A method for reducing the eddy current loss of soft magnetic strip
By constructing a cross-shaped misaligned hole array on the flexible magnetic tape, the problem of increased eddy current loss of ultrathin metal flexible magnetic tape under high-frequency conditions is solved, achieving a significant reduction in eddy current loss and an improvement in device performance, while maintaining a basically unchanged magnetic gain. The process is simple and easy to implement.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- UNIV OF SCI & TECH OF CHINA
- Filing Date
- 2026-04-14
- Publication Date
- 2026-05-29
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Figure CN122117632A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of soft magnetic material processing technology, and in particular to a method for reducing eddy current loss in soft magnetic materials. Background Technology
[0002] With the rapid development of industries such as artificial intelligence computing infrastructure, advanced electronic systems, and electric transportation, the scale of power transmission and conversion across the entire power generation, transmission, distribution, transformation, and end-user consumption chain continues to rise, placing higher demands on the efficiency and power density of power devices and magnetic devices. Soft magnetic materials, due to their high saturation magnetic induction, low coercivity, and high permeability, can achieve higher magnetic flux coupling and energy transfer in a smaller volume, making them indispensable key materials in transformers, inductors, and various electromagnetic energy conversion components. However, soft magnetic materials inevitably generate magnetic losses during alternating magnetization. These losses not only lead to device temperature rise and efficiency reduction but also restrict the development of high-frequency, miniaturized, and high-power-density applications. As wide-bandgap devices drive up switching frequencies, the losses and thermal management of magnetic devices will become one of the key bottlenecks for further improving system power density.
[0003] Soft magnetic tapes (such as amorphous / nanocrystalline alloy tapes) are widely used in various transformer cores, power inductors, and high-power-density magnetic components due to their thin tape shape and excellent soft magnetic properties. The total loss of soft magnetic materials can generally be decomposed into hysteresis loss, eddy current loss, and residual loss. Hysteresis loss is mainly related to the material's coercivity, magnetic domain structure, stress, and defects; residual loss is related to multi-scale processes such as domain wall dynamics and magnetoelastic coupling. In contrast, eddy current loss has a stronger frequency amplification effect in metallic soft magnetic materials, especially as the frequency increases, it rises rapidly and dominates the total loss. Classical thin-sheet or stacked models show that eddy current loss is approximately proportional to the square of the tape thickness, the square of the magnetization frequency, and the square of the peak magnetic flux density, and approximately inversely proportional to the material resistivity. This law reveals that the greater the thickness, the higher the frequency, the higher the magnetic flux density, or the lower the material resistivity, the greater the eddy current loss.
[0004] It is important to emphasize that the reason soft magnetic materials can significantly improve magnetic coupling and magnetic gain in inductors and transformers is precisely due to their high effective permeability. However, in metallic soft magnetic systems, the strong magnetic flux concentration and stronger induced electromotive force brought about by high permeability often make it easier for eddy current loops to form inside the material, thus leading to a more significant increase in eddy current losses under high-frequency conditions. This creates an inherent contradiction between high permeability and low eddy current losses in high-frequency applications, becoming one of the important contradictions limiting the expansion of metallic soft magnetic materials to higher frequency bands.
[0005] To reduce eddy current losses, existing technologies typically employ the following approaches: (a) Improving material resistivity (composition / microstructure design) Resistivity can be increased through alloying, microstructure control, or the use of amorphous or nanocrystalline compositions to suppress classical eddy current losses. Previous research has indicated that increasing resistivity is a direct means of reducing eddy current-related energy losses; amorphous and nanocrystalline soft magnetic materials, due to their typically small thickness and high resistivity, can suppress classical eddy current terms to some extent. However, this approach often involves long material development cycles, significant challenges in cost and consistency control, and variations in composition usually lead to changes in magnetic properties. Furthermore, since soft magnetic materials are primarily composed of metals, the range for resistivity improvement is limited.
[0006] (ii) Thinning and laminated insulation (structural processes reduce equivalent thickness) Stacking, by reducing the effective thickness of individual wafers and introducing insulating layers between wafers to suppress cross-laminated eddy current loops, is a classic engineering solution long used in electrical steels and some soft magnetic cores. Its basic principle is to divide large-loop eddy currents into multiple smaller loops, reducing the loop area and equivalent conduction cross-section. However, for ultra-thin strips (10-40 μm) and for inductors that need to balance miniaturization, planarization, and high frequency, further stacking and insulation can lead to increased process complexity and a decrease in effective permeability due to the introduction of interfacial air gaps.
