## 1 Introduction
On the other hand, other works have been developed with the purpose to provide simplified methods, often analytical, to reproduce the real MOSFET behavior. In this case, the accuracy of the approach is partially sacrificed to obtain a tool able to quickly evaluate the performances of a MOSFET. Some examples are reported in [26; 27], where, with some initial hypotheses on some of the MOSFET parameters, it is possible to have a reliable evaluation of switching losses using just the data reported on the device datasheet. In this work, the aim is to take inspiration from the simplified approaches to easily integrate the behavior of a MOSFET inside the model of a DC-DC wireless resonant converter. In this way, it is possible to quickly evaluate the impact of the electronic devices in the converter performances. An LCC-S converter has been adopted, a topology actually studied by researchers for its possibility to work with high boost voltage ratios [28]. Anyway, the proposed methodology is suitable for every kind of resonant converter. The power supply stage of resonant converters is a DC voltage combined with an inverter (made by a MOSFET's full-bridge or half-bridge), which is typically driven to provide a square wave or a Pulse Width Modulation (PWM) voltage in input to the converter. In this case, to take into account the MOSFET real behavior, its rise and fall times are considered. Due to these times, the voltage provided by the inverter to the converter acquires a trapezoidal waveform instead of a square one. This trapezoidal waveformwill be the input in the proposed converter model. The model is developed in frequency domain to make it very fast from a computational point of view. Two different commercial MOSFETs designed for power suppliers and DC-DC converters have been considered. The procedure to easily extrapolate from a MOSFET datasheet the rise and fall times will be presented. The proposed model will be compared with simulations performed in Simulink environment, where the converter behavior can be reproduced in a realistic way. Indeed, it has been proved in the literature how a SPICE environment allows for reproducing in a reliable way the datasheet information of MOSFETs [29; 30]. Typically, MOSFET SPICE models are based on the Shichman-Hodges model, and Simulink also adopts the same approach. In the text, the way to reproduce a MOSFET in a Simulink environment will be shown. The paper is organized as follows. In Section 2, the frequency domain model of the wireless resonant converter is presented, explaining how a trapezoidal input voltage can be taken into account. In Section 3, the circuital approach to model the MOSFET behavior during commutations is presented, and the way to evaluate the MOSFET rise and fall times is explained. In Section 4, the Simulink circuital scheme used to test the proposed model is shown, and a comparison between model and Simulink results is performed, calculating the resulting output voltage and output power for different values of input voltage amplitude and load resistance. These values will also be compared with the output power achievable under the hypothesis of ideal switches to understand how much the MOSFET behavior can impact on the converter performances. The way to evaluate switching losses inside the converter is presented, comparing the results with Simulink. Furthermore, the way to take into account MOSFET parasitic inductances is shown. Finally, conclusions are discussed in Section 5.