Patent Publication Number: US-8988177-B1

Title: Magnetic core having flux paths with substantially equivalent reluctance

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present disclosure is a continuation-in-part of U.S. patent application Ser. No. 13/850,080, filed Mar. 25, 2013, which is a continuation of U.S. patent application Ser. No. 12/614,843, filed Nov. 9, 2009, now U.S. Pat. No. 8,405,478, issued Mar. 26, 2013, which claims priority to U.S. Patent Application No. 61/122,526, filed Dec. 15, 2008. 
     The present disclosure also claims priority to U.S. Patent Application No. 61/831,303, filed Jun. 5, 2013. 
     Each of U.S. patent application Ser. Nos. 13/850,080, 12/614,843, 61/122,526, and 61/831,303 are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     Embodiments of the present invention relate to magnetic cores, and more particularly, to increasing energy efficiency of magnetic cores. 
     BACKGROUND 
     A magnetic core is a component in a variety of electrical and electromechanical devices including, for example, power generators, motors, transformers or inductors and can be found in Power Generation Sites, transformer substations, power supplies, direct current (DC) converters, refrigerators, air conditioners, vacuum cleaners, fluorescent lamps, and/or electrical cars, as well as a host of other devices. The magnetic core can be used, for example, to concentrate the strength and increase the effect of magnetic fields produced by electric currents and magnets. 
       FIG. 1  schematically illustrates unevenly distributed magnetic flux  102  in an example magnetic core  100 . The magnetic flux  102  is generally more highly concentrated near the inner corner regions  104 . The unevenly distributed flux  102  may result in additional generated heat at the corners, which may produce unwanted power loss and/or reduced energy efficiency. The unevenly distributed magnetic flux  102  may be apparent in a variety of cores including gaped/un-gaped magnetic cores or magnetic cores having other shapes or configurations. Magnetic flux is generally concentrated near the higher curvature radius of magnetic core structures resulting in unwanted power loss. For example, a toroid-shaped magnetic core generally has concentrated magnetic flux near an inner radius of the toroid compared to an outer radius of the toroid. 
     SUMMARY 
     In some embodiments, the present disclosure provides magnetic cores that include a first magnetic material with a first magnetic permeability, forming at least part of a body of the magnetic core, and a second magnetic material that has a second magnetic permeability positioned in a corner region of the body of the magnetic core. The second magnetic material is disposed within the body such that a plurality of magnetic flux paths of different overall lengths traverse the corner region through a first plurality of lengths of the first magnetic material and a second plurality of lengths of the second magnetic material. The plurality of potential magnetic flux paths have a corresponding plurality of effective magnetic reluctances, with different paths of the plurality of magnetic flux paths having different associated first lengths of the first plurality of lengths and different associated second lengths of the second plurality of lengths such that the corresponding plurality of magnetic reluctances of the plurality of magnetic flux paths are substantially equivalent through the different overall lengths. 
     In some embodiments, there is an inverse relationship between the plurality of different overall lengths of the plurality of magnetic flux paths that traverse the corner region and corresponding second lengths of the second plurality of lengths of the second magnetic material that the plurality of magnetic flux paths traverse. 
     In some embodiments, the body of the magnetic core is angled at the corner region at a first angle relative to a leg of the body. The corner region has an angled corner configuration in which an outside edge of the corner region is angled at a second angle relative to the leg of the body, and the second magnetic material has a triangular-shaped cross-sectional area having a straight-line base that is parallel to the outside edge of the corner region. 
     In some embodiments, the corner region has a rounded corner configuration in which an outside edge of the corner region is rounded, and the second magnetic material has a triangular-shaped cross-sectional area that has a rounded base that is concentric with the outside edge of the corner region. 
     In some embodiments, the corner region of the body of the magnetic core includes an outside edge angled at 45-degrees with respect to both the back element and the leg element, and an apex of the triangular-shaped cross-sectional area is incidental with the outside edge. 
     In some embodiments, the present disclosure describes a method of fabricating a magnetic core, including providing a body of a magnetic core that includes a first magnetic material having a first magnetic permeability, and providing a corner element into a corner region of the body of the magnetic core that is comprised of a second magnetic material having a second magnetic permeability. A plurality of magnetic flux paths of different overall lengths traverse the corner region through a first plurality of lengths of the first magnetic material and a second plurality of lengths of the second magnetic material. The plurality of potential magnetic flux paths have a corresponding plurality of effective magnetic reluctances, and the first plurality of lengths and the second plurality of lengths differ among the plurality of magnetic flux paths such that the corresponding plurality of magnetic reluctances of the plurality of magnetic flux paths are substantially equivalent through the different overall lengths. 
     In some embodiments of the method of fabricating a magnetic core, there is an inverse relationship between the plurality of different overall lengths of the plurality of magnetic flux paths that traverse the corner region and corresponding second lengths of the second plurality of lengths of the second magnetic material that the plurality of magnetic flux paths traverse. 
     In some embodiments, the method includes providing the body of the magnetic core to include a top portion and a leg portion oriented perpendicular to one another such that the corner region has an outside edge angled with respect to the top portion and the leg portion. A corner is provided with triangular-shaped cross-sectional area with a straight-line base that is parallel to the outside edge. 
