Patent Publication Number: US-2023141010-A1

Title: Reactor, converter, and power conversion device

Description:
TECHNICAL FIELD 
     The present disclosure relates to a reactor, a converter, and a power conversion device. 
     This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2020-059195 filed Mar. 27, 2020, the entire content of which is hereby incorporated by reference. 
     BACKGROUND 
     A reactor is a constituent component of a converter provided in a hybrid automobile or the like. Such a reactor includes a coil having a winding portion formed by winding a wire into a spiral, and a magnetic core combined with the coil. For example, a reactor that has one winding portion is disclosed in FIGS. 5 to 8 of Patent Document 1. The magnetic core of this reactor includes a middle core arranged inside the winding portion, side cores arranged outward of outer peripheral faces of the winding portion, and end cores arranged at end faces of the winding portion. 
     PRIOR ART DOCUMENT 
     Patent Document 
     
         
         Patent Document 1: JP 2016-201509 A 
       
    
     SUMMARY OF INVENTION 
     A reactor according to the present disclosure includes: 
     a coil including a first winding portion; and 
     a magnetic core, 
     wherein the magnetic core includes:
         a middle core arranged inside the first winding portion,   a first end core facing a first end face of the first winding portion,   a second end core facing a second end face of the first winding portion,   a first side core that is arranged outward of a first side face of the first winding portion and connects the first end core and the second end core, and   a second side core that is arranged outward of a second side face of the first winding portion and connects the first end core and the second end core,       

     the first end core includes:
         a first outer face separated from the first end face in an X direction, and   a first recessed portion provided in the first outer face,       

     in a plan view of the magnetic core from a Z direction, the first recessed portion is located in a central portion of the first end core with respect to a Y direction, 
     the X direction is a direction conforming to an axial direction of the middle core, 
     the Y direction is a direction in which the middle core, the first side core, and the second side core are side-by-side, and 
     the Z direction is a direction orthogonal to the X direction and the Y direction. 
     A converter according to the present disclosure includes: 
     the reactor of the present disclosure. 
     A power conversion device according to the present disclosure includes: 
     the converter of the present disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic perspective view of a reactor according to a first embodiment. 
         FIG.  2    is a top view of the reactor of  FIG.  1   . 
         FIG.  3    is a top view of a reactor described in a second embodiment. 
         FIG.  4    is a top view of a reactor described in a third embodiment. 
         FIG.  5    is a top view of a reactor described in a fourth embodiment. 
         FIG.  6    is a configuration diagram schematically showing a power supply system of a hybrid automobile. 
         FIG.  7    is a circuit diagram schematically showing an example of a power conversion device that includes a converter. 
         FIG.  8    is a graph showing the relationship between the width of a first recessed portion and the deterioration rate of inductance in Test Example 1. 
         FIG.  9    is a graph showing the relationship between the width of the first recessed portion and the deterioration rate of total loss in Test Example 1. 
         FIG.  10    is a graph showing the relationship between the depth of the first recessed portion and the deterioration rate of inductance in Test Example 2. 
         FIG.  11    is a graph showing the relationship between the depth of the first recessed portion and the deterioration rate of total loss in Test Example 2. 
     
    
    
     DETAILED DESCRIPTION TO EXECUTE THE INVENTION 
     Technical Problem 
     Development in hybrid automobiles and the like has led to demand for reduction in the weight of reactors. However, if the size of the magnetic core is reduced in order to reduce the weight of a reactor, magnetic characteristics of the reactor deteriorate. 
     In view of this, an object of the present disclosure is to provide a reactor that is lightweight and has excellent magnetic characteristics. Another object of the present disclosure is to provide a converter that includes a reactor that is lightweight and has excellent magnetic characteristics, and a power conversion device. 
     Advantageous Effects of Present Disclosure 
     The reactor of the present disclosure is lightweight and has excellent magnetic characteristics. Also, the converter and the power conversion device of the present disclosure are lightweight and excellent in terms of conversion efficiency. 
     Description of Embodiments of Present Disclosure 
     First, embodiments of the present disclosure will be listed and described. 
     &lt;1&gt; A reactor according to an embodiment includes: 
     a coil including a first winding portion; and 
     a magnetic core, 
     wherein the magnetic core includes:
         a middle core arranged inside the first winding portion,   a first end core facing a first end face of the first winding portion,   a second end core facing a second end face of the first winding portion,   a first side core that is arranged outward of a first side face of the first winding portion and connects the first end core and the second end core, and   a second side core that is arranged outward of a second side face of the first winding portion and connects the first end core and the second end core,       

     the first end core includes:
         a first outer face separated from the first end face in an X direction, and   a first recessed portion provided in the first outer face,       

     in a plan view of the magnetic core from a Z direction, the first recessed portion is located in a central portion of the first end core with respect to a Y direction, 
     the X direction is a direction conforming to an axial direction of the middle core, 
     the Y direction is a direction in which the middle core, the first side core, and the second side core are side-by-side, and 
     the Z direction is a direction orthogonal to the X direction and the Y direction. 
     Due to providing the first recessed portion in the first end core, the amount of material constituting the first end core is reduced, and thus the weight of the reactor is lower than in the case where the first recessed portion is not provided. 
     The central portion, with respect to the Y direction, of the first outer face of the first end core is a portion through which magnetic flux is not likely to pass. Accordingly, due to providing the first recessed portion in the central portion, with respect to the Y direction, of the first outer face of the first end core, it is possible to suppress deterioration of the magnetic characteristics of the reactor caused by the provision of the first recessed portion in the magnetic core. Here, the central portion is a region of the first end core in the Y direction that is not overlapped with the side cores. 
     &lt;2&gt; In one aspect of the reactor according to the embodiment, 
     in a plan view of the magnetic core from the Z direction, the first recessed portion fits within a range corresponding to the length of the middle core in the Y direction. 
     Due to the width of the first recessed portion being within the range of the width of the middle core, it is possible to easily suppress deterioration of the magnetic characteristics of the reactor caused by the provision of the first recessed portion in the magnetic core. 
     &lt;3&gt; In one aspect of the reactor according to the embodiment, 
     the first recessed portion is shaped as a groove extending along the Z direction. 
     If the first recessed portion is shaped as a groove that extends in the Z direction, it is possible to easily suppress deterioration of the magnetic characteristics of the reactor even if the length of the first recessed portion in the Z direction is increased in order to the further reduce the volume of the first end core. This is because even if the length of the first recessed portion in the Z direction is increased, the first recessed portion remains in a portion of the first end core where magnetic flux is not likely to pass. If the first recessed portion were shaped as a groove that extends in the Y direction, and the length of the first recessed portion in the Y direction were increased, the size of the portion of the first end core through which a large amount of magnetic flux passes could possibly be reduced due to the first recessed portion. 
     &lt;4&gt; In one aspect of the reactor according to the embodiment, 
     a cross-section of the first recessed portion orthogonal to the Z direction has a rectangular shape. 
     It is easy to form a first recessed portion having a rectangular or trapezoidal cross-sectional shape. Also, if the first end core is manufactured by being compressed in the X direction, it is possible to obtain an effect of facilitating removal of the first end core from the mold. 
     &lt;5&gt; In one aspect of the reactor according to the embodiment, 
     the magnetic core includes a plurality of core pieces, 
     one of the core pieces is a first core piece that includes at least the first end core, and 
     the first core piece is a powder compact made of a raw material powder that contains a soft magnetic powder. 
     If the magnetic core is constituted by a plurality of core pieces, the magnetic core can be attached to the coil, which includes the winding portion, at a later time. Also, if the first core piece including the first end core that has the first recessed portion is a powder compact, deterioration of the magnetic characteristics of the magnetic core can be more easily suppressed than in the case where the first core piece is a compact made of a composite material. 
     &lt;6&gt; In one aspect of the reactor according to the embodiment, 
     in a plan view of the magnetic core from the Z direction, the width of the first recessed portion in the Y direction is 5% or more and 50% or less of the length of the first end core in the Y direction. 
     If the width of the first recessed portion in the Y direction is 5% or more and 50% or less of the length of the first end core in the Y direction, the first recessed portion is not likely to be overlapped with a portion of the first end core through which a large amount of magnetic flux passes. Accordingly, deterioration of the magnetic characteristics of the reactor can be easily suppressed. 
     &lt;7&gt; In one aspect of the reactor according to the embodiment, 
     in a plan view of the magnetic core from the Z direction, the width of the first recessed portion in the Y direction is 10% or more and 150% or less of the length of the middle core in the Y direction. 
     If the width of the first recessed portion in the Y direction is 10% or more and 150% or less of the length of the middle core in the Y direction, the first recessed portion is not likely to be overlapped with a portion of the first end core through which a large amount of magnetic flux passes. Accordingly, deterioration of the magnetic characteristics of the reactor can be easily suppressed. 
     &lt;8&gt; In one aspect of the reactor according to the embodiment, 
     in a plan view of the magnetic core from the Z direction, the depth of the first recessed portion in the X direction is 10% or more and 125% or less of the length of the first end core in the X direction. 
     If the depth in the X direction of the first recessed portion is 10% or more and 125% or less of the length in the X direction of the first end core, the first recessed portion is not likely to be overlapped with a portion of the first end core through which a large amount of magnetic flux passes. Accordingly, deterioration of the magnetic characteristics of the reactor can be easily suppressed. Here, if the depth of the first recessed portion is 100% or more of the length of the first end core in the X direction, the first recessed portion extends to the middle core. In this case, the width of the first recessed portion needs to be less than the length of the middle core in the Y direction. 
     &lt;9&gt; In one aspect of the reactor according to the embodiment, 
     the second end core includes:
         a second outer face separated from the second end face in the X direction, and   a second recessed portion provided in the second outer face, and       

