# Four-Channel Buck-Type LED Driver with Automatic Current Sharing and Soft Switching
## 2 Proposed LED Driver
### Operating Principle Analysis
\begin{array}{ll}i_{C3}(t)&=C_{S3}\frac{dv_{S3}(t)}{dt}-\frac{I_{44}}{2}\\ &=-I_{04}\end{array}  \tag{51}\]  
\[ \begin{array}{ll}i_{S3}(t)=-\frac{I_{04}}{2}\end{array}  \tag{52}\]  
According to [PERSON]'s current law (KCL), the current in the switch \(S_{2}\), called \(i_{S2}(t)\), can be shown as (53), in which \(I_{02}\) and \(i_{S3}(t)\) are known. \(i_{S3}(t)\) is shown in (52). Thus, the voltage on the switch \(S_{2}\), called \(v_{S2}(t)\), can be obtained by  
\[ \begin{array}{ll}i_{S2}(t)=I_{02}+i_{S3}(t)=C_{S2}\frac{dv_{S2}(t)}{dt}\end{array}  \tag{53}\]  
\[ \begin{array}{ll}v_{S2}(t)=\frac{1}{C_{S2}}\int\limits_{t_{8}}^{t}\left(I_{ 02}-\frac{I_{04}}{2}\right)d\tau\\ &=\frac{I_{02}}{2C_{S2}}\times(t-t_{8})+0\end{array}  \tag{54}\]  
Finally, the current relationship between the switch \(S_{1}\), the energy-transferring capacitor \(C_{1}\) and the switch \(S_{2}\) is  
\[ \begin{array}{ll}i_{S1}(t)=i_{C1}(t)+i_{S2}(t)=C_{S1}\frac{dv_{S1}(t)}{dt} \end{array}  \tag{55}\]  
Since the sum of the voltages on the switches \(S_{1}\) and \(S_{2}\) is half of the input voltage, the voltage on the switch \(S_{1}\) can be obtained by  
\[ \begin{array}{ll}v_{S1}(t)&=\frac{V_{in}}{2}-v_{S2}(t)\\ &=\frac{V_{in}}{2}-\frac{I_{02}}{2C_{S2}}\times(t-t_{8})\end{array}  \tag{56}\]  
By substituting (56) into (55), the currents in the energy-transferring capacitor \(C_{1}\) and the switch \(S_{1}\) can be obtained by  
\[ \begin{array}{ll}i_{C1}(t)&=C_{S1}\frac{dv_{S1}(t)}{dt}-\frac{I_{02}}{2}\\ &=-I_{02}\end{array}  \tag{57}\]  
\[ \begin{array}{ll}i_{S1}(t)&=i_{C1}(t)+i_{S2}(t)\\ &=-I_{02}+\frac{I_{02}}{2}\\ &=\frac{-I_{02}}{2}\end{array} \] (  
\(D_{1}\), the resonant inductor \(L_{r1}\), the energy-transferring capacitor \(C_{1}\) and the body diode of the switch \(S_{1}\) form a loop; the energy-transferring capacitor \(C_{2}\), the output current \(I_{02}\), the diode \(D_{3}\), the resonant inductor \(L_{r2}\), the energy-transferring capacitor \(C_{3}\) and the body diode of 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, to achieve ZVS turn-on of \(S_{1}\) and \(S_{3}\). At this point, the currents \(i_{\text{C1}}(t)\) and \(i_{\text{C3}}(t)\) are similar to those in state 1:  
\[i_{\text{C1}}(t)=\frac{V_{in}-V_{\text{C1}}}{L_{r1}}\times(t-t_{9})-I_{02} \tag{60}\]  
\[i_{\text{C3}}(t)=\frac{V_{\text{C2}}-V_{\text{C3}}}{L_{r2}}-I_{04} \tag{61}\]  
\[i_{\text{C3}}(t)=-i_{\text{C2}}(t) \tag{62}\]  
This state ends when the switches \(S_{1}\) and \(S_{3}\) are turned on. The corresponding time elapsed and the current values of the energy-transferring capacitors \(C_{1}\) and \(C_{3}\) at the end of this state can be obtained by  
\[t_{0}+T_{s}-t_{9}=T_{d}-(t_{9}-t_{8}) \tag{63}\]  
\[i_{\text{C1}}(t_{0}+T_{s}) =i_{\text{C1}}(t_{0}) \tag{64}\] \[=\frac{V_{\text{S}}-V_{\text{C1}}}{L_{r1}}\times[T_{d}-(t_{9}-t_{ 8})]-I_{02}\] \[i_{\text{C3}}(t_{0}+T_{s}) =i_{\text{C3}}(t_{0})\] (65) \[=\frac{V_{\text{C2}}-V_{\text{C3}}}{L_{r2}}\times[T_{d}-(t_{9}-t_ {8})]-I_{04}\]  
From the above analysis, one can see that in the proposed LED driver, four switches can achieve ZVS turn-on by using the parasitic capacitors of the MOSFETs and only one coupled inductor. Moreover, to make sure each LED string has the same current, differential-mode transformers are used. Figure 22: Equivalent circuit for state 10.