Patent Publication Number: US-2022215992-A1

Title: Multilayer inductor

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a continuation application, claiming priority under § 365(c), of an International application No. PCT/KR2020/013117, filed on Sep. 25, 2020, which is based on and claims the benefit of a Russian patent application number 2019130165, filed on Sep. 25, 2019, in the Russian Intellectual Property Office, the disclosure of which is incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     1. Field 
     The disclosure relates to a multilayer inductor. 
     2. Description of Related Art 
     Inductors are circuit elements used to obtain inductance. Inductors are used in various technology fields. For example, inductors are used in wireless power transmission systems (e.g., Qi, AirFuel), energy storage, wireless engineering for noise reduction, resonance and frequency selection circuits, and the like. 
     A wireless power transmission system is operated at high frequency (e.g., 100 KHZ for Qi, 7 MHZ for AirFuel). At such a high frequency, a conductor is greatly affected by a skin-effect and a proximity effect (adjacent wiring effect or proximity effect). Accordingly, an inductor according to the related art that is manufactured with a solid conductor or a conductor based on a printed circuit board (PCB) exhibits reduced quality factor and efficiency due to the skin-effect and the proximity effect. To remove the effect of the skin-effect or the proximity effect on a conductor, Litz wires may be used. A Litz wire is a stranded wire made of twisted insulated wires. Litz wires are used in electronic devices to transmit alternating current at high operating frequency (e.g., in a wireless frequency band). As a Litz wire has a uniform current distribution and reduced resistance, an inductor made of Litz wire may exhibit a high quality factor and low heat loss. However, as Litz wires use a large number of thin insulated wires, they are relatively expensive and are difficult to manufacture and use. For example, Litz wires are more difficult to solder than general single-core or multi-core wires. Accordingly, a Litz wire-based inductor is expensive, and difficult to manufacture and use. In the related art, a solution to solve the above-described problem is known. 
     Patent Literature 1 (US 2014225705 A1) discloses a planar inductor in which a magnetic medium layer having certain dimensions and a magnetic loss coefficient is disposed. The magnetic medium layer is disposed adjacent to a side surface of a coil. The magnetic medium layer may reduce resistance loss by uniformly redistributing a current across a coil section. However, Patent Literature 1 discloses only a single layer planar inductor having a relatively low quality factor. Furthermore, Patent Literature 1 discloses only an inductor having a circular shape. 
     Patent Literature 2 (U.S. Pat. No. 9,712,209 B2) discloses a planar spiral inductor that has turns made of strip-form conductors. The coil has at least one turn. A bandwidth of a conductor varies according to a distance in a length direction from the start of a coil. As each coil has a corresponding width, an equal current flows through each coil. However, the above-mentioned solution discloses only a single layer flat inductor having a relatively low quality coefficient. 
     Patent Literature 3 (GB 2528788 A) discloses a wireless charger having a transmitter and a resonator. The resonator includes a conductive path having at least two loops of a current flow in a first direction and a current flow in a second direction opposite thereto, within a plane. In this solution, coupling efficiency may be improved by adjusting a return path of a magnetic flux by placing ferrite under the resonator. However, in Patent Literature 3, the resonator has a relatively low quality factor due to the uneven current distribution across a cross-section of the loop wiring. 
     The above information is presented as background information only to assist with an understanding of the disclosure. No determination has been made, and no assertion is made, as to whether any of the above might be applicable as prior art with regard to the disclosure. 
     SUMMARY 
     Aspects of the disclosure are to address at least the above-mentioned problems and/or disadvantages and to provide at least the advantages described below. Accordingly, an aspect of the disclosure is to provide a multilayer inductor having a high quality factor including an operation at high frequency. 
     Another aspect of the disclosure is to provide a multilayer inductor with simple, compact, and inexpensive design for mass production. 
     Additional aspects will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the presented embodiments. 
