# Four-Channel Buck-Type LED Driver with Automatic Current Sharing and Soft Switching
## 2 Proposed LED Driver
### Operating Principle Analysis
The input voltage \(V_{in}\), the switch \(S_{1}\), the energy-transferring capacitor C\({}_{1}\), the resonant inductor \(L_{r1}\) and the output current \(I_{o1}\) form one loop; the energy-transferring capacitor \(C_{2}\), the switch \(S_{3}\), the energy-transferring capacitor C\({}_{3}\), the resonant inductor \(L_{r2}\), the output current \(I_{o3}\) and the diode \(D_{2}\) form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 5:0 As the switches \(S_{1}\) and \(S_{3}\) are turned off, the operation enters state 4. Figure 5:1 Equivalent circuit for state 3. Figure 5:2 Circuit flow for state 3 in CCM. During this state, the currents in the resonant inductors \(L_{r1}\) and \(L_{r2}\) are the same as the output currents \(I_{01}\) and \(I_{03}\), respectively, so  
Figure 5:3  
Figure 5:4  
As the switches \(S_{1}\) and \(S_{3}\) are turned off, the operation enters state 4. Accordingly, the time elapsed in state 3 can be obtained to be  
Figure 5:5  
State 4 (\(t_{3}<t<t_{4}\)): As shown in Figure 12, all the switches are off, whereas the diodes \(D_{2}\) and \(D_{4}\) are forward biased but \(D_{1}\) and \(D_{3}\) are reverse biased. This state belongs to the blanking time interval. During this state, the parasitic capacitors on switches \(S_{1}\) and \(S_{3}\), called \(C_{S1}\) and \(C_{S3}\), respectively, are charged, and the parasitic capacitors on the switches \(S_{2}\) and \(S_{4}\), called \(C_{S2}\) and \(C_{S4}\), respectively, are discharged. Additionally, the corresponding equivalent circuit is shown in Figure 5:6 As the voltages across the switches \(S_{2}\) and \(S_{4}\) drop to zero, the operation enters state 5. During this state, the currents in the resonant inductors \(L_{r1}\) and \(L_{r2}\) are the same as the output currents \(I_{01}\) and \(I_{03}\), respectively, so  
Figure 5:7  
Figure 5:8 Circuit flow for state 4 in CCM. Figure 5:9 Equivalent circuit for state 4. Figure 6:0  
In order to analyze the voltage across and current in each switch, let the potential between the switches \(S_{1}\) and \(S_{2}\) be \(v_{a}(t)\), and the potential between the switches \(S_{3}\) and \(S_{4}\) be \(v_{b}(t)\). In addition, because in the previous state, the switches \(S_{1}\) and \(S_{3}\) are in the on state, the values of \(v_{a}(t)\) and \(v_{b}(t)\) at the instant \(t_{3}\) are \(V_{in}\) and \(V_{C2}\) such that \(v_{a}(t)\) and \(v_{b}(t)\) can be obtained as follows:  
Figure 6:1  
Figure 6:2  
After obtaining \(v_{a}(t)\) and \(v_{b}(t)\), the voltages on the four switches can be derived, and the resulting equations are  
Figure 6:3  
Figure 6:4  
Figure 6:5  
Figure 6:6  
As the switches \(S_{2}\) and \(S_{4}\) have zero voltage across them, the operation state enters state 5, as shown in (24). Substituting (24) into (21) and (23) can provide the time elapsed in state 4, namely,  
Figure 6:7  
Figure 6:8  
State 5 (\(t_{4}<t<t_{5}\)): As shown in Figure 14, the four switches are all off, whereas the four diodes are all forward biased. The energy-transferring capacitor \(C_{1}\), the resonant inductor \(L_{r1}\), the output current \(I_{o1}\), the diode \(D_{2}\), the energy-transferring capacitor \(C_{2}\) and the body diode of the switch \(S_{2}\) form one loop; the energy-transferring capacitor \(C_{3}\), the resonant inductor \(L_{r2}\), the output current \(I_{o3}\), the diode \(D_{4}\) and the body diode of \(S_{4}\) form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 6:9 At the same time, the resonant inductors \(L_{r1}\) and \(L_{r2}\) are demagnetized in the forward direction via the switches \(S_{2}\) and \(S_{4}\), respectively. Figure 7:0 Circuit flow for state 5 in CCM. For this state, according to the voltages on the resonant inductors \(L_{r1}\) and \(L_{r2}\), the currents \(i_{C1}(t)\) and \(i_{C3}(t)\) can be obtained as  
\[ \begin{array}{l}v_{Lr1}(t)=L_{r1}\frac{d_{iC1}(t)}{dt}=V_{C2}-V_{C1}\\ \Rightarrow i_{C1}(t)=\frac{V_{C2}V_{C1}}{L_{r1}}\times(t-t_{4})+I_{o1}\end{array}  \tag{26}\]  
\[