Patent Publication Number: US-10775195-B2

Title: Rotation angle sensing device

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     The present application is based on and claims the benefit of priority of Japanese Patent Application No. 2016-48621, filed on Mar. 11, 2016, the disclosure of which is incorporated herein by reference. 
     TECHNICAL FIELD 
     The present invention relates to a rotation angle sensing device for detecting a rotation angle of a rotating body. 
     BACKGROUND 
     Conventionally, a rotation angle sensing device for detecting a rotation angle of a rotating body is used for various purposes. One such rotation angle sensing device is provided with a magnet, which is fixed to rotate with a rotating body, and a magnetic sensor element for detecting a change in intensity of a magnetic field in association with the rotation of the magnet. In such rotation angle sensing device, the magnetic sensor element outputs a signal indicating a relative positional relationship between the rotating body and the magnetic sensor element. 
     A known conventional rotation angle sensing device, as shown in  FIG. 23A  and  FIG. 23B , includes a magnet  200  that is disk-like and is supported by and fixed to a shaft S (rotary shaft) to allow a first surface  201  and a second surface  202  of the magnet  200  to be orthogonal to the shaft S (rotary shaft). A magnetic sensor element (Hall element)  300  is arranged immediately beneath an outer circumference of the second surface  202  of the magnet  200  and in a circumferential direction about the shaft S (rotary shaft) (see Patent Literature 1). 
     In the rotation angle sensing device, because shaft wobble occurs and causes the shaft S (rotary shaft) to minutely move, the magnet  200  supported by and fixed to the shaft S (rotary shaft) minutely moves in the radial direction. In the meantime, the magnetic sensor elements (Hall elements)  300  are arranged to measure magnetic flux density in a direction parallel to the shaft S (rotary shaft) at a corner portion of the outer circumference of the magnet  200 . Consequently, a measured value for the magnetic flux density that is measured by the magnetic sensor elements (Hall elements)  300  varies greatly in association with the minute movement of the magnet  200 , and an error in measurement of a rotation angle is accentuated. 
     Conventionally, as shown in  FIG. 24A  and  FIG. 24B , a rotation angle sensing device that is provided with a magnet  210 , which is supported by and fixed to the shaft S (rotary shaft), a first surface  211  and a second surface  212  opposed the first surface  211 , and magnetic sensor elements (Hall elements)  310  arranged immediately beneath an outer circumference of the magnet  210 . The magnet  210  has a chamfering part  213  (inclined surface) formed by eliminating corners of the outer circumference at the second surface  212  side. A portion of a detector plane in the magnetic sensor elements (Hall elements)  310  is positioned immediately beneath the chamfering part  213  (inclined surface) and a remainder is arranged to be positioned outside the outer circumference of the magnet  210  (see Patent Literature 2). 
     PRIOR ART LITERATURE 
     Patent Literature 
     
         
         [Patent Literature 1] JP Laid-Open Patent Application No. 2003-75108 
         [Patent Literature 2] International Publication No. 2008/050581 
       
    
     SUMMARY OF THE INVENTION 
     Problem to be Solved by the Invention 
     However, in the rotation angle sensing device described in Patent Literature 2 above, because the magnetic sensor elements  310  are configured to detect a magnetic field in a rotary shaft direction generated from the magnet  210 , the arrangement locations of the magnetic sensor elements  310 , which are optimum to minimize a detection error of the rotation angle, happen to fluctuate due to the inclination angle of the chamfering part  213  (inclined surface) of the magnet  210 . Consequently, there is a problem that the arrangement locations of the magnetic sensor elements  310  have to be fine-tuned according to the inclination angle of the chamfering part  213  (inclined surface) of the magnet  210 . In other words, unless the chamfering part  213  (inclined surface) of the magnet  210  is formed at a highly accurate inclination angle, and the magnetic sensor elements  310  are precisely arranged at appropriate positions, a detection error of the rotation angle becomes accentuated. 
