## 2 PFC Converters Power Components Design Analysis and Selection
### The Boost Inductor Design and Manufacturing
#### 2.1.1 Conventional PFC Boost Inductor
The boost converter average input current is the same as the inductor average current (I\({}_{\text{avg}}\)) which can be calculated at full load condition and rated output voltage as given  
\[\text{I}_{\text{avg}}=\frac{\text{P}_{\text{out}}}{\text{V}_{\text{o}}}\bigg{(} \frac{1}{1-\text{D}}\bigg{)} \tag{2}\]  
The boost converter is designed to work with supply voltage wide range (85-265) V. So, the maximum and the minimum duty cycle values are calculated as  
\[\text{D}_{\text{max}}=1-\frac{\text{V}_{\text{in,min}}}{\text{V}_{\text{o}}} \text{, }\text{D}_{\text{min}}=1-\frac{\text{V}_{\text{in,max}}}{\text{V}_{\text{o}}} \tag{3}\]  
The average inductor currents at minimum and maximum supply voltage are calculated as  
\[\text{I}_{\text{avg,min}}=\frac{\text{P}_{\text{out}}}{\text{V}_{\text{o}}} \bigg{(}\frac{1}{1-\text{D}_{\text{max}}}\bigg{)}\text{, }\text{I}_{\text{avg,max}}=\frac{\text{P}_{\text{out}}}{\text{V}_{\text{o}}} \bigg{(}\frac{1}{1-\text{D}_{\text{min}}}\bigg{)} \tag{4}\]  
The inductor ripple current as the percentage (%Ripple) of the converter total input current can be expressed as  
\[\Delta\text{ILrpp}=\%\text{Ripple}\times\text{I}_{\text{avg}}\times 2 \tag{5}\]  
From (4) and (5), and from the waveforms in Figure 3, the inductor maximum peak current is calculated as  
\[\text{I}_{\text{L}\_\text{pk}}=\text{I}_{\text{avg}}+\frac{\Delta\text{ILrpp} }{2} \tag{6}\]  
Using the converter parameters given in Table 1, the required inductance, and the inductor maximum peak current for the conventional CCM PFC converter can be calculated. Based on the calculated inductance and the inductor current, the inductor core, the number of turns (N), and the size of the winding wire have to be selected. The PFC inductor core was designed to have a high saturation level which prevents the saturation at the maximum peak current (I\({}_{\text{L}\_\text{pk}}\)), support the converter operation with the designed switching frequency, also, the inductor core losses have to be accepted in accordance with the temperature rise during the PFC converter operation. Kool Mu core material's with low loss, relatively high saturation level (10,500 gausses), higher switching frequency level up to 200 kHz, and the near-zero magnetostriction (ability to expand or contract in response to a magnetic field) make the Kool Mu material good for eliminating \begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Parameter** & **Value** & **Unit** \\ \hline Supply voltage (V\({}_{\text{in}}\)) & 220 (85–265) & V \\ Supply Frequency (F) & 60 (47–63) & Hz \\ Output Voltage (V\({}_{\text{o}}\)) & 400 (320–410) & V \\ Output Power (P\({}_{\text{o}}\)) & 2000 & W \\ Efficiency (\(\eta\)) & 95\% & - \\ Switching Frequency (F\({}_{\text{sw}}\)) & 100 & kHz \\ Hold Up Time (t\({}_{\text{hold}}\)) & 10 & ms \\ Inductor ripple (\%Ripple) & 20\% & \\ voltage ripple (V\({}_{\text{rpp}}\)) & 20 & V\({}_{\text{PP}}\) \\ Current ripple & 5\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The target PFC converters stage design specifications. audible frequency noise in in-line noise filters and inductors, which also make it excellent for the implementation of the PFC circuits [34]. Choosing the inductor core in this work will be conducted by using the LI2 method to choose the core part number from the Kool Mu chart of the Magnetic inc supplier, as shown in Figure 4, where L is the inductance value and I is the inductor average current. [34,35]. From the chart and with using the calculated value of the LI2, and take in account offering the required value of the inductance with the suitable space for the wire winding around the core, the conventional PFC converter inductor is designed with using two stacked Kool Mu Toroids core with part number of 77083A7.