     In accordance with an aspect of the disclosure, a multilayer inductor is provided. The multilayer inductor includes a multilayer winding portion including a plurality of coil layers that are vertically stacked, and having an inner surface that defines a hollow of the plurality of coil layers and having an outer surface that defines an outer side, and a magnetic compensator including a soft magnetic material and including a magnetic wall located at at least one of the inner surface or the outer surface of the multilayer winding portion. 
     In various embodiments, each layer of the plurality of coil layers may include a single-turn or multi-turn field coil. 
     The magnetic wall may include first and second magnetic walls that are respectively provided on the inner surface and the outer surface of the multilayer winding portion, and the magnetic compensator may further include a lower magnetic portion that connects the first and second magnetic walls to each other and on which the multilayer winding portion may be placed. 
     The soft magnetic material of the magnetic compensator may be ferrite. 
     The magnetic wall may be attached to at least one of the inner surface or the outer surface of the multilayer winding portion. 
     The magnetic wall may be spaced apart from at least one of the inner surface or the outer surface of the multilayer winding portion. 
     A gap between the magnetic wall and the multilayer winding portion may be an air gap or may be filled with a dielectric material. 
     The magnetic wall may be perpendicular to a plane on which the plurality of coil layers are placed. 
     The magnetic wall may include the first and second magnetic walls that are respectively provided on the inner surface and the outer surface of the multilayer winding portion, and the first and second magnetic walls may be parallel to each other. 
     A surface of the magnetic wall facing the multilayer winding portion may be arranged at an inclined angle with respect to a plane on which the plurality of coil layers are placed. 
     When viewed from a plane on which the plurality of coil layers are placed, the multilayer winding portion may have an annular shape or a hollow polygonal shape, and the magnetic wall may have an annular shape or hollow polygonal shape corresponding to the shape of the multilayer winding portion. 
     The multilayer wiring portion may be provided based on a printed circuit board. 
     The plurality of coil layers may be provided on a multilayer printed circuit board. 
     The plurality of coil layers may be mutually connected by a metalized via. 
     Each of the plurality of coil layers may be formed on a single layer printed circuit board, and the plurality of coil layers may be formed by stacking single layer printed circuit boards. 
     In accordance with another aspect of the disclosure, a wireless power transmission system is provided. The wireless power transmission system includes a power transmitter including a wireless power transmission inductor, and a power receiver including a wireless power receiving inductor, wherein the inductor of the power transmitter and/or the power receiver is the multilayer inductor that includes a multilayer winding portion including a plurality of coil layers that are vertically stacked, and having an inner surface that defines a hollow of the plurality of coil layers and having an outer surface that defines an outer side, and a magnetic compensator including a soft magnetic material and including a magnetic wall located at at least one of the inner surface or the outer surface of the multilayer winding portion. 
     According to the disclosure, the multilayer inductor may improve the quality factor of an inductor when operating at high operating frequency. 
     According to the disclosure, the multilayer inductor may be simple and compact. 
     According to the disclosure, the multilayer inductor may be suitable for mass production and inexpensive. 
