## 4 Discussion  
In this section, the performances of the proposed model are compared with simulations performed in the Simulink environment. The design of a resonant converter is typically performed by selecting the values of the inductances and the desired resonant frequency. Then, capacitors are designed to resonate with the inductances. For LCC-s converter, the capacitors can be designed as follows:  
\[C_{f}=\frac{1}{\omega_{o}^{2}L_{f}};\ C_{p}=\frac{1}{\omega_{o}^{2}\big{(}L_{ p}-L_{f}\big{)}};\ C_{s}=\frac{1}{\omega_{o}^{2}L_{s}} \tag{17}\]  
In Table 1, the electric features of the LCC-s converter are reported. A standard in high-frequency Wireless Power Transfer is 6.78 MHz [44; 45]. At this frequency, inductances can be easily realized in air, so switching losses are mainly responsible for the performance drop in the converter. The working frequency has been set near, but not exactly, in resonant conditions. In this way, the output voltage is a function of the load resistance (while in resonance the output voltage value is independent by the load); at the same time, FHA can be still applied since \(f_{sw}\) is very similar to \(f_{o}\). A high coupling  
Figure 6: Flowchart representing the main steps to build the proposed model. coefficient \(k\) has been chosen (compared with the typical values for wireless power transfer). This can be assumed since, as can be seen in Table 1, the inductances of the wireless coils are very low, so it is easy to stack them, limiting the stray magnetic field. These kinds of values can be achieved with very limited distances between coils (few millimeters), typical of the electronic devices' charging applications [46; 47]. Obviously, lower \(k\) values need to be considered if other applications are taken into account. Note that the filter inductance \(L_{f}\) can be easily realized in air (since the target value is very low). The LCC-s converter has been reproduced in Simulink using Simscape library. The electric scheme is shown in Figure 7.  
The rectifier circuit has been reproduced with an equivalent resistance \(R_{e}\). The neglection of the rectifier is allowed since this converter works near the resonance condition. In this way, it is possible to evaluate the impact of MOSFETs' switching losses in the converter performances, which is the purpose of this work, without influences from other contributions. For the same reason, the parasitic resistances associated with the reactive components in the circuit have also been neglected. The MOSFETs have been reproduced using the N-Channel MOSFET block, which is programmed with the Shichman-Hodges model. This block gives the possibility to insert parameters directly taken from a datasheet. In particular, the transients during MOSFET commutations are reproduced using the values of parasitic capacitances provided in the datasheet. Producers typically provide the functions of parasitic capacitances with \(v_{DS}\). These functions can be inserted in the N-Channel MOSFET block as look-up tables. Concerning instead the proposed models, the MOSFETs' transients are reproduced evaluating the rise and fall times as shown in Section 3. Two commercial MOSFETs have been taken in consideration, a IPPB09N03L from Infineon and a PSMN1R440 YLD from Nexperia (datasheets available in [48; 49]), to compare their impact on converter performances. With the values provided in the datasheets and reported in Table 2, rise and fall times for the two MOSFETs can be evaluated with (16). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Quantity** & **Symbol** & **Value** \\ \hline Primary side inductance & \(L_{p}\) & 490 nH \\ Secondary side inductance & \(L_{s}\) & 490 nH \\ Filter inductance & \(L_{f}\) & 60 nH \\ Coupling coefficient & \(k\) & 0.85 \\ \hline Resonant frequency & \(f_{o}\) & 6.78 MHz \\ Working frequency & \(f_{sw}\) & 0.95\(f_{o}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electric features of LCC-s converter. Figure 7: Electric scheme of LCC-s converter reproduced in Simulink environment.