## 2 PFC Converters Power Components Design Analysis and Selection
### The Boost Inductor Design and Manufacturing
#### 2.1.2 Interleaved PFC Boost Inductor  
In the interleaved PFC converter, the total power is shared among the parallel channels and the PWM signals for each channel switch are at 360/n, where n is the channels number. A 2-channel interleaved CCM PFC topology is employed in this work. Since this topology uses two inductors, L\({}_{1}\) and L\({}_{2}\), each with approximately half the size of the conventional boost PFC, so that the thermal performance of the converter will improve [36]. Furthermore, the inductor current ripple in the conventional boost PFC is the same as the input current ripple while in the interleaved boost PFC, the ratio of the boost converter input ripple current to inductor's ripple current can vary depending on the duty cycle (D) as given in Equation (7), where the current ripple cancellation in the input side of interleaved type is considered as the major advantage over the conventional type as seen at the input current ripple of the converter in Figure 5[37]. \[\text{I}_{\text{In}_{\text{Ripple}}}=\sum \begin{array}{c}\text{$\Pi$}_{ \text{Ripple}}\frac{1-2\text{D}}{1-\text{D}}\text{ if D}\leq 0.5\\ \text{$\Pi$}_{\text{Ripple}}\frac{2\text{D}-1}{\text{D}}\text{ if D}>0.5\end{array}  \tag{10}\]  
As the result of the input current ripple cancellation, the size of the EMI filter can be reduced, and the required boost inductors (L\({}_{1}\) and L\({}_{2}\)) values will be reduced which leads to reducing the volume and weight of the designed boost inductors. The circuit operation of the designed interleaved PFC boost converter working in the continuous current conduction mode (CCM) can represent four operating modes and if the average duty cycle is less than 0.5, both switches will not be turned on at the same time which results in three operating modes describes the on-off states of the 2-channels switches as depicted in the converter waveforms in Figure 6, where V\({}_{\text{L1}}\), V\({}_{\text{L2}}\) represents the inductors voltages, and I\({}_{\text{L1}}\), I\({}_{\text{L2}}\) represents the inductors currents. Figure 5: Normalized input ripple current vs. duty cycle in conventional and interleaved PFC. For the interleaved PFC converter, the boost inductor at each channel can be expressed as [38; 39]. \[\mathrm{L_{1}}=\mathrm{L_{2}}=\frac{\mathrm{D_{on}}(1-\mathrm{D_{on}})\times \mathrm{V_{out}}}{\mathrm{ILr_{pk}\_pk}\times\mathrm{F_{sw}}} \tag{11}\]  
The inductor ripple current at each channel as the percentage (%Ripple) of the converter total input current can be given as  
\[\mathrm{I_{L1~{}rpk\_pk}=\mathrm{I_{L2~{}rpk\_pk}}=\frac{\text{\%Ripple}}{2} \times\frac{\mathrm{I_{avg}}}{2}} \tag{12}\]  
The peak current passing through the inductor at each channel can be given as  
\[\mathrm{I_{L1\_pk}=\frac{\mathrm{I_{avg}}}{2}+\frac{\mathrm{I_{L1~{}rpk\_pk}}} {2}} \tag{13}\]  
using the converter parameters given in Table 1, the required inductance and the inductor maximum peak current for the interleaved CCM PFC converter can be calculated. For each channel, in order to offer the required value of the inductance with the suitable space of the wire winding around the core, the core of Kool Mu material with part number of 77354A7 was used as depicted in the chart in Figure 4, the inductor number of turns (N) to obtain the required inductance value (L\({}_{1}\)) and (L\({}_{2}\)) can be calculated as:  
\[\mathrm{N_{1}}=\mathrm{N_{2}}=\sqrt{\frac{\mathrm{L_{1}}}{\mathrm{A_{L\_min} }}}=\sqrt{\frac{\mathrm{L_{2}}}{\mathrm{A_{L\_min}}}} \tag{14}\]  
Figure 6: Voltage and currents waveforms of the interleaved CCM (continues-current-conduction mode) PFC topology. where \(\text{A}_{\text{L}\_\text{min}}\) is the minimum inductance factor for the chosen core (\(\text{A}_{\text{L}\_\text{min}}\)=69.92 \(\text{nH}/\text{T}^{2}\)).