# PFC Inductor Design Considering Suppression of the Negative Effects of Fringing Flux
## 1 Introduction  
In many cases, introducing an air gap can be of great use. Often, engineers may think that introducing an air gap increases the maximum flux density a core can handle. This is not true. Instead, and more correctly, the air gap introduces a large amount of reluctance within the core. It is within the gap that much of the energy is stored. A large reluctance requires a greater magnetomotive force to push the same flux within the core than without the gap. This is much like a large resistance within an electrical circuit that requires a greater voltage to push the same current than a lower resistance would require [1; 2; 3; 4]. The efficiency of energy conversion and power density are the key criteria in the design of power converters. Packaging constraints, the demand for reduced size, and the best performance frequently force power supply engineers to re-evaluate their approach to building magnetic components. Gapped ferrite toroids can find application in compact/low profile designs and potentially be a convenient solution compared with ferrite E-cores or toroidal powder cores. Large gaps, however, produce magnetic 'fringing' causing eddy current losses in adjacent conductors, significantly impacting converter efficiency. This extra power loss can be observed in the form of 'hot spots' [5; 6; 7; 8]. Designing inductive components is a complex problem, where electrical and magnetic issues must be considered. From an electrical point of view, such aspects must be regarded as the skin and the proximity effects, current densities, and power losses of windings, insulation between turns and layers, voltages, currents, frequency, and temperature ofoperation. From a magnetic point of view, the important aspects are inductance parameters, saturation flux density level, saturation current in windings, the magnetic permeability of core material, fringing flux effects, cross-sections, and dimensions of the window area of a magnetic core [9; 10; 11; 12; 13]. Inductors, used in power electronic applications, are very often designed with an air-gapped magnetic core. Implementation of an air gap influences the shape of the B-H curve of the magnetic circuit, decreasing the effective inductance and increasing the saturation current of an inductor. Designing an inductor with an air gap is very complicated because magnetic material is described by nonlinear characteristics of the B-H curve, saturation, and power losses. Moreover, the high sensitivity of magnetic material in the manufacturing process must be taken into account. Additionally, the implementation of an air gap increases the fringing flux phenomenon which must be taken into account because of electromagnetic interferences (EMI) aspects, since fringing flux causes higher propagation of electromagnetic disturbances [14]. For power inductors, which are mainly storage chokes working at nominal currents in a range of 50-200 A and a frequency between 3 and 100 kHz, often, gapped amorphous or nanocrystalline cores are used. They offer a much higher possible saturation flux density B\({}_{\text{sat}}\) compared to ferrites (1.2-1.5 T instead of 0.3-0.4 T for ferrites), which makes them the preferred choice to build smaller inductors. To store a high amount of energy, power inductors built from amorphous or nanocrystalline materials require a relatively large air gap, in the range of 2-10 mm. Fringing flux, entering the space around a big air gap, is problematic, due to forced eddy current losses. Ways to overcome this problem are the usage of multiple small air gaps, which causes a larger manufacturing effort, or the usage of lower permeability powder materials with a permeability \(\mu_{r}\) of 10 to 26, inserted instead of an air gap. While combining two materials to form a core without an air gap, both should have a usable flux density Buse in the same range.