     Other aspects, advantages, and salient features of the disclosure will become apparent to those skilled in the art from the following detailed description, which, taken in conjunction with the annexed drawings, discloses various embodiments of the disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, features, and advantages of certain embodiments of the disclosure will be more apparent from the following description taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a schematic plan view of a multilayer inductor according to an embodiment of the disclosure; 
         FIG. 2  is a schematic cross-sectional view taken along line A-A of the multilayer inductor of  FIG. 1  according to an embodiment of the disclosure; 
         FIG. 3  is a graph showing an effect of a magnetic compensator in the multilayer inductor of  FIG. 1  according to an embodiment of the disclosure; 
         FIG. 4  is a schematic plan view of a multilayer inductor according to an embodiment of the disclosure; 
         FIG. 5  is a schematic cross-sectional view of a multilayer inductor according to an embodiment of the disclosure; 
         FIG. 6  is a schematic side view of a multilayer inductor according to an embodiment of the disclosure; 
         FIG. 7  is a schematic side view of a multilayer inductor according to an embodiment of the disclosure; 
         FIG. 8  is a schematic side view of a multilayer inductor according to an embodiment of the disclosure; 
         FIG. 9  illustrates an operation principle of a magnetic wall with respect to a conductive wire according to an embodiment of the disclosure; 
         FIG. 10  illustrates an operation principle of a magnetic wall with respect to a flat conductor according to an embodiment of the disclosure; 
         FIG. 11  illustrates a case of modeling a current density distribution in a flat conductor according to an embodiment of the disclosure; 
         FIG. 12  illustrates a case of modeling a current density distribution in a flat conductor when a magnetic wall is present at one side according to an embodiment of the disclosure; 
         FIG. 13  illustrates a case of modeling a current density distribution in a flat conductor when magnetic walls are present at both sides according to an embodiment of the disclosure; 
         FIG. 14  shows a current density distribution in each case of  FIGS. 11 to 13  according to an embodiment of the disclosure; 
         FIG. 15  illustrates a permeability of magnetic walls and a height and a thickness of the magnetic walls provided at both sides of a conductor according to an embodiment of the disclosure; 
         FIG. 16  is a graph showing a dependency of linear resistance of a conductor with respect to a height of magnetic walls according to an embodiment of the disclosure; 
         FIG. 17  is a graph showing a dependency of linear resistance of a conductor with respect to a permeability of magnetic walls according to an embodiment of the disclosure; 
         FIG. 18  is a graph showing a dependency of a quality factor of a coil with respect to a number of windings according to a presence or an absence of a magnetic compensator according to an embodiment of the disclosure; 
         FIG. 19  is a schematic perspective view of a multilayer inductor according to an embodiment of the disclosure; 
         FIG. 20  schematically illustrates an example of a wiring of coil layers of the multilayer inductor of  FIG. 19  according to an embodiment of the disclosure; and 
         FIG. 21  schematically illustrates a wireless power transmission system according to an embodiment of the disclosure. 
     
    
    
     Throughout the drawings, it should be noted that like reference numbers are used to depict the same or similar elements, features, and structures. 
     MODE OF DISCLOSURE 
     The following description with reference to the accompanying drawings is provided to assist in a comprehensive understanding of various embodiments of the disclosure as defined by the claims and their equivalents. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the various embodiments described herein can be made without departing from the scope and spirit of the disclosure. In addition, descriptions of well-known functions and constructions may be omitted for clarity and conciseness. 
     The terms and words used in the following description and claims are not limited to the bibliographical meanings, but, are merely used by the inventor to enable a clear and consistent understanding of the disclosure. Accordingly, it should be apparent to those skilled in the art that the following description of various embodiments of the disclosure is provided for illustration purpose only and not for the purpose of limiting the disclosure as defined by the appended claims and their equivalents. 
     It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a component surface” includes reference to one or more of such surfaces. 
       FIG. 1  is schematic plan view of a multilayer inductor according to an embodiment of the disclosure. 
       FIG. 2  is a schematic cross-sectional view of the multilayer inductor of  FIG. 1  taken along like A-A according to an embodiment of the disclosure. 
     Referring to  FIGS. 1 and 2 , the multilayer inductor of the present embodiment includes a multilayer winding portion  10  and a magnetic compensator  20 . 
     The multilayer winding portion  10  may be formed by vertically stacking coil layers  11 . Each layer of the coil layers  11  may include a single-turn or multi-turn field coil. The field coil may mean a coil that generates a magnetic field. For example, a circular flat coil may be a field coil. As the coil layers  11  have a shape of a winding coil, the multilayer winding portion  10  may have an inner surface  10   a  that defines a cylindrical hollow and an outer surface  10   b  that is cylindrical. Although  FIG. 2  illustrates that the multilayer winding portion  10  consists of four coil layers  11 , the disclosure is not limited thereto. 