     Further, in general, in order to reduce the size of the rotation angle sensing device, it is required to reduce the volume of the magnet; in the meantime, it is required to generate a magnetic field with an intensity that enables measurement of a change in the magnetic flux density by the magnetic sensor elements, from the magnet. In Patent Literature 2 above, since the chamfering part  213  (inclined surface) is formed at the outer circumference of the magnet  210 , even though the volume can be reduced compared to the magnet where the chamfering part  213  (inclined surface) is not formed, the magnetic field (magnetic field in a direction of the rotary shaft) that is generated toward the chamfering part  213  (inclined surface) from the magnet  210  becomes weaker. However, since the magnet  210  has to generate the magnetic field with an intensity that is strong enough to enable the magnetic sensor elements  310  to measure a change in the magnetic flux density, it becomes difficult to simultaneously fulfill the demand to increase the intensity of the magnetic field and the demand to reduce the volume of the magnet, which conflict with each other. If the volume of the magnet is increased for the purpose of increasing the intensity of the magnetic field and the mass of the magnet  210  becomes relatively greater due to the volume increase, a moment of inertia in association with the rotation of the shaft S (rotary shaft) increases. As a result, it becomes difficult to control the shaft deviation, and it may cause an increase of the detection error of the rotation angle. In addition, because it is necessary to ensure the mass of the magnet  210  to some degree, there is also a problem in that the manufacturing cost of the rotation angle sensing device is increased. 
     In the rotation angle sensing device described in Patent Literature 2 above, the rotation angle is calculated using the intensity of the magnetic field (a magnetic field in a direction of a rotary shaft C) that is generated toward the chamfering part  213  (inclined surface) side of the magnet  210 . Then, when the magnetic sensor elements  310  are arranged in a very narrow region opposed to the chamfering part  213  (inclined surface) of the magnet  210 , the detecting error of the rotation angle becomes smaller. In addition, the relative position to the magnet  210  in the region happens to fluctuate according to the inclination angle of the chamfering part  213  (inclined surface). Consequently, in order to precisely detect the rotation angle by the rotation angle sensing device described in Patent Literature 2, the magnetic sensor elements  310  have to be precisely arranged in the region to fluctuate according to the inclination angle of the chamfering part  213  (inclined surface). Therefore, a detection error of the rotation angles increases due to the shaft deviation. 
     In view of the problem above, the present invention provides a rotation angle sensing device enabling accurate detection of a rotation angle based upon magnetic fields intensity in a radial direction and/or in a circumferential direction. 
     Means for Solving the Problem 
     In order to solve the problem above, the present invention provides a rotation angle sensing device that is provided with: 
     a magnet that is placed to be integrally rotatable with a rotary shaft of a rotating body in association with a rotation of the rotating body, and where its shape as viewed along the rotary shaft is substantially circular; 
     a magnetic sensor part that outputs a sensor signal based upon a change in a direction of a magnetic field in association with the rotation of the magnet; and 
     a rotation angle detecting part that detects a rotation angle of the rotating body based upon the sensor signal output by the magnetic sensor part, wherein 
     the magnet has a magnetization vector component in a direction that is orthogonal to the rotary shaft; and 
     when a circular virtual plane that is orthogonal to the rotary shaft centered upon the rotary shaft is set in the vicinity of the magnet, the magnetic sensor part is placed at a position where amplitudes of a magnetic field intensity H r  in the radial direction and a magnetic field intensity H θ  in the circumferential direction on the virtual plane are substantially the same, and a least one of the magnetic field intensity H r  in the radial direction and the magnetic field intensity H θ  in the circumferential direction is output as the sensor signal (Invention 1). 
     In the invention above (Invention 1), it is preferable that the magnet has a first surface that is substantially orthogonal to the rotary shaft and a second surface that opposes the first surface. A size of the second surface is such that the second surface physically includes the first surface when viewed along the axial direction of the rotary shaft. The magnetic sensor part is placed at a position that opposes the second surface of the magnet (Invention 2). 
