# Four-Channel Buck-Type LED Driver with Automatic Current Sharing and Soft Switching
## 2 Proposed LED Driver
### Operating Principle Analysis
\begin{array}{l}v_{Lr2}(t)=L_{r2}\frac{d_{iC3}(t)}{dt}=-V_{C3}\\ \Rightarrow i_{C3}(t)=\frac{V_{C3}}{L_{r2}}\times(t-t_{4})+I_{03}\end{array}  \tag{27}\]  
During this state, the energy-transferring capacitors \(C_{1}\) and \(C_{2}\) are in series, so  
\[i_{C1}(t)=-i_{C2}(t) \tag{28}\]  
At the same time, this state ends when switches \(S_{2}\) and \(S_{4}\) are on, and the time elapsed can be inferred, along with the current values of the energy-transferring capacitors \(C_{1}\) and \(C_{3}\) at the end of this state:  
\[t_{5}-t_{4}=T_{d}-(t_{4}-t_{3}) \tag{29}\]  
\[i_{C1}(t_{5})= \frac{V_{C2}-V_{C1}}{L_{r1}}\times[T_{d}-(t_{4}-t_{3})]+I_{o1} \tag{30}\]  
\[i_{C3}(t_{5})= \frac{-V_{C3}}{L_{r2}}\times[T_{d}-(t_{4}-t_{3})]+I_{o3} \tag{31}\]  
State 6 (\(t_{5}<t<t_{6}\)): As shown in Figure 16, the switches \(S_{2}\) and \(S_{4}\) are turned on with ZVS but \(S_{1}\) and \(S_{3}\) are off, whereas all four diodes are forward biased. The switch \(S_{2}\), the energy-transferring capacitor \(C_{1}\), the resonant inductor \(L_{r1}\), the output current \(I_{o1}\), the diode \(D_{2}\) and the energy-transferring capacitor \(C_{2}\) form one loop; the switch \(S_{4}\), the energy-transferring capacitor \(C_{3}\), the resonant inductor \(L_{r2}\), the output current \(I_{o3}\) and the diode \(D_{4}\) form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 15. At the same time, the resonant inductors \(L_{r1}\) and \(L_{r2}\) are still demagnetized in the forward direction through the switches \(S_{2}\) and \(S_{4}\), respectively. Figure 16: Circuit flow for state 6 in CCM. Figure 15: Equivalent circuit for states 5 and 6. During this state, the currents \(i_{C1}(t)\) and \(i_{C3}(t)\), flowing through the resonant inductors \(L_{r1}\) and \(L_{r2}\), respectively, are similar to those in state 5:  
\[ \begin{array}{rl}i_{C1}(t)&=\frac{V_{C2}-V_{C1}}{L_{r1}}\int\limits_{t_{0}}^{t }d\tau\\ &=\frac{V_{C2}-V_{C1}}{L_{r1}}\times(t-t_{5})+i_{C1}(t_{5})\\ \\ i_{C3}(t)&=\frac{-V_{C3}}{L_{r2}}\int\limits_{t_{5}}^{t}d\tau\\ &=\frac{-V_{C3}}{L_{r2}}\times(t-t_{5})+i_{C3}(t_{5})\end{array}  \tag{32}\]  
where \(i_{C1}(t_{5})\) and \(i_{C3}(t_{5})\) are the currents in capacitors \(C_{1}\) and \(C_{3}\) at the instant \(t_{5}\), respectively, as shown in (32) and (33). The energy transferring-capacitors \(C_{1}\) and \(C_{2}\) are in series in this state, so  
\[i_{C1}(t)=-i_{C2}(t) \tag{34}\]  
As the current in the energy-transferring capacitor \(C_{2}\) rises to zero, state 6 ends, as shown in (35) and (36):  
\[i_{C1}(t_{6})=-i_{C2}(t_{6})=0 \tag{35}\]  
\[i_{C3}(t_{6})=0 \tag{36}\]  
Substituting (35) and (36) into (32) and (33), respectively, can provide the time elapsed in state 6, namely,  
\[t_{6}-t_{5}=\frac{i_{C1}(t_{5})\times L_{r1}}{V_{C1}-V_{C2}}=\frac{i_{C3}(t_{ 5})\times L_{r2}}{V_{C3}} \tag{37}\]  
State 7 (\(t_{6}<t<t_{7}\)): As shown in Figure 17, the switches \(S_{2}\) and \(S_{4}\) are still on but \(S_{1}\) and \(S_{3}\) are still off, whereas all four diodes are still forward biased. The switch \(S_{2}\), the energy-transferring capacitor \(C_{2}\), the output current \(l_{02}\), the diode \(D_{1}\), the resonant inductor \(L_{r1}\) and the energy-transferring capacitor \(C_{1}\) form one loop; the switch \(S_{4}\), the output current \(l_{04}\), the diode \(D_{3}\), the resonant inductor \(L_{r2}\) and the energy-transferring capacitor \(C_{3}\) form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 18. The resonant inductors \(L_{r1}\) and \(L_{r2}\) are magnetized in opposite directions through the switches \(S_{2}\) and \(S_{4}\), respectively. As soon as the currents in the resonant inductors are equal to the negative output currents, the diodes \(D_{2}\) and \(D_{4}\) are turned off with ZCS, and the operation enters state 8. Figure 17: Circuit flow for state 7 in CCM.