     A dielectric  12  may be provided between the coil layers  11 . The coil layers  11  may be formed based on a printed circuit board. In an embodiment, the coil layers  11  may be formed as a multilayer printed circuit board. In other words, the coil of the coil layers  11  may be formed as a circuit of each layer of a multilayer printed circuit board. In this case, as in an embodiment with reference to  FIG. 19  and  FIG. 20 , coils provided on the respective layers of a multilayer printed circuit board may be mutually connected by vias that are metalized. In another embodiment, each of the coil layers  11  may be formed in a conductor layer pattern on a dielectric layer of a single-layer printed circuit board (PCB), and as printed circuit boards on which these circular flat coils are formed are stacked in two or more layers, the multilayer winding portion  10  may be formed. The implementation of the multilayer winding portion  10  on a printed circuit board may be simple and at low cost, which is appropriate to mass production. 
     The magnetic compensator  20  may be formed of a soft magnetic material. The soft magnetic material is a material in which a domain wall is easily moved, and which is magnetized by applying a small magnetic field. 
     In an embodiment, the soft magnetic material of the magnetic compensator  20  may be a soft magnetic ferrite. 
     In an embodiment, the magnetic compensator  20  may be manufactured of an iron-based soft magnetic material, or an amorphous or nanocrystalline alloy-based soft magnetic material. 
     The magnetic compensator  20  is disposed at at least any one of the inner surface  10   a  and the outer surface  10   b  of the multilayer winding portion  10 . 
     In an embodiment, the magnetic compensator  20  may be first and second magnetic walls  21  and  22  having a cylindrical shape and standing from a plane (hereinafter an inductor plane) on which a plurality of the coil layers  11  are placed. 
     In an embodiment, each of the first and second magnetic walls  21  and  22  of the magnetic compensator  20 , as illustrated in  FIG. 2 , may be formed in a rectangular cross-sectional shape. 
     In an embodiment, the first and second magnetic walls  21  and  22  may be perpendicular to the inductor plane and parallel to each other. In another embodiment, the first and second magnetic walls  21  and  22  may be arranged inclined to the inductor plane. 
     In an embodiment, the first and second magnetic walls  21  and  22  are located close to an edge of the multilayer winding portion  10 . The first and second magnetic walls  21  and  22  may each be attached to the inner surface  10   a  and the outer surface  10   b  of the multilayer winding portion  10  without a gap. 
       FIGS. 1 and 2  illustrate a case in which both of the first and second magnetic walls  21  and  22  are provided, but the disclosure is not limited thereto. In an embodiment, any one of the first and second magnetic walls  21  and  22  may be provided. 
     The multilayer inductor described above may have a shape of a flat field coil. 
       FIG. 3  is a graph showing an effect of the magnetic compensator in the multilayer inductor of  FIG. 1  according to an embodiment of the disclosure. 
     Referring to the graph of  FIG. 3 , the horizontal axis denotes a location in a width direction of the multilayer winding portion  10  of the multilayer inductor, and the vertical axis denotes a current density flowing in the multilayer winding portion  10  of the multilayer inductor. In  FIG. 3 , a solid line denotes a case when there is the magnetic compensator  20 , and a dashed line denotes a case when there is no magnetic compensator  20 . The width direction of the multilayer winding portion  10  may be a diameter direction. On the horizontal axis of  FIG. 3 , a position of 0 a.u. is a position of an inner surface ( 10   a  of  FIG. 2 ) where the multilayer winding portion  10  meets the first magnetic wall  21  of the magnetic compensator  20 , and a position of 230 a.u. is a position of the outer surface  10   b  where the multilayer winding portion  10  meets the second magnetic wall  22  of the magnetic compensator  20 . 
     Referring to the dashed line of  FIG. 3 , when there is no magnetic compensator, a current density in the multilayer winding portion  10  of the multilayer inductor has “deep” in the middle of the width direction of the multilayer winding portion  10 , and the maximum value at both edges of the multilayer winding portion  10 . As is known as Lenz&#39;s law, at high operating frequency, a considerable portion of a current flows in an edge of a conductive wire of the multilayer winding portion  10 , and thus, an effective cross-sectional area of the conductive wire (conductor) is reduced. Accordingly,  FIG. 3  illustrates that, when there is no magnetic compensator, high loss and ineffective use of the conductive wire (conductor) of the multilayer winding portion  10  are accompanied. 