     In the invention above (Invention 2), it is preferable that the magnetic sensor part is placed between a first line that is parallel to the rotary shaft and passes through an outer circumference part of the first surface and a second line that is parallel to the rotary shaft and passes through an outer circumference part of the second surface (Invention 3). 
     In the invention above (Invention 2), it is preferable that the magnet includes a base portion, which comprises the second surface, and a convex portion that has the first surface and that protrudes toward the first surface from the base portion (Invention 4). 
     In the invention above (Invention 4), it is preferable that the base portion comprises a side surface that continues to an outer circumference part of the second surface and that is substantially parallel to the rotary shaft (Invention 5); it is preferable that the convex portion protrudes toward the first surface side more at a radially inner location of the magnet than the side surface of the base portion (Invention 6); it is preferable that the convex portion protrudes toward the first surface side to incline internally in the radial direction of the magnet (Invention 7); and it is preferable that a volume ratio of the base portion to the convex portion is 1:0.2 or greater (Invention 8). 
     In the invention above (Invention 1), as the magnet sensor part, a TMR element, a GMR element, an AMR element or a Hall element is usable (Invention 9). 
     In the invention above (Invention 1), it is preferable that the rotation angle sensing device has a plurality of the magnetic sensor parts, and at least two of the plurality of the magnetic sensor parts are arranged substantially at intervals (180/M)° (M is an integer greater than or equal to 2) centering on the rotary shaft along the circumferential direction on the virtual plane (Invention 10). 
     In the invention above (Invention 10), it is preferable that each of the magnetic sensor parts outputs the magnetic field intensity H r  in the radial direction or the magnetic field intensity H θ  in the circumferential direction as the sensor signal (Invention 11). 
     Effect of the Invention 
     According to the present invention, a rotation angle sensing device can be provided that accurate detection of a rotation angle based upon magnetic fields intensity in a radial direction and/or a circumferential direction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a cross-sectional view showing a schematic configuration of a rotation angle sensing device relating to the embodiment of the present invention, and  FIG. 1B  is a plan view viewing from a second surface side of a magnet in the rotation angle sensing device relating to the embodiment of the present invention. 
         FIG. 2  is a partially-enlarged side view showing a primary part of the magnet in the embodiment of the present invention. 
         FIG. 3  is a cross-sectional view showing another mode (Part  1 ) of the magnet in the embodiment of the present invention. 
         FIG. 4  is a cross-sectional view showing another mode (Part  2 ) of the magnet in the embodiment of the present invention. 
         FIG. 5  is a cross-sectional view showing another mode (Part  3 ) of the magnet in the embodiment of the present invention. 
         FIG. 6A  is a schematic view showing magnetic field intensities (magnetic field intensities in a radial direction and in a circumferential direction) that are detected by a magnetic sensor part in the embodiment of the present invention;  FIG. 6B  is a schematic view showing another mode of magnetic field intensities (magnetic field intensities in a radial direction) that are detected by the magnetic sensor parts; and  FIG. 6C  is a schematic view showing another mode of magnetic field intensities (magnetic field intensities in a circumferential direction) that are detected by the magnetic sensor parts. 
         FIG. 7  conceptually shows magnetic field intensities in a radial direction and in a circumferential direction beneath the second surface of the magnet in the embodiment of the present invention. 
         FIG. 8A  is a perspective view schematically showing the magnet and a magnet sensor arrangeable region in the embodiment of the present invention, and  FIG. 8B  is a side view of  FIG. 8A . 
         FIG. 9  is a graph showing amplitudes of magnetic field intensities that are detected in the rotation angle sensing device in the embodiment of the present invention. 
         FIGS. 10A and 10B  are a circuit diagram schematically showing one mode of a circuit configuration of the magnetic sensor part in the embodiment of the present invention, respectively. 
         FIG. 11  is a perspective view showing a schematic configuration of MR elements as magnetic detecting elements in the embodiment of the present invention. 
         FIG. 12  is a circuit schematically showing one mode of the circuit configuration of a rotation angle detecting part in the embodiment of the present invention. 
         FIG. 13  shows a simulation result of Example 1. 
         FIG. 14  shows a simulation result of Example 2. 