[0007] (III) Soft magnetic composite, coating and encapsulation technology Another common approach is to combine soft magnetic powder with an insulating phase (soft magnetic composite material SMC), or to form a layered structure through powder surface coating to suppress eddy currents. For example, biomimetic layered structures and coating systems can be used to suppress eddy currents and improve soft magnetic properties. However, powdering and compositing usually sacrifice some effective permeability and saturation magnetic induction, and introduce additional interface coatings and chemical processes, resulting in increased volume, which is detrimental to miniaturization and environmental protection.
[0008] In summary, while existing technologies have proposed various methods to address the loss problem of ultrathin metal flexible magnetic tapes under high-frequency magnetization, such as improving material resistivity, laminated insulation, and composite coatings, significant challenges remain in applications involving ultrathin (10-40 μm) tape-core inductors. On the one hand, eddy current losses increase strongly with frequency; on the other hand, many methods for suppressing eddy currents sacrifice effective permeability, introduce process complexity, or reduce device integrability, making it difficult to achieve the goal of "significantly reducing losses while maintaining essentially unchanged magnetic gain." Especially for ultrathin tapes, under typical magnetization conditions, the induced current often appears as an in-plane closed loop. Therefore, if "current blocking" can be specifically implemented on the in-plane eddy current path without significantly disrupting the main magnetic flux path, it is possible to significantly reduce eddy current losses while maintaining the inductor's magnetic gain, thereby improving the high-frequency quality factor Q. Summary of the Invention
[0009] In order to reduce the eddy current loss generated by the tape under an alternating magnetic field and improve the high-frequency efficiency of the device, this application provides a method for reducing the eddy current loss of flexible magnetic tape.
[0010] This application provides a method for reducing eddy current loss in flexible magnetic tape, which employs the following technical solution: A method for reducing eddy current losses in flexible magnetic tape includes: Provide soft magnetic tape materials; The etching area of the flexible magnetic tape is determined based on the location of eddy current concentration. A laser etching pattern is designed and imported into the laser etching equipment. The etching pattern is a cross-shaped staggered hole array, including a horizontal hole array formed by multiple horizontally spaced elongated holes and a vertical hole array formed by multiple vertically spaced elongated holes. The horizontal hole array and the vertical hole array are arranged perpendicularly and staggered to each other. Laser etching is performed on the soft magnetic tape to form an etched structure in the etched area; the etched structure can form multiple blockages in the eddy current return path, thereby reducing eddy current loss.
[0011] Furthermore, in the transverse hole array, the length of the transverse elongated holes is not less than the transverse spacing between adjacent transverse elongated holes.
[0012] Furthermore, in the longitudinal hole array, the length of the longitudinal elongated holes is not less than the longitudinal spacing between adjacent longitudinal elongated holes.
[0013] Furthermore, within the etched area, the proportion of the material area corresponding to the cross-shaped misaligned hole array to the etched area is no higher than 20%.
[0014] Furthermore, the method for determining the etching region based on the location of eddy current concentration includes: using the projection of the device on the surface of the flexible magnetic tape as a basis, and extending it outward proportionally to obtain the etching region.
[0015] Furthermore, the etching area is determined as follows: first, the projected area of the inductor coil on the soft magnetic tape is determined, and then the projection range is extended outward by 1%-200% to form an extended area, which is the etching area.
[0016] Furthermore, femtosecond lasers are used to etch the soft magnetic tape. The laser parameters are: center wavelength 1030nm, pulse width 200-300 fs, repetition frequency 50-200 kHz, average power 0.3-0.8 W, focused spot diameter 7-10 μm, scanning speed 200-500 mm / s, and scanning spacing 2-5 μm.
[0017] Furthermore, the soft magnetic tape is an amorphous alloy tape or a nanocrystalline alloy tape.
[0018] This application also provides a flexible magnetic tape for reducing eddy current loss, which is prepared by the above-mentioned method for reducing eddy current loss of flexible magnetic tape.
