# PFC Inductor Design Considering Suppression of the Negative Effects of Fringing Flux
## 1 Introduction
### Analysis of the Fringing Flux Influence on PQ-Type Ferrite Core  
The effect of the fringing flux occurs around each air gap and its magnitude depends on the size of the air gap. The displacement of the magnetic flux around the gap outside the ferromagnetic material is due to the significantly higher magnetic resistance of the air gap compared to the magnetic resistance of the ferromagnetic material. In some cases, this effect interferes with the winding of the coil, which reflects in the generation of eddy currents in the winding. Eddy currents are responsible for losses and heating of the winding. Generally, there are two ways to prevent this side effect of the fringing flux:  
* Delimitation of the space around the air gap (Figure 2) by nonconducting, nonmagnetic material, ensures that the coil winding is sufficiently distant from the magnetic flux originating from the magnetic core to the air.
* Create a distributed air gap (Figure 3) in the core by replacing the large air gap with several shorter air gaps, thus minimizing the amount of the fringing flux.  
Using the simulation program FEMM 4.2, which works on the principles of finite element methods, both discussed situations of the E-shape core were analyzed, while the focus was given to the magnetic flux distribution. The cores of the inductors were saturated with the same current, while the number of turns was the same for analyzed alternatives. For the first alternative, one air gap located on the middle column of the core was considered. The second case considered distributed air gap presented by four smaller air gaps so that the inductance and thus the same magnetic flux in the core was maintained (Figure 4).  
Figure 3: Example of the distributed air gap implementation within the E-shape core.  
Figure 2: Example of space exclusion on the magnetic core bobbin (**left**) within the space of the core air gap (**right**).  
The evaluation of magnetic field distribution around the air gaps of analyzed solutions was performed for a certain area of the air gap (distance from the air gap and length along the air gap). This is represented by the situation shown in Figure 5. Consequently, a comparison of the amplitudes of magnetic induction within the analyzed area is graphically interpreted in Figure 6 for one air gap situation and in Figure 7 for a distributed air gap.  
Figure 4: Comparison of the magnetic flux distribution within the magnetic circuit of an inductor with E-core for (**a**) one air gap and for (**b**) distributed air gap.  
Figure 5: Graphical interpretation of the evaluation of magnetic induction around the space of core air gap.  
Figure 6: Magnetic induction distribution in dependency on the distance from the air gap and the length along the airgap for inductor described by situation Figure 4a.  
As described above, the evaluation of induction took place longitudinally to the core. Figure 5 as an example indicates a red line connecting the measurement points, while this line is located at 0.4 mm from the core towards the winding. Thus, the legend of these simulation images is the distance of the measuring lines from the core.  
Figure 6 shows that at 1.8 mm from the core where the first coil winding layer was expected to be located, the value of induction was approximately 160 mT. It should be noted that the distance of 1.8 mm was the limiting distance for windings around the air gap. From the results presented for distributed air gap (Figure 7), it is seen that for the same distance from the core, the induction was 80 mT, which is half the value of the first coil alternative.