     In some embodiments, the method includes providing the body of the magnetic core to include a top portion and a leg portion oriented perpendicular to one another and such that the corner region has an rounded outside edge, and the method further includes providing the corner element to have a triangular-shaped cross-sectional area having a rounded base that is concentric with the rounded outside edge. 
     In some embodiments, the corner region of the body of the magnetic core is provided such that an outside edge is angled at 45-degrees with respect to both a back element and a leg element, and an apex of the triangular-shaped cross-sectional area is incidental with the outside edge. In some embodiments the corner element is provided to have a base length that is a function of a difference between the first magnetic permeability and the second magnetic permeability. In some embodiments, the body is provided to have an edge length that is a function of the difference between the first magnetic permeability and the second magnetic permeability. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present invention will be readily understood by the following detailed description in conjunction with the accompanying drawings. To facilitate this description, like reference numerals designate like structural elements. Embodiments of the invention are illustrated by way of example and not by way of limitation in the figures of the accompanying drawings. 
         FIG. 1  schematically illustrates unevenly distributed magnetic flux in an example magnetic core. 
         FIG. 2   a  schematically illustrates an example magnetic core, in accordance with various embodiments. 
         FIG. 2   b  schematically illustrates a substantially evenly distributed magnetic flux in an example magnetic core, in accordance with various embodiments. 
         FIG. 3  schematically illustrates a corner region of an example magnetic core, in accordance with various embodiments. 
         FIG. 4  schematically illustrates an example triangular structure coupled to a core body at a corner region of a magnetic core, in accordance with various embodiments. 
         FIG. 5   a  schematically illustrates an example triangular structure coupled to a core body of a toroid-shaped magnetic core, in accordance with various embodiments. 
         FIG. 5   b  schematically illustrates multiple example triangular structures coupled to a core body of a toroid-shaped magnetic core, in accordance with various embodiments. 
         FIG. 6  is a flow diagram of a method to fabricate a magnetic core having a substantially evenly distributed magnetic flux, in accordance with various embodiments. 
         FIG. 7  schematically illustrates an example magnetic core having an angled corner configuration and triangular structures in the corner regions, in accordance with various embodiments. 
         FIG. 8  schematically illustrates a corner region of an example magnetic core having magnetic flux paths of different lengths but substantially equivalent magnetic reluctances. 
         FIG. 9  schematically illustrates a corner region of an example magnetic core having an angled corner configuration. 
         FIG. 10  schematically illustrates an example E-shaped magnetic core having a rounded corner configuration and triangular structures in the corner regions, in accordance with various embodiments. 
         FIG. 11  schematically illustrates a corner region of an example magnetic core  1000  having a rounded corner configuration. 
         FIG. 12  is a flow diagram of a method to fabricate a magnetic core having an angled configuration or a rounded corner configuration. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION 
     The present specification describes configurations and techniques to provide a low-loss magnetic core. In the following detailed description, reference is made to the accompanying drawings which form a part hereof wherein like numerals designate like parts throughout, and in which is shown by way of illustration embodiments in which the invention may be practiced. In general, other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. Therefore, the following detailed description is not to be taken in a limiting sense, and the scope of embodiments in accordance with the present invention is defined by the appended claims and their equivalents. 
     The description may use the phrases “in an embodiment,” or “in embodiments,” which may each refer to one or more of the same or different embodiments. The phrase “in some embodiments” is used repeatedly. The phrase generally does not refer to the same embodiments; however, it may. The terms “comprising,” “having,” and “including” are synonymous, unless the context dictates otherwise. The phrase “A and/or B” means (A), (B), or (A and B). The phrase “A/B” means (A), (B), or (A and B), similar to the phrase “A and/or B.” The phrase “at least one of A, B and C” means (A), (B), (C), (A and B), (A and C), (B and C) or (A, B and C). The phrase “(A) B” means (B) or (A and B), that is, A is optional. 
       FIG. 2   a  schematically illustrates an example magnetic core  200 , in accordance with various embodiments. The illustrated magnetic core  200  comprises a first U-core  210  and a second U-core  220 , coupled as shown. In accordance with various embodiments, a magnetic core may include a variety of other shapes and configurations than what is depicted including, for example, C-cores, E-cores, I-cores, toroids, cylinders, rings, beads, planar cores, or other shapes and configurations that may benefit from the principles described herein. 
     The magnetic core  200  comprises a first magnetic material  206  having a first magnetic permeability to substantially provide a core body of the magnetic core  200 . The first magnetic material  206  includes, for example, soft or hard magnetic materials with high magnetic permeability such as soft ferrite, laminated silicon steel, and/or powder iron, or any other magnetic material that may benefit from the principles described herein. The core body generally includes components (e.g., first magnetic material  206  and second magnetic material  208 ) of the magnetic core  200  that comprise magnetic material to concentrate the strength and/or increase the effect of magnetic fields applied to the magnetic core  200 . 
