## 2 Proposed Circuit Topology and Operation Analysis  
In our particular study, a half-bridge inductor-capacitor (LC) resonant converter, a boost-typed PFC, a starter circuit, and the developed self-excited circuit were integrated to constitute the novel single-stage structure, as shown in Figure 1. A list of symbols is as follows.  
\(S_{1}\), \(S_{2}\): power switches; \(D_{51}\), \(D_{52}\): intrinsic body diodes of the power switches, \(L_{\text{PFC}}\): inductance of the boost-typed PFC, \(T_{1}\): center-tapped transformer, \(N_{p}\): turns of the primary winding, \(N_{51}\), \(N_{52}\): turns of the secondary windings, \(N_{SE1}\), \(N_{SE2}\): turns of the self-excited windings, \(D_{1}\), \(D_{2}\): full-wave rectifier diodes, \(L_{r}\): inductance of the resonant inductor, \(C_{r}\): capacitance of the resonant capacitor, \(L_{m}\): inductance of the low-pass filter, \(C_{m}\): capacitance of the low-pass filter, \(C_{bus}\): capacitance of the dc-bus capacitor, and \(C_{o}\): capacitance of the output capacitor.  
\(v_{in}\): input line voltage, \(i_{in}\): input line current, \(i_{LPFC}\): PFC inductor current, \(V_{cbus}\): dc-bus voltage, \(i_{cbus}\): dc-bus current, \(V_{o}\): output voltage, \(v_{gs1}\): gate-to-source voltage of \(S_{1}\), \(v_{gs2}\): gate-to-source voltage of \(S_{2}\), \(i_{51}\): drain-to-source current of \(S_{1}\), \(i_{52}\): drain-to source current of \(S_{2}\), \(i_{t}\): resonant current of the resonant circuit, \(v_{AB}\): input voltage of the resonant circuit, \(v_{p}\): voltage across the primary winding, \(f_{r}\): resonant frequency of the resonant circuit, \(f_{s}\): switching frequency of power switches, \(M_{cr}\): voltage gain of the resonant circuit, \(Q\): quality factor of the resonant circuit, \(s\): switching angular frequency, \(r\): resonant angular frequency, \(R_{p}\): equivalent load resistance across the primary winding, \(R_{LED}\): equivalent resistance of the LED string, and \(D\): duty ratio of the power switches.  
MOSFETs \(S_{1}\) and \(S_{2}\) acted as power switches, and the antiparallel diodes \(D_{S1}\) and \(D_{S2}\) as their intrinsic body diodes, respectively. The center-tapped transformer \(T_{1}\) and diodes \(D_{1}\) and D\({}_{2}\) formed a full-wave rectifier. The turn ratio of the primary winding to the secondary windings was n: 1:1. In addition, \(T_{1}\) had two more windings which were employed to provide power switches with self-excited driving voltages. Besides, \(T_{1}\) could provide galvanic insulation with respect to the input line. The low-pass filter (\(L_{m}\) and \(C_{m}\)) was used to remove the high-frequency current of the inductor current, because in this way, the input line current would be sinusoidal with the same frequency as the input line voltage. For simplification of the circuit analysis, the capacitances of \(C_{bus}\) and \(Co\) were assumed to be large enough that the dc-bus voltage \(V_{cbus}\) and the output voltage \(V_{0}\) could be regarded as constant. As shown in Figure 1, the power switch \(S_{2}\) should carry both currents of the PFC converter and the resonant converter. The voltage across \(S_{2}\) is equal to the dc-bus voltage when it is off. Hence, \(S_{2}\) is the crucial component of the proposed circuit and its voltage and current ratings will determine the power range.