# Design Considerations of Multi-Phase Buck DC-DC Converter
## 5 Conclusions  
Increasing the need for rapid and accurate prediction of phase numbers in the design of multi-phase buck converters to minimize ripple currents and achieve high efficiency is of particular importance to power supply designers. Analytical and graphical (3D plots) analyses of output and input current ripples in the multi-phase converter, as well as the losses in the converter circuit, were conducted using control examples. Based on the analytical results, it was demonstrated that for the considered control examples, when the output current values \(I_{0}\) are less than 20 A (\(I_{0}<20\) A), the multi-phase synchronous buck converter with \(N=2\) exhibits the highest efficiency (90.8%). Meanwhile, for output current values in the range of 20 A \(<I_{0}<35\) A, a configuration with \(N=4\) (\(\eta=90.77\%\)) achieves the highest efficiency. Other important results obtained show that for the output current range of 35 A \(<I_{0}<45\) A, the highest efficiency is achieved with a configuration using \(N=6\) phases (\(\eta=90.792\%\)). At the same time, at an output current value of \(I_{0}=40\) A, the efficiency of the \(N=4\) phase circuit is 0.21% lower than that of the \(N=6\) phase circuit. When the output current is \(I_{0}=100\) A, the efficiency of the \(N=12\) phase configuration is 0.14% higher than that of the \(N=8\) phase configuration, whereas at \(I_{0}=200\) A, the efficiency of the \(N=12\) phase circuit is 0.62% higher than that of the \(N=8\) phase circuit. Furthermore, the article assesses power losses resulting from changes in various parameters such as duty cycle (D = 0.1 \(\div\) 0.9) and operating frequency (75 kHz \(\div\) 300 kHz). It is shown that power losses increase with an increase in frequency, as significant losses are observed at low-duty cycles. The simulation results of power losses in the multi-phase synchronous buck converter with \(N=8\) are also presented in the article. The relative error between analytical and simulation results does not exceed 4%. A discussion on the optimal phase numbers for common input and output voltages is included. The choice of the optimal number of phases should be approached comprehensively to evaluate the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Quantity** & **Calc.** & **Simul.** & \(\delta\)**, \%** \\ \hline Output current \(I_{0}\), A & 200 & 196.987 & 1.5 \\ Output voltage \(U_{0}\), V & 3.3 & 3.25 & 1.5 \\ peak-to-peak inductor current \(\Delta I_{L}\) & 6.296 & 6.326 & \(-\)0.48 \\ HS MOSFET RMS current \(I_{QH\_rms}\), A & 13.145 & 13.146 & 0 \\ LS MOSFET RMS current \(I_{QL\_rms}\), A & 21.343 & 20.922 & 1.97 \\ Inductune \(L1\) RMS current \(I_{L1\_rms}\), A & 25.066 & 24.56 & 2 \\ HS MOSFETs conduction losses \(P_{Qom\_LN}\), W & 4.424 & 4.312 & 2.5 \\ LS MOSFETs conduction losses \(P_{Qom\_LN}\), W & 8.384 & 8.16 & 2.6 \\ Inductances losses \(P_{LN}\), W & 3.12 & 3 & 3.8 \\ HS MOSFETs total losses \(P_{QHN}\), W & 6.65 & 6.4 & 3.8 \\ LS MOSFETs total losses \(P_{QLN}\), W & 15.44 & 14.84 & 3.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: A comparison of the design parameters obtained from the calculations and those from the simulations—\(f_{SW}=200\) kHz, \(I_{0}=200\) A.  
advantages of increasing the number of phases in a multi-phase buck configuration. The proposed approach for a fast and accurate calculation of power losses and overall efficiency reduces preliminary computational procedures and optimizes solutions. Therefore, the methodology discussed for design can find applications both in engineering practice and in the education of students in power electronics. In further research, authors should focus their attention on calculating the induction core losses and the converter's practical implementation. [PERSON] and [PERSON] were involved in the full process of producing this paper, including conceptualization, methodology, modeling, validation, visualization, and preparing the manuscript. All authors have read and agreed to the published version of the manuscript.