## 2 The Description and Analysis of the Presented LED Tube Lamp Driver
The DC-bus capacitors \(C_{DC1}\) and \(C_{DC2}\) supply energy to resonant inductor \(L_{r}\), capacitors \(C_{r}\) and \(C_{o}\), and the LED tube lamp through switch \(S_{1}\), \(D_{1}\), and \(D_{4}\). This mode ends when inductor current \(i_{LPFC1}\) reaches its peak value at \(t_{3}\), which is denoted as \(i_{LPFC1-pk}(t)\), and can be expressed as  
\[i_{LPFC1-pk}(t)=\frac{\sqrt{2}v_{AC-rms}\sin(2\pi f_{AC}t)}{L_{PFC1}}DT_{S}. \tag{2}\]  
where \(D\) and \(T_{S}\) are the duty cycle and period, respectively, of the power switch. _Mode 4_ (\(t_{3}\leq t<t_{4}\); in Figure 3d): This mode begins when \(S_{1}\) turns off at \(t_{3}\). The utility-line voltage \(v_{AC}\) and the coupled inductor \(L_{PFC1}\) supply energy to the drain-source capacitor of \(S_{1}\) through diode \(D_{b1}\). The DC-bus capacitors \(C_{DC1}\) and \(C_{DC2}\), the drain-source capacitor of \(S_{2}\) and resonant inductor \(L_{r}\) provide energy to capacitors \(C_{r}\) and \(C_{o}\) and the LED tube lamp through diodes \(D_{1}\) and \(D_{4}\). When the drain-source voltage \(v_{DS2}\) of \(S_{2}\) is decreased to zero at \(t_{4}\), this mode ends. _Mode 5_ (\(t_{4}\leq t<t_{5}\); in Figure 3e): This mode begins when the body diode of switch \(S_{2}\) is forward-biased at \(t_{4}\). The coupled inductor \(L_{PFC1}\) provides energy to \(C_{DC1}\) through diode \(D_{b3}\). The inductor current \(i_{LPFC1}\) linearly decreases, and can be given by  
\[i_{LPFC1}(t)=\frac{\sqrt{2}v_{AC-rms}\sin(2\pi f_{AC}t)-V_{DC}/2}{L_{PFC1}}(t-t _{4}). \tag{3}\]where \(V_{DC}/2\) is the voltage of the DC-linked capacitor \(C_{DC1}\). Inductor \(L_{r}\) provides energy to capacitors \(C_{r}\) and \(C_{o}\) and the LED tube lamp through \(S_{2}\)'s body diodes, \(D_{1}\) and \(D_{4}\). When power switch \(S_{2}\) is turned on with ZVS at \(t_{5}\), this mode ends. _Mode 6_ (\(t_{5}\leq t<t_{6}\); in Figure 3f): This mode begins when switch \(S_{2}\) achieves ZVS turn-on at \(t_{5}\). Inductor \(L_{r}\) continues providing energy to capacitors \(C_{r}\) and \(C_{o}\) and the LED tube lamp through \(S_{2}\), \(D_{1}\) and \(D_{4}\). The mode ends when the resonant inductor current \(i_{L}\), decreases to zero at \(t_{6}\). _Mode 7_ (\(t_{6}\leq t<t_{7}\); in Figure 3g): This mode begins when current \(i_{Lr}\) decreases to zero at \(t_{6}\). Capacitor \(C_{r}\) provides energy to inductor \(L_{r}\), capacitor \(C_{o}\) and the LED tube lamp through \(S_{2}\) and diodes \(D_{2}\) and \(D_{3}\). The mode ends when switch \(S_{2}\) turns off at \(t_{7}\). _Mode 8_ (\(t_{7}\leq t<t_{8}\); in Figure 3h): In this mode, capacitor \(C_{r}\) and the drain-source capacitor of switch \(S_{1}\) provide energy to inductor \(L_{r}\), the drain-source capacitor of \(S_{2}\), capacitors \(C_{DC1}\), \(C_{DC2}\), \(C_{o}\), and the LED tube lamp through diodes \(D_{2}\) and \(D_{3}\). When the drain-source voltage \(v_{DS1}\) of \(S_{1}\) is decreased to zero at \(t_{7}\), this mode ends. Then, _Mode 1_ begins for the next high-frequency switching period. Figure 3: \(Cont.\)  
Figure 3: _Cont._  
Figure 4: Key waveforms of the presented LED tube lamp driver during the positive half-cycle of the input utility-line voltage. Figure 3: Operation modes of the presented driver during the positive half-cycle of input voltage \(v_{AC}\). Figure 5 shows the circuit diagram for controlling the single-stage LED tube lamp driver. Referring to Figure 5 and utilizing a constant voltage/current controller (IC1 SEA05) for regulating the LED tube lamp's output voltage and current, the output voltage \(V_{o}\) can be sensed through resistors \(R_{vs1}\), \(VR_{1}\) and \(R_{vs2}\), and the output current can be sensed through resistor \(R_{3}\). The sensed output signal from pin 5 of the IC1 feeds into the high-voltage resonant controller (IC3 ST L6599) through a photo-coupler (IC2 PC817). Two gate-driving signals \(v_{GS1}\) and \(v_{GS2}\) are generated from pin 15 and pin 11, respectively, of the IC3, to carry out regulating the LED tube lamp's output voltage and current.