Coil

Abstract

A coil (100A) is provided with an electric wire (1) that is wound around a central axis (2) by one turn or a plurality of turns in a spiral shape. An electric wire (1) includes a conductor (10) having an elongated cross-sectional shape (11) on a plane including a central axis (2). The cross-sectional shape (11) is curved such that a first end (12) and a second end (13) in the longitudinal direction are away from the central axis (2). This makes it possible to reduce loss in a coil provided with an electric wire wound one or more turns in a spiral shape.

Description

Technical Field

[0001] The present disclosure relates to coils. Background Art

[0002] Conventionally, coils obtained by winding electric wires having a conductor with a circular cross-sectional shape have been widely used. However, it is known that in such coils, the flow of current is uneven due to the skin effect and proximity effect of the electric wire. Therefore, when an alternating current flows through the coil, there is a problem that losses are generated due to these effects and the power transmission efficiency is reduced.

[0003] Therefore, research is being conducted to reduce the above-mentioned loss in the coil. For example, Japanese Patent Application Laid-Open No. 2021-100102 (Patent Document 1) discloses a coil in which an electric wire having a conductor having a non-circular cross-sectional shape is spirally wound a plurality of times.

[0004] Patent Document 1: Japanese Patent Application Publication No. 2021-100102

[0005] The method of winding the electric wire in the coil varies depending on the purpose of the coil. In the technology disclosed in Patent Document 1, the object is a coil formed by spirally winding the electric wire multiple times, and the object is not a coil formed by winding one turn or spirally winding multiple turns. In other words, Patent Document 1 does not disclose the reduction of loss in the coil formed by winding one turn or spirally winding multiple turns. Summary of the invention

[0006] The present disclosure has been made in view of the above-mentioned problem, and an object of the present disclosure is to reduce the loss in a coil including an electric wire wound once or wound a plurality of times in a spiral shape.

[0007] The coil according to one aspect of the present disclosure includes an electric wire wound once or multiple times in a spiral shape around a central axis. The electric wire includes a conductor, and the cross-sectional shape of the conductor on a plane including the central axis is elongated. The cross-sectional shape is bent in a manner such that the first end and the second end in the longitudinal direction are away from the central axis.

[0008] According to the coil, the occurrence of reverse current in the conductor and current unevenness can be suppressed. As a result, the loss in the coil including the electric wire wound once or wound a plurality of times in a spiral shape can be reduced.

[0009] According to the present disclosure, it is possible to reduce the loss in a coil including an electric wire wound once or wound a plurality of times in a spiral shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 This is a perspective view of the appearance of the coil according to the first embodiment.

[0011] Figure 2It is a cross-sectional view showing the coil of the first embodiment.

[0012] Figure 3 It is a cross-sectional view showing a coil according to the second embodiment.

[0013] Figure 4 is a cross-sectional view showing a coil according to a third embodiment.

[0014] Figure 5 It is a cross-sectional view showing an example of an electric wire including an insulating material.

[0015] Figure 6 is a cross-sectional view showing another example of an electric wire including an insulating material.

[0016] Figure 7 It is a cross-sectional view showing the coil of the first reference example.

[0017] Figure 8 It is a cross-sectional view showing a coil according to a second reference example.

[0018] Fig. 9 It is a cross-sectional view showing a coil according to a third reference example.

[0019] Fig.10 is a cross-sectional view showing a coil according to a fourth reference example.

[0020] Fig.11 It is a cross-sectional view showing a coil according to a fifth reference example.

[0021] Fig.12 It is a diagram showing the current distribution in the conductor cross section of the models No. 1A to 38A, 27A1, and 27A2 when the frequency is 100 kHz.

[0022] Fig.13 This is a graph showing the Q value of each model in the first embodiment when the coil diameter d is 50 mm and the frequency is 100 kHz.

[0023] Fig.14 This is a graph showing the Q value of each model in the first embodiment when the coil diameter d is 100 mm and the frequency is 100 kHz.

[0024] Fig.15 This is a perspective view of the appearance of a coil according to the second embodiment.

[0025] Fig.16 It is a cross-sectional view showing a coil according to a fourth embodiment.

[0026] Fig.17 is a cross-sectional view showing a coil according to a fifth embodiment.

[0027] Fig.18 is a cross-sectional view showing a coil according to a sixth embodiment.

[0028] Fig.19 is a cross-sectional view showing a coil according to a seventh embodiment.

[0029] Fig. 20 is a cross-sectional view showing a coil according to a sixth reference example.

[0030] Fig.21 It is a cross-sectional view showing a coil according to the seventh reference example.

[0031] Fig. 22 It is a cross-sectional view showing a coil according to an eighth reference example.

[0032] Fig.23 is a cross-sectional view showing a coil according to a ninth reference example.

[0033] Fig.24 is a cross-sectional view showing a coil according to a tenth reference example.

[0034] Fig.25 It is a cross-sectional view showing a coil according to an eleventh reference example.

[0035] Fig.26 This is a diagram showing the current distribution in the conductor cross section of the models No. 1B to 15B when the frequency is 100 kHz.

[0036] Fig. 27 This is a diagram showing the current distribution in the conductor cross section of the models No. 16B to 30B when the frequency is 100 kHz.

[0037] Fig.28 It is a diagram showing the current distribution in the conductor cross section of the models No. 31B to 38B, 27B1, and 27B2 at a frequency of 100 kHz.

[0038] Fig.29 It is a diagram showing the current distribution in the conductor cross section of the models No. 2B1 to 2B3, 18B1 to 18B, and 21B1 to 21B3 when the frequency is 100 kHz.

[0039] Fig.30 It is a diagram showing the current distribution in the conductor cross section of the models No. 24B1 to 24B3, 27B3 to 27B5, and 30B1 to 30B3 when the frequency is 100 kHz.

[0040] Fig.31 This is a graph showing the Q value of each model in the second embodiment when the coil diameter d is 50 mm and the frequency is 100 kHz.

[0041] Fig.32 This is a graph showing the Q value of each model in the second embodiment when the coil diameter d is 100 mm and the frequency is 100 kHz.

[0042] Fig.33 This is a perspective view of the appearance of a coil according to the third embodiment.

[0043] Fig.34 is a cross-sectional view showing a coil according to an eighth embodiment.

[0044] Fig.35 This is a graph showing the Q value of each model in the third embodiment when the coil diameter d is 50 mm and the frequency is 100 kHz.

[0045] Fig.36 This is a graph showing the Q value of each model in the third embodiment when the coil diameter d is 100 mm and the frequency is 100 kHz. DETAILED DESCRIPTION

[0046] The embodiments of the present invention are described in detail with reference to the accompanying drawings. In addition, the same reference numerals are used for the same or corresponding parts in the drawings, and their description is not repeated. In addition, the embodiments or modifications described below can also be appropriately selected and combined.

[0047] <Implementation method 1>

[0048] Figure 1 : is a perspective view of the appearance of the coil involved in the first embodiment. Figure 1 As shown, the coil 100A according to the first embodiment includes an electric wire 1 wound once around a central axis 2. The diameter of the coil 100A (hereinafter referred to as "coil diameter") is d.

[0049] Figure 2 It is a cross-sectional view showing the coil of the first embodiment. Figure 3 It is a cross-sectional view showing a coil according to the second embodiment. Figure 4 is a cross-sectional view showing a coil according to a third embodiment. Figure 2 to Figure 4 FIG. 2 shows a cross-sectional view of the coil 100A on a plane including the central axis 2. Figure 2 to Figure 4 As shown, the electric wire 1 is wound around the central axis 2 once with a distance d / 2 from the central axis 2. In addition, Figure 2 to Figure 4 Only a portion of the coil 100A is depicted. Figure 2 to Figure 4 In FIG. 1 , the cross section of the coil 100A existing on the left side of the central axis 2 is omitted from illustration.

[0050] like Figure 2 to Figure 4As shown, the electric wire 1 includes a conductor 10 whose cross-sectional shape 11 on a plane including a central axis 2 is non-circular. The cross-sectional shape 11 of the conductor 10 has a shape that avoids or bypasses a portion where a reverse current easily flows and a portion where a current is difficult to flow. As a result, the loss of the conductor 10 can be reduced. Specifically, the cross-sectional shape 11 is elongated and is bent in a manner such that a first end 12 as one end in the length direction and a second end 13 as the other end in the length direction are away from the central axis 2. As a result, when an alternating current flows through the coil 100A, the generation of a reverse current in the conductor 10 and the unevenness of the current can be suppressed.

[0051] When the first end 12 and the second end 13 are tapered, current unevenness is likely to occur in these portions. Therefore, the first end 12 and the second end 13 are preferably formed in a tapered state with rounded corners as a whole.

[0052] When a straight line passing through the center point 16 of the cross-sectional shape 11 and being orthogonal to the line segment 17 connecting the first end 12 and the second end 13 is set as a reference straight line 18, the cross-sectional shape 11 is preferably line-symmetrical with respect to the reference straight line 18. Thus, the generation of reverse current in the conductor 10 and current unevenness when the alternating current flows through the coil 100A can be further suppressed.

[0053] The reference line 18 defines the posture of the conductor 10. Figure 2 to Figure 4 As shown, the reference straight line 18 is preferably perpendicular to the central axis 2 at any portion of the electric wire 1. This can further suppress the occurrence of reverse current in the conductor 10 and current unevenness.

[0054] As described above, cross-sectional shape 11 is curved so that first end 12 and second end 13 are away from central axis 2 . Therefore, cross-sectional shape 11 has concave first edge 14 facing the outside of coil 100A and convex second edge 15 facing central axis 2 .

[0055] The cross-sectional shape 11 is preferably formed so that the interval t between the first edge 14 and the second edge 15 is constant. The interval t is preferably not more than twice the skin depth (depth at which the current becomes 1 / e of the surface current) at the operating frequency of the coil 100A.

[0056] like Figure 2 As shown, the cross-sectional shape 11a of the conductor 10 in the coil 100A of the first embodiment is an arc shape with a center angle θs. That is, the first edge 14 and the second edge 15 are arc shapes with a center angle θs. Thus, the generation of reverse current in the conductor 10 and the unevenness of the current can be further suppressed. The cross-sectional shape 11a is line symmetrical with respect to the reference straight line 18.

[0057] In the case where the conductor 10 has an arc-shaped cross-sectional shape 11a, according to the simulation results described later, the center angle θs is preferably 15° to 345°, more preferably 60° to 345°, further preferably 105° to 345°, further preferably 120° to 345°, particularly preferably 180° to 345°, and most preferably 240° to 345°. By setting the center angle θs to the above value, the generation of reverse current in the conductor 10 and the unevenness of the current can be more effectively suppressed. In addition, the center angle θs is calculated as the arithmetic mean of the measured values ​​of the angle in the cross-sectional shape 11a at an arbitrary position 10 of the electric wire 1, for example.

[0058] When the conductor 10 has an arc-shaped cross-sectional shape 11a and the interval t is constant, when the radius of the first edge 14 relative to the center point O of the arc is set to R1, the radius R1 is calculated based on the interval t, the center angle θs, and the required conductor cross-sectional area (area of ​​the cross-sectional shape 11a).

[0059] For example, at a frequency of 100kHz, the required distance is equivalent to 2mm 2 In the case of a conductor cross-sectional area of ​​​​2 × 360 / θs-πt, the radius R1 uses the interval t (mm) and the center angle θs (°), and R1 = (2 × 360 / θs-πt 2 ) / 2tπ. The interval t and the radius R1 are calculated, for example, as the arithmetic mean of the measured values ​​in the cross-sectional shape at an arbitrary position 10 of the electric wire 1 .

[0060] like Figure 3 As shown, the cross-sectional shape 11b of the conductor 10 in the coil 100A of the second embodiment is V-shaped (a shape obtained by rotating the V-shaped shape by 90°). Specifically, the cross-sectional shape 11b has a bent portion 20 at the center point 16. The region from the bent portion 20 to the first end 12 and the region from the bent portion 20 to the second end 13 extend linearly in a direction inclined relative to the center axis 2. The cross-sectional shape 11b is line-symmetrical with respect to the reference straight line 18.