[0019] This application also provides a magnetic device comprising the aforementioned soft magnetic tape for reducing eddy current losses as a magnetic core or magnetic gain material; the magnetic device is an inductor or a transformer.
[0020] In summary, this application includes at least one of the following beneficial technical effects: 1. Significant eddy current suppression effect: This application can effectively destroy the continuous conductive path of the large-scale closed loop supporting the tape by constructing a specific hole array structure on the flexible magnetic tape, thereby reducing eddy current loss over a wide frequency range. Simulation results show that the cross-shaped staggered hole array can reduce eddy current loss in the range of 1 MHz-1000 MHz, with a maximum loss reduction of about 41%, which is significantly better than the reduction of about 25% of the square hole array, demonstrating higher eddy current attenuation efficiency.
[0021] 2. Improving overall device performance while maintaining magnetic gain: This application not only reduces eddy current losses in flexible magnetic tape but also improves its performance in inductor applications. From a device perspective, the reduction in losses significantly improves the inductor's quality factor Q by approximately 35%; simultaneously, it has a minimal impact on the magnetic gain provided by the flexible magnetic tape, with a maximum reduction in inductance of only about 2% across the entire frequency range. Furthermore, in some high-frequency bands, the inductance can even increase to some extent due to the suppression of eddy current losses. Therefore, this structure can optimize device efficiency with minimal sacrifice in magnetic gain.
[0022] 3. High blocking efficiency and good structural design flexibility: The advantage of this application does not mainly rely on large-area material removal, but on reconstructing the internal conductive network topology of the strip by preferentially cutting off key flow channels. In particular, the cross-shaped staggered hole array can still achieve higher eddy current suppression effect even with a smaller proportion of material removal area, indicating that it has high structural blocking efficiency. At the same time, the perforation area, array arrangement and geometric parameters can be specifically adjusted according to different device structures, magnetic field distributions and loss concentration areas, thereby achieving localized and scenario-based optimization, with strong adaptability and scalability.
[0023] 4. Direct and easy-to-implement process: This application mainly forms structural units on flexible magnetic tape through laser drilling or etching, physically blocking eddy current loops without the need for complex functional coatings or redundant material composite steps. The process approach is straightforward and the implementation path is clear. This method is easy to integrate with existing tape processing and device fabrication processes, demonstrating good engineering feasibility. Attached Figure Description
[0024] Figure 1 This is a schematic diagram of the structure of flexible magnetic tape in inductor applications, where (a) is an unperforated flexible magnetic tape and its upper coil; (b) is a perforated flexible magnetic tape and its upper coil. Figure 2 It is the eddy current intensity distribution of unperforated soft magnetic tape at different frequencies; Figure 3 This is a schematic diagram of the cross-shaped misaligned hole array in an embodiment of this application; Figure 4 This is a schematic diagram of the square hole array structure in the comparative example of this application; Figure 5 This is a schematic diagram illustrating the mechanism by which different drilling methods reduce eddy current losses; Figure 6 This is a diagram showing the eddy current density distribution of the hole-punch strip and the cross-punch strip at 100MHz. Figure 7 It represents the eddy current loss density of the original tape and the perforated tape at different frequencies; Figure 8 These are the device inductance values of the original tape and the punched tape at different frequencies; Figure 9 It is the device quality factor Q value of the original tape and the punched tape at different frequencies. Detailed Implementation
[0025] The following is in conjunction with the appendix Figure 1-9 This application will be described in further detail.
[0026] Example This application discloses a method for reducing eddy current loss in flexible magnetic tape, comprising the following steps: Step 1: Provide soft magnetic tape.
[0027] In this embodiment, nanocrystalline flexible magnetic tape (e.g., iron-based nanocrystalline alloy) is selected, with a tape thickness of 10-40 μm, a width of 10 mm, and a length cut according to device requirements. It should be understood that this application is also applicable to amorphous alloy tapes and other metal flexible magnetic tapes.
[0028] Step 2: Determine the etching area of the soft magnetic tape based on the location of eddy current concentration, design the laser etching pattern, and import it into the laser etching equipment.
[0029] Depending on the application scenario of the inductor, eddy currents are mainly concentrated in the projection area of the inductor coil on the surface of the tape and its vicinity. Methods for determining the etching area based on the location of eddy current concentration include: using the projection of the device on the surface of the flexible magnetic tape as a basis, and proportionally extending outwards to obtain the etching area.
