# Design Considerations of Multi-Phase Buck DC-DC Converter
## 3 Design Considerations of Multi-Phase Buck DC-DC Converters
Figure 3a,b provide a graphical representation of efficiency \(\eta\) evaluated by (-23) for the control examples with the following parameters: \(Ulin=12\) V, \(Uout=1.6\) V, \(f_{SW}=200\) kHz/\(f_{SW}=300\) kHz, \(I_{0}=5\div 200\) A, \(t_{d}=100\) ns. Figure 3c,d present the graphical representation of efficiency \(\eta\) evaluated by (-23) for the next control examples: \(Ulin=12\) V, \(Uout=3.3\) V, \(f_{SW}=200\) kHz/\(f_{SW}=300\) kHz, \(I_{0}=5\div 200\) A, \(t_{d}=100\) ns. Furthermore, in Figure 3e,f are plotted (23) for the control examples with the following parameters: \(Ulin=12\) V, \(Uout=5\) V, \(f_{SW}=200\) kHz/\(f_{SW}=300\) kHz, \(I_{0}=5\div 200\) A, \(t_{d}=100\) ns. Based on Figure 3a, it can be concluded that at the output current values \(I_{0}<20\) A the multi-phase synchronous buck converter with \(N=2\) has the highest efficiency (90.8%). For output current values in the range of 20 A \(<I_{0}<35\) A, the highest efficiency \(\eta\) has a circuit with \(N=4\) (\(\eta=90.77\%\)). For output current values in the range of 35 A \(<I_{0}<45\) A, the circuit with \(N=6\) has the highest efficiency (\(\eta=90.792\%\)). On the other hand, at \(I_{0}=40\) A the efficiency of a circuit with N = 4 is \(\eta=90.58\%\), whereas for \(N=6\) it is \(\eta=90.79\%\), or in other words, the efficiency is 0.21% less than that of \(N=6\). By analyzing the efficiency for \(N=4\) and \(I_{0}=45\) A, it is observed that \(\eta=90.44\%\). Therefore, for this range of variation in output current \(I_{0}\), the efficiency decreases by 0.25% compared to the \(N=6\) configuration. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c|}{\(\Delta I_{Cout}\) A - _Ulin_ = 12 V, \(f_{SW}\) = 200 kHz} & \multicolumn{3}{c}{\(\Delta I_{Cout}\) A - _Ulin_ = 12 V, \(f_{SW}\) = 300 kHz} \\ \hline _Uout,_ V & _N =_ 4 & _N =_ 6 & _N =_ 8 & _N =_ 12** & _Uout,_ V & _N =_ 4 & _N =_ 6 & _N =_ 8 & _N =_ 12** \\ \hline
1.6 & 1.965 & 0.842 & 0.246 & 0.632 & 1.6 & 1.31 & 0.561 & 0.164 & 0.421 \\
3.3 & 0.711 & 1.197 & 0.632 & 0.553 & 3.3 & 0.474 & 0.798 & 0.421 & 0.368 \\
5 & 1.754 & 1.316 & 0.877 & 0 & 5 & 1.17 & 0.877 & 0.585 & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Multi-phase buck converter output ripple current peak-to-peak amplitude \(\Delta I_{Cout}\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c|}{\(I_{IN\_rms}\), A - _Ulin_ = 12 V, \(f_{SW}\) = 200 kHz} & \multicolumn{3}{c}{\(I_{IN\_rms}\), A - _Ulin_ = 12 V, \(f_{SW}\) = 300 kHz} \\ \hline  & _Uout_ & _N =_ 4 & _N =_ 6 & _N =_ 8 & _N =_ 12** & _Uout_ & _N =_ 4 & _N =_ 6_ & _N =_ 8_ & _N =_ 12** \\ \hline \multirow{3}{*}{\(I_{0}=45\) A} & 1.6 V & 5.665 & 3.144 & 1.662 & 1.944 & 1.6 V & 5.636 & 3.065 & 1.524 & 1.885 \\  & 3.3 V & 3.659 & 3.766 & 2.551 & 2.005 & 3.3 V & 3.504 & 3.662 & 2.389 & 1.851 \\  & 5 V & 5.503 & 3.916 & 2.911 & 2.216 & & 5 V & 5.393 & 3.825 & 2.770 & 1.477 \\ \hline \multirow{3}{*}{\(I_{0}=100\) A} & 1.6 V & 12.496 & 6.733 & 3.243 & 4.131 & & 1.6 V & 12.483 & 6.696 & 3.174 & 4.104 \\  & 3.3 V & 7.632 & 8.036 & 5.143 & 3.956 & \multirow{3}{*}{\(I_{0}=100\) A} & 1.00 & 3.3 V & 7.559 & 7.988 & 5.064 & 3.880 \\  & 5 V & 11.876 & 8.410 & 6.014 & 2.216 & & 5 V & 11.826 & 8.367 & 5.947 & 1.477 \\ \hline \multirow{3}{*}{\(I_{0}=150\) A} & 1.6 V & 18.724 & 10.044 & 4.761 & 6.156 & \multirow{3}{*}{\(I_{0}=150\) A} & 1.6 V & 18.715 & 10.02 & 4.715 & 6.138 \\  & 3.3 V & 11.339 & 11.982 & 7.596 & 5.821 & & 11.289 & 11.95 & 7.543 & 5.769 \\  & 5 V & 17.739 & 12.551 & 8.920 & 2.216 & & 5 V & 17.705 & 12.523 & 8.875 & 1.477 \\ \hline \multirow{3}{*}{\(I_{0}=200\) A} & 1.6 V & 24.956 & 13.367 & 6.299 & 8.190 & & 1.6 V & 24.95 & 13.348 & 6.264 & 8.176 \\  & 3.3 V & 15.067 & 15.942 & 10.072 & 7.707 & & 10.200 A & 3.3 V & 15.03 & 15.918 & 10.032 & 7.669 \\ \cline{1-1}  & 5 V & 23.616 & 16.705 & 11.846 & 2.216 & & 5 V & 23.591 & 16.684 & 11.812 & 1.477 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Multi-phase buck converter RMS value of input current \(I_{IN\_rms}\).