# Interleaved Boost Converter with ZVT-ZCT for the Main Switches and ZCS for the Auxiliary Switch
## 3 Basic Operating Principles
The instant \(D_{r2}\) and \(S_{a}\) are both turned on, this state comes to the end. At the same time, since \(S_{a}\) is connected in series with the resonant inductor \(L_{r}\), the current flowing through \(S_{a}\), called \(i_{\Delta a}\), is slowly increased from zero, making \(S_{a}\) turned on with zero current switching (ZCS). State 7: \([t_{6}\leq t\leq t_{7}]\). As shown in Figure 10, the main switch \(S_{1}\) is still turned on but the main switch \(S_{2}\) is still turned off but the auxiliary switch \(S_{a}\) is turned on, whereas the freewheeling diode \(D_{1}\) is still turned off but the freewheeling diode \(D_{2}\) is still turned on but the resonant diode \(D_{r1}\) is still turned off but the resonant diode \(D_{r2}\) is turned on. During this state, since \(S_{a}\) and \(D_{r2}\) are turned on, the resonant inductor \(L_{r}\) is to be magnetized. Once \(i_{Lr}=I_{L2}\), this state comes to the end. During this interval, the corresponding state equation can be expressed as follows:  
\[i_{Lr}(t)=\frac{V_{o}}{L_{r}}(t-t_{6})+i_{Lr}(t_{6}) \tag{12}\]  
Figure 10: Current flow in state 7. Figure 9: Current flow in state 6. As \(t=t_{6}\), \(i_{Lr}(t_{6})=0\), whereas as \(t=t_{7}\), \(i_{Lr}(t_{7})=l_{L2}\). Accordingly, the corresponding time elapsed is  
\[(t_{7}-t_{6})=\frac{l_{L2}L_{r}}{V_{o}} \tag{13}\]  
State 8: \([t_{7}\leq t\leq t_{8}]\). As shown in Figure 11, the main switch \(S_{1}\) is still turned on but the main switch \(S_{2}\) is still turned off but the auxiliary switch \(S_{a}\) is still turned on, whereas the freewheeling diodes \(D_{1}\) and \(D_{2}\) are turned off and the resonant diode \(D_{r1}\) is still turned off but the resonant diode \(D_{r2}\) is still turned on. During this state, the resonant capacitor \(C_{r1}\) and the parasitic capacitor \(C_{S2}\) of the main switch \(S_{2}\) resonate with the resonant inductor \(L_{r}\). Therefore, \(C_{S2}\) is discharged, \(C_{r1}\) is discharged in the opposite direction, and the resonant inductor remains demagnetized. In addition, the output capacitor \(C_{o}\) provides energy to the load. As soon as the current in \(S_{1}\) is decreased to zero, \(S_{1}\) is turned off with zero current transition (ZCT) and hence this state comes to the end. During this interval, the corresponding state equation can be represented as follows:  
\[\left\{ \begin{array}{l}i_{Lr}(t)=l_{L2}+\frac{v_{A}(t_{7})}{Z_{8}}\sin\omega _{8}(t-t_{7})-[l_{L2}-i_{Lr}(t_{7})]\cos\omega_{8}(t-t_{7})\\ \\ v_{A}(t)=Z_{8}[l_{L2}-i_{Lr}(t_{7})]\sin\omega_{8}(t-t_{7})+v_{A}(t_{7})\cos \omega_{8}(t-t_{7})\end{array} \right. \tag{14}\]  
where  
\[\omega_{8}=\sqrt{\frac{1}{L_{r}C_{A}}}\text{ and }Z_{8}=\sqrt{\frac{L_{r}}{C_{A}}} \tag{15}\]  
Accordingly, the corresponding time elapsed is as follows:  
\[(t_{8}-t_{7})=\frac{1}{\omega_{8}}\sin^{-1}\left(\frac{[i_{Lr}(t_{8})-l_{L2}]Z _{8}}{V_{o}}\right) \tag{16}\]  
State 9: \([t_{8}\leq t\leq t_{9}]\). As shown in Figure 12, the main switch \(S_{1}\) is turned off and the main switch \(S_{2}\) is still turned off and the auxiliary switch \(S_{a}\) is turned off but the auxiliary diode \(D_{a}\) is turned on, whereas the freewheeling diodes \(D_{1}\) and \(D_{2}\) are still turned off and the resonant diode \(D_{r1}\) is still turned off but the resonant diode \(D_{r2}\) is still turned on. During this state, the resonant capacitor \(C_{r1}\) is still discharged in the opposite direction, and the input inductor currents \(l_{L1}\) and \(l_{L2}\) charge the capacitors  
Figure 11: Current flow in state 8. State 11: \([t_{10}\leq t\leq t_{11}]\). As shown in Figure 14, the main switch \(S_{1}\) is turned still off and the main switch \(S_{2}\) is still turned off and the auxiliary switch \(S_{a}\) is still turned off but the auxiliary diode \(D_{a}\) is turned on, whereas the freewheeling diodes \(D_{1}\) is turned on and the freewheeling diode \(D_{2}\) is still turned on and the resonant diode \(D_{r1}\) is turned on and the resonant diode \(D_{r2}\) is still turned on.