[0030] Specifically, a three-dimensional electromagnetic field model of the flexible magnetic tape and its upper inductor coil is first established in simulation software. The eddy current energy density distribution inside the tape is calculated through simulation. The results show that the region with the highest eddy current energy density basically corresponds to the region of the coil's vertical projection on the tape. However, there is still a non-negligible eddy current contribution within approximately 10% of the outer edge of the projection, such as... Figure 2 As shown. Therefore, the etching area determined in this embodiment is: the coil projection contour extends outward by 10%, as shown. Figure 1 As shown. This expansion ratio can be determined through simulation optimization, aiming to minimize the removal ratio of magnetic material while effectively suppressing eddy currents.
[0031] The etching pattern is designed based on the application scenario's requirements for the shape, size, and local loss distribution of the flexible magnetic tape. In this embodiment, the etching pattern is a cross-shaped staggered hole array, such as... Figure 3 As shown, the cross-shaped staggered hole array includes a transverse hole array formed by multiple transverse elongated holes arranged at equal intervals along the transverse direction, and a longitudinal hole array formed by multiple longitudinal elongated holes arranged at equal intervals along the longitudinal direction; the transverse hole array and the longitudinal hole array are arranged perpendicularly and staggered to each other.
[0032] The transverse and longitudinal elongated holes can be rectangular or oblong. In this embodiment, for example... Figure 3 As shown, the horizontal and vertical elongated holes are rectangular holes with the same dimensions, and the hole length is... l 1. Hole width is w 1. The lateral spacing between two adjacent transverse elongated holes is l gap1 The transverse spacing between two adjacent columns of longitudinal strip holes is l gap3 The longitudinal spacing between two adjacent rows of horizontal elongated holes is w gap1 The longitudinal spacing between the transverse elongated hole and the adjacent longitudinal elongated hole is w gap2 .
[0033] In this embodiment, l 1 = 60μm w 1 = 10 μm; l gap1 =10μm, l gap3 =60μm, w gap1 =80μm, w gap2 =10μm.
[0034] The specific parameters of the etching patterns described above (hole size, spacing, etc.) are for illustrative purposes only. In practical applications, they can be optimized and adjusted based on the specific operating frequency, eddy current distribution simulation results, etc. For example, for higher frequency applications, the hole spacing can be reduced to enhance the blocking density.
[0035] Step 3: Perform laser etching on the soft magnetic tape to form an etched structure in the etched area.
[0036] Specifically, a femtosecond laser etching system is used, with the following laser parameters: center wavelength 1030 nm, pulse width 200-300 fs, repetition rate 50-200 kHz, average power 0.3-0.8 W, focused spot diameter 7-10 μm, scanning speed 200-500 mm / s, and scanning spacing 2-5 μm. Using these parameters, a processing feature size on the order of approximately 10 μm can be obtained, and it is beneficial for controlling the heat-affected zone.
[0037] Comparative Example The difference from the above embodiments is that the etching pattern in the comparative example is an array of square holes, such as... Figure 4 As shown. The square hole array includes square holes arranged in a two-dimensional array, with the length of each square hole being [missing information]. l The hole width is w, The lateral spacing between two adjacent square holes is l gap1 The longitudinal spacing between two adjacent square holes is w gap As an example, l = w = l gap1 = w gap =30 μm.
[0038] Figure 5 The mechanism by which different drilling methods reduce eddy current losses is demonstrated: According to Faraday's law of electromagnetic induction, a circumferential electric field will be induced in the plane of a soft magnetic material under the action of an alternating magnetic field. As long as there is a continuous conductive region inside the material, the induced electric field will drive free charge carriers to form a closed current loop, i.e., in-plane eddy current.
[0039] For metallic flexible magnetic tapes, these eddy current loops typically exhibit the following characteristics: First, the larger the loop area, the greater the change in magnetic flux it encloses, and the higher the induced electromotive force, thus making it easier to form strong eddy currents. Second, the more continuous and straight the loop path, the smaller the equivalent resistance, and the larger the eddy current amplitude. Third, when the tape has a long continuous conductive path in a certain direction, the current is more likely to expand along that direction and reclose, forming a large-scale in-plane circulation. Therefore, the key to suppressing eddy currents is not simply removing some material, but rather disrupting the continuous conductive path supporting the large-scale closed loop, making it difficult for the induced current to close along a low-resistance, short-range, large-area path.
