# Interleaved Boost Converter with ZVT-ZCT for the Main Switches and ZCS for the Auxiliary Switch
## 3 Basic Operating Principles
During this state, the parasitic diodes of the main switches \(S_{1}\) and \(S_{2}\), called \(D_{S1}\) and \(D_{S2}\), are turned on, and hence the voltages across \(S_{1}\) and \(S_{2}\), called \(v_{s1}\) and \(v_{s2}\), are zero. In addition, the output capacitor \(C_{o}\) still provides energy to the load. The instant the auxiliary switch \(S_{a}\) is turned off, \(S_{1}\) has zero-voltage-transition (ZVT) turn-on and hence this state comes to the end. During this interval, the corresponding state equation can be signified as follows:  
\[i_{Lr}(t)=I_{L}+\frac{V_{o}}{Z_{2}} \tag{6}\]  
State 4: \([t_{3}\leq t\leq t_{4}]\). As shown in Figure 7, the main switch \(S_{1}\) is turned on but the main switch \(S_{2}\) is still turned off and the auxiliary switch \(S_{a}\) is turned off, whereas the freewheeling diodes \(D_{1}\) and \(D_{2}\) are still turned off but the resonant diodes \(D_{r1}\) and \(D_{r2}\) are still turned on. During this state, the current \(i_{S1}\) begins to increase, and the auxiliary diode \(D_{a}\) is turned on due to \(S_{a}\) being turned off, thereby making the voltage across the resonant inductor \(L_{r}\) change its polarity such that \(L_{r}\) is demagnetized. Once \(i_{S1}=I_{L1}\) and \(i_{Lr}=I_{L2}\), the resonant diode \(D_{r1}\) is turned off, and hence this state comes to the end. During this interval, the corresponding state equation can be represented as follows:  
\[i_{Lr}(t)=\frac{-V_{o}}{L_{r}}(t-t_{3})+I_{L}+\frac{V_{o}}{Z_{2}} \tag{7}\]  
As \(t=t_{4}\), the corresponding time elapsed is as follows:  
\[(t_{4}-t_{3})=\frac{[I_{L}+\frac{V_{o}}{Z_{2}}-i_{Lr}(t_{4})]L_{r}}{V_{o}} \tag{8}\]  
State 5: \([t_{4}\leq t\leq t_{5}]\). As shown in Figure 8, the main switch \(S_{1}\) is still turned on but the main switch \(S_{2}\) is still turned off and the auxiliary switch \(S_{a}\) is still turned off, whereas the freewheeling diodes \(D_{1}\) and \(D_{2}\) are still turned off and the resonant diode \(D_{r1}\) is turned off but the resonant diode \(D_{r2}\) is still turned on. During this state, the inductor current \(I_{L2}\) charges the parasitic capacitor of the main switch \(S_{2}\), called \(C_{S2}\), and also charges the resonant capacitor \(C_{r1}\) in the opposite direction. Figure 6: Current flow in state 3. At the same time, the resonant inductor \(L_{r}\) still keeps demagnetized, and as the resonant current \(i_{Lr}\) is deceased to zero, the voltage across \(C_{S2}\), called \(v_{S2}\), is increased to the output voltage \(V_{o}\) and the voltage across \(C_{r1}\), called \(v_{Cr1}\), is decreased to \(-V_{o}\). The moment the auxiliary diode \(D_{a}\) is turned off, the freewheeling diode \(D_{2}\) is turned on, and hence this state comes to the end. During this interval, the corresponding state equation can be signified as follows:  
\[\left\{ \begin{array}{l}i_{Lr}(t)=l_{L2}+\frac{v_{A}(t_{4})-V_{o}}{2v_{S}}\sin \omega_{5}(t-t_{4})-\left[l_{L2}-i_{Lr}(t_{4})\right]\cos\omega_{5}(t-t_{4})\\ \\ v_{A}(t)=V_{o}+Z_{5}[l_{L2}-i_{Lr}(t_{4})]\sin\omega_{5}(t-t_{4})+\left[v_{A} (t_{4})-V_{o}\right]\cos\omega_{5}(t-t_{4})\\ \end{array} \right. \tag{9}\]  
where \(v_{A}\) is the voltage across \(C_{A}\), and  
\[C_{A}=C_{r1}+C_{S2},\omega_{5}=\sqrt{\frac{1}{L_{r}C_{A}}}\text{ and }Z_{5}=\sqrt{\frac{L_{r}}{C_{A}}} \tag{10}\]  
Hence, the corresponding time elapsed is as follows:  
\[(t_{5}-t_{4})=\frac{\pi}{2\omega_{5}} \tag{11}\]  
State 6: \([t_{5}\leq t\leq t_{6}]\). As shown in Figure 9, the main switch \(S_{1}\) is still turned on but the main switch \(S_{2}\) is still turned off and the auxiliary switch \(S_{a}\) is still turned off, whereas the freewheeling  
Figure 8: Current flow in state 5. Figure 7: Current flow in state 4.  
diode \(D_{1}\) is still turned off but the freewheeling diode \(D_{2}\) is turned on but the resonant diode \(D_{r1}\) is still turned off and the resonant diode \(D_{r2}\) is turned off. During this state, the operating behavior of this converter is the same as that of the traditional boost converter.