         FIG. 15  shows a simulation result of Example 3. 
         FIG. 16  shows a simulation result of Example 4. 
         FIG. 17  shows a simulation result of Example 5. 
         FIG. 18  shows a simulation result of Example 6. 
         FIG. 19  shows a simulation result of Example 7. 
         FIG. 20  shows a simulation result of Example 8. 
         FIG. 21  shows a simulation result of Example 9. 
         FIG. 22  shows a simulation result of Comparative Example 1. 
         FIG. 23A  is a cross-sectional view (Part  1 ) showing a schematic configuration of a conventional rotation angle sensing device, and  FIG. 23B  is a plan view (Part  1 ) viewing from a second surface side of a magnet in the conventional rotation angle sensing device. 
         FIG. 24A  is a cross-sectional view (Part  2 ) showing a schematic configuration of a conventional rotation angle sensing device, and  FIG. 24B  is a plan view (Part  2 ) viewing from a second surface side of a magnet in the conventional rotation angle sensing device. 
     
    
    
     MODE FOR CARRYING OUT THE INVENTION 
     An embodiment of the present invention is explained in detail with reference to the drawings.  FIG. 1A  is a cross-sectional view showing a schematic configuration of a rotation angle sensing device relating to the present embodiment;  FIG. 1B  is a plan view as viewed from a second surface side of a magnet in the rotation angle sensing device relating to the present embodiment; and  FIG. 2  is a partially-enlarged side view showing a primary part of the magnet in the present embodiment. 
     As shown in  FIG. 1A  and  FIG. 1B , a rotation angle sensing device  1  relating to the present embodiment is supported and fixed to the shaft S, and is provided with a magnet  2  that integrally rotates with the shaft S, a magnetic sensor part  3  that outputs a sensor signal based upon a change in a direction of a magnetic field in association with a rotation of the magnet  2 ; and a rotation angle detecting part  4  (see  FIG. 12 ) that detects a rotation angle of a rotating body based upon the sensor signal output by the magnetic sensor part  3 . 
     The shaft S is made of a magnetic metal, such as Fe or Ni, and has a circular cylindrical shape. The shaft S rotates integrally with a rotation angle of a subject to be detected (not shown), such as a motor or gear. 
     The magnet  2  has a first surface  2 A that is substantially orthogonal to the rotation axis C (shaft center) of the shaft S and a second surface  2 B opposed to the first surface  2 A. The first surface  2 A and the second surface  2 B are nearly circular when viewed along an axial direction of the rotation axis C of the shaft S. The second surface  2 B is sized to physically include the first surface  2 A. 
     The magnet  2  is supported and fixed/to the shaft S to match the centroid (center) of the first surface  2 A and the second surface  2 B of the magnet  2  with the rotation axis C of the shaft S. The magnet is magnetized in a direction that is orthogonal to the rotation axis C of the shaft S (in an in-plane direction of the first surface  2 A and the second surface  2 B). Furthermore, in the present embodiment, the magnet  2  magnetized in the direction that is orthogonal to the rotation axis C, but the present embodiment shall not be limited to such. For example, the magnet  2  should have a magnetization vector component in the direction that is orthogonal to the rotation axis C, and it is preferable that the magnetization direction of the magnet  2  is substantially orthogonal to the rotation axis C (an angle to the rotation axis C in the magnetization direction is approximately 90±10°). 
     The magnet  2  in the present embodiment has a base portion  21  having the second surface  2 B and a convex portion  22  that has the first surface  2 A and protrudes toward the first surface  2 A side from the base portion  21 . The base portion  21  continues to an outer circumference part  21 E of the second surface  2 B, and has a side surface  2 C (see  FIG. 2 ) that is substantially parallel to the rotation axis C of the shaft S. The convex portion  22  protrudes toward the first surface  2 A side from a position P (see  FIG. 2 ) internally in the radial direction of the magnet  2  from the side surface  2 C of the base portion  21  and has an inclined side surface  2 D that is inclined internally in the radial direction of the magnet  2  at a predetermined angle θ 2 D. 