     in a plan view of the magnetic core from the Z direction, the second recessed portion is provided in a central portion of the second end core with respect to the Y direction. 
     Due to providing the second recessed portion in the second end core in addition to the first recessed portion provided in the first end core, the weight of the reactor is further reduced. 
     Here, a preferred configuration of the second recessed portion is the same as the preferred configuration of the first recessed portion. In other words, the preferable configuration of the second recessed portion can be obtained by replacing “first recessed portion” of the reactor described in aspects &lt;2&gt; to &lt;8&gt; with “second recessed portion”. 
     &lt;10&gt; In one aspect of the reactor according to the embodiment, 
     the coil further includes a second winding portion and a third winding portion, 
     the first side core is arranged inside the second winding portion, and 
     the second side core is arranged inside the third winding portion. 
     Reactors that are used for certain applications and have three winding portions tend to be heavy. Even in the case of such a reactor, the weight of the reactor is reduced by providing the first recessed portion in the first end core. 
     &lt;11&gt; A converter according to an embodiment includes: 
     the reactor according to any of aspects &lt;1&gt; to &lt;10&gt;. 
     The above converter includes a reactor that is lightweight and has excellent magnetic characteristics. Accordingly, the converter is lightweight and has excellent conversion efficiency. 
     &lt;12&gt; A power conversion device according to an embodiment includes: 
     the converter according to aspect &lt;11&gt;. 
     The above power conversion device includes a converter that is lightweight and has excellent conversion efficiency. Accordingly, the power conversion device is lightweight and has excellent conversion efficiency. 
     DETAILS OF EMBODIMENTS OF PRESENT DISCLOSURE 
     Hereinafter, embodiments of a reactor according to the present disclosure will be described with reference to the drawings. Like reference numerals in the figures indicate members having like names. It should be noted that the present invention is not limited to the configurations shown in the embodiments, but rather is indicated by the scope of claims, and is intended to include all modifications within a meaning and scope equivalent to the scope of claims. 
     First Embodiment 
     The configuration of a reactor  1  will be described in a first embodiment with reference to  FIGS.  1  and  2   . The reactor  1  shown in  FIG.  1    is obtained by combining a coil  2  and a magnetic core  3 . One of the features of the reactor  1  is that a first recessed portion  4  is provided in a portion of the magnetic core  3 . Hereinafter, configurations provided in the reactor  1  will be described in detail. 
     1. Coil 
     The coil  2  includes one first winding portion  21  ( FIGS.  1  and  2   ). The first winding portion  21  is constituted by one jointless coil wire that has been wound into a spiral. A known coil wire can be used as the coil wire. A covered flat wire is used as the coil wire in this embodiment. The conductor wire of the covered flat wire is constituted by a copper flat wire. The insulating coating of the covered flat wire is made of an enamel. The first winding portion  21  is constituted by an edgewise coil in which a covered flat wire has been wound edgewise. 
     The first winding portion  21  is shaped as a rectangular cylinder. The term “rectangular” includes a square. In other words, the end faces of the first winding portion  21  are shaped as a rectangular frame. Due to the first winding portion  21  being shaped as a rectangular cylinder, the area of contact between the first winding portion  21  and the installation target is likely to be larger than in the case where the winding portion is shaped as a cylinder having the same cross-sectional area. For this reason, heat generated by the reactor  1  can be easily dissipated to the installation target via the first winding portion  21 . Moreover, the first winding portion  21  can be easily disposed stably on the installation target. The winding portion  21  has rounded corner portions. 
     An end portion  2   a  and an end portion  2   b  of the first winding portion  21  extend circumferentially outward from the first winding portion  21  on one end side and the other end side, respectively, in the axial direction of the first winding portion  21 . At the end portion  2   a  and the end portion  2   b  of the first winding portion  21 , the insulating coating has been peeled off to expose the conductor wire. A terminal member (not shown) is connected to each of the exposed portions of the conductor wire. An external device is connected to the coil  2  via the terminal members. The external device is not shown in the drawings. One example of the external device is a power source that supplies electric power to the coil  2 . 
     2. Magnetic Core 
     As shown in  FIG.  2   , the magnetic core  3  includes a middle core  30 , a first end core  31 , a second end core  32 , a first side core  33 , and a second side core  34 . In  FIG.  2   , the boundaries of the cores  30 ,  31 ,  32 ,  33 , and  34  are shown by dashed double-dotted lines. The middle core  30  is a section of the magnetic core  3  that has a portion arranged inside the first winding portion  21 . The first end core  31  is a portion of the magnetic core  3  that faces a first end face  211  of the first winding portion  21 . The second end core  32  is a portion of the magnetic core  3  that faces a second end face  212  of the first winding portion  21 . The first side core  33  is a portion of the magnetic core  3  that is arranged outward of a first side face  213  of the first winding portion  21 . The second side core  34  is a portion of the magnetic core  3  that is arranged outward of a second side face  214  of the first winding portion  21 . 
     In the magnetic core  3 , an annular closed magnetic path shown by a bold dashed line is formed in the middle core  30 , the first end core  31 , the first side core  33 , and the second end core  32 . Also, an annular closed magnetic path shown by a bold dashed line is formed in the middle core  30 , the first end core  31 , the second side core  34 , and the second end core  32 . 
     Here, directions in the reactor  1  are defined based on the magnetic core  3 . First, the direction along the axial direction of the middle core  30  is an X direction. A direction that is orthogonal to the X direction and is the direction in which the middle core  30 , the first side core  33 , and the second side core  34  are side-by-side is a Y direction. A direction that intersects both the X direction and the Y direction is a Z direction ( FIG.  1   ). 
     2.1. Middle Core 
     The middle core  30  is a portion of the magnetic core  3  that is arranged inside the first winding portion  21  of the coil  2 . Accordingly, the middle core  30  extends along the axial direction of the first winding portion  21 . In this example, the two end portions of the magnetic core  3  along the axial direction of the first winding portion  21  respectively project from the end faces  211  and  212  of the first winding portion  21 . The protruding portions are also portions of the middle core  30 . 
     The shape of the middle core  30  is not particularly limited as long as it conforms to the shape of the interior of the first winding portion  21 . The middle core  30  of this example has a substantially rectangular parallelepiped shape. 
     2.2. First End Core and Second End Core 
     The first end core  31  and the second end core  32  have a larger width in the Y direction than the first winding portion  21 . Specifically, the first end core  31  projects outward in the Y direction from the first end face  211  of the first winding portion  21 , and the second end core  32  projects outward in the Y direction from the second end face  212  of the first winding portion  21 . 
     The shapes of the first end core  31  and the second end core  32  are not particularly limited as long as sufficient magnetic paths are formed inside the end cores  31  and  32 . The first end core  31  and the second end core  32  of this example have a substantially rectangular parallelepiped shape. Among the four corner portions of the first end core  31  and the second end core  32  in a view from the Z direction, the two corner portions that are distant from the side cores  33  and  34  may be rounded. If these two corner portions are rounded, the weight of the end cores  31  and  32  is lowered. These two corner portions are portions where magnetic flux is not likely to flow. Therefore, even if these two corner portions are rounded, the magnetic characteristics of the reactor  1  are not likely to deteriorate. 
     The first end core  31  in this example includes the first recessed portion  4  provided in a first outer face  310  thereof. Out of the two faces of the first end core  31  that are orthogonal to the X direction, the first outer face  310  is the face that is distant from the middle core  30 . The weight of the first end core  31  is lowered due to the first recessed portion  4 . The first recessed portion  4  will be described in detail later. 
     2.3. First Side Core and Second Side Core 
     The first side core  33  connects the first end core  31  and the second end core  32  at a position outward of the first side face  213  of the first winding portion  21 . The axial direction of the first side core  33  is parallel with the axial direction of the middle core  30 . The first side face  213  is a face of the first winding portion  21  that faces the Y direction. 