     The magnetic core  200  further comprises a second magnetic material  208  having a second magnetic permeability that is lower than the first magnetic permeability of the first magnetic material  206 . The second magnetic material  208  may be coupled to or positioned in the core body in a manner that substantially evenly distributes magnetic flux in the magnetic core  200 . In other words, as used herein substantially evenly distributed magnetic flux means that the magnetic core  200 , as well as other magnetic cores according to various embodiments described herein—having a second magnetic material such as the second magnetic material  208  coupled as shown—generally have a more evenly distributed magnetic flux than a magnetic core that solely comprises only one magnetic material, such as magnetic material  206 . 
       FIG. 2   b  schematically illustrates a substantially evenly distributed magnetic flux  202  in an example magnetic core  250 , in accordance with various embodiments. The second magnetic material  208  forces a more even distribution of the magnetic flux  202  at the inner corners and the rest of the magnetic core  250  by making a magnetic reluctance associated with different loops or paths of the magnetic flux  202  more similar or substantially the same. In other words, the second magnetic material  208  is generally configured in the core body to provide similar or substantially equal reluctance for different loops of the magnetic flux  202 . For example, a magnetic reluctance for an inner loop of the magnetic flux  202  that is closer to the inner corners of the magnetic core  250  may be similar or substantially equal to a magnetic reluctance for an outer loop of the magnetic flux  202  that is closer to the outer corners of the magnetic core  250 . 
     Coupling a lower permeability magnetic material such as the second magnetic material  208  to the first magnetic material  206 , as shown, generally reduces or substantially eliminates the localized heating and/or power loss described with respect to the inner corner regions  104  of  FIG. 1  and provides a more energy efficient magnetic core  250 . Example design principles for the shape and configuration of the second magnetic material  208  are described with respect to  FIGS. 3-5 . 
       FIG. 3  schematically illustrates a corner region  330  of an example magnetic core  300 , in accordance with various embodiments. The magnetic core  300  comprises a first U-core  310  and a second U-core  320 , coupled as shown. The magnetic core  300  further includes a corner region  330  defined by a region of the core body where a first portion  332  of the core body meets or coincides with a second portion  334  of the core body in a manner that is substantially perpendicular. The first portion  332  of the U-core  310 , for example, coincides with the second portion  334  at the corner region  330  in a manner that roughly forms a right angle where the first portion  332  and the second portion  334  meet. According to various embodiments, the components of the magnetic core  300  may have rounded edges and/or corners without departing from the scope of this disclosure. 
     The corner region  330  has an area of about axd or slightly larger, where a is a width of the first portion  332  and where d is a width of the second portion  334 , as illustrated. An inner perimeter  340  of the magnetic core  300  generally represents a shortest path for magnetic flux and an outer perimeter  350  generally represents a longest path for magnetic flux. The shortest magnetic flux path around the inner perimeter  340  has a distance equal to 2p+2q, where p and q represent the illustrated dimensions associated with the inner perimeter  340 . The longest magnetic flux path around the outer perimeter  350  has a distance equal to 4a+4d+2p+2q. An evenly distributed flux can be obtained in the magnetic core  300  by making reluctance for the longest path, the shortest path, and paths in between, substantially similar. The same reluctance for the various paths (e.g., inner perimeter  340  and outer perimeter  350 ) may be achieved by coupling a lower permeability material at one or more corner regions such as the corner region  330  of the magnetic core  300 . An example configuration for coupling a lower permeability material at the corner region  330  is described further with respect to  FIG. 4 . 
       FIG. 4  schematically illustrates an example triangular structure  402  coupled to a core body  400  at a corner region  412  (e.g.,  330 ) of a magnetic core (e.g., magnetic core  200  or magnetic core  300 ), in accordance with various embodiments. The term “coupled to” as used with respect to the triangular structure  402  broadly includes connection relationships such as “physically connected to” or “part of”, meaning that the triangular structure  402  may be “formed in”, “positioned in”, “placed in”, or “inserted in” the core body, or other similar meanings. As alluded to earlier, the core body  400  includes a first magnetic material  406  having a first magnetic permeability. The corner region  412  includes the triangular structure  402  comprising a second magnetic material  408  having a second magnetic permeability that is lower than the first magnetic permeability. 
     According to various embodiments, the triangular structure  402  may be only substantially triangular in form. In other words, the triangular structure  402  may not be an exact triangle, but may include triangular structures having rounded corners, uneven sides, or other deviations from a triangular shape. The term triangular structure  402  is intended to describe a general shape of the second magnetic material  408 . 
     In an embodiment, the triangular structure  402  is an isosceles triangle having a base with length, c, that is positioned near an inner corner of the corner region  412  and having an apex that is positioned near an outer corner of the corner region  412 , as illustrated. The base having length, c, may form an angle that is substantially 45° relative to an inner surface (e.g.,  410 ,  414 ) of the core body  400 . An angle, α, defines the angle between an outer surface (e.g.,  416 ,  418 ) of the first magnetic material  406  and the substantially triangular structure  402 , as illustrated. 
     Distance, b, defines a distance that is normal to an inner surface (e.g.,  410 ) and spans from the inner surface of the first magnetic material  406  to a position where an end of the base having length, c, coincides with an inner surface  414  that is substantially perpendicular to the other inner surface  410 , as depicted. The distance, b, may be determined according to the following equation, where a is a width of a portion of the core body  400 , cot represents a cotangent function, and where a defines the angle between the outer surface (e.g.,  416 ,  418 ) of the first magnetic material  406  and the substantially triangular structure  402 , as illustrated:
 