[0040] Existing methods for suppressing eddy current losses by perforation include a representative structure such as the square hole array shown in the comparative example. This method periodically removes a portion of the conductive magnetic material, dividing the originally continuous strip into multiple locally conductive regions, thereby weakening the ability to form large-area closed loops. Compared to unperforated strips, the square hole array can split the original large-scale circulation into multiple smaller loops, reducing the effective magnetic flux enclosed by a single loop and increasing the equivalent resistance of the loop, thus reducing the total eddy current loss.
[0041] However, the blocking effect of the square hole array is still limited. The main reason is that relatively regular lateral and longitudinal bridging channels are usually retained between the holes. These residual conductive regions have strong geometric continuity and periodicity, allowing the induced current to still bypass the holes and reconstruct local closed loops between adjacent holes. In other words, although the square hole array can divide the original large-scale single circulation into several smaller circulations, it does not sufficiently disrupt the continuous flow capability in the two dominant lateral and longitudinal directions. From the current distribution perspective, the current often flows around the edges of the holes and experiences local congestion at the corners or narrow bridges; however, because the alternative paths are still relatively clear, the overall blocking is not complete. This can also be verified by finite element simulation results.
[0042] In contrast, the advantage of the cross-shaped staggered hole array lies not in simply increasing the strip removal area, but in actively reconstructing the internal conductive topology of the strip by staggering narrow blocking regions, thereby simultaneously constraining the continuous flow capability in both the lateral and longitudinal directions. Its mechanism can be summarized in the following two points: First, the cross-shaped staggered hole array provides stronger bidirectional interruption of the eddy current main path: In unperforated strips, induced current can form a large-scale closed loop along the continuous metal surface; while the square hole array cuts off part of the area, regular bridging is usually still maintained in the transverse and longitudinal directions, and the current can still form a local loop around the hole. The cross-shaped staggered hole array introduces staggered blocking in both main conduction directions simultaneously, making it easier for the current to be restricted by the blocking unit in the other direction when it extends in either direction, thus making it difficult to form a long-range, continuous, low-resistance large-area closed loop. Under this topological constraint, the original large-scale eddy current loop is further compressed or even destroyed, and the residual current can only be distributed in a smaller local area and flow around along a more tortuous and narrower path. As a result, on the one hand, the effective magnetic flux area surrounded by the local loop decreases, and the induced electromotive force decreases; on the other hand, the flow path lengthens, the local conduction cross section shrinks, and the equivalent loop resistance increases. The combined effect of these two effects makes the cross-shaped staggered hole array exhibit a stronger eddy current suppression capability than the square hole array.
[0043] Secondly, the cross-shaped staggered hole array exhibits higher blocking efficiency: its advantage does not primarily stem from removing more material, but rather from the preferential cutting off of critical flow channels. In other words, this structure targets bridging paths that facilitate large-scale circulation closure, rather than uniformly and extensively reducing the area of material. Taking the perforation parameters in the embodiment as an example, the cross-shaped array requires only 17.5% material removal in the smallest repeating unit of 190μm × 90μm, while the square hole array requires 29.8%. This means that the structure can retain more magnetic material while reducing losses, thus better balancing low losses and magnetic gain, and providing a physical basis for reducing device power consumption without significantly sacrificing inductance enhancement.
[0044] To verify the above technical effects, the flexible magnetic tapes prepared in the examples and comparative examples were assembled into identical planar inductor devices for simulation testing: Figure 6 The effects of cross-shaped staggered aperture arrays and square aperture arrays on eddy current suppression at 100 MHz are demonstrated. It can be seen that the intensity and spatial distribution of eddy currents are significantly reduced with the cross-shaped staggered aperture array. Further analysis, combined with the extracted eddy current loss energy density, shows... Figure 7 As shown, both square hole arrays and cross-shaped staggered hole arrays can effectively reduce eddy current losses in the 1 MHz–1000 MHz range. The cross-shaped staggered hole array exhibits the highest loss reduction of approximately 41%, significantly better than the approximately 25% reduction of the square hole array. This indicates that, thanks to its unique structural design, the cross-shaped staggered hole array can still achieve higher eddy current suppression efficiency even with a smaller material removal area ratio.