     When the magnetic compensator  20  in a wall shape is present at both side surfaces of the multilayer winding portion  10 , the current density of the multilayer winding portion  10  is more uniformly distributed, as indicated by the solid line of  FIG. 3 , compared with a case without a magnetic compensator. The maximum value of the current density at the edge, that is, the inner surface  10   a  and the outer surface  10   b  of the multilayer winding portion  10  is considerably reduced, compared with the case without a magnetic compensator, and the current density in the middle portion of the multilayer winding portion  10  is increased. 
     As described above,  FIG. 3  shows that, as the magnetic compensator  20  provides a more uniform current distribution across the cross-section of the multilayer winding portion  10 , the effective cross-section of the conductive wire (conductor) of the multilayer winding portion  10  is increased and loss is decreased. 
     Although the multilayer inductor according to the embodiment of  FIGS. 1 and 2  is described as having a shape of a circular inductor having a circular coil, the disclosure is not limited thereto. 
       FIG. 4  is a schematic plan view of a multilayer inductor according to an embodiment of the disclosure. 
     Referring to  FIG. 4 , the multilayer inductor may have a rectangle inductor shape and include a multilayer winding portion  10 ′ formed of coils having a hollow rectangular shape and a magnetic compensator  20 ′ having first and second magnetic walls  21 ′ and  22 ′ that are provided on an inner surface and an outer surface of the multilayer winding portion  10 ′ and each have a rectangular shape. 
       FIG. 5  is a schematic plan view of a multilayer inductor according to an embodiment of the disclosure. 
     Referring to  FIG. 5 , the multilayer inductor may have a hexagonal inductor shape including a multilayer winding portion  10 ″ formed of coils having a hollow hexagonal shape and a magnetic compensator  20 ″ having first and second magnetic walls  21 ″ and  22 ″ that are provided on an inner surface and an outer surface of the multilayer winding portion  10 ″ and each have a hexagonal shape. 
     The inductor may have any suitable geometric shape in a plan view, for example, triangular, polygonal, oval, etc., depending on the purpose, design features, and required parameters. 
     The multilayer inductor of the embodiment with reference to  FIGS. 1 and 2  is described with an example in which the first and second magnetic walls  21  and  22  have a rectangular cross-sectional shape, but the disclosure is not limited thereto. 
       FIG. 6  is a schematic side view of a multilayer inductor according to an embodiment of the disclosure. 
     Referring to  FIG. 6 , first and second magnetic walls  21 ″′ and  22 ″′ may have an inclined shape on sides facing the multilayer winding portion  10 . In another example, the first and second magnetic walls  21 ″′ and  22 ″′ may have a shape such as trapezoidal, triangular, etc. 
       FIG. 7  is a schematic side view of a multilayer inductor according to an embodiment of the disclosure. 
     Referring to  FIG. 7 , the first and second magnetic walls  21  and  22  may be arranged adjacent to each other to be a certain distance apart from each of the inner surface  10   a  and the outer surface  10   b  of the multilayer winding portion  10 . In other words, a gap G may be present between the magnetic compensator  20  and the multilayer winding portion  10 . The gap G may be present between the magnetic compensator  20  and the multilayer winding portion  10  may be an air gap, a gap filled with a dielectric, or a combination thereof. When the gap G is filled with a dielectric, the dielectric may be the dielectric  12  located between the coil layers  11 , for example, a dielectric of a printed circuit board. 
     Although  FIG. 7  illustrates a case in which both of the first and second magnetic walls  21  and  22  are spaced apart from the multilayer winding portion  10 , only any one of the first and second magnetic walls  21  and  22  may be spaced apart from the multilayer winding portion  10 . 
       FIG. 8  is a schematic side view of a multilayer inductor according to an embodiment of the disclosure. 