[0061] When the bent portion 20 is sharp, current unevenness is likely to occur in this portion. Figure 3 The side opposite to the central axis 2 is preferably a chamfered shape.

[0062] When the conductor 10 has a V-shaped cross-sectional shape 11b, according to the simulation results described later, the angle θv formed inside the bent portion 20 is preferably 90° to 165°, more preferably 105° to 165°, further preferably 120° to 165°, and particularly preferably 120° to 150°. In addition, the angle θv is calculated as the arithmetic mean of the measured values ​​of the angle in the cross-sectional shape at an arbitrary position 10 of the electric wire 1, for example.

[0063] When the conductor 10 has a V-shaped cross-sectional shape 11b and the interval t is constant, assuming that half the length of the first edge 14 is L1, the length L1 is calculated based on the interval t, the angle θv, and the required conductor cross-sectional area (area of ​​the cross-sectional shape 11b).

[0064] like Figure 4 As shown, the cross-sectional shape 11c of the conductor 10 in the coil 100A of the third embodiment is U-shaped (the U is rotated 90 degrees). Specifically, the cross-sectional shape 11c has two bent portions 21 and 22. The portion between the bent portions 21 and 22 in the cross-sectional shape 11 extends linearly parallel to the central axis 2. The area from the bent portion 21 to the first end 12 and the area from the bent portion 22 to the second end 13 extend linearly in a direction inclined relative to the central axis 2, respectively. The cross-sectional shape 11c is linearly symmetrical with respect to the reference straight line 18. Therefore, the angle θu formed inside the bent portions 21 and 22 is the same.

[0065] When the bent portions 21 and 22 are sharp, current unevenness is likely to occur in the portion. Figure 4 The side opposite to the central axis 2 is preferably a chamfered shape.

[0066] When the conductor 10 has a U-shaped cross-sectional shape 11c, according to the simulation results described later, the angle θu formed inside the bent portions 21 and 22 is preferably 105 to 165°, and more preferably 105 to 150°. The angle θu is calculated, for example, as the arithmetic mean of the measured values ​​of the angle in the cross-sectional shape at any position 10 of the electric wire 1.

[0067] When the conductor 10 has a U-shaped cross-sectional shape 11c and the interval t is constant, when the length from the bend portion 21 to the first end 12 (or the length from the bend portion 22 to the second end 13) in the first edge 14 is set to L2 and the length between the bend portions 21 and 22 in the first edge 14 is set to L3, the lengths L2 and L3 are calculated based on the interval t, the angle θu, and the required conductor cross-sectional area (the area of ​​the cross-sectional shape 11).

[0068] The conductor 10 is made of, for example, a plain braided copper wire, a copper plate, a copper tape, a copper foil, etc. In addition, the material of the conductor 10 is not limited to copper, and may be a metal other than copper.

[0069] The electric wire 1 may include an insulating material covering the conductor 10. Alternatively, the conductor 10 may not be covered with an insulating material but may be a bare conductor.

[0070] Figure 5 It is a cross-sectional view showing an example of an electric wire including an insulating material. Figure 5The electric wire 1 is shown in which the conductor 10 is entirely covered by an insulating material 30. For example, Figure 5 As shown in (a) of FIG. 1 , the electric wire 1 may also include an insulating material 30 that covers the entire conductor 10 and has a peripheral edge having a shape corresponding to the peripheral edge of the conductor 10. Alternatively, Figure 5 As shown in (b) of FIG. 1 , the electric wire 1 may include an insulating material 30 that covers the entire conductor 10 and has a rectangular peripheral edge.

[0071] Figure 6 is a cross-sectional view showing another example of an electric wire including an insulating material. Figure 6 The electric wire 1 is shown in which only a portion of the conductor 10 is covered by the insulating material 30. For example, Figure 6 As shown in (a) of FIG. 1 , the electric wire 1 may also include a hollow cylindrical insulating material 30 having an outer periphery in contact with the first edge 14 of the conductor 10. Alternatively, Figure 6 As shown in FIG. 2 (b), the electric wire 1 may include a hollow cylindrical insulating material 30 having an inner circumference in contact with the second edge 15 of the conductor 10 .

[0072] The material of the insulating material 30 is not limited to the following materials, but is preferably an electrically insulating polymer composition, more preferably a 1×10 12 A polymer composition having a volume resistivity of Ω·cm or more.

[0073] (simulation)

[0074] Using the analysis software Femtet (registered trademark) (Version 2018.1.2.70140), under the analysis conditions shown in Table 1, the models of each of a plurality of coils having different conductor cross-sectional shapes and conductor postures were evaluated.

[0075] [Table 1]

[0076]

[0077] The model of the evaluation object is in addition to Figure 2 to Figure 4 In addition to the models corresponding to the coil 100A of the first to third embodiments shown respectively, there are also models corresponding to the coils of the first to fifth reference examples shown below. Figure 1 The coil 100A shown also includes an electric wire wound once around the central axis 2 .

[0078] Figure 7 is a cross-sectional view showing the coil of the first reference example. Figure 7 As shown, the electric wire included in the coil of the first reference example has a conductor 10 having a circular cross-sectional shape 11d on a plane including the central axis 2. The diameter D of the cross-sectional shape 11d is calculated based on the required conductor cross-sectional area (area of ​​the cross-sectional shape 11d).

[0079] Figure 8 is a cross-sectional view showing a coil of the second reference example. Figure 8 As shown, the wire included in the coil of the second reference example has a conductor 10 whose cross-sectional shape 11e on a plane including the central axis 2 is an I-shaped conductor. The cross-sectional shape 11e is elongated like the cross-sectional shapes 11a to 11c. However, the cross-sectional shape 11e is a straight line. A reference straight line 18 passing through the center point 16 of the cross-sectional shape 11e and orthogonal to the line segment 17 connecting the first end 12 and the second end 13 defines the posture of the conductor 10 having the cross-sectional shape 11e. Figure 8 As shown, the reference straight line 18 is orthogonal to the central axis 2. That is, the cross-sectional shape 11e extends along the central axis 2. The length L4 of the cross-sectional shape 11e in the longitudinal direction is calculated based on the interval t between the edge of the cross-sectional shape 11e on the central axis 2 side and the edge on the opposite side of the central axis 2 and the required conductor cross-sectional area (area of ​​the cross-sectional shape 11e).

[0080] Fig. 9 is a cross-sectional view showing a coil of the third reference example. Fig. 9 As shown, the electric wire provided in the coil of the third reference example has a conductor 10 having an O-shaped cross-sectional shape 11f on a plane including the central axis 2. The inner diameter R2 of the cross-sectional shape 11f is calculated based on the interval t between the outer periphery and the inner periphery of the cross-sectional shape 11f and the required conductor cross-sectional area (area of ​​the cross-sectional shape 11d).

[0081] Fig.10 is a cross-sectional view showing a coil of the fourth reference example. Fig.10 As shown, the wires provided in the coil of the fourth reference example have Figure 2 The conductor 10 has the same cross-sectional shape 11a as the first embodiment shown in the figure. However, in the fourth reference example, the conductor 10 is arranged so that the reference straight line 18 is parallel to the central axis 2. That is, the conductor 10 in the fourth reference example takes a posture obtained by rotating the reference straight line 18 by 90° on a plane including the central axis 2 from the posture of the conductor 10 in the first embodiment.

[0082] Fig.11 is a cross-sectional view showing a coil of the fifth reference example. Fig.11 As shown, the wires provided in the coil of the fifth reference example have Figure 2 The conductor 10 has the same cross-sectional shape 11a as the first embodiment shown in the figure. However, in the fifth reference example, the conductor 10 is arranged so that the concave first edge 14 faces the central axis 2 and the convex second edge 15 faces the outside of the coil. That is, the conductor 10 in the fifth reference example takes a posture obtained by rotating the reference straight line 18 by 180° on a plane including the central axis 2 from the posture of the conductor 10 in the first embodiment.

[0083] Table 2 shows a list of cross-sectional shapes of conductors used in the model to be evaluated. The cross-sectional shapes were designed so that the cross-sectional area on the plane including the central axis 2 was 2 mm. 2 The cross-sectional shape of No.1 is Figure 7 The cross-sectional shape of the circular shape 11d is shown. The cross-sectional shape of No.2 is Figure 8 The cross-sectional shape 11e of the letter I is shown. The length L4 of the cross-sectional shape of No. 2 is designed so that the interval t is 0.4 mm. The cross-sectional shape of No. 3 is Fig. 9 The cross-sectional shape 11f of the O-shaped cross section is shown. The inner diameter R2 of the cross-sectional shape of No. 3 is designed so that the interval t is 0.4 mm. The cross-sectional shapes of No. 4 to 9 are Figure 3 The V-shaped cross-sectional shapes 11b shown have different angles θv. The length L1 of the cross-sectional shapes of No. 4 to 9 is designed so that the interval t is 0.4 mm and the angle θv is 90° to 165° (interval 15°). The cross-sectional shapes of No. 10 to 15 are Figure 4 The U-shaped cross-sectional shapes 11c shown have different angles θu. The cross-sectional shapes of No. 10 to 15 are designed with a length L3 of 0.4 mm, a length L2 of 2.5 mm, and an angle θu of 90° to 165° (15° interval). The cross-sectional shapes of No. 16 to 38 are Figure 2 The arc-shaped cross-sectional shapes 11a shown have different central angles θs from each other. The radii R1 of the cross-sectional shapes of No. 16 to 38 are designed to have a central angle θs of 15° to 345° (at intervals of 15°) at intervals t of 0.4 mm.

[0084] [Table 2]

[0085]

[0086] The models to be evaluated include models No. 1A to 38A, 27A1, and 27A2. Model No. 1A corresponds to a coil formed by winding a conductor wire having a cross-sectional shape of No. 1 around a central axis 2 ( Figure 7 The model No.2A corresponds to a coil in which a conductor wire having a cross-sectional shape of No.2 is wound once around the central axis 2, and the reference straight line 18 of the cross-sectional shape is orthogonal to the central axis 2 ( Figure 8 The model No.3A corresponds to a coil formed by winding a conductor wire having a cross-sectional shape of No.3 around the central axis 2 ( Fig. 9 ) of the coil of the third reference example shown.

[0087] The models No. 4A to 9A correspond to coils formed by winding a conductive wire having a cross-sectional shape of No. 4 to 9 around the central axis 2 ( Figure 3 The coil 100A of the second embodiment is shown.

[0088] The models No. 10A to 15A correspond to coils formed by winding a conductive wire having a cross-sectional shape of No. 10 to 15 around the central axis 2 ( Figure 4 The coil 100A of the third embodiment is shown.

[0089] The models No. 16A to 38A correspond to coils formed by winding a conductive wire having a cross-sectional shape of No. 16 to 38 around the central axis 2 ( Figure 2 The coil 100A of the first embodiment shown in FIG. 4A to FIG. 38A corresponds to a coil having a conductor in which the second edge 15 faces the central axis 2 and the reference straight line 18 is perpendicular to the central axis 2 .

[0090] The model No. 27A1 corresponds to a coil formed by winding a conductive wire having a cross-sectional shape of No. 27 around the central axis 2 in such a manner that the reference straight line 18 is parallel to the central axis 2 ( Fig.10 ) of the coil of the fourth reference example shown.

[0091] The model No. 27A2 corresponds to a coil formed by winding a conductive wire having the cross-sectional shape of No. 27 once around the central axis 2 in a manner such that the first edge 14 faces the central axis 2 and the reference straight line 18 is orthogonal to the central axis 2 ( Fig.11 ) of the coil of the fifth reference example shown.