     The second side core  34  connects the first end core  31  and the second end core  32  at a position outward of the second side face  214  of the first winding portion  21 . The second side face  214  is a face of the first winding portion  21  that faces the Y direction, but faces the side opposite to the first side face  213 . The axial direction of the second side core  34  is parallel with the axial direction of the middle core  30 . In this example, the axis of the middle core  30 , the axis of the first side core  33 , and the axis of the second side core  34  are arranged on the XY plane. 
     2.4. Division 
     The magnetic core  3  is constituted by a plurality of core pieces so as to enable attachment to the coil  2 . The magnetic core  3  in this example is a combination of two core pieces, namely a first core piece  3 A and a second core piece  3 B. The first core piece  3 A is constituted by the first end core  31  and a portion of the middle core  30 . The first core piece  3 A is approximately T-shaped in a view from the Z direction. On the other hand, the second core piece  3 B is constituted by the second end core  32 , the first side core  33 , the second side core  34 , and a portion of the middle core  30 . The second core piece  3 B is approximately E-shaped in a view from the Z direction. Here, the magnetic core  3  may be divided into three or more pieces as shown in a second embodiment, for example. 
     The sum of the X direction length of the portion of the first core piece  3 A corresponding to the middle core  30  and the X direction length of the portion of the second core piece  3 B corresponding to the middle core  30  is shorter than the X direction length of the first side core  33  and the X direction length of the second side core  34 . Accordingly, a gap portion  3   g  is formed between the first core piece  3 A and the second core piece  3 B inside the first winding portion  21 . The gap portion  3   g  in this example is an air gap. A gap plate (not shown) may be arranged in the gap portion  3   g . In contrast to this example, the end face of the first core piece  3 A and the end face of the second core piece  3 B may be in contact with each other inside the first winding portion  21 . In this case, a gap portion may be provided at least either between the first end core  31  and the first side core  33  or between the first end core  31  and the second side core  34 . 
     2.5. Magnetic Characteristics, Materials, Etc. 
     It is preferable that the cores  30 ,  31 ,  32 ,  33 , and  34  of the magnetic core  3  are each a powder compact formed by pressure molding a raw material powder containing a soft magnetic powder, or a compact made of a composite material including a soft magnetic powder and a resin. All of the cores  30 ,  31 ,  32 ,  33 , and  34  may be powder compacts, or all of the cores  30 ,  31 ,  32 ,  33 , and  34  may be composite material compacts. Also, a configuration is possible in which some of the cores  30 ,  31 ,  32 ,  33 , and  34 , are powder compacts and the rest are composite material compacts. In the case where some of the cores are powder compacts and the rest are composite material compacts, the magnetic core  3  has resistance to magnetic saturation. 
     The soft magnetic powder of the powder compact is an aggregate of soft magnetic particles constituted by an iron group metal such as iron, or an iron alloy such as an Fe—Si (iron-silicon) alloy or an Fe—Ni (nickel) alloy. An insulating coating made of phosphate or the like may be formed on the surfaces of the soft magnetic particles. The raw material powder may contain a lubricant or the like. 
     The composite material compact can be produced by filling a mold with a mixture of a soft magnetic powder and an unsolidified resin, and then solidifying the resin. The soft magnetic powder contained in the composite material can be the same as that used in the powder compact. Also, examples of the resin contained in the composite material include a thermosetting resin, a thermoplastic resin, a room temperature curing resin, and a low temperature curing resin. Examples of thermosetting resins include unsaturated polyester resin, epoxy resin, urethane resin, and silicone resin. Examples of thermoplastic resins include polyphenylene sulfide (PPS) resin, polytetrafluoroethylene (PTFE) resin, liquid crystal polymer (LCP), a polyamide (PA) resin such as nylon 6 or nylon 66, polybutylene terephthalate (PBT) resin, and acrylonitrile butadiene styrene (ABS) resin. It is also possible to use millable silicone rubber, millable urethane rubber, or a BMC (Bulk Molding Compound), which is obtained by adding calcium carbonate and glass fiber to unsaturated polyester, for example. 
     If the composite material contains a non-magnetic and non-metallic powder filler made of alumina, silica, or the like in addition to the soft magnetic powder and the resin, the heat dissipation characteristic can be further improved. The content of the non-magnetic and non-metal powder is 0.2% by mass or more and 20% by mass or less, 0.3% by mass or more and 15% by mass or less, or 0.5% by mass or more and 10% by mass or less, for example. 
     The content of the soft magnetic powder in the composite material is 30% by volume or more and 80% by volume or less, for example. From the viewpoint of improving saturation magnetic flux density and heat dissipation, the content of the soft magnetic powder can also be set to 50% by volume or more, 60% by volume or more, or 70% by volume or more. From the viewpoint of improving fluidity in the manufacturing process, it is preferable that the content of the soft magnetic powder is 75% by volume or less. The relative magnetic permeability of the composite material compact can be easily reduced by lowering the filling rate of the soft magnetic powder. The relative magnetic permeability of the composite material compact is 5 or more and 50 or less, for example. The relative magnetic permeability of the composite material compact may also be 10 or more and 45 or less, 15 or more and 40 or less, or 20 or more and 35 or less. In this example, the second core piece  3 B is entirely constituted by a composite material compact. 
     A powder compact has a higher content of soft magnetic powder than a composite material compact. For example, the content of soft magnetic powder in a powder compact is over 80% by volume, or 85% by volume or more. A core piece made of a powder compact tends to have a high saturation magnetic flux density and a high relative magnetic permeability. The powder compact has a relative magnetic permeability of 50 or more and 500 or less, for example. The powder compact may have a relative magnetic permeability of 80 or more, 100 or more, 150 or more, or 180 or more. In this example, the entirety of the first core piece  3 A including the first recessed portion  4  is constituted by a powder compact. 
     2.6. Size 
     When the reactor  1  in this example is for in-vehicle use, a length L of the magnetic core  3  in the X direction is 30 mm or more and 150 mm or less, for example, a width W of the magnetic core  3  in the Y direction is 30 mm or more and 150 mm or less, for example, and a height H in the Z direction is 15 mm or more and 75 mm or less, for example. 
     A length TO of the middle core  30  in the Y direction is 10 mm or more and 50 mm or less, for example. A length T 1  of the first end core  31  in the X direction and a length T 2  of the second end core  32  in the X direction are 5 mm or more and 40 mm or less, for example. Also, a length T 3  of the first side core  33  in the Y direction and a length T 4  of the second side core  34  in the Y direction are 5 mm or more and 40 mm or less, for example. These lengths are related to the magnitude of the sectional area of the magnetic path of the magnetic core  3 . 
     3. First Recessed Portion 
     The first end core  31  includes the first recessed portion  4  in the first outer face  310 . The first recessed portion  4  is provided in a central portion, with respect to the Y direction, of the first end core  31  in a plan view of the magnetic core  3  from the Z direction. The central portion is a region of the first end core  31  in the Y direction that is not overlapped with the side cores  33  and  34 . It is preferable that the first recessed portion  4  is symmetrical about the center of the first end core  31  in the Y direction. The two closed magnetic paths formed in the magnetic core  3  in this example face directions away from the central portion in the Y direction. For this reason, magnetic flux is not likely to pass through the central portion of the first outer face  310 . Accordingly, even if the first recessed portion  4  is provided in the central portion of the first outer face  310 , the sectional area of the magnetic path of the first end core  31  is not likely to decrease, and the magnetic characteristics of the reactor  1  are not likely to deteriorate. 
     The first recessed portion  4  in this example is shaped as a groove that extends in the Z direction. The first recessed portion  4  in this example has a length extending from the upper face of the first end core  31  to the lower face of the same in the Z direction. If the first recessed portion  4  has such a length, the effect of reducing the weight of the first end core  31  is improved. In contrast to this example, a configuration is possible in which the first recessed portion  4  does not reach the upper face or the lower face of the first end core  31 . 