     Referring to  FIG. 8 , a multilayer inductor of the present embodiment includes the multilayer winding portion  10  and a magnetic compensator  20 . The multilayer winding portion  10  may be substantially the same as the multilayer winding in the multilayer inductor of the above-described embodiments. The magnetic compensator  20  may further include a lower magnetic portion  30  in addition to the first and second magnetic walls  21  and  22  in the multilayer inductor of the above-described embodiments. The lower magnetic portion  30  may be located on a lower surface of the multilayer winding portion  10 . 
     The lower magnetic portion  30  may be formed of a soft magnetic material. In an embodiment, the soft magnetic material of the lower magnetic portion  30  may be a soft magnetic ferrite. In an embodiment, the lower magnetic portion  30  may be manufactured of an iron-based soft magnetic material, or an amorphous or nanocrystalline alloy-based soft magnetic material. The first and second magnetic walls  21  and  22  and the lower magnetic portion  30  may all be formed of the same material. 
     The lower magnetic portion  30  may be attached on lower surfaces of the first and second magnetic walls  21  and  22 . Although  FIG. 8  illustrates that the first and second magnetic walls  21  and  22  and the lower magnetic portion  30  are provided separately, the first and second magnetic walls  21  and  22  and the lower magnetic portion  30  may be formed integrally. 
     The lower magnetic portion  30  may connect the first and second magnetic walls  21  and  22  that are respectively provided on an inner wall and an outer wall of the multilayer winding portion  10 , thereby shielding the multilayer inductor from the effect of an external environment. 
       FIG. 9  illustrates an operation principle of a magnetic wall with respect to a conductive wire according to an embodiment of the disclosure. 
     The left side of  FIG. 9  illustrates a case in which a conductive wire perpendicular to a plane is present at some distance away from a magnetic wall. When the ground is assumed to be an x-y plane, the magnetic wall is located on a y-z plane and a conductor is arranged parallel to a Z-axis. A current flows in the conductive wire in a Z-axis direction. A tangential component of a magnetic field generated by a current flowing in the conductive wire is 0. 
     The right side of  FIG. 9  illustrates a configuration that is magnetically equivalent to the left configuration of  FIG. 9 . The magnetic field generated by the current of the conductive wire is equivalent to the magnetic field generated by the current flowing in two conductive wires arranged parallel to each other, due to the presence of the magnetic wall, as in an example illustrated in  FIG. 9 . A second conductive wire is located symmetrically to a first conductive wire with respect to the magnetic wall. In other words, with respect to the first conductive wire located in the right (x&gt;0) with respect to the magnetic wall, the second conductive wire is located in the left (x&lt;0) with respect to the magnetic wall. The current flowing in the second conductive wire has the same amount as the current flowing in the first conductive wire, and flows in the same direction as the current flowing in the first conductive wire. The tangential component of the magnetic field generated by the two conductive wires becomes 0 at the location of the magnetic wall. 
       FIG. 10  illustrates an operation principle of a magnetic wall with respect to a flat conductor according to an embodiment of the disclosure. 
     The left side of  FIG. 10  illustrates a case in which there is a flat conductor that is perpendicular to a magnetic wall. When the ground is assumed to be an x-y plane, the magnetic wall is located on a y-z plane and a conductor is arranged on a z-x plane. A current flows in the conductive wire in a Z-axis direction. A current distribution j z  across the cross-section of the conductor may have a shape as shown in a curved graph marked above the conductor. 
     The right side of  FIG. 10  illustrates a configuration that is magnetically equivalent to the left configuration of  FIG. 10 . The magnetic field generated by the conductor illustrated in the left side of  FIG. 10  is equivalent to the magnetic field generated by a current flowing in a flat conductor consisting of two parts that are symmetrically located with respect to the position of the magnetic wall, as illustrated in the right side  FIG. 10 , considering the presence of the magnetic wall therearound. The equivalent relationship of  FIG. 10  as above may be understood in a similar manner to  FIG. 9 . 
