}\) should be maximized to achieve the maximum \(\eta_{\text{2-coil}}\) based on (1). The optimum \(k_{23}\), \(Q_{2}\), and \(Q_{3}\) can be derived by the proper outer and inner diameter of Tx coil, inner diameter of Rx coil, and number of turns for Tx and Rx coils at given design constraints [8]. The three-coil link optimization procedure maximizes \(\eta_{23}\) and \(Q_{4}\) in (2), and additionally adjust \(k_{34}\) in the Rx to provide the maximum PTE, \(\eta_{\text{3-coil}}\). A more detailed flow chart is discussed in [9]. In this optimization procedure, the additional \(L_{3}\) coil in the Rx plays the role of an impedance-matching circuit, which can convert an arbitrary \(R_{\text{L}}\) to \(R_{\text{L,PTE}}\) for optimal PTE compared to the conventional two-coil link. In other words, the reflected load on the Tx can be adjustable for maximizing the PTE if the designer can choose the suitable \(k_{23}\) and \(k_{34}\) in the design of a three-coil link. As shown in Figure 5 which shows the exemplar designs of two- and three-coil inductive links, the three-coil link can maintain the maximum PTE by adjusting \(k_{34}\) while the two-coil link only reaches the optimal PTE for a specific \(R_{\text{L}}=200\)\(\Omega\)[9]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{3}{c}{**Inductive Link Configurations**} \\ \cline{3-4}  & & **2-Coil** & **3-Coil** & **4-Coil** \\ \hline \multirow{5}{*}{**Application Conditions**} & Size constrain & \(\surd\) & \(\times\) & \(\times\) \\  & Strong coupling (\(k\)) & \(\surd\) & \(\surd\) & \(\times\) \\  & Weak coupling (\(k\)) & \(\times\) & \(\surd\) & \(\surd\) \\  & Large PDL (small \(R_{\text{s}}\)) & \(\surd\) & \(\surd\) & \(\times\) \\  & Small PDL (large \(R_{\text{s}}\)) & \(\times\) & \(\times\) & \(\surd\) \\  & \(k\) variation w/small \(R_{\text{s}}\) & \(\surd\) & \(\surd\) & \(\times\) \\  & \(k\) variation w/large \(R_{\text{s}}\) & \(\times\) & \(\times\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between two-, three-, and four-coil inductive links. Figure 4: The lumped circuit model for (**a**) two-coil, (**b**) three-coil, and (**c**) four-coil inductive links. The four-coil link is sometimes very useful especially for large coil distance between the Tx and Rx and the large source impedance, \(R_{\rm s}\), since it provides the additional degree of freedom on the Tx side. Therefore, the four-coil link is widely implemented in the high carrier frequency applications because \(R_{\rm s}\) in the PA is typically increased in the higher frequency. The four-coil link can tolerate the variations in \(k_{23}\) caused by the coil separation varying and maintain the high PTE by keeping \(k_{12}\) large. The four-coil link optimization maximizes the individual parameters of \(k_{23}Q_{2}Q_{3}\), \(Q_{1}\), \(Q_{4}\), \(k_{12}\) as similar in the two- and three-coil link optimization. Then, the optimal \(k_{34}\) is chosen to provide the maximum PTE as discussed in [9]. The optimization geometries of two-, three-, or four-coil links should satisfy the specific absorption rate (SAR) limit which can be verified by a field solver. If the resulted design cannot satisfy the SAR limit, the designer needs to modify the design constraints and perform the optimization procedure again. The segmented coil design in [10] helps to reduce the average SAR while the loss of the overall link is decreased by using a segmented Tx coil. In Figure 6, the segmented coil shows a more uniform E-field distribution compared to a normal coil with the same geometry, resulting in the reduced peak E-field. Therefore, more Tx power is allowable under the same tissue environment and SAR limit.