     Thickness T 21  of the base portion  21  of the magnet  2  is not particularly limited, and for example, can be set to approximately 1 to 4 mm. Thickness T 22  of the convex portion  22  is also not particularly limited, and for example, can be set to approximately 1 to 4 mm. 
     It is preferable that a ratio of a diameter D 2A  of the first surface  2 A to a diameter D 2   B  of the second surface  2 B in the magnet  2  is 1:2 or greater. If the ratio of the diameter D 2A  of the first surface  2 A to the diameter D 2B  of the second surface  2 B is within the range above, when a circular virtual plane Vf, which is orthogonal to the rotation axis C beneath the second surface  2 B and is centered upon the rotation axis C is set, the amplitude of a magnetic field intensity H r  in the radial direction and that of a magnetic field intensity H 0  in the circumferential direction at a predetermined position on the virtual plane Vf are substantially the same. Here, the virtual plane Vf is a plane optionally set within a predetermined space (a space in the vicinity of the second surface  2 B) beneath the second surface  2 B of the magnet  2 . Furthermore, the diameter D 2A  of the first surface  2 A can be set to, for example, approximately 8 mm to 20 mm, and the diameter D 2B  of the second surface  2 B can be set to, for example, approximately 16 mm to 40 mm. 
     The Length L (length along the radial direction of the magnet  2 ) from the side surface  2 C of the base portion  21  to a rising position of the inclined side surface  2 D of the convex portion  22  (position P internally in the radial direction of the magnet  2 ) can be set to, for example, approximately 8 mm or less, and preferably approximately 1 mm to 4 mm. 
     In the magnet  2  of the present embodiment, a ratio of volume V 21  of the base portion  21  to volume V 22  of the convex portion  22  (V 21 :V 22 ) is preferably 1:0.2 or greater, is more preferably 1:0.2-5, and is particularly preferably 1:0.2-1. If the volume ratio (V 21 :V 22 ) is within the range above, a region where the amplitude of the magnetic field intensity H r  in the radial direction and that of the magnetic field intensity H θ  in the circumferential direction become substantially identical. 
     Furthermore, the magnet  2  in the present embodiment is not limited to the modes shown in  FIG. 1A  and  FIG. 2 . For example, as shown in  FIG. 3 , a mode having the base portion  21 , which includes the side surface  2 C, continuing to the second surface  2 B and the outer circumference part  21 E of the second surface  2 B and having the convex portion  22 , which includes the inclined side surface  2 D, continuing to the upper end of the side surface  2 C and the first surface  2 A is also acceptable. Further, as shown in  FIG. 4 , another mode with a nearly trapezoidal cross-sectional shape having the base portion  21 , which includes the second surface  2 B, and the convex portion  22 , which includes the inclined side surface  2 D continuing to the outer circumference part  21 E of the second surface  2 B, and the first surface  2 A is also acceptable. In addition, as shown in  FIG. 5 , another mode with a nearly stepwise cross-sectional shape having the base portion  21 , which includes the second surface  2 B and the side surface  2 C continuing to the outer circumference part  21 E of the second surface  2 B, and the convex portion  22 , which includes the side surface  2 E rising substantially in parallel to the rotation axis C of the shaft S from the position P more internally in the radial direction of the magnet  2  than the side surface  2 C and the first surface  2 A is also acceptable. 
     When the circular virtual plane Vf that is orthogonal to the rotation axis C beneath the second surface  2 B of the magnet  2 , and that is centered upon the rotation axis C is set, the magnetic sensor part  3  in the present embodiment is placed at a position where the amplitude of the magnetic field intensity H r  in the radial direction and that of the magnetic field intensity Ho in the circumferential direction are substantially the same at a predetermined position on the virtual plane Vf. Furthermore, in the present embodiment, as shown in  FIG. 6A , while one magnetic sensor part  3  that can detect the magnetic field intensity H r  in the radial direction and the magnetic field intensity H θ in the circumferential direction is exemplified, but the present embodiment shall not be so limited. For example, as shown in  FIG. 6B  and  FIG. 6C , may be provided with two magnetic sensor parts  3  that are arranged at intervals of 90° about the rotation axis C of the shaft S. In this case, the two magnetic sensor parts  3  may detect the magnetic field intensity H r  in the radial direction (see  FIG. 6B ) and may detect the magnetic field intensity H θ in the circumferential direction, respectively (see  FIG. 6C ). 