[0092] The simulation results when the coil diameter d of each model is set to 50 mm are shown in Table 3. In addition, the simulation results when the coil diameter d of each model is set to 100 mm are shown in Table 4. Tables 3 and 4 show the Q value at each frequency. The Q value is expressed by 2πfL / R using inductance L and resistance R. The higher the Q value, the less the loss.

[0093] [Table 3]

[0094] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 1A 0.0 0.0 0.1 0.6 5.3 24.3 82.1 262.1 708.9 2A 0.0 0.0 0.0 0.5 4.3 27.5 96.5 303.4 809.5 3A 0.0 0.0 0.1 0.5 5.0 30.4 96.3 306.3 822.0 4A 0.0 0.0 0.0 0.5 4.6 27.6 93.4 293.0 787.0 5A 0.0 0.0 0.0 0.5 4.5 28.0 95.8 301.6 802.4 6A 0.0 0.0 0.0 0.5 4.5 28.3 97.3 306.2 819.5 7A 0.0 0.0 0.0 0.5 4.4 28.2 97.9 308.3 825.3 8A 0.0 0.0 0.0 0.5 4.4 28.1 97.9 308.2 825.3 9A 0.0 0.0 0.0 0.5 4.3 27.8 97.4 306.5 820.6 10A 0.0 0.0 0.0 0.5 4.8 27.9 91.2 285.6 778.2 11A 0.0 0.0 0.0 0.5 4.7 28.7 95.3 299.8 796.3 12A 0.0 0.0 0.0 0.5 4.6 29.0 97.8 308.0 823.7 13A 0.0 0.0 0.0 0.5 4.5 28.9 98.9 311.8 840.0 14A 0.0 0.0 0.0 0.5 4.4 28.6 98.9 311.6 834.6 15A 0.0 0.0 0.0 0.5 4.4 28.0 98.0 308.5 824.1 16A 0.0 0.0 0.0 0.5 4.3 27.7 97.2 305.9 817.7 17A 0.0 0.0 0.0 0.5 4.3 28.0 97.9 308.3 824.8 18A 0.0 0.0 0.0 0.5 4.4 28.2 98.5 310.4 836.0 19A 0.0 0.0 0.0 0.5 4.4 28.5 99.1 311.1 832.3 20A 0.0 0.0 0.0 0.5 4.4 28.7 99.6 313.1 848.6 21A 0.0 0.0 0.0 0.5 4.4 29.0 100.1 315.9 860.4 22A 0.0 0.0 0.0 0.5 4.4 29.2 100.5 317.3 856.7 23A 0.0 0.0 0.0 0.5 4.5 29.4 100.8 318.1 854.1 24A 0.0 0.0 0.0 0.5 4.5 29.6 101.1 318.5 879.1 25A 0.0 0.0 0.0 0.5 4.5 29.8 101.3 320.5 870.4 26A 0.0 0.0 0.0 0.5 4.6 30.0 101.4 320.0 855.2 27A 0.0 0.0 0.0 0.5 4.6 30.2 101.4 319.8 879.5 28A 0.0 0.0 0.0 0.5 4.6 30.4 101.4 320.1 874.3 29A 0.0 0.0 0.0 0.5 4.6 30.6 101.3 320.6 880.7 30A 0.0 0.0 0.0 0.5 4.7 30.7 101.2 319.5 874.6 31A 0.0 0.0 0.0 0.5 4.7 30.8 101.0 319.2 862.8 32A 0.0 0.0 0.0 0.5 4.8 30.9 100.7 318.6 858.9 33A 0.0 0.0 0.0 0.5 4.8 31.0 100.3 318.5 877.0 34A 0.0 0.0 0.0 0.5 4.8 31.1 99.9 317.8 875.4 35A 0.0 0.0 0.0 0.5 4.9 31.1 99.4 315.5 864.3 36A 0.0 0.0 0.0 0.5 4.9 31.1 98.8 312.7 843.3 37A 0.0 0.0 0.0 0.5 5.0 31.0 98.0 310.9 833.4 38A 0.0 0.0 0.1 0.5 5.0 30.8 97.2 308.6 835.8 27A1 0.0 0.0 0.0 0.5 4.5 28.1 95.3 299.5 819.5 27A2 0.0 0.0 0.0 0.5 4.4 26.5 91.0 285.1 780.3

[0095] [Table 4]

[0096] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 1A 0.0 0.0 0.1 0.7 6.3 29.1 98.8 315.6 853.9 2A 0.0 0.0 0.1 0.6 5.3 33.9 119.6 376.6 1005.0 3A 0.0 0.0 0.1 0.6 6.1 36.9 117.4 373.8 1005.4 4A 0.0 0.0 0.1 0.6 5.6 33.3 113.9 358.2 963.8 5A 0.0 0.0 0.1 0.6 5.5 33.9 116.8 368.2 978.4 6A 0.0 0.0 0.1 0.6 5.4 34.2 118.8 374.2 1000.8 7A 0.0 0.0 0.1 0.6 5.4 34.3 119.9 377.8 1011.3 8A 0.0 0.0 0.1 0.6 5.3 34.3 120.3 379.1 1012.6 9A 0.0 0.0 0.1 0.6 5.3 34.1 120.2 378.8 1013.5 10A 0.0 0.0 0.1 0.6 5.8 33.6 111.0 348.4 948.3 11A 0.0 0.0 0.1 0.6 5.6 34.6 115.8 364.8 971.2 12A 0.0 0.0 0.1 0.6 5.5 35.0 118.9 374.8 1003.6 13A 0.0 0.0 0.1 0.6 5.4 35.0 120.5 380.1 1023.1 14A 0.0 0.0 0.1 0.6 5.4 34.7 121.0 381.6 1023.5 15A 0.0 0.0 0.1 0.6 5.3 34.3 120.6 380.1 1013.3 16A 0.0 0.0 0.1 0.6 5.3 34.1 120.1 378.6 1013.5 17A 0.0 0.0 0.1 0.6 5.3 34.2 120.6 380.3 1015.4 18A 0.0 0.0 0.1 0.6 5.3 34.4 121.0 381.7 1025.4 19A 0.0 0.0 0.1 0.6 5.3 34.6 121.4 381.5 1020.3 20A 0.0 0.0 0.1 0.6 5.4 34.8 121.8 382.9 1035.8 21A 0.0 0.0 0.1 0.6 5.4 35.0 122.1 385.6 1047.5 22A 0.0 0.0 0.1 0.6 5.4 35.2 122.4 386.7 1042.6 23A 0.0 0.0 0.1 0.6 5.4 35.5 122.6 385.7 1042.0 24A 0.0 0.0 0.1 0.6 5.5 35.7 122.7 386.8 1063.6 25A 0.0 0.0 0.1 0.6 5.5 35.9 122.8 389.0 1057.0 26A 0.0 0.0 0.1 0.6 5.5 36.1 122.9 388.3 1037.9 27A 0.0 0.0 0.1 0.6 5.6 36.3 122.9 387.3 1062.3 28A 0.0 0.0 0.1 0.6 5.6 36.5 122.8 387.6 1056.9 29A 0.0 0.0 0.1 0.6 5.6 36.7 122.7 388.5 1065.0 30A 0.0 0.0 0.1 0.6 5.7 36.8 122.5 387.3 1060.8 31A 0.0 0.0 0.1 0.6 5.7 37.0 122.3 387.4 1043.1 32A 0.0 0.0 0.1 0.6 5.7 37.2 122.1 386.7 1040.9 33A 0.0 0.0 0.1 0.6 5.8 37.3 121.8 386.2 1062.0 34A 0.0 0.0 0.1 0.6 5.8 37.5 121.3 385.7 1061.6 35A 0.0 0.0 0.1 0.6 5.9 37.5 120.8 384.2 1057.6 36A 0.0 0.0 0.1 0.6 5.9 37.6 120.1 380.9 1028.4 37A 0.0 0.0 0.1 0.6 6.0 37.5 119.3 378.8 1015.3 38A 0.0 0.0 0.1 0.6 6.0 37.3 118.3 376.1 1020.1 27A1 0.0 0.0 0.1 0.6 5.5 34.8 118.7 373.7 1023.9 27A2 0.0 0.0 0.1 0.6 5.4 33.6 115.3 362.3 990.3

[0097] Fig.12 It is a diagram showing the current distribution in the conductor cross section of the models No. 1A to 38A, 27A1, and 27A2 when the frequency is 100 kHz. Fig.12The current distribution when the coil diameter d of each model is set to 50 mm is shown. Fig.12 The current distribution in the conductor cross section where the central axis 2 exists on the left is shown.

[0098] Fig.13 This is a graph showing the Q value of each model in the first embodiment when the coil diameter d is 50 mm and the frequency is 100 kHz. Fig.14 Graph showing the Q value of each model in Embodiment 1 when the coil diameter d is 100 mm and the frequency is 100 kHz. Fig.13 and Fig.14 In the figure, the horizontal axis represents the center angle θs, angles θv, θu, and the vertical axis represents the Q value. Fig.13 and Fig.14 In FIG. 1 , the point at θs=360° shows the value obtained from the model corresponding to the coil of the third reference example. In addition, the point at θs=0° and the points at θv and θu=180° show the values ​​obtained from the model corresponding to the coil of the second reference example.

[0099] like Fig.13 and Fig.14 As shown, the Q values ​​of the models No. 4A to 38A corresponding to the coils of the first to third embodiments are higher than the model No. 1 corresponding to the first reference example having a circular cross-sectional shape. This is because Fig.12 As shown, in the model No. 1A corresponding to the first reference example having a circular cross-sectional shape, the current unevenness is obvious, whereas in the models No. 4A to 38A corresponding to the coils of the first to third embodiments, the current unevenness is suppressed.

[0100] It can be observed that the Q values ​​of the models No. 16A to 38A corresponding to the coil (arc shape) of the first embodiment tend to be higher than the Q values ​​of the models No. 4A to 15A corresponding to the coils (V-shaped and U-shaped) of the second and third embodiments. This is because Fig.12 As shown, in V-shaped and U-shaped conductors having bent portions 20 to 22, current is easily uneven in the bent portions 20 to 22. In contrast, in arc-shaped conductors, current unevenness due to the bent portions can be suppressed.

[0101] The models No. 27A, 27A1, and 27A2 all correspond to coils having an arc-shaped conductor with θs = 180°. However, it can be considered that the Q value of the model No. 27A corresponding to the coil of the first embodiment is higher than that of the models No. 27A1 and 27A2 corresponding to the coils of the fourth and fifth reference examples. This is because the convex second edge 15 (refer to Figure 2 ) is opposite to the central axis 2 and Fig.12 As shown, the current unevenness can be suppressed.

[0102] like Fig.13 and Fig.14 As shown in FIG. 1 , it was confirmed that the Q value of the model corresponding to the coil with the arc-shaped conductor in which the center angle θs was 15° to 345° was higher than that of the model corresponding to the coil with the conductor having a circular and I-shaped cross-sectional shape. In addition, it was confirmed that the Q value of the model corresponding to the coil with the center angle θs of 105° to 345° was higher than that of the model corresponding to the coil with the conductor having other cross-sectional shapes. It was confirmed that the Q value was further increased when the center angle θs was 180° to 345°, and the Q value was further increased when the center angle θs was 240° to 345°.

[0103] It was confirmed that in the model corresponding to the coil having the V-shaped conductor, the Q value was high when the angle θv was 105° to 165°, and the Q value was particularly high when the angle θv was 120° to 150°.

[0104] It was confirmed that in the model corresponding to the coil having the U-shaped conductor, the Q value was high when the angle θu was 105° to 165°, and the Q value was particularly high when the angle θu was 105° to 150°.

[0105] <Implementation method 2>

[0106] Fig.15 2 is a perspective view of the appearance of the coil involved in Embodiment 2. Fig.15 As shown, the coil 100B according to the second embodiment is different from the coil 100A according to the first embodiment in that the electric wire 1 is wound helically a plurality of times around the central axis 2 .

