## 6 LLC resonant Converter Drive  
As mentioned in section 2, the control strategy of the LLC resonant converter is based on the Frequency Modulation (FM) of the gate input signals of primary bridge switches. If the primary stage is a half bridge, the leg is driven in a complementary way with \(\sim\)50% duty cycle, with adequate deadtime, as defined in Equation (10). In the case of a full bridge on the primary stage, the second leg is driven at the opposite of the first one. If the rectifier is made up of controllable switches, i.e., it is a synchronous rectifier, it also needs an accurate driving circuit that can minimize power dissipation by bypassing the body diodes for the majority of each conduction period. Normally, the synchronous rectifier is controlled by a smart IC driver that senses the drain to the source voltage of each rectifier MOSFET to determine the source to drain current and turn on each gate rapidly at the start of each conduction cycle and turn off in close proximity to the zero current transitions for each branch of the output rectifier circuit. The switching frequency, \(f_{sw}\), is changed in order to stabilize the output voltage to the desired value thanks to a closed loop control whose simple block scheme is reported in Figure 3. The relationship between the switching frequency and the output voltage is defined in Equation (4), since \(f_{sw}=f_{n}f_{r}\). Considering the gate drive losses, for a common driver, they can be estimated according to the equation:  
\[P_{d}=C_{g}V_{D}^{2}f_{sw} \tag{11}\]  
This equation shows a linear relationship between the driver losses and the switching frequency. For this reason, increasing the switching frequency in modern applications requires the optimization of the driving technique to avoid more power loss in the  
Figure 3: LLC converter and its closed loop control scheme. driver [84, 85]. Moreover, another important aspect for the gate drive is the presence of parasitic components in the circuit. As the frequency is increased, the variation of voltage and current becomes faster, involving the dynamic of stray capacitances and inductances of the circuit. Phenomena like false trigger, voltage overshoot and ringing can occur, thus increasing the total power dissipation on the driver and causing the gate-source voltage to have an unexpected behavior, which can compromise the correct operations of the switch [86, 87]. Overall, during the last years, some different works concerning the optimal driving of MOSFETs and GaN HEMTs have been published; in some cases, novel driver topologies have been developed [88, 89, 90]. Thus, the only way to achieve very high switching frequencies and keep power losses low is using resonant drivers, as shown in [84, 85, 91, 92]. This technique exploits the resonance between the input capacitance of the power device and an external small inductor in order to create a series resonance, as shown in Figure 4. By modulating the driver's p-MOSFET and n- MOSFET in an appropriate way, it is possible to control the resonance current flowing through the inductor to obtain an impulsive current that turns on and off the gate of the power device. At the same time, the commutations of the driver's devices are soft and the switching power losses are heavily reduced. In fact, the power dissipation of the driver circuit can be reduced at:  
\[P_{d}=kC_{g}V_{D}^{2}f_{sw} \tag{12}\]  
where \(k\) is a constant depending on the characteristic impedance of the resonant circuit and gate resistance; it is less than 1 [90]. With the aim of working with GaN HEMTs at very high switching frequencies, there are some commercial drivers recommended by the manufacturers to achieve good performances in terms of rise and fall time, maximum propagation delay, thermal shutdown and jitter, both for low-side applications and half bridge [93, 94, 95]. While the low-side driving is quite easy to realize, the high-side requires more care, especially in terms of noise coupling and isolation.