     There are no particular limitations on the shape of a cross section of the first recessed portion  4  orthogonal to the extending direction thereof. In this example, a cross section of the first recessed portion  4  orthogonal to the extending direction has a rectangular shape. This cross-sectional shape is a shape defined by a bottom face  40  of the first recessed portion  4 , two inner wall faces  41  and  42  of the same that face each other in the Y direction, and the opening on the outer side in the X direction. The corner portions of the rectangle may be rounded. If the cross-sectional shape of the first recessed portion  4  is rectangular, the volume of the first end core  31  can be significantly lower than in the case where the first recessed portion has a semicircular or triangular cross-sectional shape. The first core piece  3 A provided with the first recessed portion  4  is a compressed powder compact that was compressed in the X direction. If the cross-sectional shape of the first recessed portion  4  is rectangular, the first core piece  3 A can be easily removed from the mold. Also, since a portion of the middle core  30  is provided on the side of the first core piece  3 A opposite to the first recessed portion  4 , differences are not likely to arise in the compression length of the first core piece  3 A in the X direction. For this reason, it is easy to produce a dense first core piece  3 A. In contrast to this example, the cross-sectional shape of the first recessed portion  4  may be a trapezoid that has a wide opening. In other words, if the first recessed portion  4  has a trapezoidal cross-sectional shape, the distance between the inner wall face  41  and the inner wall face  42  of the first recessed portion  4  increases from the bottom face  40  toward the opening. The corner portions of the trapezoid may be rounded. 
     It is preferable that the first recessed portion  4  fits within a range corresponding to the length TO of the middle core  30  in the Y direction in a plan view of the magnetic core  3  from the Z direction. Such a first recessed portion  4  is not likely to be overlapped with a portion of the first end core  31  through which a large amount of magnetic flux passes. Accordingly, the sectional area of the magnetic path of the first end core  31  is not likely to decrease, and the magnetic characteristics of the reactor  1  are not likely to deteriorate. 
     It is preferable that a width W 1  of the first recessed portion  4  in the Y direction is 5% or more and 50% or less of the length of the first end core  31  in the Y direction, that is to say the width W of the magnetic core  3 . It is more preferable that the width W 1  is 10% or more and 35% or less of the width W. In this case as well, the first recessed portion  4  is not likely to be overlapped with a portion of the first end core  31  through which a large amount of magnetic flux passes. Accordingly, the sectional area of the magnetic path of the first end core  31  is not likely to decrease, and the magnetic characteristics of the reactor  1  are not likely to deteriorate. Here, the width W 1  of the first recessed portion  4  is the width of the opening of the first recessed portion  4 . 
     The width W 1  of the first recessed portion  4  in the Y direction may be 10% or more and 150% or less of the length TO of the middle core  30  in the Y direction. It is more preferable that the width W 1  is 25% or more and 125% or less of the length TO. In this case as well, the first recessed portion  4  is not likely to be overlapped with a portion of the first end core  31  through which a large amount of magnetic flux passes. Accordingly, the sectional area of the magnetic path of the first end core  31  is not likely to decrease, and the magnetic characteristics of the reactor  1  are not likely to deteriorate. 
     On the other hand, it is preferable that the depth D 1  of the first recessed portion  4  in the X direction is 10% or more and 125% or less of the length T 1  of the first end core  31  in the X direction. It is more preferable that the depth D 1  is 20% or more and 100% or less of the length T 1 . In this case as well, the first recessed portion  4  is not likely to be overlapped with a portion of the first end core  31  through which a large amount of magnetic flux passes. Accordingly, the sectional area of the magnetic path of the first end core  31  is not likely to decrease, and the magnetic characteristics of the reactor  1  are not likely to deteriorate. Here, the depth D 1  of the first recessed portion  4  is the length from the opening of the first recessed portion  4  to the deepest portion. 
     4. Second Recessed Portion 
     Here, the second end core  32  may include a second recessed portion  5 , which is indicated by a dashed double-dotted line. The second recessed portion  5  has the same configuration as the first recessed portion  4 . A description of the second recessed portion  5  can be obtained from the description of the first recessed portion  4  by replacing “first recessed portion  4 ” with “second recessed portion  5 ”, replacing “first outer face  310 ” with “second outer face  320 ”, replacing “first end core  31 ” with “second end core  32 ”, and replacing “length T 1 ” with “length T 2 ”. 
     5. Other Remarks 
     The reactor  1  may further include at least one component among a case, an adhesive layer, a holding member, and a molded resin portion. The case is a member that houses the assembly of the coil  2  and the magnetic core  3 . The assembly housed in the case may be embedded in a sealing resin portion. The adhesive layer fixes the assembly to a mounting face, fixes the assembly to the inner bottom face of the case, or fixes the case to a mounting face. The holding member is a member interposed between the coil  2  and the magnetic core  3  to ensure insulation between the coil  2  and the magnetic core  3 . The molded resin portion surrounds the assembly and is interposed between the coil  2  and the magnetic core  3  to integrate the coil  2  and the magnetic core  3 . 
     6. Effects 
     The reactor  1  in this example having the first recessed portion  4  is lighter than a conventional reactor not having the first recessed portion  4 . 
     In the reactor  1  in this example, the first recessed portion  4  is provided in the first end core  31  so as to reduce the amount of material constituting the first end core  31 . This therefore reduces the weight of the reactor  1 . Also, since the amount of material constituting the first end core  31  is reduced, it is possible to improve the productivity of the magnetic core  3 , including the cost, that is to say improve the productivity of the reactor  1 . Also, if the second recessed portion  5  is provided in the second end core  32 , the weight of the reactor  1  is further reduced. 
     The reactor  1  in this example has magnetic characteristics equivalent to those of a reactor that does not have the first recessed portion  4 . 
     In the reactor  1  in this example, the first recessed portion  4  is provided in the central portion, with respect to the Y direction, of the first outer face  310  of the first end core  31 . This central portion is a portion through which magnetic flux is not likely to pass. This therefore suppresses the case where the magnetic characteristics of the reactor  1  deteriorate due to providing the first recessed portion  4  in the magnetic core  3 . 
     Second Embodiment 
     A reactor  1  according to a second embodiment will be described below with reference to  FIG.  3   . The magnetic core  3  of the reactor  1  of the second embodiment is divided differently from that of the reactor  1  of the first embodiment. Besides how the magnetic core  3  is divided, the configuration of the reactor  1  in this example is the same as that of the reactor  1  of the first embodiment. 
     The magnetic core  3  of the reactor  1  in this example is a combination of a first core piece  3 A, a second core piece  3 B, a third core piece  3 C, and a fourth core piece  3 D. The first core piece  3 A in this example is constituted by a first end core  31  and a portion of the middle core  30 . The first end core  31  includes a first recessed portion  4 . The second core piece  3 B in this example is constituted by a second end core  32  and a portion of the middle core  30 . The second end core  32  includes a second recessed portion  5 . The first core piece  3 A and the second core piece  3 B are approximately T-shaped in a view from the Z direction. The first core piece  3 A and the second core piece  3 B in this example have the same shape and are manufactured by one mold. 
     On the other hand, the third core piece  3 C in this example is constituted by the first side core  33 , and the fourth core piece  3 D in this example is constituted by the second side core  34 . The third core piece  3 C and the fourth core piece  3 D are approximately I-shaped in a view from the Z direction. The third core piece  3 C and the fourth core piece  3 D in this example have the same shape and are manufactured by one mold. 
     The core pieces  3 A,  3 B,  3 C, and  3 D are each a powder compact or a composite material compact. For example, the core pieces  3 A and  3 B are powder compacts, and the core pieces  3 C and  3 D are composite material compacts. 
     The reactor  1  in this example has effects similar to those of the reactor  1  of the first embodiment. In other words, the reactor  1  in this example is lightweight and has excellent magnetic characteristics. 
