# Design Considerations of Multi-Phase Buck DC-DC Converter
## 3 Design Considerations of Multi-Phase Buck DC-DC Converters  
_Optimum Phase Numbers for Some Common Input and Output Voltages_  
The growing necessity for rapid and accurate phase number prediction in designing multi-phase buck converters, so as to minimize the ripple currents and achieve high efficiency is of particular importance to power supply designers. For this purpose, using the results from different control examples, this section discusses the selection of the optimum phase numbers for various common input and output voltages. Analytical examples (with an application in modern microprocessors) are based on the following parameters:  
* _Uin_ = 12 V, _Uout_ = 1.6 V/3.3 V/5 V, _f_SW = 75 kHz \(\div\) 300 kHz, \(I\)0 = 5\(\div\) 200 A, _t_\({}_{d}\) = 100 ns;  
To increase the efficiency of the multi-phase synchronous buck converter, transistors with small reverse recovery charge Qrr and R\({}_{\text{D}\text{S}\text{o}\text{n}}\). are selected. Table 1 presents the MOSFET data used in the considered examples [39; 40; 41; 42; 43]. The used capacitors _Cout_ and _Cin_ (Figure 1) have equivalent series resistances \(ESRout=ESRin=0.8\) m\(\Omega\). The value of the used inductances \(LI=\ldots=LN=L=1.9\) uH and the equivalent series resistances of the output inductances \(DCR1=\ldots=DCRN=DCR=0.62\) m\(\Omega\) (high current shielded power inductors AGM2222 [44]). A proper starting point is to select an inductor such that its ripple current amplitude is about 40% of the maximum channel current [35]. It is well known that increasing the number of units helps to reduce the maximum ripple current [32; 33; 34; 35; 36; 37; 38]. Also, the ripple output current and output voltage will reach zero if the duty cycle is equal to one of the following critical points:  
\[\text{D}_{\text{crit}}=i/N\;i=1,2,N-1. \tag{24}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Part Number**} & & **Id @** & **R\({}_{\text{D}\text{S}\text{n}}\)** & **Coss** & **Q\({}_{\text{G}}\)**,** & **Qrr** & **trr @** & \\  & **V\({}_{\text{DS}}\), V** & **Tc = 25 \({}^{\circ}\)C,** & **GTj = 25 \({}^{\circ}\)C,** & **PF** & **nC (Vgs = 10 V)** & **nC** & **Tj = 25 \({}^{\circ}\)C,** & **V\({}_{\text{SD}}\), V** \\  & **A** & **m\(\Omega\)** & **m\(\Omega\)** & **nC** & **nC** & **nS** & **nS** & **nS** \\ \hline SiRA10 BDP & 30 & 60 & 2.3 & 655 & 24.1 & 36 & 38 & 0.75 \\ SiRC10 DP (SkyFET & & & & & & & & \\ with monolithic & 30 & 60 & 2.9 & 760 & 24.0 & 27 & 35 & 0.51 \\ Schottky diode & & & & & & & & \\ SiRC06 DP & 30 & 60 & 2.2 & 350 & 38.5 & 19 & 31 & 0.47 \\ CSD17581Q3A & 30 & 60 & 3.2 & 342 & 41.0 & 10.2 & 9.8 & 0.80 \\ CSD17581Q5A & 30 & 60 & 2.9 & 342 & 41.0 & 13 & 11 & 0.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: N-Channel Power MOSFETs—typical values. For the considered examples, based on (2) and (3) the presented results in Tables 2 and 3 are for the RMS value of input current \(I_{IN\_rms}\) and the output ripple current peak-to-peak amplitude \(\Delta I_{Cout}\) of the multi-phase buck converter. The used transistors are SiRA10 BDP (\(QI\)) and SiRC10 DP (\(Q2\)). It can be seen that, for all \(N\), the RMS value of the input current \(I_{IN\_rms}\) and the peak-to-peak ripple current amplitude \(\Delta I_{Cout}\) decrease as the frequency increases. Furthermore, at \(Uout=5\) V and \(N=12\), the output ripple current will be zero. Therefore, theoretically, the output filter capacitor can be eliminated in the circuit. Thus, the size of the converter can be reduced significantly, and the response time will be faster. However, from a practical point of view, most of the converters operate with a variable duty cycle due to compatibility considerations with varied power supplies, and eliminating the output capacitor is impossible. However, providing less ripple current contributes to the use of less bulky capacitors. Another crucial criterion in selecting the optimal number of phases is the circuit's efficiency.