## 2 The Description and Analysis of the Presented LED Tube Lamp Driver  
Figure 2 shows the presented driver, which integrates the dual buck-boost converter with coupled inductors (one buck-boost converter includes a diode \(D_{b1}\), a coupled inductor \(L_{PFC1}\), a switch \(S_{1}\), a body diode of the switch \(S_{2}\), and a DC-linked capacitor \(C_{DC1}\); another buck-boost converter includes a diode \(D_{b2}\), a coupled inductor \(L_{PFC2}\), a switch \(S_{2}\), a body diode of the switch \(S_{1}\), and the capacitor \(C_{DC2}\)) with the half-bridge series resonant converter cascaded with a bridge rectifier (including two DC-linked capacitors \(C_{DC1}\) and \(C_{DC2}\), two switches \(S_{1}\) and \(S_{2}\), a resonant inductor \(L_{r}\), a resonant capacitor \(C_{r}\), a full-bridge rectifier (including diodes \(D_{1}\), \(D_{2}\), \(D_{3}\) and \(D_{4}\)), and an output capacitor \(C_{o}\)) into a single-stage topology for supplying an LED tube lamp [17]. In addition, an LC filter (an inductor \(L_{f}\) and a capacitor \(C_{f}\)) is connected with the input utility-line voltage. In order to analyze the operations of the presented LED tube lamp driver, the following assumptions are made. Figure 1: The commercial two-stage driver for supplying a T8-Type LED (light-emitting diode) tube lamp. Figure 2: The presented single-stage driver for supplying a T8-type LED tube lamp. Since the switching frequencies of the two switches (\(S_{1}\) and \(S_{2}\)) are much higher than that 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. Power switches are complementarily operated, and their intrinsic diodes and inherent drain-source capacitors are considered. 3. The conducting voltage drops of all diodes (including \(D_{b1}\), \(D_{b2}\), \(D_{b3}\), \(D_{b4}\), \(D_{1}\), \(D_{2}\), \(D_{3}\) and \(D_{4}\)) are neglected. 4. Two coupled inductors (\(L_{PFC1}\) and \(L_{PFC2}\)) are designed to be operated in discontinuous-conduction mode (DCM) for naturally achieving power-factor correction (PFC). The operating modes and key waveforms of the presented LED tube lamp driver during the positive half-cycle of input utility-line voltage are shown in Figures 3 and 4, respectively, and the analysis of operations for the presented driver are described in detail as follows. _Mode 1_ (\(t_{0}\leq t<t_{1}\); in Figure 3a): The drain-source voltage \(v_{DS1}\) of \(S_{1}\) is decreased to zero at time \(t_{0}\); thus, the body diode of switch \(S_{1}\) is forward-biased. The resonant capacitor \(C_{r}\) provides energy to resonant inductor \(L_{r}\), capacitors \(C_{DC1}\), \(C_{DC2}\), \(C_{o}\) and the LED tube lamp through \(S_{1}\)'s body diode, \(D_{2}\), and \(D_{3}\). When power switch \(S_{1}\) turns on with zero-voltage switching (ZVS) at \(t_{1}\), this mode ends. _Mode 2_ (\(t_{1}\leq t<t_{2}\); in Figure 3b): This mode begins when switch \(S_{1}\) achieves ZVS turn-on at \(t_{1}\). The input voltage \(v_{AC}\) provides energy to coupled inductor \(L_{PFC1}\) through diode \(D_{b1}\) and switch \(S_{1}\). The inductor current \(i_{LPFC1}\) linearly increases from zero, and can be expressed as  
\[i_{LPFC1}(t)=\frac{\sqrt{2}v_{AC-rms}\sin(2\pi f_{AC}t)}{L_{PFC1}}(t-t_{1}). \tag{1}\]  
where \(v_{AC-rms}\) is the root-mean-square (rms) value of the input utility-line voltage, and \(f_{AC}\) is the utility-line frequency. The resonant capacitor \(C_{r}\) still provides energy to inductor \(L_{r}\), capacitors \(C_{DC1}\), \(C_{DC2}\), \(C_{o}\) and the LED tube lamp through \(S_{1}\), \(D_{2}\), and \(D_{3}\). This mode finishes when the resonant inductor current \(i_{Lr}\) is zero at \(t_{2}\). _Mode 3_ (\(t_{2}\leq t<t_{3}\); in Figure 3c): The input voltage \(v_{AC}\) still provides energy to the coupled inductor \(L_{PFC1}\) through diode \(D_{b1}\) and switch \(S_{1}\).