     Third Embodiment 
     A reactor  1  according to a third embodiment will be described below with reference to  FIG.  4   . The magnetic core  3  of the reactor  1  of the third embodiment is divided differently from that of the reactor  1  of the first and second embodiments. Besides how the magnetic core  3  is divided, the configuration of the reactor  1  in this example is the same as that of the reactor  1  of the first and second embodiments. 
     The magnetic core  3  of the reactor  1  in this example is a combination of a first core piece  3 A and a second core piece  3 B. The first core piece  3 A in this example is constituted by a first end core  31 , a second end core  32 , a first side core  33 , and a second side core  34 . The first end core  31  includes a first recessed portion  4 . The second end core  32  includes a second recessed portion  5 . The first core piece  3 A is approximately O-shaped in a view from the Z direction. On the other hand, the second core piece  3 B in this example is constituted by the middle core  30 . The second core piece  3 B is approximately I-shaped in a view from the Z direction. 
     The core pieces  3 A and  3 B are each a powder compact or a composite material compact. For example, the first core piece  3 A is a powder compact and the second core piece  3 B is a composite material compact. 
     The reactor  1  in this example has effects similar to those of the reactor  1  of the first embodiment. In other words, the reactor  1  in this example is lightweight and has excellent magnetic characteristics. 
     Fourth Embodiment 
     A reactor  1  provided with three winding portions  21 ,  22 , and  23  of a fourth embodiment will be described below with reference to  FIG.  5   . 
     The coil  2  in this example includes a first winding portion  21 , a second winding portion  22 , and a third winding portion  23 . The three winding portions  21 ,  22 , and  23  may be continuous or independent as long as they can form a closed magnetic path as shown in  FIG.  2   . A middle core  30  is arranged inside the first winding portion  21 , a first side core  33  is arranged inside the second winding portion  22 , and a second side core  34  is arranged inside the third winding portion  23 . The three winding portions  21 ,  22 , and  22  are arranged in parallel in the Y direction, and the axes of the three winding portions  21 ,  22 , and  23  are on the XY plane. 
     The magnetic core  3  in this example is a combination of a first core piece  3 A and a second core piece  3 B. The first core piece  3 A in this example is constituted by a first end core  31 , a portion of the middle core  30 , a portion of the first side core  33 , and a portion of the second side core  34 . On the other hand, the second core piece  3 B in this example is constituted by a second end core  32 , a portion of the middle core  30 , a portion of the first side core  33 , and a portion of the second side core  34 . The first core piece  3 A and the second core piece  3 B are approximately E-shaped in a view from the Z direction. The first core piece  3 A and the second core piece  3 B in this example have the same shape and are manufactured by one mold. 
     The core pieces  3 A and  3 B are each a powder compact or a composite material compact. For example, the first core piece  3 A is a powder compact and the second core piece  3 B is a composite material compact. 
     The reactor  1  in this example has effects similar to those of the reactor  1  of the first embodiment. In other words, the reactor  1  in this example is lightweight and has excellent magnetic characteristics. 
     Fifth Embodiment 
     Converter and Power Conversion Device 
     The reactor  1  according to the first to fourth embodiments can be used for applications that satisfy the following power conduction conditions. The power conduction conditions include, for example, that the maximum direct current is 100 A or more and 1000 A or less, the average voltage is 100 V or more and 1000 V or less, and the operating frequency is 5 kHz or more and 100 kHz or less. The reactor  1  according to the first to fourth embodiments can be typically used as a component of a converter mounted in a vehicle such as an electric automobile or a hybrid automobile, or a component of a power conversion device that includes the converter. 
     As shown in  FIG.  6   , a vehicle  1200  such as a hybrid automobile or an electric automobile includes a main battery  1210 , a power conversion device  1100  connected to the main battery  1210 , and a motor  1220  that is used for traveling and is driven by power supplied from the main battery  1210 . The motor  1220  is typically a three-phase AC motor that drives wheels  1250  during travel, and functions as a generator during regeneration. In the case of a hybrid automobile, the vehicle  1200  includes an engine  1300  in addition to a motor  1220 . The vehicle  1200  in  FIG.  6    includes an inlet as a charging point, but can include a plug instead. 
     The power conversion device  1100  includes a converter  1110  connected to the main battery  1210 , and an inverter  1120  that is connected to the converter  1110  and performs conversion between direct current and alternating current. During traveling of the vehicle  1200 , the converter  1110  shown in this example steps up the input voltage from the main battery  1210 , which is about 200 V or more and 300 V or less, to about 400 V or more and 700 V or less, and supplies the boosted power to the inverter  1120 . During regeneration, the converter  1110  steps down the input voltage output from the motor  1220  via the inverter  1120  to a DC voltage suitable for the main battery  1210 , and charges the main battery  1210 . The input voltage is DC voltage. During traveling of the vehicle  1200 , the inverter  1120  converts the DC voltage boosted by the converter  1110  into a predetermined AC voltage and supplies the power to the motor  1220 , whereas during regeneration, the inverter  1120  converts AC voltage output from the motor  1220  into DC voltage and outputs the power to the converter  1110 . 
     As shown in  FIG.  7   , the converter  1110  includes a plurality of switching elements  1111 , a drive circuit  1112  that controls the operation of the switching elements  1111 , and a reactor  1115 , and performs conversion of an input voltage by repeated ON/OFF operations. Here, the conversion of the input voltage is stepping up and stepping down. Power devices such as field effect transistors or insulated gate bipolar transistors are used as the switching elements  1111 . The reactor  1115  utilizes the property of a coil that attempts to prevent a change in the current flowing in the circuit to achieve a function of smoothing a change in the current when the current attempts to increase or decrease due to the switching operation. The reactor  1  according to any one of the first to fourth embodiments is provided as the reactor  1115 . The power conversion device  1100 , the converter  1110 , or the like is lightweight and has excellent conversion efficiency due to including the reactor  1  that is lightweight and has excellent magnetic characteristics. 
     In addition to the converter  1110 , the vehicle  1200  includes a power supply device converter  1150  connected to the main battery  1210 , and an auxiliary power supply converter  1160  that is connected to a sub battery  1230  (power supply for accessories  1240 ) and the main battery  1210  and converts a high voltage from the main battery  1210  to a low voltage. The converter  1110  typically performs DC-DC conversion, whereas the power supply device converter  1150  and the auxiliary power supply converter  1160  typically perform AC-DC conversion. Some power supply device converters  1150  perform DC-DC conversion. The reactor of the power supply device converter  1150  and the auxiliary power supply converter  1160  has the same configuration as the reactor  1  of any one of the first to fourth embodiments, and the size, shape, and the like of the reactor can be changed appropriately. Also, the reactor  1  or the like of any one of the first to fourth embodiments can be used in a converter that performs conversion on input power but only performs stepping up or stepping down. 
     Tests 
     Test Example 1 
     In Test Example 1, the influence of the width W 1  of the first recessed portion  4  shown in  FIG.  2    on the inductance and the total loss of the reactor  1  was investigated. Specifically, the reactor of Sample No. 1 not including the first recessed portion  4  and the reactor  1  of Samples No. 2 to No. 6 including the first recessed portion  4  were analyzed. The only difference between the reactor of Sample No. 1 and the reactor  1  of Samples No. 2 to No. 6 is the presence or absence of the first recessed portion  4 . Also, the only difference between the reactors of Samples No. 2 and No. 6 is the width W 1  of the first recessed portion  4 . The dimensions of the main portions of the magnetic core  3  of each sample are as follows. 
     Sample No. 1
         Does not include first recessed portion  4     Length L of magnetic core  3 : 70 mm   Width W of magnetic core  3 =width W of first end core  31  and second end core  32 : 75 mm   Height H of magnetic core  3 : 30 mm   Length T 0  of middle core  30  in Y direction: 30 mm   Lengths T 1  and T 2  of first end core  31  and second end core  32  in X direction: 12 mm   Lengths T 3  and T 4  of first side core  33  and second side core  34  in Y direction: 11 mm       

     Sample No. 2
         Width W 1  of first recessed portion  4 : 6 mm       

     The width W 1  of the first recessed portion  4  is 8% of the width W of the magnetic core  3  and 20% of the length T 0  of the middle core  30  in the Y direction.
         Depth D 1  of first recessed portion  4 : 4 mm   Length of first recessed portion  4  in Z direction: 30 mm       

     Sample No. 3
         Width W 1  of first recessed portion  4 : 12 mm       

     The width W 1  of the first recessed portion  4  is 16% of the width W of the magnetic core  3  and 40% of the length T 0  of the middle core  30  in the Y direction. 
     Sample No. 4
         Width W 1  of first recessed portion  4 : 18 mm       

     The width W 1  of the first recessed portion  4  is 24% of the width W of the magnetic core  3  and 60% of the length T 0  of the middle core  30  in the Y direction. 
     Sample No. 5
         Width W 1  of first recessed portion  4 : 24 mm       

     The width W 1  of the first recessed portion  4  is 32% of the width W of the magnetic core  3  and 80% of the length T 0  of the middle core  30  in the Y direction. 
     Sample No. 6
         Width W 1  of first recessed portion  4 : 30 mm       

     The width W 1  of the first recessed portion  4  is 40% of the width W of the magnetic core  3  and 100% of the length T 0  of the middle core  30  in the Y direction. 
     The commercially available software JMAG-Designer 18.1 (manufactured by JSOL Corporation) was used to simulate the inductance and total loss of each sample. The inductance (pH) when a current was passed through the coil  2  was obtained in the inductance analysis. The current was changed in the range of 0 A to 300 A. Table 1 shows the inductance when the current value is 0 A, 100 A, 200 A, and 300 A. The inductance is shown as a percentage relative to an inductance of 100% for Sample No. 1 at 0 A. 
     In the total loss analysis, the total loss (W) was obtained based on the magnetic flux density distribution and the current density distribution when driven at a direct current of 0 A, an input voltage of 200 V, an output voltage of 400 V, and a frequency of 20 kHz. The total loss in this example includes iron loss of the magnetic core  3 , coil loss, and the like. The results are shown in Table 1. The total loss is shown as a percentage relative to a total loss of 100% for Sample No. 1. 
     Table 1 also shows the volume reduction amount (mm 3 ) of the magnetic core  3  due to the provision of the first recessed portion  4 . 
     
