## 2 Descriptions and Operational Modes Analysis of the Presented Single-Stage LED Driver
The coupled-inductor current \(i_{LB11}\) linearly decreases from its peak level, and can be given by:  
\[i_{LB11}(t)=\frac{V_{DC}}{2L_{B11}}(t-t_{3}), \tag{3}\]  
where \(V_{DC}\) is the voltage of the DC bus capacitor \(C_{DC}\). Capacitors \(C_{DC}\) and \(C_{DS2}\) and resonant inductor \(L_{r}\) continue providing energy to capacitors \(C_{DS1}\), \(C_{r}\) and \(C_{o}\) and to the LED through diodes \(D_{o1}\) and \(D_{o4}\). When the drain-source voltage \(v_{DS2}\) of \(S_{2}\) decreases to zero at \(t_{4}\), this mode ends. Mode 5 (\(t_{4}\leq t<t_{5}\); in Figure 5e): The body diode of switch \(S_{2}\) is forward-biased at time \(t_{4}\), and this mode begins. The resonant inductor \(L_{r}\) provides energy to capacitors \(C_{DS2}\), \(C_{r}\) and \(C_{o}\) and to the LED through the body diode of power switch \(S_{2}\) and diodes \(D_{o1}\) and \(D_{o4}\). The diode \(D_{B12}\) is forward-biased and coupled inductors \(L_{B11}\) and \(L_{B12}\) provide energy to capacitor \(C_{DS1}\) through diode \(D_{B12}\). At time \(t_{5}\), the drain-source voltage \(v_{DS2}\) of power switch \(S_{2}\) is zero and \(S_{2}\) turns on with ZVS; then this mode ends. Mode 6 (\(t_{5}\leq t<t_{6}\); in Figure 5f): When switch \(S_{2}\) achieves ZVS turn-on at \(t_{5}\), this mode starts. The rectified input voltage source \(V_{REC2}\) provides energy to coupled inductor \(L_{B22}\) through diode \(D_{B22}\) and switch \(S_{2}\), and diode \(D_{B21}\) is reverse-biased during this mode. The DC bus capacitor \(C_{DC}\) and resonant capacitor \(C_{r}\) provide energy to inductor \(L_{r}\), capacitors \(C_{DS1}\) and \(C_{o}\) and to the LED through diodes \(D_{o2}\) and \(D_{o3}\). Coupled inductors \(L_{B11}\) and \(L_{B12}\) continue providing energy to capacitor \(C_{DS1}\) through diode \(D_{B12}\). This mode ends when current \(i_{LB11}\) decreases to zero at \(t_{6}\). Mode 7 (\(t_{6}\leq t<t_{7}\); in Figure 5g): Voltage source \(V_{REC2}\) continues providing energy to coupled inductor \(L_{B22}\) through diode \(D_{B22}\) and switch \(S_{2}\). The resonant capacitor \(C_{r}\) provides energy to resonant inductor \(L_{r}\), output capacitor \(C_{o}\) and the LED through diodes \(D_{o2}\) and \(D_{o3}\). This mode ends when diode \(D_{B21}\) is forward-biased at \(t_{7}\). Mode 8 (\(t_{7}\leq t<t_{8}\); in Figure 5h): This mode begins when power switch \(S_{2}\) turns off at \(t_{7}\). The diode \(D_{B21}\) is forward-biased and coupled inductors \(L_{B21}\) and \(L_{B22}\) provide energy to capacitor \(C_{DS2}\). The resonant capacitor \(C_{r}\) continues providing energy to resonant inductor \(L_{r}\), capacitors \(C_{DS2}\) and \(C_{o}\) and to the LED through diodes \(D_{o2}\) and \(D_{o3}\). When the drain-source voltage \(v_{DS1}\) of \(S_{1}\) decreases to zero at \(t_{8}\), this mode ends. Then Mode 1 begins for the next high-frequency switching period. Figure 5: _Cont._  
Figure 5: Operation modes of the presented LED driver; (**a**) Model 1; (**b**) Model 2; (**c**) Model 3; (**d**) Model 4; (**e**) Model 5; (**f**) Model 6; (**g**) Model 7; (**h**) Model 8.