 b=a *cot(α)− a=a (cot(α)−1)  (1)
 
     For clarity and ease of discussion of the principles described herein, the core body  400  will be described for an example case where distance a of  FIG. 3  is equal to distance d of  FIG. 3 . In such a case, within the corner region  412 , the longest distance for magnetic flux is through the first magnetic material  406  around the outer perimeter (e.g.,  2   a ) of the core body  400  and the shortest distance for magnetic flux is across the base length (e.g., c) of the triangular structure  402  comprising the second magnetic material  408 . The following equations set the shortest path (e.g., c) reluctance to be the same as the longest path reluctance (e.g.,  2   a ), and provide a way to calculate the angle α, where S unit     —     area  is a unit cross-section area of the magnetic flux, μ 1  is the magnetic permeability of the first magnetic material  406 , and μ 2  is the magnetic permeability of the second magnetic material  408 . 
                       2   ⁢           ⁢   a         S   unit_area     ⁢     μ   1         =         2     ⁢     a   ⁡     (       cot   ⁡     (   α   )       -   1     )             S   unit_area     ⁢     μ   2                 (   2   )               
becomes
 
                     cot   ⁡     (   α   )       =           2     ⁢     μ   2       +     μ   1         μ   1               (   3   )               
becomes
 
     
       
         
           
             
               
                 
                   α 
                   = 
                   
                     
                       cot 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               2 
                             
                             ⁢ 
                             
                               μ 
                               2 
                             
                           
                           + 
                           
                             μ 
                             1 
                           
                         
                         
                           μ 
                           1 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Thus, if magnetic permeability for the first magnetic material  406  and the second magnetic material  408  are known, then the angle, α, can be determined. In an embodiment, the first magnetic material  406  comprises ferrite and the second magnetic material  408  comprises iron powder. Subject matter is not limited in this regard, and the first and second magnetic materials (e.g.,  406 ,  408 ) may include any of a variety of magnetic materials that may benefit from the principles described herein. The base length, c, can be determined according to the following: 
                   c   =       2     ⁢     a   ⁡     (       cot   ⁡     (   α   )       -   1     )                 (   5   )               
Equation (5) is reduced to the following using equation (4):
 
     
       
         
           
             
               
                 
                   c 
                   = 
                   
                     
                       2 
                       ⁢ 
                       a 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         μ 
                         2 
                       
                     
                     
                       μ 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     An angle, β, of the apex of the triangular structure  402  may be determined according to the following:
 
β=90°−2α  (7)
 
     A triangular structure  402  may be implemented in core bodies having other shapes and the triangular structure  402  may be positioned in regions other than the corner region  412  of the core body, according to various embodiments. Such an example is described further with respect to  FIG. 5   a.    
       FIG. 5   a  schematically illustrates an example triangular structure  502  coupled to a core body of a toroid-shaped magnetic core  500 , in accordance with various embodiments. The magnetic core  500  includes a first magnetic material  506  having a first magnetic permeability and a second magnetic material  508  having a second magnetic permeability that is lower than the first magnetic permeability. 
     In an embodiment, the second magnetic material  508  forms a substantially triangular structure  502  having a base positioned near an inner radius, r, of the core body and having an apex positioned near an outer radius, R, of the core body. The base length, f, may be determined according to the following, where μ 1  is the magnetic permeability of the first magnetic material  506 , and μ 2  is the magnetic permeability of the second magnetic material  508 : 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                         π 
                         ⁡ 
                         
                           ( 
                           
                             R 
                             - 
                             r 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         μ 
                         2 
                       
                     
                     