[0107] Fig.16 It is a cross-sectional view showing a coil according to a fourth embodiment. Fig.17 is a cross-sectional view showing a coil according to a fifth embodiment. Fig.18 is a cross-sectional view showing a coil according to a sixth embodiment. Figure 16 to Figure 18 FIG. 2 shows a cross-sectional view of the coil 100B on a plane including the central axis 2. Figure 16 to Figure 18 As shown, the electric wire 1 is spirally wound around the central axis 2 multiple times at a distance d / 2 from the central axis 2. d is the coil diameter. In addition, Figure 16 to Figure 18 Only a portion of the coil 100B is depicted. Figure 16 to Figure 18 In FIG. 1 , the cross section of the coil 100B existing on the left side of the central axis 2 is omitted from illustration.

[0108] like Figure 16 to Figure 18 As shown, the electric wire 1 according to the second embodiment has the same features as those of the first embodiment.

[0109] That is, the electric wire 1 includes a conductor 10 having a non-circular cross-sectional shape 11 on a plane including the central axis 2. In order to avoid or bypass a portion where it is difficult for current to flow, the cross-sectional shape 11 is elongated and bent so that a first end 12 as one end in the length direction and a second end 13 as the other end in the length direction are away from the central axis 2. In addition, the first end 12 and the second end 13 are preferably formed in a state where the entirety is rounded and the front ends are tapered.

[0110] In addition, cross-sectional shape 11 is preferably line-symmetric with respect to reference straight line 18 passing through center point 16 and perpendicular to line segment 17 connecting first end 12 and second end 13. Reference straight line 18 is preferably perpendicular to central axis 2 at any position of electric wire 1.

[0111] Furthermore, the concave first edge 14 faces the outside of the coil 100B, and the convex second edge 15 faces the central axis 2. The cross-sectional shape 11 is preferably formed so that the interval t between the first edge 14 and the second edge 15 is constant. The interval t is preferably less than or equal to twice the skin depth (the depth at which the current becomes 1 / e of the surface current) at the operating frequency of the coil 100B.

[0112] like Fig.16 As shown, the cross-sectional shape 11a of the conductor 10 of the coil 100B of the fourth embodiment is similar to Figure 2 The first example of the embodiment 1 shown is also in the shape of an arc. When the conductor 10 having the cross-sectional shape 11a is wound in a manner such that the coil diameter d is 50 mm, according to the simulation results described later, the center angle θs is preferably 15° to 330°, more preferably 60° to 285°, further preferably 90° to 240°, and particularly preferably 105° to 240°. When the conductor 10 having the cross-sectional shape 11a is wound in a manner such that the coil diameter d is 100 mm, the center angle θs is preferably 60° to 345°, more preferably 120° to 345°, and further preferably 180° to 300°. By making the center angle θ S By setting the above value, the current unevenness can be suppressed more effectively.

[0113] like Fig.17 As shown, the cross-sectional shape 11b of the conductor 10 of the coil 100B of the fifth embodiment is similar to Figure 3The second example of the embodiment 1 shown is also V-shaped. When the conductor 10 having the cross-sectional shape 11b is wound in a manner such that the coil diameter d is 50 mm, the angle θv formed inside the bent portion 20 is preferably 120° to 165° according to the simulation results described later. When the conductor 10 having the cross-sectional shape 11b is wound in a manner such that the coil diameter d is 100 mm, the angle θv is preferably 90° to 165°, more preferably 105° to 165°, and further preferably 120° to 165°. By setting the angle θv to the above value, the unevenness of the current can be more effectively suppressed.

[0114] like Fig.18 As shown, the cross-sectional shape 11c of the conductor 10 of the coil 100B of the sixth embodiment is similar to Figure 4 The third example of the embodiment 1 shown is also U-shaped. When the conductor 10 having the cross-sectional shape 11c is wound in a manner such that the coil diameter d is 50 mm, the angle θu formed inside the bent portions 21 and 22 is preferably 105° to 165°, more preferably 120° to 165°, and further preferably 120° to 150°, according to the simulation results described later. When the conductor 10 having the cross-sectional shape 11c is wound in a manner such that the coil diameter d is 100 mm, the angle θu is preferably 90° to 165°, more preferably 90° to 150°, and further preferably 105° to 135°. By setting the angle θu to the above value, the unevenness of the current can be more effectively suppressed.

[0115] Fig.19 FIG. 2 is a cross-sectional view showing a coil of the seventh embodiment. Fig.19 As shown, the cross-sectional shape 11a of the conductor 10 of the coil 100B of the seventh embodiment is similar to Fig.17 The first embodiment shown is also in an arc shape. However, the coil 100B of the seventh embodiment is different from the coil 100B of the fourth embodiment in that the reference straight line 18 and the central axis 2 are not orthogonal to each other in a part of the electric wire 1 .

[0116] The electric wire 1 is spirally wound three or more times around the target section 3 of the central axis 2. Fig.19In the example shown, the electric wire 1 is wound 10 times. The electric wire 1 has: a first portion 1a wound around a first section 3a located on one end side of the target section 3; a second portion 1b wound around a second section 3b located on the other end side of the target section 3; and a third portion 1c wound around a third section 3c located between the first section 3a and the second section 3b of the target section 3. The reference straight line 18c in the third portion 1c is orthogonal to the central axis 2. The reference straight line 18a in the first portion 1a is inclined relative to the reference straight line 18c corresponding to the third portion 1c in a direction in which the intersection points 40a and 40c with the central axis 2 are separated from each other. The reference straight line 18b in the second portion 1b is inclined relative to the reference straight line 18c corresponding to the third portion 1c in a direction in which the intersection points 40b and 40c with the central axis 2 are separated from each other. The degree of inclination is determined by the angle formed by the reference straight lines 18a and 18c and the line orthogonal to the central axis 2. express.

[0117] The postures of the conductor 10 in the first portion 1a, the second portion 1b, and the third portion 1c may be made different from each other by twisting the electric wire 1 or by joining the first portion 1a, the second portion 1b, and the third portion 1c in a state where the postures of the conductor 10 are different from each other.

[0118] In addition, Fig.19 In the example shown, the number of turns in the first part 1a and the second part 1b is three, and the number of turns in the third part 1c is four. However, the number of turns in the first part 1a, the second part 1b, and the third part 1c is not limited thereto.

[0119] As shown in the simulation results described later, in the conductor 10 of the first part 1a and the second part 1b, the current tends to flow to the side farther from the third part 1c. Fig.19 As shown, by inclining the reference straight lines 18 a and 18 b in the first portion 1 a and the second portion 1 b , the conductor 10 is located in a portion where current easily flows, and current variation in the conductor 10 can be suppressed.

[0120] In the second embodiment, the electric wire 1 may also include an insulating material covering the conductor 10. The insulating material may be Figure 5 As shown in the figure, the entire conductor 10 can also be covered as shown in the figure. Figure 6 As shown, the conductor 10 is partially covered. Alternatively, the insulating material may also cover the conductor 10 extending along the central axis 2 and wound a plurality of times in a spiral shape.

[0121] (simulation)

[0122] The models of each of a plurality of coils having different conductor cross-sectional shapes and conductor postures were evaluated using the same method as in the first embodiment.

[0123] The model of the evaluation object is in addition to Figure 16 to Figure 19 In addition to the models corresponding to the coils of the fourth to seventh embodiments shown respectively, there are also models corresponding to the coils of the sixth to eleventh reference examples shown below. Fig.15 The coil 100B shown also includes an electric wire that is spirally wound a plurality of times around the central axis 2 .

[0124] Fig. 20 is a cross-sectional view showing a coil of the sixth reference example. Fig. 20 As shown, the cross-sectional shape 11d of the conductor 10 included in the coil of the sixth reference example is similar to Figure 7 The first reference example shown is also circular in shape and has a diameter D (refer to Figure 7 ) to define.

[0125] Fig.21 is a cross-sectional view showing the coil of the seventh reference example. Fig.21 As shown, the cross-sectional shape 11e of the conductor 10 provided in the coil of the seventh reference example is similar to Figure 8 The second reference example shown is also I-shaped, and has a length L4 in the longitudinal direction (refer to Figure 8 ), the distance t between the edge on the central axis 2 side and the edge on the opposite side of the central axis 2 (refer to Figure 8 The reference straight line 18 is perpendicular to the central axis 2 at any part of the electric wire.

[0126] Fig. 22 is a cross-sectional view showing the coil of the eighth reference example. Fig. 22 As shown, the cross-sectional shape 11f of the conductor 10 included in the coil of the eighth reference example is Fig. 9 The third reference example shown is also in an O-shape, and the distance t between the outer periphery and the inner periphery (refer to Fig. 9 ) and inner diameter R2 (refer to Fig. 9 ) to define.

[0127] Fig.23 is a cross-sectional view showing a coil of the ninth reference example. Fig.23 As shown, the wires of the coil of the ninth reference example have Fig.16 The conductor 10 has the same cross-sectional shape 11a as the fourth embodiment shown in the figure. However, in the ninth reference example, the electric wire 1 is arranged so that the reference straight line 18 is parallel to the central axis 2 at any part. That is, the cross-sectional shape 11a in the ninth reference example takes a posture obtained by rotating the reference straight line 18 by 90° on a plane including the central axis 2 from the posture in the fourth embodiment.

[0128] Fig.24 is a cross-sectional view showing a coil of the tenth reference example. Fig.24As shown, the wires provided in the coil of the tenth reference example have Fig.16 The conductor 10 has the same cross-sectional shape 11a as the fourth embodiment shown in the figure. However, in the tenth reference example, the electric wire 1 is arranged so that the concave first edge 14 faces the central axis 2 and the convex second edge 15 faces the outside of the coil. That is, the cross-sectional shape 11a in the tenth reference example is a posture obtained by rotating the reference straight line 18 by 180° on a plane including the central axis 2 from the posture in the fourth embodiment.

[0129] Fig.25 is a cross-sectional view showing the coil of the eleventh reference example. Fig.25 As shown, the conductor 10 of the electric wire provided in the coil of the eleventh reference example has Fig.21 The cross-sectional shape 11e is the same as that of the seventh reference example shown in the figure. However, the coil of the eleventh reference example is different from the coil of the seventh reference example in that the reference straight line 18 and the central axis 2 are not orthogonal in a part of the electric wire. Specifically, as in the seventh embodiment, the electric wire has: a first portion 1a wound around a first section 3a located on one end side of the target section 3; a second portion 1b wound around a second section 3b located on the other end side of the target section 3; and a third portion 1c wound around a third section 3c located between the first section 3a and the second section 3b of the target section 3. The reference straight line 18c in the third portion 1c is orthogonal to the central axis 2. The reference straight line 18a in the first portion 1a is inclined in a direction in which the intersection points 40a and 40c with the central axis 2 are separated from each other relative to the reference straight line 18c corresponding to the third portion 1c. The reference straight line 18b in the second portion 1b is inclined in a direction in which the intersection points 40b and 40c with the central axis 2 are separated from each other relative to the reference straight line 18c corresponding to the third portion 1c. The degree of inclination is determined by the angle between the reference straight lines 18a, 18c and the normal to the central axis 2. The number of turns in the first part 1a and the second part 1b is three, and the number of turns in the third part 1c is four.

[0130] The models to be evaluated include models No. 1B to 38B, 2B1 to 2B3, 18B1 to 18B3, 21B1 to 21B3, 24B1 to 24B3, 27B1 to 27B5, and 30B1 to 30B3. Model No. 1B corresponds to a coil ( Fig. 20 The model No.2B corresponds to a coil in which a conductor wire having a cross-sectional shape of No.2 is spirally wound ten times around the central axis 2, and the reference straight line 18 of the cross-sectional shape is orthogonal to the central axis 2 ( Fig.21The model No. 3B corresponds to a coil formed by spirally winding a conductor wire having a cross-sectional shape of No. 3 around the central axis 2 for ten turns ( Fig. 22 ) of the coil of the eighth reference example shown.

