# Single-Switch Non-Isolated Resonant DC-DC Converter for Single-Input Dual-Output Applications
## 2 Proposed Single-Switch SIDO ZVS-QRC Configuration Description
### Operation Mode  
In a static way, the operation mode of the ZVS-QR SEPIC-Cuk combination converter shown in Figure 3 can be analyzed by assuming that the inductors' currents (\(L_{1}\), \(L_{2}\) and \(L_{3}\)) and the capacitors' voltages (\(C_{1}\), \(C_{2}\), \({C_{o}}^{+}\) and \({C_{o}}^{-}\)) remain relatively constant during a switching period (\(T_{s}\)), close to their average values. In these conditions, the operation  
Figure 3: SIDO ZVS-QR SEPIC–Cuk combination converter.  
Figure 2: ZVS-QR \(M\)-type half-wave SEPIC converter.  
mode can be divided into four time intervals during \(T_{s}\). Therefore, it can be analyzed by the four equivalent circuits shown in Figure 4, assuming half-wave operation with respect to the resonant action (\(D_{Q}\) conducts for a time interval and prevents the voltage across the resonant capacitor from changing its sign). The analysis begins with the capacitor \(C_{R}\) voltage being zero, the load currents \(I_{o1}\) and \(I_{o2}\) circulating across the resonant inductor \(L_{R}\) and the switch \(Q\) being on.  
Linear Interval [\(t_{1}-t_{0}\)]:  
At \(t_{0}\), \(Q\) is turned off. The supply current is provided from \(V_{g}\) through \(L_{R}\) and \(C_{R}\). The voltage across \(C_{R}\) (and across \(Q\)) grows linearly from zero (zero-voltage switching), and this time interval ends when the voltage across \(C_{R}\) reaches \(V_{g}+V_{o}/2\) and the freewheel diodes (\(D_{1}\) and \(D_{2}\)) are directly biased (at time \(t_{1}\)).  
Resonant Interval [\(t_{2}-t_{1}\)]:  
At \(t_{1}\), the freewheel diodes \(D_{1}\) and \(D_{2}\) are turned on and conduct the current of the load, and that is due to \(I_{g}\) and \(i_{LR}\) (half for a balanced load). The voltage across \(C_{R}\) varies sinusoidally, the inductor current \(L_{R}\) varies cosinusoidally and the capacitor \(C_{R}\) and the inductor \(L_{R}\) are in resonance. The energy of the inductor is transferred to the capacitor, which increases its voltage from \(V_{g}+V_{o}/2\) to the resonant wave amplitude. This time interval ends when the voltage across \(C_{R}\) returns to zero and \(D_{Q}\) is directly biased (at time \(t_{2}\)).  
Inductor-Discharging Interval [\(t_{3}-t_{2}\)]:  
At \(t_{2}\), \(D_{Q}\) turns on. The voltage across \(C_{R}\) attempts to reverse, but it is clamped to zero by \(D_{Q}\), which is turned on. The inductor current grows linearly. \(Q\) should be turned on before \(D_{Q}\) is turned off. This time interval ends when \(Q\) starts supplying the load currents (\(I_{o1}\) and \(I_{o2}\)) again and the freewheel diodes (\(D_{1}\) and \(D_{2}\)) are reverse-biased (at time \(t_{3}\)). Thus, \(Q\) is turned on with zero-voltage switching.  
Figure 4: Equivalent circuits of the ZVS-QR SEPIC–Cuk combination converter during a switching period. (**a**) Linear State. Interval [\(t_{1}-t_{0}\)]. (**b**) Resonant State. Interval [\(t_{2}-t_{1}\)]. (**c**) Inductor-Discharging State. Interval [\(t_{3}-t_{2}\)]. (**d**) Passive State. Interval [\(t_{4}-t_{3}\)].  
Passive State Interval [\(t_{4}-t_{3}\)]:  
At \(t_{3}\), \(Q\) turns on and supplies the load currents (\(I_{01}\) and \(I_{02}\)) again, and the conditions return to the initial ones. This time interval ends when \(Q\) is turned off again, starting a new switching cycle. This time interval is also used to regulate the output voltages.