                       
                         μ 
                         1 
                       
                       - 
                       
                         μ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     The use of a triangular structure  502  in the magnetic core  500  may make magnetic reluctance the same between the inner radius, r, and the outer radius, R, which may force the magnetic flux to be evenly distributed. The same principle may be applied to other circular-type magnetic cores. 
       FIG. 5   b  schematically illustrates multiple example triangular structures  502  coupled to a core body  506  of a toroid-shaped magnetic core  525 , in accordance with various embodiments. In an embodiment, a base length for each of the multiple triangular structures  502 , is determined by calculating base length, f, according to equation (8) for a single triangular structure and dividing the base length, f, by the number of triangular structures  502  used. For example, in the illustrated embodiment of  FIG. 5   b , the base length is f/ 3  for each of the three triangular structures  502 . In a case where only two triangular structures are used (not shown), the base length for each triangular structure is f/ 2 . In another case where only four triangular structures are used, the base length for each triangular structure is f/ 4 . 
     This principle can be used to calculate the base length for any number of triangular structures used to evenly distribute magnetic flux in a circular-type magnetic core. An increasing number of triangular structures may provide more evenly distributed flux distribution, but may cost more to manufacture. A desired number of triangular structures  502  may account for these considerations. 
       FIG. 6  is a flow diagram of a method to fabricate a magnetic core having a substantially evenly distributed magnetic flux, in accordance with various embodiments. At block  602 , method  600  includes providing a first magnetic material to form a core body of a magnetic core. The first magnetic material comprises a first magnetic permeability and may be used to form a substantial portion of the core body. The magnetic core may be formed according to any suitable well-known process. 
     According to various embodiments, the first magnetic material is formed into a core of desired shape and then one or more portions of the first magnetic material are removed such that a second magnetic material may be positioned, at block  604 , in the core body to substantially evenly distribute the magnetic flux in the magnetic core. In other embodiments, the first magnetic material is formed into a core having vacant regions to anticipate where the second magnetic material is to be placed, at block  604 . Other suitable techniques to provide a first magnetic material to form a core body of the magnetic core may be used in other embodiments. 
     At block  604 , a second magnetic material is coupled into the core body to substantially evenly distribute magnetic flux in the magnetic core. The term “couple” as used with respect to coupling the second material into the core body may broadly include connection relationships such as to “physically connect”, “become part”, “position”, “place”, “insert”, or other similar meanings. The second magnetic material may, for example, first be formed into a triangular structure and then inserted into the core body. In another example, the triangular structure may be formed in place as part of a curing process. In an embodiment, the second magnetic material is formed into a triangular structure first, and then placed into the core body prior to a baking process that cures the magnetic core to reduce manufacturing costs. 
     The triangular structure may be formed to conform with design principles disclosed herein such as determining a length of a base and/or associated angles of the triangular structure. The triangular structure may be placed in a variety of structures, including a corner region or in a toroid as described herein. Such principles may be applied to other similar shapes and configurations, such as U-cores, C-cores, E-cores, I-cores, toroids, cylinders, rings, beads, planar cores, or other shapes and configurations that may benefit from principles taught in this disclosure. 
     Additional embodiments are described below in which some magnetic core materials or portions are omitted from corner portions of the magnetic cores. Corner regions of the magnetic cores described below include an angled corner configuration and a rounded corner configuration in which portions of the corner regions are omitted, although embodiments may include other configurations such as a three-sided corner configuration in which an outside edge of the corner includes three straight-line edges each angled 30 degrees from adjacent edge segments. Omitting the portions of the corner regions enables the magnetic cores to be manufactured using less material, resulting in lighter magnetic cores. Since no flux lines would traverse these omitted portions if they were formed as part of the magnetic cores, the omitted portions would be redundant. As with the embodiments described herein with respect to  FIGS. 2-6 , the magnetic flux paths in the magnetic cores that are described below are substantially uniform, thereby providing relatively higher magnetic core efficiency and heat distribution and reduced power losses of the magnetic core  700  compared with magnetic cores having only one magnetic material or different magnetic materials with different magnetic reluctances. These additional embodiments are applicable to generators, electric motors, inductors, and transformers in electrical power industries. Embodiments are also applicable to high-power industries such as wind power industries, solar power industries; they are also applicable to battery chargers for electric vehicles, and so forth. 
     Although the embodiments described below are depicted in the figures, and described herein, as being E-cores, magnetic cores according to various embodiments include a variety of other shapes and configurations than what is depicted herein including, for example, C-cores, U-cores, I-cores, or other shapes and configurations that may benefit from the principles described herein. 