[0131] The models No. 4B to 9B correspond to coils formed by spirally winding a conductive wire having a cross-sectional shape of No. 4 to 9 around a central axis 2 for ten turns, respectively ( Fig.17 The coil 100B of the fifth embodiment is shown.

[0132] The models No. 10B to 15B correspond to coils formed by spirally winding a conductive wire having the cross-sectional shape of No. 10 to 15 around the central axis 2 for ten turns, respectively ( Fig.18 The coil 100B of the sixth embodiment is shown.

[0133] The models No. 16B to 38B correspond to coils formed by spirally winding a conductive wire having a cross-sectional shape of No. 16 to 38 around a central axis 2 for ten turns ( Fig.16 The coil 100B of the fourth embodiment is shown.

[0134] Furthermore, the models No. 4B to 38B correspond to coils having a conductor in which the second edge 15 faces the central axis 2 and the reference straight line 18 is perpendicular to the central axis 2 .

[0135] The model No. 27B1 corresponds to a coil formed by spirally winding a conductor wire having the cross-sectional shape of No. 27 ten times around the central axis 2 in a manner such that the reference straight line 18 is parallel to the central axis 2 ( Fig.23 ) of the coil of the ninth reference example shown.

[0136] The model of No. 27B2 corresponds to a coil formed by spirally winding a conductive wire having the cross-sectional shape of No. 27 around the central axis 2 ten times in a manner such that the first edge 14 faces the central axis 2 and the reference straight line 18 is perpendicular to the central axis 2 ( Fig.24 ) of the coil of the tenth reference example shown.

[0137] Models No. 2B1 to 2B3 correspond to coils formed by spirally winding a conductor wire having a cross-sectional shape of No. 2 around the central axis 2 in ten turns in such a manner that the reference straight lines 18a and 18b of the first part 1a and the second part 1b are inclined relative to the normal line of the central axis 2 and the reference straight line 18c of the third part 1c is orthogonal to the central axis 2 ( Fig.25 The coil of the eleventh reference example shown in FIG. 11 ) The models of No. 2B1 to 2B3 correspond to the angles (Refer to Fig.25) are designed as coils of 30°, 45°, and 60°, respectively. The number of turns of the first part 1a and the second part 1b is set to three, and the number of turns of the third part 1c is set to four.

[0138] Models No. 18B1 to 18B3, 21B1 to 21B3, 24B1 to 24B3, 27B3 to 27B5, and 30B1 to 30B3 correspond to coils formed by spirally winding a conductor having a cross-sectional shape 11a around the central axis 2 in ten turns in such a manner that the reference straight lines 18a and 18b of the first portion 1a and the second portion 1b are inclined relative to the normal line of the central axis 2 and the reference straight line 18c of the third portion 1c is orthogonal to the central axis 2 ( Fig.19 The number of turns of the first part 1a and the second part 1b is set to three, and the number of turns of the third part 1c is set to four.

[0139] Models No. 18B1 to 18B3 correspond to the coil 100B having a conductor with a cross-sectional shape 11a of No. 18. Models No. 21B1 to 21B3 correspond to the coil 100B having a conductor with a cross-sectional shape 11a of No. 21. Models No. 24B1 to 24B3 correspond to the coil 100B having a conductor with a cross-sectional shape 11a of No. 24. Models No. 27B3 to 27B5 correspond to the coil 100B having a conductor with a cross-sectional shape 11a of No. 27. Models No. 30B1 to 30B3 correspond to the coil 100B having a conductor with a cross-sectional shape 11a of No. 30.

[0140] Models No.18B1, 21B1, 24B1, 27B3, 30B1 correspond to angles (Refer to Fig.19 ) is designed as a 30° coil. Models No.18B2, 21B2, 24B2, 27B4, 30B2 correspond to angles (Refer to Fig.19 ) is designed as a 45° coil. Models No.18B3, 21B3, 24B3, 27B5, 30B3 correspond to angles (Refer to Fig.19 ) is designed as a 60° coil.

[0141] In each model, the pitch P1 between the wound electric wires 1 (refer to Figures 16 to 25 ) is set to 6mm.

[0142] The simulation results when the coil diameter d of each model was 50 mm are shown in Tables 5 and 6. The simulation results when the coil diameter d of each model was 100 mm are shown in Tables 7 and 8. Tables 5 to 8 show the Q value at each frequency.

[0143] [Table 5]

[0144] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 1B 0.0 0.0 0.1 1.4 13.3 57.4 192.6 613.7 1659.5 2B 0.0 0.0 0.1 1.4 12.3 72.1 233.3 718.1 1931.0 3B 0.0 0.0 0.1 1.4 13.0 70.4 221.4 701.3 1878.9 4B 0.0 0.0 0.1 1.4 12.8 68.8 217.9 671.2 1794.8 5B 0.0 0.0 0.1 1.4 12.8 72.1 230.2 715.1 1876.6 6B 0.0 0.0 0.1 1.4 12.7 74.0 237.5 737.6 1959.9 7B 0.0 0.0 0.1 1.4 12.6 74.9 241.2 749.8 2007.1 8B 0.0 0.0 0.1 1.4 12.5 74.5 240.6 746.6 1992.8 9B 0.0 0.0 0.1 1.4 12.4 73.3 236.9 733.1 1959.6 10B 0.0 0.0 0.1 1.4 12.8 68.8 217.9 671.2 1794.8 11B 0.0 0.0 0.1 1.4 12.8 72.1 230.2 715.1 1876.6 12B 0.0 0.0 0.1 1.4 12.8 76.1 241.1 752.4 2010.2 13B 0.0 0.0 0.1 1.4 12.7 77.0 246.0 767.6 2078.8 14B 0.0 0.0 0.1 1.4 12.6 76.2 244.7 761.0 2042.2 15B 0.0 0.0 0.1 1.4 12.4 74.1 239.3 741.7 1971.7 16B 0.0 0.0 0.1 1.4 12.4 73.0 236.0 730.1 1945.9 17B 0.0 0.0 0.1 1.4 12.4 73.9 238.6 739.2 1975.2 18B 0.0 0.0 0.1 1.4 12.5 74.8 241.2 748.7 2008.3 19B 0.0 0.0 0.1 1.4 12.5 75.8 244.2 756.1 2014.0 20B 0.0 0.0 0.1 1.4 12.6 76.6 246.5 763.8 2048.2 21B 0.0 0.0 0.1 1.4 12.6 77.2 248.1 774.4 2114.1 22B 0.0 0.0 0.1 1.4 12.6 77.6 248.9 778.7 2104.8 23B 0.0 0.0 0.1 1.4 12.7 78.3 250.7 783.4 2092.5 24B 0.0 0.0 0.1 1.4 12.7 78.7 251.3 787.4 2163.8 25B 0.0 0.0 0.1 1.4 12.8 78.8 251.1 789.7 2151.1 26B 0.0 0.0 0.1 1.4 12.8 78.9 250.5 785.2 2093.6 27B 0.0 0.0 0.1 1.4 12.9 78.7 249.4 781.3 2141.3 28B 0.0 0.0 0.1 1.4 12.9 78.4 247.6 777.6 2135.2 29B 0.0 0.0 0.1 1.4 12.9 78.0 245.8 774.3 2129.8 30B 0.0 0.0 0.1 1.4 12.9 77.6 244.1 767.6 2091.1 31B 0.0 0.0 0.1 1.4 13.0 77.2 242.3 762.1 2056.3 32B 0.0 0.0 0.1 1.4 13.0 76.7 240.5 756.2 2038.5 33B 0.0 0.0 0.1 1.4 13.0 76.1 238.4 753.6 2082.4 34B 0.0 0.0 0.1 1.4 13.0 75.3 235.7 746.3 2054.8 35B 0.0 0.0 0.1 1.4 13.0 74.5 233.0 736.5 2006.1 36B 0.0 0.0 0.1 1.4 13.0 73.6 230.2 726.1 1955.4 37B 0.0 0.0 0.1 1.4 13.0 72.6 227.3 718.1 1924.8 38B 0.0 0.0 0.1 1.4 13.0 71.7 224.5 710.3 1911.8 27B1 0.0 0.0 0.1 1.3 11.2 60.4 198.5 617.4 1671.5 27B2 0.0 0.0 0.1 1.4 11.6 56.7 190.6 586.1 1572.4

[0145] [Table 6]

[0146] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 2B1 0.0 0.0 0.1 1.4 13.0 79.4 255.3 791.5 2123.1 2B2 0.0 0.0 0.1 1.4 12.8 75.4 244.5 757.7 2029.4 2B3 0.0 0.0 0.1 1.4 12.4 70.1 229.9 712.1 1901.4 18B1 0.0 0.0 0.1 1.4 13.2 84.1 267.6 838.0 2262.2 18B2 0.0 0.0 0.1 1.4 13.1 81.1 259.1 810.4 2176.7 18B3 0.0 0.0 0.1 1.4 12.7 75.9 244.8 764.6 2048.2 21B1 0.0 0.0 0.1 1.4 13.3 85.7 270.6 852.0 2356.3 21B2 0.0 0.0 0.1 1.4 13.2 84.7 267.4 841.6 2318.5 21B3 0.0 0.0 0.1 1.4 12.9 80.4 255.5 802.8 2203.6 24B1 0.0 0.0 0.1 1.4 13.3 84.9 266.8 838.7 2303.7 24B2 0.0 0.0 0.1 1.4 13.3 85.3 267.2 840.7 2308.1 24B3 0.0 0.0 0.1 1.4 13.1 82.8 260.6 819.6 2252.7 27B3 0.0 0.0 0.1 1.4 13.3 83.0 259.7 815.5 2241.8 27B4 0.0 0.0 0.1 1.4 13.4 83.7 261.3 820.8 2253.1 27B5 0.0 0.0 0.1 1.4 13.2 82.8 258.9 814.3 2236.4 30B1 0.0 0.0 0.1 1.4 13.3 80.3 250.7 788.9 2152.3 30B2 0.0 0.0 0.1 1.4 13.3 81.0 252.4 795.0 2169.0 30B3 0.0 0.0 0.1 1.4 13.2 80.8 252.1 794.5 2166.8

[0147] [Table 7]