     In the case of the provision of a plurality of the magnetic sensor parts  3 , at least two of the plurality of the magnetic sensor parts  3  should be placed at intervals of substantially (180/M) ° (M is an integer greater than or equal to 2, and is preferably an integer of  2  to  5 ) about the rotation axis C of the shaft S. A signal that is output from the magnetic sensor parts  3  includes an M t -order high-frequency error component, but since the M th -order high-frequency error component can be removed by placing the magnetic sensor parts  3  at intervals of (180/M) ° about the rotation axis C, a detection error of the rotation angle can be further reduced. 
     In the present embodiment, the magnetic field intensity H r  in the radial direction and the magnetic field intensity H θ  in the circumferential direction on the circular virtual plane Vf set beneath the second surface  2 B of the magnet  2  can be handled as a sum of a magnetic field M r21  in the radial direction that is generated by the base portion  21  of the magnet  2  and a magnetic field M r22  in the radial direction that is generated by the convex portion  22  and a sum of a magnetic field M θ21  in the circumferential direction that is generated by the base portion  21  and a magnetic field M θ22  in the circumferential direction that is generated by the convex portion  22 , respectively (see  FIG. 7 ). 
     In the case the magnet  2  is magnetized in the in-plane direction of the magnet  2  as in the present embodiment, the magnitude of the magnetic field intensity H r  in the radial direction on the virtual plane Vf becomes maximal in the vicinity of an N pole side edge NP and in the vicinity of an S pole side edge SP, respectively, and becomes minimal at a position rotated by 90° about the shaft  5  from the N pole side edge NP and the S pole side edge SP, respectively. In the meantime, the magnitude of the magnetic field intensity H θ  in the circumferential direction becomes maximal at a position rotated by 90° from the N pole side edge NP and the S pole side edge SP centering upon the shaft  5 , respectively, and becomes minimal in the vicinity of the N pole side edge NP and the in the vicinity of the S pole side edge SP, respectively. 
     In the present embodiment, a direction of the magnetic field M r21  in the radial direction that is generated by the base portion at the N pole side edge NP and the S pole side edge SP is anti-parallel to a magnetization direction DM of the magnet  2 , respectively, and a direction of the magnetic field M r22  in the radial direction that is generated by the convex portion  22  is parallel to the magnetization direction DM of the magnet  2 . Then, the intensity of the magnetic field M r21  (magnetic field intensity H r21 ) in the radial direction that is generated by the base portion  21  is greater than that of the magnetic field M r22  (magnetic field intensity H r22 ) in the radial direction that is generated by convex portion  22  (H r21 &gt;H r22 ). Furthermore, in  FIG. 7 , the intensities of the magnetic field M r21 , M r22 , M θ21  and M θ22  (magnetic field intensities H r21 , H r22 . H θ21  and H θ22 ) are expressed with arrow length, respectively. 
     In the meantime, the direction of the magnetic field M θ21  in the circumferential direction that is generated by the based portion  21  and the direction of the magnetic field M θ22  in the circumferential direction at a position rotated by 90° about the shaft S from the N pole side edge NP and the S pole side edge SP are anti-parallel to the magnetization direction DM of the magnet  2 , and the intensities of those magnetic fields H θ21  and H θ22  are smaller than the intensity of the magnetic field M r21  (magnetic field intensity H r21 ) in the radial direction that is generated by the base portion  21  at the N pole side edge NP and the S pole side edge SP (H r21 &gt;H θ21 , H θ22 ). Consequently, the amplitude of the magnetic field intensity H r  in the radial direction and that of the magnetic field intensity H θ  in the circumferential direction become substantially the same. 
