# PFC Inductor Design Considering Suppression of the Negative Effects of Fringing Flux
## 1 Introduction
### Analysis of the Fringing Flux Suppression on Toroid Ferrite Core  
_Airgap Distribution_  
Another experiment we conducted was the effect of the distributed air gap. Table 2 lists the main properties of the PFC inductors used for this experiment. We focused on the identification of the magnetic field reduction (FEM analysis), and a later experiment related to inductance stability was performed. Figure 8: Practical realization of PFC inductor v1 for experimental verifications. Figure 9: Temperature distribution during converter PFC operation at nominal power equipped with (a) inductor with one centered air gap, (b) inductor with excluded space around air gap. Two alternatives of inductor design made on toroid core were analyzed. The first alternative was made in the way of an inductor made on a gapped core, while the division of this gap (shortening) was performed by insertion of two non-conductive plates (FR4) and magnetically conductive material placed between these plates (Figure 10). This way, the air gap was distributed, but not evenly within the inductor volume. Therefore, the second alternative was made with distributed air gaps with smaller dimensions distributed moderately around the perimeter of the core (Figure 11). The analysis of the magnetic field distribution for v2 inductor alternatives was performed once using the simulation program FEMM 4.2. For the first alternative (delimitated space around air gap), the results are shown in Figure 12 left, while the highlighted areas indicate the evaluation points of magnetic induction. Figure 12 right refers to the situation with distributed air gap, whereby evaluation points are indicated around one of the air gaps of the core. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Core type** & R50 \(\times\) 30 \(\times\) 20 & R50 \(\times\) 30 \(\times\) 20 \\
**Inductance** & 254 \(\mu\)H & 267 \(\mu\)H \\
**Max. current** & 12.034 A & 11.5 A \\
**Length of airgap** & On the inner circuit 2 \(\times\) 1.5 mm & 4 \(\times\) 0.4 mm \\
**Saturation induction of the core** & 280 mT & 280 mT \\
**Nr. of turns** & 42 & 42 \\
**Nr. of winding layers** & 1 & 1 \\
**Type of wire** & 2 \(\times\) 20 \(\times\) 0.2 mm litz wire & 2 \(\times\) 20 \(\times\) 0.2 mm litz wire \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of PFC inductor v2 for analysis of distributed airgap influence. Figure 10: Alternative of the toroidal inductor with air gap given by product type (**left**) and modification by shortening airgap by ferrite material inserted within air gap (**right**). Figures 13 and 14 show results of the magnetic induction amplitudes within the selected space of the air gap for the inductor within one air gap filled with magnetically conductive material (see Figure 12a). For this case, two surroundings were evaluated, i.e., the area on the outer and inner diameter of the core. Results valid for the area on the outer diameter are shown in Figure 13. Here it is seen that the peak values of the magnetic induction were located at the edges of the magnetic core as well as on the edges of inserted magnetically conductive material. Figure 12: Comparison of the magnetic flux distribution within the magnetic circuit of an inductor with toroidal core for (**a**) delimitated air gap, (**b**) distributed air gap. Figure 13: Magnetic induction distribution along the outer diameter of the air gap of the inductor described by situation Figure 12a. Evaluation of the values of magnetic induction on the inner diameter of the air gap was provided as well, while the results are graphically interpreted in Figure 14. Similar to the previous case, the highest values were present on the edges (boundaries) between air gap and core or magnetically conductive material. Moreover, comparing results in Figure 14, it is seen that the peak value of magnetic induction was two times higher for the closest vicinity of the evaluation field (0.2 mm). Above this value, the intensity of the magnetic induction around the airgap was similar comparing the inner and outer parts.