       FIG. 7  schematically illustrates an example magnetic core  700  having an angled corner configuration and triangular structures in the corner regions, in accordance with various embodiments. A body of the magnetic core  700  includes two E-core structures  702  and  704  placed onto one another. The body of the magnetic core  700  includes a corner region  706 , a back portion  708 , and a leg portion  710 , which includes a first magnetic material having a first magnetic permeability. The first magnetic material therefore forms part of a body of the magnetic core  700 . The body of the magnetic core  700  has positioned within it a triangular-shaped portion  712 , which is composed of a second magnetic material having a second magnetic permeability that is different from the first magnetic permeability. Thus, the corner regions, such as the corner region  706 , are comprised of the triangular-shaped portion  712  as well as parts of the back portion  708  and the leg portion  710 . Other corner regions of the magnetic core  700  have the same or similar configurations as the corner region  706 . In the example illustrated in  FIG. 7 , the back portion  708  and the leg portion  710  are oriented perpendicular to one another; but embodiments include magnetic cores in which such portions are oriented at other angles with respect to one another. In the example illustrated in  FIG. 7  (as well as in the other examples illustrated in the present disclosure, different corner regions of the magnetic cores all have the same angles (e.g., 90 degrees); but different corner regions of the same magnetic cores have, in some embodiments, different angles from one another, such that the magnetic cores have shapes that are deflected, skewed, or otherwise non-uniform. Generally, the angles of the corners of each loop of the magnetic cores sum to 360 degrees. Generally, the bend or angled portions of the magnetic cores according to embodiments include triangular portions similar to or the same as those described herein. The first magnetic material and the second magnetic material include, for example, soft or hard magnetic materials with high magnetic permeability such as soft ferrite, laminated silicon steel, and/or powder iron, or any other magnetic material. Subject matter is not limited in this regard, and the first and second magnetic materials may include any of a variety of magnetic materials that may benefit from the principles described herein. 
     A plurality of magnetic flux paths of different overall lengths traverses the corner region  706 . The magnetic flux paths traverse through different lengths of the first magnetic material and the second magnetic material. In general, and as described in more detail below, the magnetic flux paths having longer lengths through the corner region  706  pass through a relatively shorter length of the lower permeability second magnetic material of the triangular-shaped portion  712  than do the magnetic flux paths with shorter lengths through the corner region  706 . Conversely, the magnetic flux paths having longer lengths through the corner region pass through a longer length of the higher permeability magnetic material of the back portion  708  and the leg portion  710 . Thus, there is an inverse relationship between the overall length of a magnetic flux path that traverses the corner region  706  and the corresponding length of the second magnetic material that the magnetic flux path traverses. 
     For example, referring to  FIG. 8 , magnetic flux path  800  has a shorter overall length through the corner region  706  compared with magnetic flux path  802 . But magnetic flux path  800  passes through a relatively long segment X through the triangular portion  712  compared with the segment Y of the triangular portion  712  through which the magnetic path  802  passes. The size and angles of the triangular-shaped portion  712 , as well as the relative magnetic permeability of the first and second magnetic materials, result in magnetic flux paths that traverse the corner region  706 —such as the magnetic flux paths  800  and  802 —having effective magnetic reluctances that are substantially equivalent, or in other words generally more uniform than the magnetic reluctances of the magnetic flux paths in magnetic cores having only one magnetic material or having different magnetic materials with the same magnetic reluctances. The effective magnetic reluctances are functions of the distances and magnetic permeability of the magnetic materials that the flux lines pass through. Thus, by selecting magnetic materials having different magnetic reluctances, and selecting appropriate dimensions and angles for the second magnetic material, the effective magnetic reluctances are substantially similar through the different overall lengths of the magnetic flux paths. And having substantially similar magnetic reluctances results in the magnetic flux lines that are substantially evenly distributed throughout the body of the magnetic core  700 , including the corner region  706 . 
       FIG. 9  schematically illustrates a corner region  706  of an example magnetic core having an angled corner configuration. The corner region  706  has an angled corner configuration in which an outside edge BF of the corner region is angled relative to the leg portion  710  and the back portion  708 . In the example shown in  FIG. 7 , the outside edge BF is angled at 45-degrees with respect to the leg portion  710  (as well as 45-degrees with respect to the back portion  708 ), although other angles are possible without departing from the scope of the present disclosure. 
     The triangular-shaped portion  712  has a triangular-shaped cross sectional area with a straight-line base CD that is parallel to the outside edge BF of the corner region  706 . Length a is the cross-sectional width of both the back portion  708  and the leg portion  710 . Length b is a vertical distance from point C of the triangular-shaped portion  712  to point D of the triangular-shaped portion  712 . Length c is the length of a base CD of the triangular-shaped portion  712 . The base CD is parallel to the outside edge BF of the corner region  706 , and is thus also angled at the same angle as the outer edge BF, e.g., 45-degrees, with respect to the leg portion  710  and the back portion  712 . The apex E of the triangular-shaped portion  712  is incidental with the outside edge BF. 
     A particular design example for a magnetic core having an angled corner configuration is described mathematically below. However, other designs are possible without departing from the scope of embodiments. As will be described below, the length of the base CD, as well as the length of the outer edge BF is, in embodiments, a function of at least the difference between the first magnetic permeability and the second magnetic permeability. The following equations describe the dimensions of the corner region  706 . 
                   GE   =           2     ⁢     (     a   +   b     )       -   a   -     b     2         =       a   ⁡     (       2     -   1     )       +     b   ⁢       2     2                   (   9   )                 AB =( a+b )− GB   (10)
 
