## 1 Introduction  
Wireless power transfer is actually one of the most interesting and studied techniques to transfer electric power, thanks to its possibility to strongly reduce the usage of cables for the connections between power suppliers (also called transmitters) and loads (also called receivers). The physical separation between transmitters and receivers significantly improve the versatility and the safety of the system. In addition, the extremely low necessity of magnetic materials (limited to some inductances possibly requested in the circuit) strongly reduce the problem related to magnetic losses, which typically have an important impact on the final system efficiency. With these premises, it is not a surprise to find them in a plethora of applications, such as renewable energies [1, 2, 3, 4], electric vehicles [5, 6, 7, 8, 9], underwater systems [10, 11], railways [12, 13] and DC microgrids [14, 15]. High efficiency and high-power density are the main requirements asked of these devices, so academic research in this field is actually focused in providing solutions in these directions [16; 17; 18]. The key aspect in the increase in power density is the converter working frequency. Since the reactance associated with inductors and capacitors are a function of the frequency, an increase in the working frequency allows a reduction in the inductances or capacitance values [19; 20], optimizing, in this way, their dimensions. However, the increase in working frequency typically has side effects. Firstly, high-frequency magnetic fields (especially over the MHz range) can have an impact on both electronic devices and human bodies; for this reason, specific strategies for the design of wireless converters have been proposed in the literature to limit the amount of these fields [21; 22]. Secondly, the increase in the working frequency causes a reduction in the converter efficiency; this work puts the focus on this second aspect. The converter efficiency drop is mainly due to two aspects: the first one is related to the switching losses in electronic devices (switches in particular); the second one concerns the magnetic losses in the magnetic materials of inductive components. Thinking to very high-frequency power applications (several MHz), the main problem is represented by switching losses, since inductances can be realized directly in air. Switching losses occur during the state commutation (from ON to OFF and vice versa) of electronic devices (the most used devices for high-frequency power electronics applications are the MOSFETs). Since the commutation is not instantaneous (it requires a finite time to be completed), there is a time interval in which the voltage across the device and the current flowing in it are both non-zero. Consequently, there is an amount of dissipated energy associated with each commutation. For each period, there is a total energy loss given by the sum of the energies lost in the switching on and switching off phases. Since power losses are defined as \(\text{P}_{\text{loss}}=f\text{ E}_{\text{loss}}\), the higher is the frequency, the higher are the switching power losses. Switching losses can have a strong impact in the performances of the converter, reducing the power that could be supplied to the load. For this reason, many works are available in the literature to estimate these kinds of losses. A good review is presented in [23]. On one hand, several works try to reproduce in the most accurate way as possible the behavior of MOSFETs, modeling the transients during commutations with a set of variable capacitances, which are functions of the voltage across the MOSFET itself [24; 25]. These methods achieved really good results, but the implementation of these approaches could be challenging from the computational point of view. Indeed, time-domain simulations of the converter are required, which often take a long time when variable parameters are considered.