[0148] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 1B 0.0 0.0 0.2 2.2 20.9 91.6 309.5 987.9 2673.2 2B 0.0 0.0 0.2 2.2 18.5 103.3 337.3 1033.0 2779.9 3B 0.0 0.0 0.2 2.2 20.6 114.3 360.7 1144.8 3074.4 4B 0.0 0.0 0.2 2.2 19.7 106.7 345.5 1072.0 2878.7 5B 0.0 0.0 0.2 2.2 19.5 109.4 356.0 1108.4 2930.1 6B 0.0 0.0 0.2 2.2 19.2 110.1 359.4 1116.9 2971.8 7B 0.0 0.0 0.2 2.2 19.0 109.1 356.8 1105.1 2942.3 8B 0.0 0.0 0.2 2.2 18.8 107.2 350.5 1081.7 2870.1 9B 0.0 0.0 0.2 2.2 18.6 105.1 343.0 1055.8 2802.9 10B 0.0 0.0 0.2 2.2 20.3 109.4 348.4 1083.8 2950.2 11B 0.0 0.0 0.2 2.2 20.0 113.7 363.6 1135.4 2998.7 12B 0.0 0.0 0.2 2.2 19.6 115.0 370.5 1156.6 3086.2 13B 0.0 0.0 0.2 2.2 19.2 113.6 368.8 1148.8 3094.5 14B 0.0 0.0 0.2 2.2 18.9 110.3 359.4 1114.5 2984.7 15B 0.0 0.0 0.2 2.2 18.6 106.4 346.9 1069.2 2832.1 16B 0.0 0.0 0.2 2.2 18.5 104.4 340.8 1048.6 2781.0 17B 0.0 0.0 0.2 2.2 18.6 105.7 344.9 1062.3 2820.4 18B 0.0 0.0 0.2 2.2 18.7 107.2 349.7 1079.3 2885.2 19B 0.0 0.0 0.2 2.2 18.8 108.8 355.0 1093.6 2906.3 20B 0.0 0.0 0.2 2.2 18.9 110.5 360.6 1113.6 2992.7 21B 0.0 0.0 0.2 2.2 19.0 112.2 365.9 1138.1 3097.1 22B 0.0 0.0 0.2 2.2 19.1 113.9 370.8 1155.8 3112.7 23B 0.0 0.0 0.2 2.2 19.2 115.4 375.1 1167.1 3128.4 24B 0.0 0.0 0.2 2.2 19.3 116.7 378.6 1181.2 3228.5 25B 0.0 0.0 0.2 2.2 19.5 117.9 381.5 1197.2 3250.8 26B 0.0 0.0 0.2 2.2 19.6 118.9 383.5 1200.3 3207.4 27B 0.0 0.0 0.2 2.2 19.7 119.6 384.8 1204.1 3298.6 28B 0.0 0.0 0.2 2.2 19.8 120.2 385.4 1209.3 3310.5 29B 0.0 0.0 0.2 2.2 20.0 120.5 385.4 1213.2 3330.6 30B 0.0 0.0 0.2 2.2 20.1 120.7 384.9 1209.9 3301.3 31B 0.0 0.0 0.2 2.2 20.2 120.7 383.8 1207.4 3245.1 32B 0.0 0.0 0.2 2.2 20.3 120.5 382.4 1203.8 3241.5 33B 0.0 0.0 0.2 2.2 20.4 120.2 380.5 1202.6 3311.7 34B 0.0 0.0 0.2 2.2 20.5 119.7 378.2 1197.5 3293.6 35B 0.0 0.0 0.2 2.2 20.6 119.1 375.6 1189.1 3251.2 36B 0.0 0.0 0.2 2.2 20.6 118.3 372.5 1176.5 3169.4 37B 0.0 0.0 0.2 2.2 20.6 117.2 368.8 1166.5 3126.9 38B 0.0 0.0 0.2 2.2 20.7 116.0 365.0 1156.0 3119.4 27B1 0.0 0.0 0.2 2.1 18.8 102.1 337.5 1054.9 2876.6 27B2 0.0 0.0 0.2 2.2 18.3 94.7 318.4 986.3 2674.7

[0149] [Table 8]

[0150] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 2B1 0.0 0.0 0.2 2.2 20.0 121.8 398.1 1238.0 3336.5 2B2 0.0 0.0 0.2 2.2 20.2 121.4 398.0 1238.8 3376.8 2B3 0.0 0.0 0.2 2.2 20.1 117.3 386.8 1205.2 3247.6 18B1 0.0 0.0 0.2 2.2 20.3 127.3 411.5 1287.5 3472.2 18B2 0.0 0.0 0.2 2.2 20.6 129.4 417.7 1309.4 3535.3 18B3 0.0 0.0 0.2 2.2 20.5 126.2 409.3 1283.5 3456.6 21B1 0.0 0.0 0.2 2.2 20.5 129.5 415.3 1303.8 3584.3 21B2 0.0 0.0 0.2 2.2 20.9 134.0 427.3 1344.8 3703.9 21B3 0.0 0.0 0.2 2.2 20.9 132.8 424.0 1334.8 3672.7 24B1 0.0 0.0 0.2 2.2 20.6 129.5 412.5 1292.8 3537.2 24B2 0.0 0.0 0.2 2.2 21.1 134.6 425.9 1339.1 3679.5 24B3 0.0 0.0 0.2 2.2 21.1 135.6 428.3 1347.3 3699.5 27B3 0.0 0.0 0.2 2.2 20.7 128.4 406.7 1275.5 3500.2 27B4 0.0 0.0 0.2 2.2 21.1 132.6 417.6 1311.6 3602.7 27B5 0.0 0.0 0.2 2.2 21.2 134.4 422.3 1328.7 3657.0 30B1 0.0 0.0 0.2 2.2 20.8 126.6 398.9 1255.5 3426.2 30B2 0.0 0.0 0.2 2.2 21.1 129.2 405.7 1277.6 3487.8 30B3 0.0 0.0 0.2 2.2 21.2 130.6 409.6 1291.1 3524.0

[0151] Fig.26 This is a diagram showing the current distribution in the conductor cross section of the models No. 1B to 15B when the frequency is 100 kHz. Fig. 27 This is a diagram showing the current distribution in the conductor cross section of the models No. 16B to 30B when the frequency is 100 kHz. Fig.28 It is a diagram showing the current distribution in the conductor cross section of the models No. 31B to 38B, 27B1, and 27B2 at a frequency of 100 kHz. Fig.29 It is a diagram showing the current distribution in the conductor cross section of the models No. 2B1 to 2B3, 18B1 to 18B3, and 21B1 to 21B3 when the frequency is 100 kHz. Fig.30 It is a diagram showing the current distribution in the conductor cross section of the models No. 24B1 to 24B3, 27B3 to 27B5, and 30B1 to 30B3 when the frequency is 100 kHz. Figure 26 to Figure 30 The current distribution when the coil diameter d of each model is set to 50 mm is shown. Figure 26 to Figure 30 The current distribution in the conductor cross section where the central axis 2 exists on the left is shown.

[0152] Fig.31 This is a graph showing the Q value of each model in the second embodiment when the coil diameter d is 50 mm and the frequency is 100 kHz. Fig.32 Graph showing the Q value of each model in Embodiment 2 when the coil diameter d is 100 mm and the frequency is 100 kHz. Fig.31 and Fig.32 In the figure, the horizontal axis represents the center angle θs, angles θv, θu, and the vertical axis represents the Q value. Fig.31 and Fig.32 In the figure, the point where θs=360° shows the value obtained from the model corresponding to the coil of the eighth reference example. In addition, the point where θs=0° and the points where θv and θu=180° show the values ​​obtained from the model corresponding to the coil of the seventh reference example or the eleventh reference example.

[0153] As in the first embodiment, the Q values ​​of the models No. 4B to 38B corresponding to the coils of the fourth to sixth embodiments are considered to be higher than the model No. 1B corresponding to the sixth reference example in which the cross-sectional shape of the conductor is circular.

[0154] In addition, it can be observed that the Q value of the model No. 16B to 38B corresponding to the coil (arc shape) of the fourth embodiment is higher than the Q value of the model No. 4B to 15B corresponding to the coil (V-shaped and U-shaped) of the fifth and sixth embodiments.

[0155] Models No. 27B, 27B1, and 27B2 all correspond to coils having arc-shaped conductors with θs = 180°. However, it can be considered that the Q value of model No. 27B corresponding to the coil of the fourth embodiment is higher than that of models No. 27B1 and 27B2 corresponding to the coils of the ninth and tenth reference examples.

[0156] According to the simulation results of the model corresponding to the coil having an arc-shaped conductor, it can be considered that the Q value depends on the center angle θs. Specifically, when the coil diameter d is 50 mm, the Q value becomes higher when the center angle θs is 15° to 330°, and the Q value becomes higher when the center angle θs is 60° to 285°, and the Q value becomes higher when the center angle θs is 90° to 240°, and the Q value becomes higher when the center angle θs is 105° to 240°. When the coil diameter d is 100 mm, the Q value becomes higher when the center angle θs is 60° to 345°, and the Q value becomes higher when the center angle θs is 120° to 345°, and the Q value becomes higher when the center angle θs is 180° to 300°.

[0157] Furthermore, it is considered that the Q value is significantly increased by inclining the reference straight lines 18a and 18b of the first portion 1a and the second portion 1b of the electric wire 1 wound around the first section 3a and the second section 3b located at both ends of the target section 3 of the central axis 2. Fig. 27 and Fig.28 As shown in FIG. 1 , in the conductor of the first portion 1a at the upper end, the current tends to concentrate on the upper side. On the other hand, in the conductor of the second portion 1b at the lower end, the current tends to concentrate on the lower side. Fig.29 and Fig.30 As shown, by inclining the posture of the conductor in a direction where the current is likely to concentrate, it is possible to suppress the unevenness of the current in the conductor.

[0158] According to the simulation results of the model corresponding to the coil having a V-shaped conductor, it can be considered that the Q value depends on the angle θv. When the coil diameter d is 50 mm, the Q value becomes higher when the angle θv is 120° to 165°. When the coil diameter d is 100 mm, the Q value becomes higher when the angle θv is 90° to 165°, and the Q value becomes higher when the angle θv is 90° to 150°, and the Q value becomes higher when the angle θv is 105° to 135°.

[0159] According to the simulation results of the model corresponding to the coil having a U-shaped conductor, it can be considered that the Q value depends on the angle θu. When the coil diameter d is 50 mm, the Q value becomes higher when the angle θu is 105° to 165°, and the Q value becomes higher when the angle θu is 120° to 165°, and the Q value becomes higher when the angle θu is 120° to 150°. When the coil diameter d is 100 mm, the Q value becomes higher when the angle θu is 90° to 165°, and the Q value becomes higher when the angle θu is 90° to 150°, and the Q value becomes higher when the angle θu is 105° to 135°.

[0160] <Implementation method 3>

[0161] Fig.33 : is a three-dimensional diagram of the appearance of the coil involved in the third embodiment. Fig.33 As shown, the coil 100C according to the third embodiment is different from the coil 100B according to the second embodiment in that the distance between the central axis 2 and the electric wire 1 increases or decreases along the central axis 2. Fig.33 In the example shown, the distance between the central axis 2 and the electric wire 1 increases as the distance between the central axis 2 and the electric wire 1 increases. Fig.33 As shown, the coil diameter d is the diameter of the portion of the electric wire 1 that is wound closest to the central axis 2 .

[0162] Fig.34 is a cross-sectional view showing a coil of the eighth embodiment. The coil 100C of the eighth embodiment is obtained by applying the structure of the third embodiment to Fig.16 The coil 100B of the fourth embodiment shown in FIG. Fig.34 As shown, the coil 100C of the eighth embodiment is different from the coil 100B of the fourth embodiment only in that the distance between the central axis 2 and the electric wire 1 is increased by a pitch P2 while the electric wire 1 is spirally wound once around the central axis 2 .

[0163] Similarly, by applying the structure of Embodiment 3 to Figure 17 to Figure 19 The coils 100B of the fifth to seventh embodiments shown in the figure are combined to obtain the coils of the ninth to eleventh embodiments (not shown). That is, the coil 100C of the ninth embodiment and the coil 100B of the fifth embodiment (see Fig.17) is different from the coil 100B of the sixth embodiment only in that the distance between the central axis 2 and the electric wire 1 is increased by a pitch P2 during the period in which the electric wire 1 is spirally wound around the central axis 2. Fig.18 ) is different from the coil 100B of the seventh embodiment only in that the distance between the central axis 2 and the electric wire 1 is increased by a pitch P2 during the period of spirally winding the electric wire 1 around the central axis 2. Fig.19 ) is different only in that the distance between the central axis 2 and the electric wire 1 becomes larger by a pitch P2 during the period in which the electric wire 1 is spirally wound around the central axis 2 once.

[0164] (simulation)

[0165] The models of each of a plurality of coils having different conductor cross-sectional shapes were evaluated using the same method as in the second embodiment.

[0166] The evaluation object models include models corresponding to coils 100C of the eighth to eleventh embodiments and models corresponding to coils of the twelfth to seventeenth reference examples (not shown). The coils of the twelfth to seventeenth reference examples are obtained by applying the structure of the third embodiment to the coils of the twelfth to seventeenth reference examples. Figure 20 to Figure 25 That is, the coils of the twelfth to seventeenth reference examples are different from the coils of the sixth to eleventh reference examples respectively in that the distance between the center axis 2 and the electric wire 1 is increased by a pitch P2 during the period in which the electric wire 1 is spirally wound around the center axis 2 for one turn.

[0167] The models to be evaluated include models No. 1C to 38C, 2C1 to 2C3, 18C1 to 18C3, 21C1 to 21C3, 25C1 to 25C3, 27C1 to 27C5, and 29C1 to 29C3. The models of No.1C to 38C, 2C1 to 2C3, 18C1 to 18C3, 21C1 to 21C3, 25C1 to 25C3, 27C1 to 27C5, 29C1 to 29C3 are different from the above-mentioned models of No.1B to 38B, 2B1 to 2B3, 18B1 to 18B3, 21B1 to 21B3, 25B1 to 25B3, 27B1 to 27B5, 29B1 to 29B3 only in that the distance between the center axis 2 and the electric wire 1 becomes larger by a pitch P2 while the electric wire 1 is spirally wound around the center axis 2 once.

[0168] That is, the model of No. 1C corresponds to the coil of the twelfth reference example having a conductor with a cross-sectional shape of No. 1 shown in Table 2. The model of No. 2C corresponds to the coil of the thirteenth reference example having a conductor with a cross-sectional shape of No. 2. The model of No. 3C corresponds to the coil of the fourteenth reference example having a conductor with a cross-sectional shape of No. 3. The models of No. 4C to 9C correspond to the coil 100C of the ninth embodiment having conductors with cross-sectional shapes of No. 4 to 9, respectively. The models of No. 10C to 15C correspond to the coil 100C of the tenth embodiment having conductors with cross-sectional shapes of No. 10 to 15, respectively. The models of No. 16C to 38C correspond to the coil 100C of the eighth embodiment having conductors with cross-sectional shapes of No. 16 to 38, respectively. The model of No. 27C1 corresponds to the coil of the fifteenth reference example having a conductor with a cross-sectional shape of No. 27. The model of No. 27C2 corresponds to the coil of the sixteenth reference example having a conductor with a cross-sectional shape of No. 27.

[0169] The models No. 2C1 to 2C3 correspond to the coil of the seventeenth reference example having the conductor having the cross-sectional shape of No. 2, and the angles formed by the reference straight lines 18a and 18b and the normal to the central axis 2 are The coils are designed to have angles of 30°, 45°, and 60°, respectively. The models No. 18C1 to 18C3 correspond to the coil 100C of the eleventh embodiment having a conductor with a cross-sectional shape of No. 18, and the angles formed by the reference straight lines 18a, 18b and the normal to the central axis 2 are The coils 100C are designed to be 30°, 45°, and 60°, respectively. The models No. 21C1 to 21C3 correspond to the coils 100C of the eleventh embodiment having the conductor having the cross-sectional shape of No. 21, and the angles formed by the reference straight lines 18a and 18b and the normal to the central axis 2 are The coils 100C are designed to have angles of 30°, 45°, and 60°, respectively. The models No. 24C1 to 24C3 correspond to the coils 100C of the eleventh embodiment having the conductor having the cross-sectional shape of No. 24, and the angles formed by the reference straight lines 18a and 18b and the normal to the central axis 2 are The coils 100C are designed to be 30°, 45°, and 60°, respectively. The models No. 27C3 to 27C5 correspond to the coils 100C of the eleventh embodiment having the conductor having the cross-sectional shape of No. 27, and the angles formed by the reference straight lines 18a, 18b and the normal to the central axis 2 are The coils 100C are designed to have angles of 30°, 45°, and 60°, respectively. The models No. 30C1 to 30C3 correspond to the coils 100C of the eleventh embodiment having a conductor with a cross-sectional shape of No. 30, and the angles formed by the reference straight lines 18a and 18b and the normal to the central axis 2 are The coils 100C are designed to have angles of 30°, 45°, and 60° respectively.

[0170] In each model, the pitch P1 between the wound electric wires 1 (refer to Fig.34 ) is set to 6mm and the pitch P2 is set to 3mm.

[0171] The simulation results when the coil diameter d of each model was 50 mm are shown in Tables 9 and 10. The simulation results when the coil diameter d of each model was 100 mm are shown in Tables 11 and 12. Tables 9 to 12 show the Q value at each frequency.

[0172] [Table 9]

[0173] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 1C 0.0 0.0 0.2 1.8 17.1 74.2 250.2 797.9 2158.2 2C 0.0 0.0 0.2 1.7 15.7 89.9 294.1 912.0 2463.0 3C 0.0 0.0 0.2 1.8 16.7 92.0 289.6 918.0 2462.8 4C 0.0 0.0 0.2 1.8 16.4 88.1 281.9 874.3 2350.8 5C 0.0 0.0 0.2 1.8 16.3 91.3 293.4 915.0 2418.5 6C 0.0 0.0 0.2 1.8 16.2 93.3 300.6 937.4 2499.8 7C 0.0 0.0 0.2 1.7 16.1 94.0 303.7 947.4 2537.2 8C 0.0 0.0 0.2 1.7 16.0 93.4 302.8 943.9 2518.7 9C 0.0 0.0 0.2 1.7 15.8 92.0 299.2 931.9 2488.6 10C 0.0 0.0 0.2 1.8 16.8 88.4 279.4 867.6 2366.3 11C 0.0 0.0 0.2 1.8 16.6 92.7 293.8 916.8 2423.5 12C 0.0 0.0 0.2 1.8 16.4 95.2 303.3 947.8 2533.5 13C 0.0 0.0 0.2 1.8 16.2 96.0 307.5 961.7 2600.6 14C 0.0 0.0 0.2 1.7 16.1 95.4 307.4 960.1 2574.4 15C 0.0 0.0 0.2 1.7 15.9 93.3 302.4 942.9 2507.7 16C 0.0 0.0 0.2 1.7 15.8 91.4 297.6 927.3 2473.6 17C 0.0 0.0 0.2 1.7 15.9 92.8 301.6 940.4 2511.4 18C 0.0 0.0 0.2 1.7 15.9 94.0 304.3 949.4 2549.5 19C 0.0 0.0 0.2 1.7 16.0 95.2 307.7 957.5 2557.6 20C 0.0 0.0 0.2 1.7 16.1 96.0 309.6 963.8 2596.6 21C 0.0 0.0 0.2 1.7 16.1 96.8 311.6 976.1 2669.6 22C 0.0 0.0 0.2 1.7 16.2 97.5 313.2 981.9 2658.1 23C 0.0 0.0 0.2 1.7 16.3 97.9 314.1 982.1 2636.7 24C 0.0 0.0 0.2 1.8 16.3 98.3 314.5 984.8 2707.6 25C 0.0 0.0 0.2 1.8 16.4 98.6 314.7 989.3 2691.0 26C 0.0 0.0 0.2 1.8 16.4 98.7 314.7 986.2 2638.8 27C 0.0 0.0 0.2 1.8 16.5 98.8 314.4 985.0 2702.4 28C 0.0 0.0 0.2 1.8 16.5 98.9 313.9 985.9 2704.4 29C 0.0 0.0 0.2 1.8 16.6 98.8 313.0 985.4 2707.1 30C 0.0 0.0 0.2 1.8 16.6 98.6 312.0 980.5 2675.3 31C 0.0 0.0 0.2 1.8 16.7 98.4 310.7 976.5 2628.0 32C 0.0 0.0 0.2 1.8 16.7 98.0 309.0 972.1 2621.7 33C 0.0 0.0 0.2 1.8 16.7 97.4 306.7 969.0 2668.3 34C 0.0 0.0 0.2 1.8 16.8 97.0 305.0 965.6 2659.1 35C 0.0 0.0 0.2 1.8 16.8 96.3 302.4 956.6 2609.1 36C 0.0 0.0 0.2 1.8 16.8 95.5 299.6 945.6 2547.5 37C 0.0 0.0 0.2 1.8 16.8 94.5 296.4 937.1 2512.0 38C 0.0 0.0 0.2 1.8 16.8 93.4 293.1 927.8 2501.9 27C1 0.0 0.0 0.2 1.7 14.7 79.6 262.3 817.4 2222.0 27C2 0.0 0.0 0.2 1.8 15.0 74.1 249.8 772.5 2089.0

[0174] [Table 10]

[0175] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 2C1 0.0 0.0 0.2 1.7 16.2 95.6 312.5 972.3 2614.6 2C2 0.0 0.0 0.2 1.7 16.1 93.5 306.4 952.9 2587.0 2C3 0.0 0.0 0.2 1.7 15.8 89.2 293.4 912.5 2452.1 18C1 0.0 0.0 0.2 1.7 16.5 101.7 328.3 1027.7 2769.3 18C2 0.0 0.0 0.2 1.7 16.4 99.8 322.5 1009.5 2717.6 18C3 0.0 0.0 0.2 1.7 16.1 95.3 309.2 966.5 2593.9 21C1 0.0 0.0 0.2 1.8 16.8 105.3 336.3 1057.6 2908.4 21C2 0.0 0.0 0.2 1.7 16.7 104.2 333.1 1047.7 2877.4 21C3 0.0 0.0 0.2 1.7 16.4 100.2 321.4 1009.2 2759.3 24C1 0.0 0.0 0.2 1.8 16.9 106.1 336.1 1055.1 2892.8 24C2 0.0 0.0 0.2 1.7 16.9 105.9 335.5 1054.0 2891.4 24C3 0.0 0.0 0.2 1.7 16.6 103.0 327.2 1027.3 2820.0 27C3 0.0 0.0 0.2 1.8 17.0 104.7 330.0 1036.1 2846.0 27C4 0.0 0.0 0.2 1.8 17.0 105.2 331.3 1040.3 2855.5 27C5 0.0 0.0 0.2 1.8 16.8 103.5 326.5 1025.5 2815.5 30C1 0.0 0.0 0.2 1.8 17.0 102.3 321.2 1010.9 2758.1 30C2 0.0 0.0 0.2 1.8 17.0 103.0 323.2 1017.7 2777.6 30C3 0.0 0.0 0.2 1.8 16.9 102.3 321.3 1011.8 2761.5

[0176] [Table 11]

