Magnetic cores for power supply inductors require careful selection because of the important role they play. An inductor core must be able to retain inductance with dc bias and handle any ripple current without excessive core loss. Therefore, inductor cores generally need to have high saturation flux density, low permeability, and low loss. Besides these ideal material characteristics, selecting inductor cores often involves their shape, cost, and size. The following are some commonly used magnetic materials for inductors.
 Gapped ferrites.
 Nibased powder cores, such as Molypermalloy (MPP) and high flux powder cores.
 FeSiAl powder cores, such as Sendust/Kool Mμ powder cores.
 Powdered iron cores.
Formerly available only as toroids, Kool Mμ now comes in “E” shape, which allows the ease of bobbin winding. The “Ecore also has a larger window area, which provides more space for winding.
Kool Mμ is a ferrous alloy material (FeSiAl) with low losses at high frequencies. It has a saturation flux density of 10.5kG that's twice that of gapped ferrites, which allows higher storage capability, therefore reducing the core size. Pressed from insulated powder, the cores have a distributed gap structure. This results in low permeability currently available at permeability values of 26, 40, 60, and 90 and gradual saturation characteristics. These properties are well suited for dc bias applications such as inductors for switchmode power supplies (SMPS), power factor correction (PFC) circuits, UPS systems, flyback transformers, and “EMI filter inductors.
Energy Capacity vs. DC Bias
The sole function of inductors is to store energy. It's therefore useful to plot the energy capacity of inductor cores. The general expression for the energy of an inductor is:
Where:
ε=Energy in Joules [J]
L=Inductance in Henries [H]
I=Current in Amps [A]
The energy needed for a design is the product of the required inductance and the square of the peak dc current:
You can calculate the energy capacity of a core at a given dc bias from the permeability of the core with the dc bias field and the magnitude of the field. From this, you can derive an expression for the core's energy/volume as a function of dc bias field ^{[1][2]}.
Since:
Therefore:
Where:
μ_{H}=Relative permeability of core with dc bias field
A_{e}=Core area in cm^{2}
l_{e}=Magnetic path length in cm
H=dc bias field in Oersteds [Oe]
V_{e}=Core volume in cm^{3}
Inductor cores must satisfy the energy requirement of the design: Fig. 1 shows the energy/volume of gapped ferrites vs. Kool Mμ powder cores at various dc bias fields. Ferrite curves utilize the optimum gapped permeability for each bias level.
To handle the maximum dc bias current without saturating, you can optimize ferrite permeability through gapping. Thus, for low bias application, you can maximize permeability to increase energy storage capability. However, Kool Mμ E cores are made to lower permeabilities a maximum of 90μ. As with other powder core materials, lower permeabilities handle higher dc current.
The energy/volume of the materials becomes equal when it's necessary to gap ferrite to achieve the same effective permeability as Kool Mμ at the maximum dc bias field. To handle higher dc current, Kool Mμ E, with twice the saturation flux density of ferrites, has much higher energy storage ability per volume than ferrites. When designing at a typical 50% permeability rolloff point, this can result in a 35% reduction in core size. Ferrites, on the other hand, are limited to a lower maximum gapped permeability. To increase energy storage ability at a given bias field, you must increase core volume (Equation 3).
Temperature rise can affect energy capacity. Ferrite's saturation flux density decreases with increasing temperature, mandating lower gapped permeability or increased core size. As you can see in Fig. 1, on page 16, ferrite's energy capacity reduces at 100°C.
You can't independently use energy storage ability to determine the most suitable core for a design; however, it's useful as a guide. Consider other effects, such as core loss including material loss and gap loss associated with fringing flux on a ferrite core at the site of a large gap. The window area available to support the needed current and inductance can limit full utility of the energy capacity of a material. Core selector charts given in powder core manufacturers' catalogs take these considerations into account.
Saturation Characteristic
Fig. 2 shows the saturation characteristics of 60μ gapped ferrites and a Kool Mμ E core. Ferrites are usually gapped at the center leg while Kool Mμ E cores are pressed with varying amounts of insulation to obtain the desired initial permeability. As a result of having a single “discrete” gap, gapped ferrite cores maintain constant permeability until the core abruptly saturates, at which point, the inductance plunges. Kool Mμ E cores consist of a distributed gap structure. Individual particles of core material don't saturate all at once. As a result, the cores exhibit a “soft” saturation characteristic, where the initial permeability gradually and predictably rolls off with applied dc bias (Fig. 2) ^{[4]}.
In applications where maintaining constant inductance is important, such as a power supply inductor operating at fixed current, gapped ferrites may be a good choice. Otherwise, the swinging inductance characteristic of Kool Mμ is usually an advantage because cores accommodate any unexpected current surges without concern for sudden drop in inductance. Also, an inductor using Kool Mμ would have higher inductance at lower load, only swinging to a lower, controlled inductance value at higher loads. The result is a more robust design that allows a wider operating range and provides overcurrent protection, improving overall efficiency. As you can see in Fig. 2, you need to design ferrites at a lower current to anticipate sudden current surges with the same gapped permeability; otherwise, lower gapped permeability is necessary. Designers typically create Kool Mμ E cores at a 50% initial permeability rolloff point.
