# Design Considerations of Multi-Phase Buck DC-DC Converter
## 4 Analytical and Simulation Study of Power Losses in an 8-Phase Synchronous Buck Converter  
### Analytical Study of Power Losses in an 8-Phase Synchronous Buck Converter  
In this paragraph, power losses as a function of switching frequency \(f_{SW}\) and duty cycle \(D\) are investigated for a control example with the following data: _Uout_ = 1.6 V, \(I_{0}\) = 200 A, \(f_{SW}\) = 75 kHz \(\div\) 300 kHz; dead time \(t_{d}\) = 100 ns. Based on the data shown in Table 6, the multi-phase synchronous buck converter with \(N\) = 8 is chosen. The used transistors are SiRA10 BDP and SiRC10 DP.  
For the proper choice of the circuit elements, the estimation of the losses resulting from the changes in different parameters is of particular importance. All power losses plotted in Figure 5 consider the 8-phase synchronous buck converter (\(N\) = 8). Figure 5a shows the total power loss distribution \(P_{out}(D,f_{SW})\) as a function of the duty cycle D and the switching frequency \(f_{SW}\). Figure 5b illustrates the total HS MOSFETs power losses \(P_{QHN}(D,f_{SW})\) and Figure 5c shows the total LS MOSFETs power losses \(P_{QLN}(D,f_{SW})\). The inductance losses of the considered multi-phase synchronous buck converter versus the duty cycle D and the switching frequency \(f_{SW}\) are given in Figure 5d. The power losses in the output \(P_{Cout}(D,f_{SW})\) and input capacitors \(P_{Cin}(D,f_{SW})\  
Power losses increase with increasing frequency, as at small duty cycles, the power losses are significant. In addition, power losses in the low-side transistors are considerable.  
The following Figure 6a,b show the dependencies of total HS MOSFETs losses versus the total converter's power losses \(P_{QHN}/P_{out}\), % and HS MOSFETs switching losses versus the HS MOSFETs total power losses \(P_{QSW\_HN}/P_{Q_{HN}}\), % in the 8-phase synchronous buck converter, respectively. In Figure 6c, the dependencies of the total LS MOSFETs losses versus the total power losses \(P_{QLN}/P_{out}\), % are plotted. The dependencies of the inductance losses of the considered 8-phase synchronous buck converter versus the total power losses \(P_{LN}/P_{out}\), % are illustrated in Figure 6d.  
Figure 5: Multi-phase synchronous buck converter losses at \(N=8\): (**a**) Total power losses \(P_{out}(D,f_{SW}),W\); (**b**) total HS MOSFETs power losses \(P_{QHN}(D,f_{SW}),W\); (**c**) total LS MOSFETs power losses \(P_{QLN}(D,f_{SW}),W\); (**d**) the inductances losses \(P_{LN}(D,f_{SW}),W\); (**e**) the power losses in the output capacitor \(P_{Cout}(D,f_{SW})\), W; (**f**) power losses in the input capacitor \(P_{Cin}(D,f_{SW})\), W.  
Based on these results, it is evident that in the range up to the duty cycle D \(\approx\) 0.4, for the studied frequency range, the losses in the low-side transistors at frequencies up to \(f_{SW}\approx\) 100 kHz are a significant part of the total losses in the converter (\(\approx\)45%), whereas the losses in the high-side transistors are \(\approx\)35% of the total losses in the converter. Switching losses are the highest percentage of the total losses in the upper transistors (\(\approx\)80%) at small values of duty cycle D regardless of the operation frequency range. With increasing the  
Figure 6: Multi-phase synchronous buck converter losses at \(Lout=\) 1.6 V, \(I_{0}=\) 200 A, \(N=\) 8: (**a**) The total HS MOSFETs losses vs. to the total power losses \(P_{QHN}/P_{out}\), %; (**b**) the HS MOSFETs switching losses vs. the total power losses in HS MOSFETs \(P_{QSW\_HN}/P_{QHN}\), %; (**c**) the total LS MOSFETs losses vs. the total power losses \(P_{QLN}/P_{out}\), %; (**d**) the inductances losses vs. the total power losses—\(P_{LN}/P_{out}\), %.  
frequency, the losses in the high-side transistors increase, and at a frequency of 300 kHz, the losses in the high-side transistors are \(\approx\)50% of the total losses in the circuit.