## 5 Simulation Results and Discussion  
A Differential Evolution algorithm is proposed to obtain the best values for the primary and secondary inductances, aiming to maximize the efficiency of the system. In Figure 17c, the curve of the efficiency of the best individual in relation to the number of generations of the Differential Evolution is presented. Note that the algorithm showed rapid convergence to the global maximum of 94.79% for the PS WPT stage efficiency. The initial population was generated within a predefined range. Figure 17a shows the distribution of the initial individuals. As expected, the position of the individuals was dispersed, since the population was randomly generated. Figure 17b shows the individual distribution after performing all iterative processes. Note that the position of all individuals converged to the global maximum, where \(L_{2}\) was equal to 430.2 nH. Since the efficiency dependency of \(L_{1}\) was neglected, the \(L_{1}\) values were distributed throughout the defined range. As mentioned before, the WPT circuit parameters were sized considering an output power of 1 W. However, aiming to evaluate the practical non-idealities and the effective  
Figure 17: Differential Evolution performance evaluation. (**a**) First generation population. (**b**) Last generation population. (**c**) Efficiency improvement across generations. \begin{table}
\begin{tabular}{l c} \hline \hline
**Description** & **Value** \\ \hline DC supply voltage (\(V_{\mathrm{CC}}\)) & 12.0 V \\ RE choke (\(RFC\)) & 1.0 mH \\ Choke resistance (\(R_{FC}\)) & 0.5 \(\Omega\) \\ Shunt capacitance (\(C_{\mathrm{c}}\)) & 25.9 pF \\ Series inductance (\(L_{\mathrm{r}}\)) & 12.4 \(\upmu\)H \\ Series resistance (\(R_{\mathrm{c}}\)) & 6.8967 \(\Omega\) \\ Series capacitance (\(C_{\mathrm{c}}\)) & 14.13 pF \\ Match capacitance (\(C_{\mathrm{m}}\)) & 63.3 pF \\ Primary capacitance (\(C_{\mathrm{i}}\)) & 219 pF \\ Primary coil resistance (\(R_{\mathrm{i}}\)) & 0.3381 \(\Omega\) \\ Primary coil inductance (\(L_{\mathrm{i}}\)) & 610.0 nH \\ Secondary capacitance (\(C_{\mathrm{2}}\)) & 320.2 pF \\ Secondary coil resistance (\(R_{\mathrm{2}}\)) & 0.2328 \(\Omega\) \\ Secondary coil inductance (\(L_{\mathrm{2}}\)) & 430.2 nH \\ Capacators’ ESR & 0.050 \(\Omega\) \\ Switch RDS\({}_{\mathrm{m}}\) (\(S\)) & 0.025 \(\Omega\) \\ Load resistance (\(R_{\mathrm{L}}\)) & 12.96 \(\Omega\) \\ Mutual inductance (M) & 128.1 nH \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Circuit parameters. losses in each stage depicted in Figure 16, a 1 W input power was imposed for the Class-E amplifier. Thus, the currents and voltages across the circuit elements, as well as the output power were expected to be lower than those previously calculated. Before analyzing the PS WPT circuit, it is reasonable to check the operation of the Class-E circuit. Looking at Figure 18, the input current \(I_{IN}\) is depicted in (a). As observed, its value was slightly superior to 80 mA, draining about 1 W from the DC power source. In Figure 18b,c, the \(I_{e}\) and \(C_{m}\) currents prove the resonance at 13.56 MHz; however, a small DC level was present, which denotes some mismatch caused by the values' divergences and dissipative elements; this behavior did not make the circuit operation unfeasible; however, it increased the switch losses due to the current peaks, a consequence of the remanent voltage noticed in Figure 18e. Figure 18d shows the C\({}_{e}\) voltage, and it is important to note its peak value, which can reach almost 150 V, being important data for a practical design. Carrying out the analysis of the circuit for the WPT part, it can be concluded that the current in the primary inductor added to the current in the primary capacitor resulted in the input current \(I_{1}\). Figure 19a,b illustrate the respective primary inductor and capacitor currents over time. The RMS currents in \(L_{1}\) and \(C_{1}\) were 311 mA and 306 mA, respectively. The current across all secondary elements (\(I_{2}\)) is presented in Figure 19c.