The maximum current of the Lr1 can be given by Im1=uCr(t2)/ZLC (5) The impedance of the resonant ZLC can be given by Model 4〔 t3～t4〕 At t3, the current through the resonant tank increases to Io/n, the current through S1 decreases to zero, the anti-parallel diode begins to work, because the current through resonant tank increases from zero, according to i(t3)=Io/n (7) The time interval can be derived from Model 5〔 t4～t5〕 At t4, when turning off the S1, the S1 is in zero-current state, but the anti-parallel diode is still in conducting state. The current through resonant tank decreases from Im1 to Io/n, The total time interval of model 4 and model 5 is By the equation (2) and (9), the voltage of Cr at t5 can be expressed as Model 6〔 t5～ t6〕 At t5, the current of resonant tank decreases to Io/n, the diode D1 turns off naturally, then the current through the resonant tank will keep to be Io/n, the voltage of S1 begins to increase, while the voltage of S2 to decrease.Because the capacitor discharges in constant current, so the voltage of resonant capacitor can be given as From the equation(11) we can see that the voltage value of resonant capacitor increases gradually, at t6, to Uin/2. From equation (10) and (11), we know that the time interval of this model can be expressed as Model 7〔 t6～ t7〕 At t6, the voltage of Cr begins to increase from Uin/2, the rectifier composed of D5 to D8 begins to conduct, the voltage of S2 continues to decrease. The resonant network is composed of inductor Lr3, resonant capacitor Cr and leakage inductor Lk, and the network cooperation with link capacitor C1, the initial state of the resonant network is Therefore this model should meet the following equation: where At t7, when the voltage of Cr is Vin, the D2 begins to work, the voltage of the leakage inductor is fixed at (Lk＋ Lr)Uin/Lk. From equation (15) and (16). We can see that the time interval of model 7 can be given by Model 8〔 t7～ t8〕 At t7, the voltage of S2 decreases to zero, the anti-parallel diode D2 begins to work, the current through the transformer will be reduced to zero by the capacitor C2. In this model, the current of Lr3 should meet the following equation: The current of leakage inductor can be given by Model 9〔 t8～ t10〕 At t8, the current through the transformer is zero. The resonant tank composed of Cr,Lr3 and Lr2 will begin to work, and the current through Lr3 will change the direction. At t9, when turning off S3, the S3 is in ZCS model. After half of the resonant period, the current of Lr3 decreases back to zero and the anti-parallel diode D3 turns off natu rally. The time interval of this model can be given by The work process of S2 is accordant with above, so in this paper the work process of S1 is mainly discussed. Fig.3 The equivalent circuits of the work process by S1 2 The Discussion to the Circuit Model 2.1 The Duty Ratio Loss The duty ratio loss is concentrated in time interval t0 to t1, therefore the duty ratio loss is where Ts is the switch cycle period. 2.2 Minimum Duty Ratio To ensure soft switching off, there should be enough time for the current of S1 to decrease to zero before the switch turns off. From model 3, equation (8), we can deduce the minimum duty ratio is 2.3 Soft Commutation Conditions 1)From the analysis for model 4, 5 and equation (8) and (9), we can see that, if there is enough time for S1 to realize turning at zero current, the maximum current of the resonant network must meet the following expression: 2)If the output current Io is small, and the Io meet the following expression: From equation (15), we know that the voltage of Cr will not increase to Uin, the D2 would not conduct, the time interval of model 7 would delay until the current of the Lk decreases to zero, therefore the model 8 would disappeared. But still the IGBT is switched in ZCS, and the D3 turns off naturally. 3)From the above analysis to topology, we can see that in the topology, if the maximum current is larger enough to meet the expression (27), and the time t4 correspended to main switch turning off satisfies the following condition: and the time t9 correspended to auxiliary switch turning off meets the following condition: