**2. Converter Operation**

The proposed configuration is depicted in Figure 3. The input voltage is represented by *E*, the currents and voltages through *L*<sup>1</sup> and *L*<sup>2</sup> are denoted by *iL*<sup>1</sup> , *vL*<sup>1</sup> , *iL*<sup>2</sup> , and *vL*<sup>2</sup> , respectively. The voltages and currents through *Cp*, and *C*<sup>0</sup> are denoted by *vC<sup>p</sup>* , *iC<sup>p</sup>* , *v*0, and *iC*<sup>0</sup> , respectively. On the other hand, the voltages through *S*1, *DS*<sup>1</sup> , *S*<sup>2</sup> and *DS*<sup>2</sup> are denoted by *vS*<sup>1</sup> , *vDS*<sup>1</sup> , *vS*<sup>2</sup> , and *vDS*<sup>2</sup> . Finally, the current through the load *R* is denoted by *I*0.

**Figure 3.** Quadratic boost converter with non-series power transfer.

The analysis is carried out considering the following points:


• For steady-state operation, *T<sup>s</sup>* = *tON* + *tOFF*, where *tON* = *DT<sup>s</sup>* and *tOFF* = (1 − *D*)*T<sup>s</sup>* .

Due to the above assumptions, the proposed configuration operates in two modes. The power transfer from the input to the output of the proposed configuration is shown in Figure 4. As can be seen, a non-series power transfer between the input source and the load occurs due to the transfer capacitor *Cp*.

**Figure 4.** Power flows of the proposed configuration: (**a**) Equivalent scheme when both inductor are storing energy, and (**b**) equivalent scheme when both inductors are delivering energy.

The two operating modes of the converter are described as follows:

Mode I [*tON*]: Both active switches (*S*1, *S*2) are turned ON. The diodes *DS*<sup>1</sup> and *DS*<sup>2</sup> are not conducting; then, the input source *E* delivers energy to the inductor *L*1. The inductor *L*<sup>2</sup> is charged through capacitor *C<sup>p</sup>* by the energy stored in the capacitor *C*0, which also supplies energy to the load. The circuit that describes this operating mode is exhibited in Figure 5.

**Figure 5.** Circuit for the intervale *tON*.

Mode II [*tOFF*]: Both active switches (*S*1, *S*2) are turned OFF. For this interval, the output capacitor *C*<sup>0</sup> and the load *R* are supplied by the energy stored in inductor *L*1, through capacitor *Cp*. The inductor *L*<sup>2</sup> delivers energy to the output (*C*<sup>0</sup> and *R*) through the diode *DS*<sup>2</sup> . The circuit that describes this operating mode is exhibited in Figure 6.

The analysis, modeling, and the expressions in steady-state are easy to develop in two operating modes. On the other hand, the capacitor *C<sup>p</sup>* acts as a power transfer element between the first converter and the output capacitor *C*0. Due to this arrangement, the cascade power transfer between the first and second converter is avoided; thus, there is an improvement in the converter efficiency.

**Figure 6.** Circuit for the interval *tOFF*.