       FIG. 11  illustrates a case of modeling a current density distribution in a flat conductor according to an embodiment of the disclosure. 
       FIG. 12  illustrates a case of modeling a current density distribution in a flat conductor when a magnetic wall is present at one side according to an embodiment of the disclosure. 
       FIG. 13  illustrates a case of modeling a current density distribution in a flat conductor when magnetic walls are present at both sides according to an embodiment of the disclosure. 
       FIG. 14  shows a current density distribution in each case of  FIGS. 11 to 13  according to an embodiment of the disclosure. 
     For example,  FIG. 14  illustrates a modeling result of a case in which a current flows at a frequency of 100 kHz in a flat conductor that is 60 μm thick and 10 mm wide. 
     The distribution of a current density in a case of  FIG. 11  is illustrated as Case 1 in the graph of  FIG. 14 . The “deep” is in the middle of the conductor and two maximum values are at edges of the conductor. 
     The distribution of a current density in a case of  FIG. 12  is illustrated as Case 2 in the graph of  FIG. 14 . The magnetic wall removes a sharp increase in the current density of the conductor in the vicinity of a contact point with the magnetic wall. 
     The distribution of a current density in a case of  FIG. 13  is illustrated as Case 3 in the graph of  FIG. 14 . Two magnetic walls at both sides of the conductor remove a sharp increase in the current density of the conductor in the vicinity of a contact point with the magnetic wall. As an ideal case that is a simulation of a flat conductor with two magnetic walls is the same as a flat conductor with an infinite width, a current density is uniformly distributed across the width of a conductor. Accordingly, the maximum efficiency using a conductor cross-section is achieved and loss of a conductor is reduced. 
       FIG. 15  illustrates the permeability of magnetic walls and the height and thickness of the magnetic walls provided at both sides of a conductor according to an embodiment of the disclosure. 
       FIG. 16  is a graph showing the dependency of linear resistance of the conductor with respect to the height of magnetic walls according to an embodiment of the disclosure. 
       FIG. 17  is a graph showing the dependency of linear resistance of the conductor with respect to the permeability of magnetic walls according to an embodiment of the disclosure. 
     Referring to  FIG. 15 , the magnetic wall is substituted with a wall of a soft magnetic material having finite dimension and permeability in a specific embodiment. In an example,  FIG. 15  illustrates a flat copper conductor that is 60 μm thin and 10 mm wide in which a current of a frequency of 100 kHz flows. The magnetic wall of the magnetic compensator is located at both sides of the conductor. In an embodiment, the magnetic wall is formed of ferrite. “μ” denotes permeability of the magnetic wall. The finite geometric dimension and permeability reduce the effect of eliminating a sharp increase in current density near the edge of the conductor. 
     To determine the dependency of resistance (ohm/m) per unit length of a conductor of a magnetic compensator with respect to the height of a magnetic wall, it is assumed that the thickness of the magnetic wall is 2 mm and permeability μ is 1000. 
     Referring to  FIG. 16 , in an embodiment, it may be seen that almost minimum linear resistance of the conductor is achieved from a magnetic wall height of about 4 mm of the magnetic compensator. 
     To determine the dependency of linear resistance of a conductor with respect to permeability of a magnetic wall of a magnetic compensator, it is assumed that the thickness and the height of the magnetic wall are 2 mm and 4 mm, respectively. 
     Referring to  FIG. 17 , in an embodiment, it may be seen that, even when a permeability value is 30, substantially minimum linear resistance of a conductor is achieved. 
     As active resistance of a conductor of inductor winding decreases, heating loss during inductor operation is reduced. 
     Accordingly, the disclosed multilayer inductor may implement a flat inductor having a high quality factor from a simple design having a magnetic compensator. 
       FIG. 18  is a graph showing the dependency of a quality factor of a coil with respect to the number of windings according to the presence of the magnetic compensator according to an embodiment of the disclosure. 
