## 2 Proposed Topology and Working Principle
\[i_{A1}(t)=i_{A\_peak}-\frac{V_{\text{in}}-2V_{\text{CA1}}}{2L_{A}}t \tag{3}\]  
where \(i_{A\_peak}\) is the peak value of the auxiliary current, \(0<t\leq DT_{\text{s}}\) and \(D\) is the duty cycle, and \(T_{\text{s}}\) is the PWM period. With the proposed ACACs, all the main switches realized zero-voltage turn-on even at no load condition, and the auxiliary switch realized zero current turn-on and zero-voltage turn-off. The auxiliary current \(i_{A1}\) is controllable by adjusting the turn-on time of the auxiliary switch \(S_{A}\), and the auxiliary current \(i_{A1}\) will be zero if the auxiliary switch \(S_{A1}\) is not turned on. If the load is heavy enough, the ACACs will not work and the ITLDC achieves natural ZVS. When the load is light, the auxiliary current \(i_{A1}\) can be controlled to a suitable value to realize ZVS. Then, a full load range ZVS of the ITLDC can be realized; thus, the efficiency will be high. The detailed working process is analyzed as follows. The main theoretical waveforms of the ITLDC with ACACs are shown in Figure 4, and the positive directions of currents and voltages are marked in Figure 2. Since the working principle of the ITLDC has already been described in [7], here, we focus on the realization of ZVS. One switching period is divided into ten time intervals and the equivalent circuits for each time interval are shown in Figure 5. Before the analysis, the following assumptions are made: (1) the output inductor \(L_{\text{o}}\) is large enough, and thus the output current \(i_{\text{o}}\) can be assumed to be constant; (2) the magnetizing current is negligibly small; (3) the equivalent parallel capacitors have the same value, i.e., \(C_{1}=C_{2}=C_{3}=C_{4}=C_{\text{s}}\); (4) the auxiliary inductors have the same value, i.e., \(L_{A1}=L_{A2}=L_{A}\). Detailed analysis for each time interval is described as follows. Interval 1 (Figure 5a, \(t_{0}\)-\(t_{1}\)): During this interval, the auxiliary current \(i_{A1}\) will decrease from the maximum value \(i_{A\_peak}\) to \(-i_{A\_peak}\), which can be expressed as (3). The current \(i_{S1}\) flows though the main switch \(S_{1}\) and the value of \(i_{S1}\) is equal to \((i_{L}-i_{A1})\). Interval 2 (Figure 5b, \(t_{1}\)-\(t_{2}\)): At \(t_{1}\), the main switch \(S_{1}\) is turned off and the auxiliary current \(i_{A1}\) reaches the peak value \(-i_{A\_peak}\). The current \(i_{A1}\) and \(i_{L}\) will charge \(C_{1}\) and discharge \(C_{2}\) until the voltage of \(C_{2}\) reaches zero; thus, the zero-voltage turn-on condition for the switch \(S_{2}\) is realized. At \(t_{1}\), the auxiliary switch \(S_{A1}\) is turned off at zero-voltage condition. Interval 3 (Figure 5c, \(t_{2}\)-\(t_{3}\)): At \(t_{2}\), the switch \(S_{2}\) is turned on at zero-voltage condition and the converter reaches a freewheeling stage. At \(t_{2}\), the current \(i_{A1}\) reaches \(-i_{A\_peak}\). Since the voltage of \(V_{\text{CA1}}\) is assumed to be constant, the charge variation of the capacitance \(C_{A1}\) should be zero. The voltage \(V_{\text{CA1}}\) is applied to the auxiliary inductance; thus, the auxiliary current \(i_{A1}\) increases linearly, which can be expressed as (4). The current \(i_{A1}\) will reach zero quickly. \[i_{A1}(t)=-i_{A\_peak}+\frac{V_{\text{CA1}}}{L_{A}}t \tag{4}\]Figure 1:0 Theoretical waveforms of the ITLDC with proposed ACACs. Figure 1:1 _Cont_. Interval 4 (Figure 5d, \(t_{3}\)-\(t_{4}\)): The auxiliary switch S\({}_{\rm A2}\) is turned on at zero-current condition and the auxiliary current \(i_{\rm A2}\) is built up in a short time. The auxiliary current  
Figure 1:2 Equivalent circuits for each time interval. (**a-j**) are the equivalent circuits of interval 1–interval 10 respectively. increases from zero; thus, the auxiliary switch S\({}_{\text{A2}}\) realizes zero-current turn-on. At \(t_{4}\), the main switch S\({}_{4}\) is turned off and the current \(i_{\text{A2}}\) reaches the maximum value \(i_{\text{A\_peak}}\).