     becomes 
                   AB   =       (     a   +   b     )     -       2     ⁢   GE               (   11   )               
becomes
 
                   AB   =     a   +   b   -       2     ⁢     a   ⁡     (       2     -   1     )         -       2     ⁢   b   ⁢       2     2                 (   12   )               
becomes
 
     
       
         
           
             
               
                 
                   AB 
                   = 
                   
                     a 
                     ⁡ 
                     
                       ( 
                       
                         
                           2 
                         
                         - 
                         1 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     From equation 13 it follows that: 
                     tan   ⁢           ⁢   θ     =         a   ⁡     (       2     -   1     )       a     =       2     -   1               (   14   )               
θ is therefore 22.5 degrees, and is unrelated to the magnetic permeability of the magnetic materials of the magnetic core  700 .
 
     So that the effective magnetic reluctances are equivalent along all magnetic flux paths through the corner region  706 , the magnetic resistance along triangle base CD is equal to the magnetic resistance of the path along the edge ABFV of the corner region  712 . Thus, 
     
       
         
           
             
               
                 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           ( 
                           
                             a 
                             + 
                             b 
                             - 
                             
                               
                                 2 
                               
                               ⁢ 
                               GE 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         2 
                         ⁢ 
                         GE 
                       
                     
                     
                       μ 
                       1 
                     
                   
                   = 
                   
                     
                       
                         2 
                       
                       ⁢ 
                       b 
                     
                     
                       μ 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
                         4   ⁢     a   ⁡     (       2     -   1     )         +     b   ⁢     2           μ   1       =         2     ⁢   b       μ   2               (   16   )               
where μ 1  is the magnetic permeability of the first magnetic material of the body of the magnetic core  700 , and μ 2  is the magnetic permeability of the second magnetic material of the triangular-shaped portion  712 , and μ 1 &gt;&gt;μ 2 . Based on equation 16, it is possible to extrapolate the length c of the triangle base CD.
 
     
       
         
           
             
               
                 
                   c 
                   = 
                   
                     
                       4 
                       ⁢ 
                       
                         ( 
                         
                           
                             2 
                           
                           - 
                           1 
                         
                         ) 
                       
                       ⁢ 
                       a 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         μ 
                         2 
                       
                     
                     
                       
                         μ 
                         1 
                       
                       - 
                       
                         μ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Using equation 17, the height GE of the omitted triangle portion BGF is calculated as: 
                   GE   =         a   ⁡     (       2     -   1     )       +     b   ⁢       2     2         =         a   ⁡     (       2     -   1     )       +       4   ⁢     2     ⁢     a   ⁡     (       2     -   1     )       ⁢     μ   2         2   *     2     ⁢     (       μ   1     -     μ   2       )           =         (       2     -   1     )     ⁢     (       μ   1     -     μ   2       )     ⁢   a         μ   1     -     μ   2                     (   18   )               
becomes
 
     
       
         
           
             
               
                 
                   GE 
                   = 
                   
                     
                       
                         ( 
                         
                           2 
                           - 
                           
                             2 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             μ 
                             1 
                           
                           + 
                           
                             μ 
                             2 
                           
                         
                         ) 
                       
                       ⁢ 
                       a 
                     
                     
                       
                         μ 
                         1 
                       
                       - 
                       
                         μ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Using equation 19, the hypotenuse GB of the omitted triangle portion BGF is calculated as: 
     
       
         
           
             
               
                 
                   GB 
                   = 
                   
                     
                       
                         ( 
                         
                           
                             2 
                           
                           - 
                           1 
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             μ 
                             1 
                           
                           + 
                           
                             μ 
                             2 
                           
                         
                         ) 
                       
                       ⁢ 
                       a 
                     
                     
                       
                         μ 
                         1 
                       
                       - 
                       
                         μ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Equations 17, 19, and 20 present a design formula for an example corner region  706 , including the triangular-shaped portion  712 , according to some embodiments of the present disclosure. In one specific example, μ 1 =3000 and μ 2 =280 and α is 5.9 mm; therefore using equation 17, the length c of the base of the triangular-shaped portion  712  is 1.0 mm. The height UE of the triangular-shaped portion is also α=5.9 mm; the triangular-shaped portion  712  in this specific example is therefore long and narrow. In some embodiments the ratio of the magnetic permeability of μ 1 :μ 2  is approximately 10:1, although other ratios of magnetic permeability may be used without departing from the scope of embodiments. The magnetic resistance of the shortest magnetic flux path in the magnetic core  700  is approximately 0.2% greater than in a conventional magnetic core, such as in  FIG. 1 , having the same overall dimensions and using the first magnetic material having μ 1 . However, overall efficiency of the magnetic core  700  is increased over conventional designs by many percentage points. 
     The magnetic lines of force (magnetic flux paths) in the corner region  706 , which are parallel to one another, rotate to the right by 45-degrees at diagonal line BC, the magnetic flux paths then penetrate the second magnetic material of the triangular-shaped portion  712  following this direction, and then rotate to the right by another 45-degrees at a second diagonal line FD and change to the horizontal direction at the diagonal line FD. Because of the parallel nature of the magnetic flux paths, and because the magnetic reluctances of the magnetic flux paths are equivalent or substantially equivalent, the magnetic flux paths will be evenly or substantially evenly distributed along the widths a of the corner region  706 . Because the magnetic flux paths in the non-corner portions of the magnetic core  700  also have magnetic reluctances that are equivalent or substantially equivalent magnetic resistances, the magnetic flux paths will be evenly or substantially evenly distributed throughout the entire magnetic core  700 . 
       FIG. 10  schematically illustrates an example E-shaped magnetic core  1000  having a rounded corner configuration and triangular structures in the corner regions, in accordance with various embodiments. A body of the magnetic core  1000  includes two E-core structures  1002  and  1004  placed onto one another. The body of the magnetic core  1000  includes a corner region  1006 , a back portion  1008 , and a leg portion  1010 , which include a first magnetic material having a first magnetic permeability. The first magnetic material therefore at least partly forms a body of the magnetic core  1000 . The body of the magnetic core  1000  has positioned within it a triangular-shaped portion  1012 , which is composed of a second magnetic material having a second magnetic permeability that is different from the first magnetic permeability. Thus, the corner portions, such as the corner region  1006 , are comprised of the triangular-shaped portion  1012  as well as parts of the back portion  1008  and the leg portion  1010 . Other corner regions of the magnetic core  1000  have the same or similar configurations as the corner region  1006 . In the example illustrated in  FIG. 10 , the back portion  1008  and the leg portion  1010  are oriented perpendicular to one another; but embodiments include magnetic cores in which such portions are oriented at other angles with respect to one another. 
     The triangular-shaped portion  1012  has a rounded base that is concentric with the rounded outside edge of the corner region  1006 . The principle of operation of the magnetic core  1000  is similar to the principle of operation of the magnetic core  700 ; in particular, the magnetic flux paths through the corner regions—such as the corner region  1006 —have magnetic reluctances that are equivalent or substantially equivalent. Thus, the distribution of the magnetic flux paths will be evenly or substantially evenly distributed through the corner region  1006 . And because the magnetic flux paths will have equivalent or substantially equivalent magnetic reluctances through the non-corner portions of the magnetic core  1000 , the magnetic flux paths will be evenly distributed throughout the body of the magnetic core  1000  and the efficiency of operation of the magnetic core  1000  is improved over conventional magnetic cores of similar configuration (e.g., conventional E-cores). 
       FIG. 11  schematically illustrates a corner region  1006  of an example magnetic core  1000  having a rounded corner configuration. The corner region  1006  has an outside edge  1100  and inside edge  1102 , which includes the rounded base  1104  of the triangular-shaped portion  1012 . The outside edge  1100  and the rounded base  1104  are concentric one quarter circular arcs. The radius of circular arc of the outside edge  1100  is d+e, and the radius of the circular arc of the inside edge is e, where d is the width of the back portion  1008  and the width of the leg portion  1010 , and where: 
     