     Referring to  FIG. 18 , the magnetic compensator may improve the quality factor of the multilayer inductor as the number of windings increases. When there is no magnetic compensator, the quality factor is much low, as illustrated in  FIG. 18 . In other words, where there is a magnetic compensator, the quality factor increase much according to the increase of the number of windings, whereas when there is no magnetic compensator, actually, the quality factor remains unchanged in spite of an increase in the number of windings (or the number of coil layers). This is because a current in a coil layer is not uniformly distributed. 
       FIG. 19  is a schematic perspective view of a multilayer inductor according to an embodiment of the disclosure. 
       FIG. 20  schematically illustrates an example of a wiring of coil layers of the multilayer inductor of  FIG. 19  according to an embodiment of the disclosure. 
     Referring to  FIGS. 19 and 20 , a multilayer winding portion of the multilayer inductor is formed based on a printed circuit board. Each layer of the multilayer winding portion may be a printed circuit board, that is, the dielectric  12  on which a conductor, that is, a circuit layer  11 , is deposited. To manufacture the multilayer winding portion, the layers of the multilayer winding portion are connected to each other by punching and plating holes of the printed circuit board, and a current path is formed between the conductors of winding layers. The multilayer inductor consists of eight coil layers M 1 , M 2 , M 3 , M 3 , M 4 , M 5 , M 6 , M 7 , and M 8  that are connected in series, and each coil layer is based on a printed circuit board. The conductor of each layer of the coil layers M 1 , M 2 , M 3 , M 3 , M 4 , M 5 , M 6 , M 7 , and M 8  is formed on the dielectric  12  of the printed circuit board, and the coil layers M 1 , M 2 , M 3 , M 3 , M 4 , M 5 , M 6 , M 7 , and M 8  are separated from each other by the dielectric  12 . The conductors of the coil layers M 1 , M 2 , M 3 , M 3 , M 4 , M 5 , M 6 , M 7 , and M 8  may be electrically connected to each other via, for example, a metalized via. In an embodiment, VIA 1 , VIA 3 , VIA 4 , and VIAE may be punched in the printed circuit board in an initial production process before forming the multilayer winding portion by bonding the printed circuit board. VIA 2  and VIA 3  may be drilled after the first bonding of M 1 -M 4  layers and M 5 -M 8  layers. VIA 0  (through-hole) may be punched after the final bonding. The coil layers and the corresponding VIAs for connecting the coil layers may be designed to provide a current flow direction that is required by the multilayer inductor to form a desired magnetic field. Alternatively, the coil layers M 1 , M 2 , M 3 , M 3 , M 4 , M 5 , M 6 , M 7 , and M 8  may be connected to each other by other well-known electrical connection devices. 
       FIG. 21  schematically illustrates a wireless power transmission system according to an embodiment of the disclosure. 
     Referring to  FIG. 21 , the multilayer inductors of the above-described embodiments may be applied in a wireless power transmission system. In an embodiment, the wireless power transmission system may include a power transmitter  100  including a wireless power transmission inductor  110 , and a power receiver  200  including a wireless power receiving inductor  210 . The multilayer inductors of the above-described embodiments may be the wireless power transmission inductor  110  and/or the wireless power receiving inductor  210 , and accordingly, the wireless power transmission system may have a simple structure and highly efficient power transmission. 
     In an embodiment, the wireless power transmission system may be used in a wireless charging system of a mobile electronic device. The mobile electronic device needs to increase power transmission efficiency and reduce the overall size of the wireless power transmission system in order to make the mobile electronic device compact, and the multilayer inductors of the above-described embodiments may be of great help to achieve the required levels of a mobile electronic device. 
     In an embodiment, the above-described wireless power transmission system may be used to exclude wired connections having low mechanical and strength characteristics by transmitting power between different parts of a robot connected to each other through joints or other movable joints. 
     The features recited in the various dependent claims as well as the implementations disclosed in various parts of this specification may be combined to achieve advantageous effects even if the possibility of such combinations is not explicitly disclosed. 
     While the disclosure has been shown and described with reference to various embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the disclosure as defined by the appended claims and their equivalents.