## 3 The Load Adaptive Auxiliary Current Control  
### Principle  
Essentially, the ZVS realization of the main switches is to obtain a proper initial resonant current \(I_{r}\), in order to discharge the resonant capacitors to zero voltage before the main switches are turned on. Figure 3 shows the key waveforms to realize ZVS of S\({}_{1}\) and S\({}_{4}\), where \(v_{ds}\) is the drain-source voltage of a MOSFET, \(i_{d}\) is the drain current of a MOSFET, \(v_{g}\) is the gate signal, \(i_{tf}\) is the filter inductor current, \(i_{tf,l}\) is the lower envelope of \(i_{tf}\), \(i_{tf,u}\) is the upper envelope of \(i_{tf}\), and \(i_{Lr}\) is the auxiliary current. When \(i_{tf,l}<-I_{r\_min}\), \(i_{tf,l}\) can create natural ZVS (NZVS) conditions for S\({}_{1}\) and S\({}_{4}\) without the operation of auxiliary switches. When \(i_{tf,l}>-I_{r\_min}\), S\({}_{1}\) is turned on before S\({}_{2}\) and S\({}_{3}\) are turned off. The resonant inductor \(L_{r}\) is charged, resulting in the linear increase of the auxiliary current. Therefore,  
Figure 2: Control diagram of the ARSI. a proper \(I_{r}\) can be obtained with the operation of S\({}_{\rm{r1}}\). The auxiliary ZVS (AZVS) of S\({}_{\rm{1}}\) and S\({}_{\rm{4}}\) is realized. In order to fully discharge the resonant capacitors, the minimum initial resonant current must meet the following requirement:  
\[I_{r\_\_\_\_\_\_\_\_\_\_}\geq\frac{2C_{r}V_{s}}{t_{dead}}. \tag{1}\]  
The principle of ARSI without LC filter was introduced in [21]. The initial resonant current is the difference between the auxiliary current and the output current. Namely, the required auxiliary current is the sum of the output current and initial resonant current. As for the ARSI with LC filter, the auxiliary current is the sum of the filter inductor envelope current and the initial resonant current, which is different from that of the ARSI without LC filter. The filter current ripple can be calculated as follows:  
\[\Delta i_{Lf}=\frac{V_{s}-v_{o}}{L_{f}}DT_{s}=\frac{(2-2D)DV_{s}T_{s}}{L_{f}}, \tag{2}\]  
where \(v_{o}\) is the output voltage, \(D\) is the duty ratio, and \(T_{s}\) is the switching period. The upper and lower envelopes of the filter inductor current can be calculated as follows:  
\[i_{Lf\_\_\_\_}=i_{o}+\frac{1}{2}\Delta i_{Lf}=i_{o}+\frac{(1-D)DV_{s}T_{s}}{L_{ f}} \tag{3}\]  
\[i_{Lf\_\_\_}=i_{o}-\frac{1}{2}\Delta i_{Lf}=i_{o}-\frac{(1-D)DV_{s}T_{s}}{L_{ f}}. \tag{4}\]  
The ZVS realization of S\({}_{\rm{1}}\) and S\({}_{\rm{4}}\) is related to the lower envelope of the filter inductor current \(i_{Lf\_\_\_}\) shown in Figure 3. Similarly, the ZVS realization of S\({}_{\rm{2}}\) and S\({}_{\rm{3}}\) is related to the upper envelope of the filter inductor current \(i_{Lf\_\_\_}u\). Table 1 shows the ZVS types under different load conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Switch** & \(i_{Lf\_\_\_}1\) & \(<-I_{r\_\_\_\_\_}min\) & \(i_{Lf\_\_\_}1>-I_{r\_\_\_\_\_}min\) & **Switch** & \(i_{Lf\_\_\_}1<I_{r\_\_\_\_}min\) & \(i_{Lf\_\_\_}1>I_{r\_\_\_\_\_\_}min\) \\ \hline S\({}_{\rm{1}}\) \& S\({}_{\rm{4}}\) & NZVS & AZVS (S\({}_{\rm{r1}}\)) & S\({}_{\rm{2}}\) \& S\({}_{\rm{3}}\) & AZVS (S\({}_{\rm{r2}}\)) & NZVS \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Zero-voltage switching (ZVS) types of switches under different output currents. The output current can be obtained through the current sensor. Therefore, the required auxiliary current can be calculated as follows:  
\[I_{Lrm}=\left\{ \begin{array}{ll}I_{r}+i_{Lf\_l}&forS_{r1}\\ I_{r}-i_{Lf\_u}&forS_{r2}\end{array} \right.. \tag{5}\]  
The charging rate and the discharging rate of the resonant inductor are the same because of the same voltage \(V_{s}\).