       
         
           
             
               
                 
                   e 
                   = 
                   
                     
                       d 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         μ 
                         2 
                       
                     
                     
                       
                         μ 
                         1 
                       
                       - 
                       
                         μ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     Where μ 1  is the magnetic permeability of the first magnetic material and μ 2  is the magnetic permeability of the second magnetic material of which the triangular-shaped portion  1012  is composed. 
     The magnetic cores  700  and  1000  in  FIGS. 7-11  are illustrated as having triangular-shaped corner portions that are comprised of a second magnetic material with lower permeability than the first magnetic material that is included in the magnetic cores, and that have a straight-line or curved bases along the inner surface of the corner region and apexes that are incidental with an outside edge of the corner region. But magnetic cores may have other configurations without departing from the scope of embodiments. For example, corner regions of magnetic cores according to some embodiments include triangular-shaped corner portions, comprised of a higher permeability magnetic material than the magnetic material that is included the body of the magnetic core, with bases that form parts of the outside surfaces of the corner regions and apexes that are incidental with the inner surfaces of the corner regions. Other example configurations include corner regions having more than one triangular-shaped corner portion in a single corner region. Still other examples include magnetic cores having corner portions with outside and/or inside edges that are curved but not perfectly circular or that are either more or less than quarter circles, and so forth. Some magnetic cores according to some embodiments include corner regions with curved outside surfaces and angled but straight-line inner surfaces, which have a similar principal of operation as the magnetic cores illustrated in  FIGS. 3-11 . Similarly, magnetic cores include corner portions with angled, straight-line outside surfaces and curved inner surfaces without departing from the scope of embodiments. 
       FIG. 12  is a flow diagram of a method  1200  to fabricate a magnetic core having an angled configuration or a rounded corner configuration. At  1202 , one or more triangular-shaped corner portions, such as the corner portions  402 ,  502 ,  712 , and  1012 , are compression molded. For example, to mold the magnetic core  700 , eight triangular-shaped corner portions are compression molded. 
     At  1204 , the one or more triangular-shaped corner portions are fixed into the corner regions of a core mold, such as a conventional E-core, U-core, or other core type mold. Where angled or rounded corner configurations are desired, as with magnetic cores  700  and  1000 , either the mold is modified (or special-built) to produce the angled or rounded corner regions, or additional mold pieces are added to the mold at the corner regions to prevent magnetic material from forming the omitted portions of the core. 
     At  1206 , the first magnetic material, as described above, is poured into the mold having the fixed triangular-shaped corner portions in the corner regions. At  1208 , a secondary compression is performed to produce the magnetic core having the triangular-shaped corner portions as described here, according to various embodiments. 
     Various operations may have been described as multiple discrete actions or operations in turn, in a manner that is most helpful in understanding the claimed subject matter. However, the order of description should not be construed as to imply that these operations are necessarily order dependent. In particular, these operations may not be performed in the order of presentation. Operations described may be performed in a different order than the described embodiment. Various additional operations may be performed and/or described operations may be omitted in additional embodiments. 
     Although certain embodiments have been illustrated and described herein, a wide variety of alternate and/or equivalent embodiments or implementations calculated to achieve the same purposes may be substituted for the embodiments illustrated and described without departing from the scope of the present invention. This application is intended to cover any adaptations or variations of the embodiments discussed herein. Therefore, it is manifestly intended that embodiments in accordance with the present invention be limited only by the claims and the equivalents thereof.