## 2 Descriptions and Operational Modes Analysis of the Presented Single-Stage LED Driver
In order to analyze the operations of the presented LED driver, the following assumptions are made. 1. Since the switching frequencies of the two switches \(S_{1}\) and \(S_{2}\) are much higher than those of the utility-line voltage \(v_{AC}\), the sinusoidal utility-line voltage can be considered as a constant value for each high-frequency switching period. 2. \(V_{REC1}\) and \(V_{REC2}\), respectively, represent the rectified input voltage sources for the capacitors \(C_{in1}\) and \(C_{in2}\). 3. Power switches are complementarily operated, and their inherent body diodes and drain-source capacitors (\(C_{DS1}\) and \(C_{DS2}\)) are considered. 4. The conducting voltage drops of diodes \(D_{B11}\), \(D_{B12}\), \(D_{B21}\), \(D_{B22}\), \(D_{o1}\), \(D_{o2}\), \(D_{o3}\) and \(D_{o4}\) are neglected. 5. Coupled inductors (including \(L_{B11}\) and \(L_{B12}\); \(L_{B21}\) and \(L_{B22}\)) are designed to be operated in DCM for naturally achieving PFC. The operating modes and the key waveform of the presented LED driver for streetlight applications are shown in Figures 5 and 6, respectively, and the analyses of operations are described in detail in the following. Mode 1 (\(t_{0}\leq t<t_{1}\); in Figure 5a): The body diode of switch \(S_{1}\) is forward-biased at time \(t_{0}\), and this mode begins. The resonant capacitor \(C_{r}\) provides energy to the inductor \(L_{r}\), capacitors \(C_{DS2}\) and  
Figure 4: Simplified circuit of the presented single-stage LED driver for streetlight applications. Figure 3: The utilized control circuit of the presented single-stage LED driver for streetlight applications. and to the LED through diodes \(D_{o2}\) and \(D_{o3}\). The diode \(D_{B21}\) is forward-biased and coupled inductors \(L_{B21}\) and \(L_{B22}\) provide energy to capacitor \(C_{DS2}\) through diode \(D_{B21}\). At time \(t_{1}\), the drain-source voltage \(v_{DS1}\) of power switch \(S_{1}\) is zero and \(S_{1}\) turns on with zero-voltage switching (ZVS); then this mode ends. Mode 2 (\(t_{1}\leq t<t_{2}\); in Figure 5b): When switch \(S_{1}\) achieves ZVS turn-on at \(t_{1}\), this mode starts. The rectified input voltage source \(V_{REC1}\) provides energy to coupled inductor \(L_{B11}\) through diode \(D_{B11}\) and switch \(S_{1}\), and diode \(D_{B12}\) is reverse-biased during this mode. The inductor current \(i_{LB11}\) linearly increases from zero, and can be expressed as:  
\[i_{LB11}(t)=\frac{\left|\sqrt{2}v_{AC-rms}\sin(2\pi f_{AC}t)\right|}{2L_{B11}}( t-t_{1}), \tag{1}\]  
where \(v_{AC-rms}\) is the root-mean-square (rms) value of input utility-line voltage, and \(f_{AC}\) is the utility-line frequency. The DC bus capacitor \(C_{DC}\) and resonant inductor \(L_{r}\) provide energy to capacitors \(C_{DS2}\), \(C_{r}\) and \(C_{o}\) and to the LED through diodes \(D_{o1}\) and \(D_{o4}\). Coupled inductors \(L_{B21}\) and \(L_{B22}\) continue providing energy to capacitor \(C_{DS2}\) through diode \(D_{B21}\). This mode ends when current \(i_{LB22}\) decreases to zero at \(t_{2}\). Mode 3 (\(t_{2}\leq t<t_{3}\); in Figure 5c): Voltage source \(V_{REC1}\) continues providing energy to coupled inductor \(L_{B11}\) through diode \(D_{B11}\) and switch \(S_{1}\). Capacitors \(C_{DC}\) and \(C_{DS2}\), along with resonant inductor \(L_{r}\) provide energy to capacitors \(C_{r}\) and \(C_{o}\) and to the LED through diodes \(D_{o1}\) and \(D_{o4}\). At \(t_{3}\), the coupled-inductor current reaches its peak value, defined as \(i_{LB11-pk}(t)\), and is given by:  
\[i_{LB11-pk}(t)=\frac{\left|\sqrt{2}v_{AC-rms}\sin(2\pi f_{AC}t)\right|}{2L_{B1 1}}DT_{S}, \tag{2}\]  
where \(D\) and \(T_{S}\) are the duty cycle and period of the power switch, respectively. This mode ends when diode \(D_{B12}\) becomes forward-biased at \(t_{3}\). Mode 4 (\(t_{3}\leq t<t_{4}\); in Figure 5d): This mode begins when power switch \(S_{1}\) turns off at \(t_{3}\). The diode \(D_{B12}\) is forward-biased and coupled inductors \(L_{B11}\) and \(L_{B12}\) provide energy to capacitor \(C_{DS1}\).