       
         
           
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Sample No. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Item 
                 Unit 
                 No. 1 
                 No. 2 
                 No. 3 
                 No. 4 
                 No. 5 
                 No. 6 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Width W1 of first 
                 mm 
                 0 
                 6 
                 12 
                 18 
                 24 
                 30 
               
               
                 recessed portion 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Inductance 
                  0 A 
                 % 
                 100 
                 99.97 
                 99.93 
                 99.86 
                 99.78 
                 99.64 
               
               
                   
                 100 A 
                   
                 79.43 
                 79.40 
                 79.35 
                 79.22 
                 78.97 
                 78.56 
               
               
                   
                 200 A 
                   
                 55.71 
                 55.67 
                 55.54 
                 55.18 
                 54.55 
                 53.80 
               
               
                   
                 300 A 
                   
                 33.42 
                 33.40 
                 33.31 
                 33.14 
                 33.08 
                 32.88 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Total loss 
                 % 
                 100 
                 100.15 
                 100.44 
                 100.99 
                 101.68 
                 102.55 
               
               
                 Volume reduction 
                 mm 3   
                 — 
                 720 
                 1440 
                 2160 
                 2880 
                 3600 
               
               
                   
               
            
           
         
       
     
     As shown in Table 1, compared with the reactor of Sample No. 1 serving as the base model, as the width W 1  of the first recessed portion  4  increase and as the volume reduction amount of the magnetic core  3  increases, the inductance of the reactor  1  tends to decrease, and the total loss tends to increase. In other words, there is a trade-off relationship between reduction of the weight of the reactor  1  and the magnetic characteristics of the reactor  1 . However, since the first recessed portion  4  is located in a central portion of the first outer face  310  of the first end core  31 , the decrease in inductance and the increase in total loss are insignificant. Here, from the viewpoint of maintaining the magnetic characteristics of the reactor  1 , it is preferable that the rate of decrease in inductance and the rate of increase in total loss due to the provision of the first recessed portion  4  are 1% or less. From this point of view, it can be said that Sample No. 3 and Sample No. 4 have a good balance between the volume reduction amount and the extent of deterioration of magnetic characteristics. In other words, it is preferable that the width W 1  of the first recessed portion  4  is about 12 mm or more and 18 mm or less. 
     Furthermore, in order to investigate the relationship between the width W 1  of the first recessed portion  4  and the extent of change in the magnetic characteristics of the reactor  1 , the deterioration rate of inductance performance and the deterioration rate of total loss were investigated as shown below. These deterioration rates are unique indicators in this specification. 
     Deterioration Rate of Inductance Performance 
       (deterioration rate of inductance performance)=(decrease in inductance)/(volume reduction amount of magnetic core) 
     Here, the amount of decrease in inductance in the above expression is the sum of the difference in inductance from the base model when the current value is 0 A, the difference in inductance from the base model when the current value is 100 A, the difference in inductance from the base model when the current value is 200 A, and the difference in inductance from the base model when the current value is 300 A. For example, the amount of decrease in inductance of Sample No. 2 based on the results in Table 1 is |100−99.97|+|79.43−79.40|+|55.7|−55.67|+β3.42−33.40|=0.12. 
     The deterioration rate of inductance of Samples No. 2 to No. 6 is shown in the graph of  FIG.  8   . The horizontal axis of the graph indicates the width W 1  (mm) of the first recessed portion  4 , and the vertical axis indicates the deterioration rate of inductance performance. In the graph of  FIG.  8   , the plotted points of the samples are connected by lines. When the slope of the line between the plotted points shown in  FIG.  8    is small, it can be said that the rate of deterioration of inductance performance relative to an increase in the width W 1  is small 
     Deterioration Rate of Total Loss 
       (deterioration rate of total loss)=(increase in total loss)/(volume reduction amount of magnetic core) 
     Here, the amount of increase in total loss in the above equation is the difference in total loss from the base model. For example, the increase in total loss of Sample No. 2 based on the results in Table 1 is 100.15-100.00=0.15. 
     The deterioration rate of total loss of Samples No. 2 to No. 6 is shown in the graph of  FIG.  9   . The horizontal axis of the graph indicates the width W 1  (mm) of the first recessed portion  4 , and the vertical axis indicates the deterioration rate of total loss. In the graph of  FIG.  9   , the plotted points of the samples are connected by lines. When the slope of the line between the plotted points shown in  FIG.  9    is small, it can be said that the rate of deterioration of total loss relative to an increase in the width W 1  is small. 
     As shown in  FIGS.  8  and  9   , the slope of the line connecting Sample No. 4 with a width W 1  of 18 mm and Sample No. 5 with a width W 1  of 24 mm is smaller than the slope of the other lines. Accordingly, it can be said that the extent of deterioration of the magnetic characteristics of the reactor  1  is comparatively moderate when the width W 1  is in the range of 18 mm to 24 mm. Accordingly, from the viewpoint of reducing the weight of the magnetic core  3 , the width W 1  of the first recessed portion  4  may be 18 mm or more and 24 mm or less. 
     Test Example 2 
     In Test Example 2, the influence of the depth D 1  of the first recessed portion  4  shown in  FIG.  2    on the inductance and the total loss of the reactor  1  was investigated. Specifically, the reactor of Sample No. 1 not including the first recessed portion  4  and the reactor  1  of Samples No. 7 to No. 11 including the first recessed portion  4  were analyzed. The reactor of Sample No. 1 is the same as the reactor of Sample No. 1 of Test Example 1. The only difference between the reactor  1  of Samples No. 7 to No. 11 is the depth D 1  of the first recessed portion  4 . The dimensions of the main portions of the magnetic core  3  of each sample are as follows. 
     Sample No. 7
         Depth D 1  of first recessed portion  4 : 2 mm       

     The depth D 1  of first recessed portion  4  is 16% f the length T 1  of the first end core  31  in the X direction.
         Width W 1  of first recessed portion  4 : 12 mm   Length of first recessed portion  4  in Z direction: 30 mm       

     Sample No. 8
         Depth D 1  of first recessed portion  4 : 4 mm       

     The depth D 1  of the first recessed portion  4  is 33% of the length T 1  of the first end core  31  in the X direction. 
     Sample No. 9
         Depth D 1  of first recessed portion  4 : 6 mm       

     The depth D 1  of the first recessed portion  4  is 50% of the length T 1  of the first end core  31  in the X direction. 
     Sample No. 10
         Depth D 1  of first recessed portion  4 : 8 mm       

     The depth D 1  of the first recessed portion  4  is 66% of the length T 1  of the first end core  31  in the X direction. 
     Sample No. 11
         Depth D 1  of first recessed portion  4 : 10 mm       

     The depth D 1  of the first recessed portion  4  is 83% of the length T 1  of the first end core  31  in the X direction. 
     The inductance and total loss of each sample were determined by the same method as in Test Example 1. The results are shown in Table 2. 
     
       
         
           
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                 Sample No. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Item 
                 Unit 
                 No. 1 
                 No. 7 
                 No. 8 
                 No. 9 
                 No. 10 
                 No. 11 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Depth D1 of first 
                 mm 
                 0 
                 2 
                 4 
                 6 
                 8 
                 10 
               
               
                 recessed portion 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Inductance 
                  0 A 
                 % 
                 100 
                 99.96 
                 99.93 
                 99.88 
                 99.82 
                 99.75 
               
               
                   
                 100 A 
                   
                 79.43 
                 79.39 
                 79.35 
                 79.26 
                 79.13 
                 78.93 
               
               
                   
                 200 A 
                   
                 55.71 
                 55.66 
                 55.54 
                 55.29 
                 54.89 
                 54.34 
               
               
                   
                 300 A 
                   
                 33.42 
                 33.39 
                 33.31 
                 33.17 
                 33.05 
                 32.93 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Total loss 
                 % 
                 100 
                 100.18 
                 100.44 
                 100.92 
                 101.45 
                 102.17 
               
               
                 Volume reduction 
                 mm 3   
                 — 
                 720 
                 1440 
                 2160 
                 2880 
                 3600 
               
               
                   
               
            
           
         
       
     
