## 1 Introduction  
As well known, the switching power supply is widely used today. This is because of its small volume, high efficiency, etc. However, it has some disadvantages due to its hard switching, such as high switching loss, large voltage/current stress and strong electromagnetic interference. To overcome the demerits mentioned above, the quasi-resonant converter (QRC) [1; 2; 3; 4; 5; 6] has been investigated since 1980, mainly on the condition that the voltage/current waveform is sinusoidal. This converter contains the resonant inductor in a series with the switch or the diode, and hence resonates with the switch parasitic capacitor or the diode parasitic capacitor so that the zero-voltage switching (ZVS) during the turn-on period or the zero-current switching (ZCS) during the turn-off period can be realized. However, this inductor locates on the path of the main power stage such that the high voltage/current on/in the switch or diode will occur and hence the circulation current is unavoidable, thereby creating a large conduction loss. Moreover, the resonant energy comes from the input and the load such that the soft switching can be achieved only for some input voltage range as well as some load range. To overcome the demerits of QRCs, a resonant network paralleled with the main power stage path was developed. Some derived structures were presented, such as active clamp [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21], zero-voltage transition (ZVT) and zero-current transition (ZCT) [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. The last two structures use resonant networks, which will make the main switch have ZVS and ZCS according to the auxiliary switch. Furthermore, the voltage on the switch and the current in the switch are of sinusoidal form. By doing so, the voltage stress and current stress for the switch are effectively alleviated, causing the circulation current to be small and hence the unavoidable conduction loss to be reduced. Moreover, the required resonant energy is not all determined by the input voltage and output load. Accordingly, in design of the resonant parameters for soft switching all over the range of input voltage and output load, only the minimum input voltage and the maximum output load were considered. On the other hand, to increase the output current as well as to upgrade the corresponding overall efficiency, the multiphase converter along with interleaved control are commonly utilized. Since the AC components of the inductor currents for multiple phases are cancelled with each other to some extent, not only is the output current ripple thereby decreased but also the frequency of the output current ripple is increased. Accordingly, not only will the design of the required filter be easier, but the corresponding size will also be smaller. Generally, the total loss generated from multiple phases will be smaller than that generated from one phase. Furthermore, the soft switching multiphase converter is proposed so that the overall efficiency is further upgraded. The literature [34; 35; 36; 37] takes multiple phases with the accompanying number of auxiliary resonance circuits, thereby resulting in increasing the number of components and hence increasing not only the conduction loss but also the cost. In the literature [36], the two-phase converter utilizes the same auxiliary resonant circuit. However, only the ZVS is employed so that the improvement in efficiency is restricted. In the literature [37], a two-phase converter adopts one snubber circuit to force the main switches to realize soft switching. Nevertheless, the resonant inductor is put on the power path, thus increasing the conduction loss. In addition, since there are differences in component features and line impedance between the two phases, the current-balancing control will be required. Regarding current balance, there are two types of current-balancing control strategies. One method is passive; the other method is active.