At elevated temperature, the permeability of ferrite drops even sooner with dc bias because of ferrite's reduction in saturation flux density (Fig. 3). Kool Mμ E core's saturation characteristics remain the same, with permeability slightly reduced at each bias field ^{[3]}.
Core Loss
You can group core loss into two categories material loss and gap loss. Losses are mainly in terms of eddy current losses in the material as well as in the copper windings surrounding a gapped structure.
Ferrites have an advantage over many magnetic materials because they are inherently high in material resistivity. This reduces the eddy current losses, which would otherwise inhibit operation at high frequencies. In contrast, Kool Mμ E cores are made from insulated alloy powder. Higher conductivity results in higher eddy current losses, even though the powder microstructure mitigates the loss at high frequency. Information is available characterizing material losses for Kool Mμ E and ungapped ferrites.
Although you can estimate expected material loss from published data, gap losses in ferrites are difficult to predict. When a core is gapped, magnetic flux exiting the core structure fringes away from the gap (Fig. 3) ^{[4]}. Gap loss mainly results from fringing flux intersecting copper windings, generating eddy current loss. While fringing flux occurs in a Kool Mμ E core, you can't see the effect since the gaps distribute throughout the core structure. A single large gap on ferrites results in fringing flux that can bow quite a distance from the core structure. Unless you take special care to space copper windings away from the gap, gap loss will occur.
Even though ferrites have very low material loss, gap loss can significantly increase the total losses. This effect is particularly significant at high frequencies and where wide copper strips are used ^{[5]}. Fringing flux can also create high temperature “hot spots” on the ferrite core at the corner of the gaps where flux is concentrated before bowing out into the gap area. This uneven heat distribution can reduce core efficiency.
Figs. 4 and 5a and 5b show the core loss at 1000 gauss for Kool Mμ E core and gapped ferrites one requiring a small gap (90μ) and another requiring a larger gap (26μ) ^{[6]}. Core loss for gapped ferrites is lower than that of the Kool Mu E core when the gap is small. As the gap size increases, core loss surpasses that of the Kool Mμ E core.
Other Considerations
Leakage Effects: Low permeability materials, like Kool Mμ E cores, exhibit a leakage effect around the core. Therefore, you shouldn't use metal clips to hold Kool Mμ E cores together because they will concentrate flux lines and generate loss (Fig. 6) ^{[4]}.
Magnetostriction: While ferrites and to a larger extent, powder iron cores suffer rapid expansion and compression that results in audible noise when operating in the 20 Hz to 20 kHz region. Kool Mμ material has a very low to zero magnetostrictive effect, thus generating no audible noise.
Geometry: Ferrites are available in a variety of sizes. Kool Mμ is currently available only in toroid and E shapes (E cores are in standard industrial ferrite sizes). Designers are currently considering different shapes of Kool Mμ for tooling.
Cost: Kool Mμ E cores are competitively priced against gapped ferrites, especially since Kool Mμ typically results in smaller core size.
Inductor design parameters (Design example):
L=250 μH
I_{dc}=1.8A
I_{ripple}=0.20A
f≤150 kHz
You can select core based on required energy storage capacity, LI_{peak}^{2}:
I_{peak}=I_{dc}+I_{ripple}/2=1.8+0.10=1.90A
LI_{peak}^{2}=250×10^{6}×1.90^{2}=0.9025 mHA^{2}
Based on LI_{peak}^{2} value, choose Kool Mμ E core size and permeability from the core selector chart you can find in Table 1^{[4]}, on page 17: K2510E060 (60μ). For the gapped ferrite part, choose a power material, such as Pmaterial and choose the size and gapped A_{L}: 0P43515A440 (A_{L}=440, = 290). Table 1 compares the performance of both cores.
Wound cores were measured for inductance vs. dc current at temperatures 25°C, 50°C, 75°C, 100°C, and 125°C (Figs. 7 and 8). Figs. 9a and 9b, on page 22, show the comparison in core size for this design and finished units for similar designs.
Some advantages of gapped ferrites over Kool Mμ E are as follows.
 You obtain a lower material loss; lower overall loss when using small gap.
 You can gap to any desired effective permeability.
 You can obtain much higher effective permeability values.
 With a variety of core shapes available, you can secure cores with metal clips.
Some advantages of the Kool Mμ E core over gapped ferrites include:
 Lower overall core loss at high frequency when compared to ferrites with large gap.
 Lower permeability available without large discrete gap.
 Soft predictable saturation.
 Higher saturation flux, better dc bias handling.
 Saturation flux density is constant over a large temperature range.
 Smaller structure possible.
Gapped ferrites and Kool Mμ E also share some advantages. The price of Kool Mμ E core is comparative against gapped ferrites, and Kool Mμ E core offers the same winding facility as gapped ferrite Ecores.
References:

G.D. Smith, “Designing Toroidal Inductors with DC bias,” technical note, Goddard Space Flight Center (1964).

P.Cattermole, “Optimizing Flyback Transformer Design,” Power Conversion International, p. 74, Feb (1981).

Magnetics Div. of Spang & Co., “Designing with Magnetic Cores at High Temperatures,” technical bulletin, publication pending (1999).

Magnetics Div. of Spang & Co., “Magnetics Kool Mμ E” Cores,” product bulletin, KMCE1 6H (2000).

Khai D.T. Ngo, M.H. Kuo, “Effects of Air Gaps on Winding Loss in High Frequency Planar Magnetics,” PESC, p. 1112, April (1988).

M.Horgan, “Leakage Flux Considerations on Kool Mμ E” Cores,” technical bulletin, KMCE2, Magnetics Div. of Spang & Co. (2000).

Magnetics Div. of Spang & Co., Ferrite Cores, product catalog, FC60111H, p. 4.16 (2001).
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