     As shown in Table 2, compared with the reactor of Sample No. 1 serving as the base model, as the depth D 1  of the first recessed portion  4  increases, that is to say as the volume reduction amount of the magnetic core  3  increases, the inductance of the reactor  1  tends to decrease, and the total loss tends to increase. However, since the first recessed portion  4  is located in a central portion of the first outer face  310  of the first end core  31 , the decrease in inductance and the increase in total loss are insignificant. However, from the viewpoint of maintaining the magnetic characteristics of the reactor  1 , it is preferable that the rate of decrease in inductance and the rate of increase in total loss due to the provision of the first recessed portion  4  are 1% or less. From this point of view, it can be said that Sample No. 8 and Sample No. 9 have a good balance between the volume reduction amount and the extent of deterioration of magnetic characteristics. In other words, it is preferable that the depth D 1  of the first recessed portion  4  is about 4 mm or more and 6 mm or less. 
     Furthermore, in order to investigate the relationship between the depth D 1  of the first recessed portion  4  and the extent of change in the magnetic characteristics of the reactor  1 , the deterioration rate of inductance and the deterioration rate of total loss of each sample were investigated. The definitions of both deterioration rates are the same as the definitions of the deterioration rates in Test Example 1. The results are shown in  FIGS.  10  and  11   . 
       FIG.  10    is a graph showing the deterioration rate of inductance of Samples No. 7 to No. 11. The horizontal axis of the graph in  FIG.  10    indicates the depth D 1  (mm) of the first recessed portion  4 , and the vertical axis indicates the rate of deterioration of inductance.  FIG.  11    is a graph showing the deterioration rate of total loss of Samples No. 7 to No. 11. The horizontal axis of the graph indicates the depth D 1  (mm) of the first recessed portion  4 , and the vertical axis indicates the deterioration rate of total loss. In the graphs of  FIGS.  10  and  11   , the plotted points of the samples are connected by lines. 
     When the slope of the line between the plotted points shown in  FIGS.  10  and  11    is small, it can be said that the rate of deterioration of inductance and total loss relative to an increase in the depth D 1  is small. As shown in  FIGS.  10  and  11   , the slope of the line connecting Sample No. 9 with a depth D 1  of 6 mm and Sample No. 10 with a depth D 1  of 8 mm is smaller than the slope of the other lines. Accordingly, it can be said that the rate of deterioration of the magnetic characteristics of the reactor  1  is comparatively moderate when the depth D 1  is in the range of 6 mm to 8 mm. Accordingly, from the viewpoint of reducing the weight of the magnetic core  3 , the depth D 1  of the first recessed portion  4  may be 6 mm or more and 8 mm or less. 
     Test Example 3 
     In Test Example 3, it was investigated whether the rate of decrease in magnetic characteristics due to the provision of the first recessed portion  4  is different according to whether the magnetic core  3  is a powder compact or a composite material. The characteristics of the samples are as follows. The dimensions L, W, H, T 0 , T 1 , T 2 , T 3 , and T 4  of the magnetic core  3  of each sample are the same as in Sample No. 1 of Test Example 1. 
     Sample No. 20
         Magnetic core  3  is entirely a powder compact.   Does not include first recessed portion  4 .       

     Sample No. 21
         Magnetic core  3  is entirely a powder compact.   Includes first recessed portion  4 .   Width W 1  of first recessed portion  4 : 12 mm   Depth D 1  of first recessed portion  4 : 4 mm       

     Sample No. 22
         Magnetic core  3  is entirely a composite material.   Does not include first recessed portion  4 .       

     Sample No. 23
         Magnetic core  3  is entirely a composite material.   Includes first recessed portion  4 .   Width W 1  of first recessed portion  4 : 12 mm   Depth D 1  of first recessed portion  4 : 4 mm       

     The inductance and the total loss of Samples No. 20 to No. 23 were measured. The measurement method is the same as in Test Example 1. The measurement results are shown in Table 3. The inductance in Table 3 is shown as a percentage relative to an inductance of 100% for Sample No. 20 at 0 A. The total loss in Table 3 is shown as a percentage relative to a total loss of 100% for Sample No. 20. In the columns for Sample No. 21 and Sample No. 23 in Table 3, the deterioration rates relative to Sample No. 20 and Sample No. 22 are shown as a percentage in parentheses. When the rate of deterioration of inductance is negative, it can be considered that the magnetic characteristics of the reactor  1  have deteriorated. When the rate of change in total loss is positive, it can be considered that the magnetic characteristics of the reactor  1  have deteriorated. 
     
       
         
           
               
               
             
               
                   
                 TABLE 3 
               
             
            
               
                   
                   
               
               
                   
                 Sample No. 
               
            
           
           
               
               
               
               
               
               
            
               
                 Item 
                 Unit 
                 No. 20 
                 No. 21 
                 No. 22 
                 No. 23 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Inductance 
                  0 A 
                 % 
                 100.0 
                 99.81 
                 12.99 
                 12.94 
               
               
                   
                   
                   
                   
                 (−0.2%) 
                   
                 (−0.4%) 
               
               
                   
                 100 A 
                   
                 12.97 
                 12.89 
                 10.95 
                 10.91 
               
               
                   
                   
                   
                   
                 (−0.7%) 
                   
                 (−0.4%) 
               
               
                   
                 200 A 
                   
                 7.16 
                 7.13 
                 8.64 
                 8.61 
               
               
                   
                   
                   
                   
                 (−0.5%) 
                   
                 (−0.3%) 
               
               
                   
                 300 A 
                   
                 3.69 
                 3.69 
                 6.19 
                 6.19 
               
               
                   
                   
                   
                   
                 (−0.1%) 
                   
                 (−0.1%) 
               
            
           
           
               
               
               
               
               
               
            
               
                 Total loss 
                 % 
                 10.00 
                 100.33 
                 104.62 
                 105.68 
               
               
                   
                   
                   
                 (+0.3%) 
                   
                 (+1.0%) 
               
               
                   
               
            
           
         
       
     
     As shown in Table 3, the deterioration rate of Sample No. 21 in which the magnetic core  3  was made of a powder compact was smaller than the deterioration rate of Sample No. 23 in which the magnetic core  3  was made of a composite material. Accordingly, if the first recessed portion  4  is provided in the first end core  31 , it is preferable that the first end core  31  is a powder compact. 
     LIST OF REFERENCE NUMERALS 
     
         
         
           
               1  reactor 
               2  coil
             21  first winding portion,  22  second winding portion,  23  third winding portion,  2   a ,  2   b  end portion     211  first end face,  212  second end face     213  first side face,  214  second side face   
         
               3  magnetic core
             3   g  gap portion     3 A first core piece,  3 B second core piece,  3 C third core piece,  3 D fourth core piece     30  middle core,  31  first end core,  32  second end core     33  first side core,  34  second side core     310  first outer face,  320  second outer face   
         
               4  first recessed portion
             40  bottom face,  41 ,  42  inner wall face   
         
               5  second recessed portion 
               1100  power conversion device
             1110  converter,  1111  switching element,  1112  drive circuit     1115  reactor,  1120  inverter     1150  power supply device converter,  1160  auxiliary power supply converter   
         
               1200  vehicle
             1210  main battery,  1220  motor,  1230  sub battery     1240  accessory,  1250  wheel     1300  engine   D 1  depth   H height   L, T 0 , T 1 , T 2 , T 3 , T 4  length   W, W 1  width