## 3 Analysis of Semiconductor Power Loss
### Switching Loss  
The switching loss of MOSFET, \(P_{S,SW}\) is divided into switch turn-on loss, \(P_{S,SW,ON}\) switch turn-off loss \(P_{S,SW,OFF}\), and output capacitance loss \(P_{S,SW,Coss}\) as [5; 15; 17]:  
Figure 5: Switch and diode current of the proposed TSBB converter: (**a**) Buck; (**b**) Boost; (**c**) Buck-boost.  
\[P_{S,SW}=P_{S,SW,ON}+P_{S,SW,OFF}+P_{S,SW,Coss} \tag{7}\]  
The switch turn-on and turn-off losses are difficult to calculate because of the nonlinear characteristics of the drain-source voltage \(v_{DS}\) and drain current \(i_{D}\). Therefore, they can be determined by applying linear approximation in the rising and falling sections of \(v_{DS}\) and \(i_{D}\). The output capacitance loss of MOSFET can be determined by calculating the stored energy of the capacitor because the energy is charged in the output capacitance when the MOSFET turns off, and is discharged when the MOSFET turns on. The MOSFET switching loss can be represented by using the turn-on time \(t_{on}\), turn-off time \(t_{off}\), switching frequency \(f_{sw}\), and output capacitance \(C_{oss}\) of the MOSFET as [5; 17; 18]:  
\[\begin{array}{l}P_{S,SW}=\frac{1}{2}\cdot v_{DS}\cdot i_{D}\cdot t_{on}\cdot f _{sw}+\frac{1}{2}\cdot v_{DS}\cdot i_{D}\cdot t_{off}\cdot f_{sw}+\frac{1}{2} \cdot C_{oss}\cdot v_{DS}\cdot^{2}\cdot f_{sw}\\ \\ =\frac{1}{2}\cdot v_{DS}\cdot i_{D}\cdot(t_{on}+t_{off})\cdot f_{sw}+\frac{1}{2} \cdot C_{oss}\cdot v_{DS}\cdot^{2}\cdot f_{sw}\end{array} \tag{8}\]  
The output capacitance of the MOSFET is several tens to hundreds of picofarads. Therefore, it is negligible compared to the switch turn-on and turn-off losses and can be represented as [5; 6; 17; 18]:  
\[P_{S,SW}=\frac{1}{2}\cdot v_{DS}\cdot i_{D}\cdot(t_{on}+t_{off})\cdot f_{sw} \tag{9}\]  
The switching loss \(P_{D,SW}\) of the diode can be divided into the switch turn-on loss \(P_{D,SW,ON}\) and the switch turn-off loss \(P_{D,SW,OFF}\) it is represented as:  
\[P_{D,SW}=P_{D,SW,ON}+P_{D,SW,OFF}\cong P_{D,SW,OFF} \tag{10}\]  
The switching loss of the diode can be approximated as the switch turn-off loss because the loss of the diode caused by the reverse recovery in the turn-off section is considerably larger than the turn-on loss [19; 20].  
Figure 6 shows the reverse recovery characteristic of the diode [6]. In an ideal diode, the current flows when the voltage is applied in the forward direction, and no current flows when the voltage is applied in the reverse direction. However, in an actual operation, the reverse current flows for a certain time before it reaches zero when the diode is turned off after a forward current flow. Here, the time during which the reverse current flows is referred to as the reverse recovery time (\(t_{tr}\)); the maximum value of the reverse current that flows in the diode is referred to as the repetitive peak reverse current (\(I_{RRM}\)). The turn-off loss \(P_{D,SW,OFF}\) of the diode when the reverse voltage applied to the diode is \(V_{R}\) and the switching frequency is \(f_{sw}\) can be expressed as [21; 22]:  
\[P_{D,SW}=\frac{1}{2}\cdot V_{R}\cdot I_{RRM}\cdot t_{rr}\cdot f_{sw} \tag{11}\]  
Figure 6: Diode reverse recovery characteristics.