## 3 Design Procedure and Simulation Results  
The procedure for designing the 3-coil inductive link is shown in Figure 3b. Firstly, the procedure begins with optimizing the design parameters that aids in achieving a high PTE. The external and implantable coils of the 3-coil inductive link is designed using the obtained optimized parameters at 13.56 MHz and 40.68 MHz to investigate the effects of low and high ISM band frequencies on the human tissue model. This iterative design procedure is carried out by the high frequency structure simulator (HFSS) and the input power is set to 1 W.  
_Step 1: Assign Design Constraints:_ The implant size, operating frequency, and distance between the coils are the main constraints to design the 3-coil inductive link. These design constraints are assigned and optimized based on the application and printed circuit board (PCB) fabrication process. Figure 3: (**a**) Orientation of the external and implantable coils; (**b**) Flowchart of the optimization procedure of a 3-coil inductive link. Step 2: Assign the Initial Parameters:The initial parameters which are assigned and optimized for designing the 3-coil inductive link are copper wire width (\(W_{L_{1}-L_{3}}\)), copper wire height (\(H_{L_{1}-L_{3}}\)), spacing between the wires (\(S_{L_{1}-L_{3}}\)), number of turns of a coil (\(N_{L_{1}-L_{3}}\)), and inner radius of the coil (\(r_{inL_{1}-L_{3}}\)). The initial parameter \(H_{L_{1}-L_{3}}\) are assigned considering the PCB fabrication constraints. Step 3: \(M_{ab}\) and \(Q_{ab}\):The \(M_{ab}\) and \(Q_{ab}\) of the coils play a vital role in achieving a higher PTE. The \(M_{ab}\) and \(Q_{ab}\) depend on the initial parameters and therefore optimizing the initial values lead to a high \(M_{ab}\) and \(Q_{ab}\). The \(C_{1}\), \(C_{2}\) and \(C_{3}\) are 100 pF, 423 pF, and 300 pF respectively, and the resistors \(R_{S}\) and \(R_{L}\) are set to 50 \(\Omega\) each. If the resulting \(M_{ab}\) is low and \(Q_{ab}\) lies outside the expected range, then the initial parameters are optimized further to achieve a high PTE [2; 28]. At \(f_{0}\) = 13.56 MHz, \(M_{ab}\) = 905.1 nH and \(Q_{ab}\) = 25.3 and at \(f_{0}\) = 40.68 MHz, \(M_{ab}\) = 2516.6 nH and \(Q_{ab}\) = 15. Figure 4a,b shows the \(M_{ab}\) with respect to \(d_{ab}\) at 13.56 MHz and 40.68 MHz and Figure 4c,d shows the \(Q_{ab}\) with respect to resonance frequency at 13.56 MHz and 40.68 MHz. Step 4: PTEThis step discusses the effects of \(W_{L_{3}}\) and \(N_{L_{3}}\) on PTE as one of the applications of this paper is to design an implantable coil less than 2 cm. The PTE is evaluated based on the optimal design parameters obtained above and for a low PTE, _step-_2 is repeated iteratively as optimizing the initial parameters ameliorates the \(M_{ab}\) and \(Q_{ab}\), thereby increasing the PTE of the system. At perfect alignment, the maximum PTE achieved with \(W_{L_{3}}\) = 0.3 mm and \(N_{L_{3}}\) = 10 for 10 mm \(d_{ab}\) and 13.56 MHz is 53.3%. The same iterative procedure is repeated at 40.68 MHz and at perfect alignment, the system achieved a maximum PTE of 70.8% with \(W_{L_{3}}\) = 0.8 mm and \(N_{L_{3}}\) = 6. Figure 5a,b show the change in PTE with respect to distance at 13.56 MHz and 40.68 MHz respectively. The results show that the PTE decreases gradually with increasing \(d_{ab}\). Table 2 presents the final optimized values of the design examples at 13.56 MHz and 40.68 MHz. Generally, the PTE declines under misalignment conditions, so, the system is also analyzed under lateral and/or angular misalignments. Figure 4: (**a**) Mutual inductance vs. distance between the coils at 13.56 MHz; (**b**) Mutual inductance vs. distance between the coils at 40.68 MHz; Q-factor vs. resonance frequency at (**c**) 13.56 MHz operating frequency; (**d**) 40.68 MHz operating frequency. _Lateral Misalignment_: The implantable coil is laterally displaced from a perfectly aligned position of 0 mm to 10 mm. The system has been simulated at laterally displaced misalignment positions of 5 mm and 10 mm.