## 5 Unconventional Phase Shift Approach  
As seen in Figure 5c, the attenuation requirement and filter corner frequency are slightly different for one unit non-interleaved and two units and three units with a conventional phase shift. Hence, the interleaving technique does not have any benefits at some switching frequency ranges, such as 75-150 kHz, for two units interleaved in comparison to one unit in Band B. Hence, observing the carrier frequency harmonics behavior based on the phase to get the unconventional phase shift is essential in that frequency range. Notably, analytical EMI estimation can be predicted on EMI noise level in any order of carrier frequency harmonics based on the selective phase angle. Therefore, an unconventional phase shift can be selected by looking at the first appeared carrier harmonics behavior in the different phases in Band B. Hence, Table 3 provides an unconventional phase shift from  
Figure 7: Norton equivalent circuit of the interleaved boost PFC converter.  
an analytical estimation approach to get a low filter attenuation requirement based on the switching frequency and the number of interleaved units. Figure 8 depicts the first carrier harmonics behavior in Band B for several interleaved case studies in different phases and switching frequencies. The first carrier harmonics can be removed by proper phase shift selection. On the other hand, by eliminating the first noise peak, which is important in EMI filter design in Band B, the filter design frequency shifts to a high frequency. So, (17) and (18) representing unconventional phase shift formulation are obtained from Table 3 by assessing the relation between \(N\), \(k\), and \(\theta\).  
\[\theta=\frac{360^{o}}{N}\hskip 28.452756 pt\text{if $k$ is not a multiple of $N$} \tag{17}\]  
\[\theta=\frac{360^{o}}{\min\{factor(N)\,.k\}}\hskip 28.452756 pt\text{if $k$ is a multiple of $N$} \tag{18}\]  
where \(k\) denotes the harmonic order of the switching frequency, that is the first noise peak in Band B.  
Figure 8: First carrier harmonics behavior with various switching frequencies in Band-B for three interleaved units with different phases.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency (kHz)**} & \multirow{2}{*}{**Harm. Order (k):**} & \multicolumn{4}{c}{**Number of Interleaved (N)**} \\ \cline{3-5}  & & **2** & **3** & **4** \\ \hline
20 & 8 th & 22.5\({}^{\circ}\) & 120\({}^{\circ}\) & 22.5\({}^{\circ}\) \\
25 & 6 th & 30\({}^{\circ}\) & 20\({}^{\circ}\) & 90\({}^{\circ}\) \\
30 & 5 th & 180\({}^{\circ}\) & 120\({}^{\circ}\) & 90\({}^{\circ}\) \\
35 & 5 th & 180\({}^{\circ}\) & 120\({}^{\circ}\) & 90\({}^{\circ}\) \\
37.5 & 4 th & 45\({}^{\circ}\) & 120\({}^{\circ}\) & 45\({}^{\circ}\) \\
45 & 4 th & 45\({}^{\circ}\) & 120\({}^{\circ}\) & 45\({}^{\circ}\) \\
50 & 3 th & 180\({}^{\circ}\) & 40\({}^{\circ}\) & 90\({}^{\circ}\) \\
70 & 3 th & 180\({}^{\circ}\) & 40\({}^{\circ}\) & 90\({}^{\circ}\) \\
75 & 2 th & 90\({}^{\circ}\) & 120\({}^{\circ}\) & 90\({}^{\circ}\) \\
140 & 2 th & 90\({}^{\circ}\) & 120\({}^{\circ}\) & 90\({}^{\circ}\) \\
150 & 1 th & 180\({}^{\circ}\) & 120\({}^{\circ}\) & 90\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The Unconventional Phase Shift Angles at the Switching Frequency Range (20–150 kHz) up to Four Units Interleaved for Band B.  
Notably, unconventional phase shift does not affect the DM EMI filter loss. Since the DM capacitor takes most of the switching ripple, the DM inductor loss is almost the same no matter which phase shift is applied. In addition, Figure 9 illustrates the RMS input current of the DC-link capacitor for conventional phase shift and unconventional phase shift based on the number of the interleaved converters. As it is clear from Figure 9, the unconventional phase shift increases the RMS capacitor input current in some cases. Notably, it does not affect the DC capacitor size regarding ripple current is lower than non-interleaved PFC.