[0045] From a device perspective, such as Figure 9As shown, reduced losses can significantly improve the inductor's quality factor Q (approximately 35%), while having a smaller impact on the magnetic gain provided by the flexible magnetic tape, resulting in a maximum reduction in inductance of only about 2% across the entire frequency domain. Figure 8 As shown. Furthermore, at high frequencies, the inductance can be further improved due to the suppression of eddy current losses. These results demonstrate that the cross-hole drilling strategy only requires the removal of a small proportion of material to achieve efficient suppression of eddy current losses while essentially maintaining magnetic gain.
[0046] In summary, the method for reducing eddy current losses in flexible magnetic tape provided in this application offers high processing precision, minimal heat-affected zone, and eliminates the need for additional materials. Furthermore, the etched area can be precisely located based on simulation, avoiding a significant decrease in permeability during full-area processing. Verification by the above embodiments shows that flexible magnetic tape using a cross-shaped staggered hole array maintains high inductance while reducing eddy current losses and improving the quality factor. This method is particularly suitable for high-frequency power inductors, planar transformers, and integrated magnetic core devices, significantly improving system efficiency and power density.
[0047] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.
Claims
1. A method for reducing eddy current loss in flexible magnetic tape, characterized in that: include: Provide soft magnetic tape materials; The etching area of the flexible magnetic tape is determined based on the location of eddy current concentration, and the laser etching pattern is designed and imported into the laser etching equipment. The etching pattern is a cross-shaped staggered hole array, including a horizontal hole array formed by multiple horizontally spaced elongated holes arranged horizontally, and a vertical hole array formed by multiple vertically spaced elongated holes arranged vertically; the horizontal hole array and the vertical hole array are arranged perpendicularly and staggered to each other. Laser etching is performed on the soft magnetic tape to form an etched structure in the etched area; the etched structure can form multiple blockages in the eddy current return path, thereby reducing eddy current loss.
2. The method for reducing eddy current loss in flexible magnetic tape according to claim 1, characterized in that: In the transverse hole array, the length of the transverse elongated holes is not less than the transverse spacing between adjacent transverse elongated holes.
3. The method for reducing eddy current loss in flexible magnetic tape according to claim 2, characterized in that: In the longitudinal hole array, the length of the longitudinal elongated holes is not less than the longitudinal spacing between adjacent longitudinal elongated holes.
4. The method for reducing eddy current loss in flexible magnetic tape according to claim 3, characterized in that: Within the etched area, the proportion of the material area corresponding to the cross-shaped misaligned hole array to the etched area is no higher than 20%.
5. The method for reducing eddy current loss in flexible magnetic tape according to claim 1, characterized in that: Methods for determining the etching region based on the location of eddy current concentration include: using the projection of the device on the surface of the flexible magnetic tape as a basis, and extending it outward proportionally to obtain the etching region.
6. The method for reducing eddy current loss in flexible magnetic tape according to claim 5, characterized in that: The etching area is determined as follows: first, the projected area of the inductor coil on the soft magnetic tape is determined, and then the projection range is extended outward by 1%-200% to form an extended area, which is the etching area.
7. A method for reducing eddy current loss in flexible magnetic tape according to claim 1, characterized in that: Femtosecond lasers were used to etch the soft magnetic tape. The laser parameters were: center wavelength 1030 nm, pulse width 200-300 fs, repetition frequency 50-200 kHz, average power 0.3-0.8 W, focused spot diameter 7-10 μm, scanning speed 200-500 mm / s, and scanning spacing 2-5 μm.
8. The method for reducing eddy current loss in flexible magnetic tape according to claim 1, characterized in that: The soft magnetic tape is an amorphous alloy tape or a nanocrystalline alloy tape.
9. A flexible magnetic tape for reducing eddy current losses, characterized in that: It is prepared by the method described in any one of claims 1-8.
10. A magnetic device, characterized in that: The magnetic magnetic material described in claim 9 is used as a magnetic core or magnetic gain material; the magnetic device is an inductor or a transformer.