# Four-Channel Buck-Type LED Driver with Automatic Current Sharing and Soft Switching
## 2 Proposed LED Driver
### Operating Principle Analysis  
State 1 (\(t_{0}<t<t_{1}\)): As shown in Figure 7, the switches \(S_{1}\) and \(S_{3}\) are turned on with zero voltage switching (ZVS) but \(S_{2}\) and \(S_{4}\) are turned off, whereas all the four diodes are forward biased. The input voltage \(V_{in}\), the diode \(D_{1}\), the resonant inductor \(L_{r1}\), the energy-transferring capacitor \(C_{1}\) and the switch \(S_{1}\) form a loop; the energy-transferring capacitor \(C_{2}\), the output current \(I_{o2}\), the diode \(D_{3}\), the resonant inductor \(L_{r2}\), the energy-transferring capacitor \(C_{3}\) and the switch \(S_{3}\) form a loop. Additionally, the corresponding equivalent circuit is shown in Figure 8. At the same time, \(L_{r1}\) and \(L_{r2}\) are demagnetized in opposite directions via \(S_{1}\) and \(S_{3}\), respectively. Figure 4: Illustrated waveforms relevant to the proposed circuit operating in CCM. Figure 5: Equivalent circuit after combining the equivalent output inductors, output capacitors and LED strings. Figure 6: Equivalent circuit after decoupling the coupled inductors. Figure 7: Current flow in state 1 in CCM. In this state, the current \(i_{C1}(t)\) and \(i_{C3}(t)\) can be obtained according to the voltages across the resonant inductors \(L_{r1}\) and \(L_{r2}\):  
\[v_{Lr1}(t)=L_{r1}\frac{di_{C1}(t)}{dt}=V_{in}-V_{C1}\Rightarrow i_{C1}(t)=\frac {V_{in}-V_{C1}}{L_{r1}}\times(t-t_{0})+i_{C1}(t_{0}) \tag{1}\]  
\[v_{Lr2}(t)=L_{r2}\frac{di_{C3}(t)}{dt}=V_{C2}-V_{C3}\Rightarrow i_{C3}(t)=\frac {V_{C2}-V_{C3}}{L_{r1}}\times(t-t_{0})+i_{C3}(t_{0}) \tag{2}\]  
where \(i_{C1}(t_{0})\) and \(i_{C3}(t_{0})\) are the currents in the energy-transferring capacitors \(C_{1}\) and \(C_{3}\) at \(t_{0}\), respectively. Since the energy-transferring capacitors \(C_{2}\) and \(C_{3}\) are connected in series in this state,  
\[i_{C2}(t)=-i_{C3}(t) \tag{3}\]  
As the current in \(C_{1}\) rises to zero, the state ends, as shown in (4) and (5). Substituting (4) and (5) into (1) and (2) can provide the time elapsed in state 1:  
\[i_{C1}(t_{1})=0 \tag{4}\]  
\[i_{C3}(t_{1})=-i_{C2}(t_{1})=0 \tag{5}\]  
Figure 4:0  
State 2 (\(t_{1}<t<t_{2}\)): As shown in Figure 9, the switches \(S_{1}\) and \(S_{3}\) are turned on but \(S_{2}\) and \(S_{4}\) are turned off, whereas all the four diodes are forward biased. The input voltage \(V_{in}\), the switch \(S_{1}\), the energy-transferring capacitor \(C_{1}\), the resonant inductor \(L_{r1}\) and the output current \(l_{01}\) 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 \(l_{03}\) and the diode \(D_{2}\) form the other loop. Additionally, the corresponding equivalent circuit is shown in Figure 4:1 At the same time, the resonant inductors \(L_{r1}\) and \(L_{r2}\) are magnetized in the forward direction. Once the currents in the resonant inductors are equal to the output currents, the diodes \(D_{1}\) and \(D_{3}\) are turned off with zero current switching (ZCS) and the operation enters state 3 immediately. Figure 4:2 Equivalent circuit for states 1, 2 and 10. Figure 4:3 Current flow in state 2 in CCM. The currents in the resonant inductors \(L_{r1}\) and \(L_{r2}\) are positive, and their expressions are the same as in state 1; that is,  
Figure 4:4  
Figure 4:5  
Figure 4:6  
As the currents in the resonant inductors are the same as the output currents, the state ends, as shown in (10) and (11). Substituting (10) and (11) into (7) and (8) can provide the time elapsed in state 2:  
Figure 4:7  
Figure 4:8  
Figure 4:9  
State 3 (\(t_{2}<t<t_{3}\)): As shown in Figure 10, the switches \(S_{1}\) and \(S_{3}\) are turned on but \(S_{2}\) and \(S_{4}\) are turned off, whereas the diodes \(D_{2}\) and \(D_{4}\) are forward biased but \(D_{1}\) and \(D_{3}\) are reverse biased.