[0177] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 1C 0.0 0.0 0.2 2.4 22.9 101.3 343.1 1095.9 2965.6 2C 0.0 0.0 0.2 2.4 20.8 120.7 402.1 1249.9 3389.7 3C 0.0 0.0 0.2 2.4 22.7 127.4 402.8 1279.3 3436.6 4C 0.0 0.0 0.2 2.4 21.9 119.9 390.4 1215.5 3265.9 5C 0.0 0.0 0.2 2.4 21.7 123.3 403.4 1260.8 3337.6 6C 0.0 0.0 0.2 2.4 21.5 125.0 410.6 1282.9 3423.4 7C 0.0 0.0 0.2 2.4 21.4 125.3 413.3 1290.6 3444.7 8C 0.0 0.0 0.2 2.4 21.2 124.6 412.2 1287.0 3432.3 9C 0.0 0.0 0.2 2.4 21.0 122.9 408.2 1273.4 3396.4 10C 0.0 0.0 0.2 2.4 22.4 120.7 386.0 1202.4 3279.8 11C 0.0 0.0 0.2 2.4 22.1 125.6 403.8 1262.9 3342.8 12C 0.0 0.0 0.2 2.4 21.9 128.1 414.7 1298.2 3469.4 13C 0.0 0.0 0.2 2.4 21.6 128.4 419.0 1312.3 3545.1 14C 0.0 0.0 0.2 2.4 21.3 127.0 417.7 1306.7 3503.1 15C 0.0 0.0 0.2 2.4 21.0 124.3 411.6 1285.2 3418.7 16C 0.0 0.0 0.2 2.4 20.9 122.3 406.6 1268.8 3380.5 17C 0.0 0.0 0.2 2.4 21.0 123.8 410.7 1282.9 3421.7 18C 0.0 0.0 0.2 2.4 21.1 125.3 414.4 1295.4 3475.4 19C 0.0 0.0 0.2 2.4 21.2 126.6 417.8 1301.4 3473.2 20C 0.0 0.0 0.2 2.4 21.3 127.7 420.7 1311.8 3539.6 21C 0.0 0.0 0.2 2.4 21.4 128.8 423.2 1327.2 3621.8 22C 0.0 0.0 0.2 2.4 21.5 129.8 425.3 1334.5 3604.5 23C 0.0 0.0 0.2 2.4 21.6 130.6 427.0 1336.7 3589.9 24C 0.0 0.0 0.2 2.4 21.7 131.4 428.3 1341.7 3682.9 25C 0.0 0.0 0.2 2.4 21.8 132.1 429.3 1351.1 3672.6 26C 0.0 0.0 0.2 2.4 21.9 132.7 430.0 1348.8 3611.6 27C 0.0 0.0 0.2 2.4 22.0 133.1 430.1 1349.0 3700.3 28C 0.0 0.0 0.2 2.4 22.1 133.5 430.2 1352.1 3716.8 29C 0.0 0.0 0.2 2.4 22.2 133.8 429.9 1354.6 3715.7 30C 0.0 0.0 0.2 2.4 22.3 134.0 429.3 1350.7 3687.3 31C 0.0 0.0 0.2 2.4 22.4 134.0 428.2 1348.2 3633.5 32C 0.0 0.0 0.2 2.4 22.5 133.9 426.7 1344.2 3622.1 33C 0.0 0.0 0.2 2.4 22.5 133.7 424.8 1343.1 3698.3 34C 0.0 0.0 0.2 2.4 22.6 133.2 422.4 1338.5 3683.6 35C 0.0 0.0 0.2 2.4 22.7 132.6 419.5 1330.0 3639.4 36C 0.0 0.0 0.2 2.4 22.7 131.8 416.0 1315.3 3550.0 37C 0.0 0.0 0.2 2.4 22.8 130.7 412.0 1304.5 3498.6 38C 0.0 0.0 0.2 2.4 22.8 129.2 407.5 1292.3 3491.3 27C1 0.0 0.0 0.2 2.4 20.6 114.1 378.0 1181.7 3223.1 27C2 0.0 0.0 0.2 2.4 20.4 106.2 358.9 1114.8 3032.9

[0178] [Table 12]

[0179] No. 1Hz 10Hz 100Hz 1kHz 10kHz 100kH 1MHz 10MHz 100MH 2Cl 0.0 0.0 0.2 2.4 21.7 128.9 428.4 1334.6 3613.2 2C2 0.0 0.0 0.2 2.4 21.8 128.8 427.9 1332.5 3628.6 2C3 0.0 0.0 0.2 2.4 21.6 125.5 417.4 1300.4 3529.1 18C1 0.0 0.0 0.2 2.4 22.0 136.1 447.0 1401.5 3775.9 18C2 0.0 0.0 0.2 2.4 22.2 136.7 448.3 1406.3 3791.2 18C3 0.0 0.0 0.2 2.4 22.0 133.6 438.6 1375.4 3697.5 21C1 0.0 0.0 0.2 2.4 22.4 141.0 458.1 1441.9 3956.2 21C2 0.0 0.0 0.2 2.4 22.5 142.3 461.4 1453.3 3985.8 21C3 0.0 0.0 0.2 2.4 22.4 139.8 453.8 1428.9 3910.1 24C1 0.0 0.0 0.2 2.4 22.6 143.0 460.4 1446.4 3967.8 24C2 0.0 0.0 0.2 2.4 22.8 144.9 465.1 1463.2 4021.8 24C3 0.0 0.0 0.2 2.4 22.7 143.4 460.4 1448.3 3978.0 27C3 0.0 0.0 0.2 2.4 22.8 142.5 455.3 1430.8 3930.3 27C4 0.0 0.0 0.2 2.4 22.9 144.5 460.5 1447.9 3976.3 27C5 0.0 0.0 0.2 2.4 22.9 144.0 458.6 1442.4 3959.7 30C1 0.0 0.0 0.2 2.4 22.9 140.4 445.7 1404.6 3838.3 3()C2 0.0 0.0 0.2 2.4 23.0 142.1 450.1 1419.4 3877.6 30C3 0.0 0.0 0.2 2.4 23.0 142.2 450.1 1419.9 3879.3

[0180] Fig.35 This is a graph showing the Q value of each model in the third embodiment when the coil diameter d is 50 mm and the frequency is 100 kHz. Fig.36 Graph showing the Q value of each model in Embodiment 3 when the coil diameter d is 100 mm and the frequency is 100 kHz. Fig.35 and Fig.36 In the figure, the horizontal axis represents the center angle θs, angles θv, θu, and the vertical axis represents the Q value. Fig.35 and Fig.36 In FIG. 1 , the point where θs=360° shows the value obtained from the model corresponding to the coil of the thirteenth reference example. In addition, the point where θs=0° and the points where Qv and θu=180° show the values ​​obtained from the model corresponding to the coil of the thirteenth reference example or the seventeenth reference example.

[0181] As in the first embodiment, it is considered that the Q values ​​of the models No. 4C to 38C corresponding to the coils of the eighth to tenth embodiments are higher than the model No. 1C corresponding to the twelfth reference example in which the cross-sectional shape of the conductor is circular.

[0182] In addition, it can be observed that the Q values ​​of the models No. 16C to 38C corresponding to the coils (arc shape) of the fourth embodiment are higher than the Q values ​​of the models No. 4C to 15C corresponding to the coils (V-shaped and U-shaped) of the ninth and tenth embodiments.

[0183] Models No. 27C, 27C1, and 27C2 all correspond to coils having arc-shaped conductors with θs = 180°. However, it can be considered that the Q value of model No. 27C corresponding to the coil of the eighth embodiment is higher than that of models No. 27C1 and 27C2 corresponding to the coils of the fifteenth and sixteenth reference examples.

[0184] According to the simulation results of the model corresponding to the coil having an arc-shaped conductor, it can be considered that the Q value depends on the center angle θs. Specifically, when the coil diameter d is 50 mm, the Q value becomes higher when the center angle θs is 60° to 345°, the Q value becomes higher when the center angle θs is 90° to 300°, and the Q value becomes higher when the center angle θs is 120° to 255°. When the coil diameter d is 100 mm, the Q value becomes higher when the center angle θs is 60° to 345°, the Q value becomes higher when the center angle θs is 90° to 345°, the Q value becomes higher when the center angle θs is 120° to 330°, and the Q value becomes particularly high when the center angle θs is 180° to 300°.

[0185] Furthermore, it is considered that the Q value is significantly increased by inclining the reference straight lines 18a and 18b of the first and second portions 1a and 1b of the electric wire 1 wound around the first and second sections 3a and 3b located at both ends of the target section 3 of the central axis 2.

[0186] According to the simulation results of the model corresponding to the coil having the V-shaped conductor, it is considered that the Q value depends on the angle θv. The Q value is high when the angle θv is 105° to 165°, and the Q value is further high when the angle θv is 120° to 150°.

[0187] According to the simulation results of the model corresponding to the coil having the U-shaped conductor, it is considered that the Q value depends on the angle θu. The Q value is high when the angle θu is 105° to 165°, and the Q value is further high when the angle θu is 120° to 150°.

[0188] <Modification>

[0189] In the above description, arc, V, and U shapes are shown as the cross-sectional shape 11 of the conductor 10, but the cross-sectional shape 11 is not limited to these shapes. For example, the cross-sectional shape 11 of the conductor 10 may have three or more bent portions in a manner such that the first end 12 and the second end 13 are away from the central axis 2. As the number of bent portions increases and approaches an arc shape, it is difficult to generate uneven current, so the number of bent portions is preferably large. In this case, the outer side of the bent portion is preferably chamfered.

[0190] <Application Examples>

[0191] The coils 100A to 100C involved in the above-mentioned embodiments 1 to 3 can be applied as magnetic field coupling type wireless power supply coils. As magnetic field coupling type wireless power supply coils, for example, relatively small wearable device charging coils, smartphone charging coils, and relatively large electric vehicle battery charging coils can be listed. In addition, in such contactless power supply coils, AC currents of 85kHz, 6.78MHz, 13.56MHz, etc. usually flow, and the coils 100A to 100C of this embodiment can be applied to the use of AC currents above 10kHz or above 100kHz.

[0192] In addition, the coils 100A to 100C involved in the above-mentioned embodiments 1 to 3 can be applied as resonant coils for electric field resonance coupling type wireless power supply. As the application of electric field resonance coupling type wireless power supply, electric vehicles and trams can be listed. In such electric field resonance coupling type wireless power supply, an alternating current of 6.78MHz, 13.56MHz, 27.12MHz, etc. usually flows. The coils 100A to 100C of this embodiment can be applied to the use of an alternating current of 10kHz or more or 100kHz or more. The resonant coil for electric field resonance coupling type wireless power supply refers to a coil inserted in an electrical circuit including a power transmission coupler on the power transmitting side or the power receiving side of the electric field coupling type wireless power supply in order to improve the power factor and produce a resonant state.

[0193] The invention is not limited to magnetic field coupling type wireless power supply coils and electric field resonance coupling type wireless power supply resonant coils. In particular, in high frequency applications where the resistance of a Litz wire, which is usually used as a coil wire, increases, or in small applications where it is difficult to use a Litz wire, the coils 100A to 100C according to the above-mentioned embodiments 1 to 3 can be appropriately used instead of a coil using a Litz wire. "High frequency" refers to a frequency preferably of 1 MHz or more, and more preferably of 5 MHz or more.

[0194] The embodiments disclosed this time should be considered in all respects as illustrative and not restrictive. The scope of the present invention is indicated by the claims rather than the above description, and is intended to include all modifications within the meaning and scope equivalent to the claims.

[0195] Description of Reference Numerals

[0196] 1…electric wire; 1a…first section; 1b…second section; 1c…third section; 2…central axis; 3…object section; 3a…first section; 3b…second section; 3c…third section; 10…conductor; 11, 11a to 11f…cross-sectional shape; 12…first end; 13…second end; 14…first edge; 15…second edge; 16…center point; 17…line segment; 18, 18a to 18c…reference straight line; 20 to 22…bend portion; 30…insulating material; 40a to 40c…intersection; 100A to 100C…coil.

Claims

1. A coil, wherein: The electric wire is wound once or multiple times in a spiral shape around a central axis. The electric wire includes a conductor having an elongated cross-sectional shape on a plane including the central axis. The cross-sectional shape is curved such that a first end and a second end in a longitudinal direction are away from the central axis.

2. The coil according to claim 1, wherein When a straight line that passes through the center point of the cross-sectional shape and is orthogonal to a line segment connecting the first end and the second end is set as a reference straight line, the cross-sectional shape is line-symmetric with respect to the reference straight line.

3. The coil according to claim 2, wherein: The reference straight line is orthogonal to the central axis.

4. The coil according to claim 1, wherein The electric wire is spirally wound three or more times around the target section of the central axis, The wire has: A first portion is wound around a first section located on one end side of the target section; a second portion wound around a second section located on the other end side of the target section; and The third portion winds around a third section of the target section located between the first section and the second section. When a straight line passing through the center point of the cross-sectional shape and being orthogonal to a line segment connecting the first end and the second end is set as a reference straight line, The reference straight line in the third portion is orthogonal to the central axis, The reference straight line in the first portion is inclined in a direction away from the intersection point with the central axis relative to the reference straight line corresponding to the third portion. The reference straight line in the second portion is inclined in a direction in which an intersection point with the central axis is separated from the reference straight line corresponding to the third portion.

5. The coil according to any one of claims 1 to 4, wherein: The electric wire is spirally wound more than two times, The distance between the central axis and the electric wire increases or decreases along the central axis.

6. The coil according to any one of claims 1 to 4, wherein: This is a coil for magnetic field coupling type wireless power supply.

7. The coil according to any one of claims 1 to 4, wherein: This is a resonant coil for electric field resonance coupling type wireless power supply.

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