     As described above, a region where the amplitude of magnetic field intensities H r  and H θ in the radial direction and the circumferential direction on the virtual plane Vf set beneath the second surface  2 B of the magnet  2  in the present embodiment are substantially identical (magnetic sensor arrangeable region  5 ) is created. This magnetic sensor arrangeable region  5 , as shown in  FIG. 8A  and  FIG. 8B , is a ring-shaped region beneath the second surface  2 B between a first virtual line L 1 , which is parallel to the rotation axis C and passes through the outer circumference part  22 E of the first surface  2 A of the magnet  2 , and a second virtual line L 2 , which is parallel to the rotation axis C and passes through the outer circumference part  21 E of the second surface  2 B. Therefore, since the amplitude of the magnetic field intensity H r  in the radial direction and that of the magnetic field intensity H θ in the circumferential direction are substantially the same by placing the magnetic sensor part or parts  3  in this magnetic sensor arrangeable region  5  (see  FIG. 9 ), a detection error of the rotation angle by the rotation angle sensing device  1  relating to the present embodiment can be reduced. 
     The magnetic sensor part  3  in the present embodiment includes at least one magnetic detecting element. The magnetic sensor part  3  may include a pair of magnetic detecting elements connected in series as at least one magnetic detecting element. In this case, the magnetic sensor part  3  has first and second detecting circuits including the first pair of magnetic detecting elements connected in series and the second pair of magnetic detecting elements connected in series. 
     As shown in  FIG. 10A , the first detecting circuit  31  in the magnetic sensor part  3  has a power source port V 1 , a ground port G 1 , two output ports E 11  and E 12 , and a first Wheatstone bridge circuit  311 . The first Wheatstone bridge circuit  311  has a first signal generation part  31 A including a first pair of magnetic detecting elements R 11  and R 12  connected in series and a second signal generation part  31 B including a second pair of magnetic detecting elements R 13  and R 14  connected in series. A connecting point J 12  of the magnetic detecting elements R 11  and R 13  is connected to the power source port V 1 . A connecting point J 11  of the magnetic detecting elements R 11  and R 12  is connected to the output port E 11 . A connecting point J 14  of the magnetic detecting elements R 13  and R 14  is connected to the output port E 12 . A connecting point J 13  of the magnetic detecting elements R 12  and R 14  is connected to the ground port G 1 . Power-supply voltage with predetermined magnitude is applied to the power source port V 1 , and the ground port G 1  is connected to the ground. A first signal S 1  generated by the first signal generating part  31 A is output from the output port E 11 , and a second signal S 2  generated by the second signal generating part  31 B is output from the output port E 12 . 
     Further, as shown in  FIG. 10B , the second detecting circuit  32  in the magnetic sensor part  3  has a power source port V 2 , a ground port G 2 , output ports E 21  and E 22  and a second Wheatstone bridge circuit  312 . The second Wheatstone bridge circuit  312  has a third signal generation part  32 A including a third pair of magnetic detecting elements R 21  and R 22  connected in series and a fourth signal generation part  32 B including a fourth pair of magnetic detecting elements R 23  and R 24  connected in series. A connecting point J 22  of the magnetic detecting elements R 21  and R 23  is connected to the power source port V 2 . A connecting point J 21  of the magnetic detecting elements R 21  and R 22  is connected to the output port E 21 . A connecting point J 24  of the magnetic detecting elements R 23  and R 24  is connected to the output port E 22 . A connecting point J 23  of the magnetic detecting elements R 22  and R 24  is connected to the ground port G 2 . Power-supply voltage with predetermined magnitude is applied to the power source port V 2 , and the ground port G 2  is connected to the ground. A third signal S 3  generated by the third signal generating part  32 A is output from the output port E 21 , and a fourth signal S 4  generated by the fourth signal generating part  32 B is output from the output port E 22 . 
     In the present embodiment, all magnetic detecting elements R 11  to R 14  and R 21  to R 24  included in the first and second detecting circuits  31  and  32  can be magnetoresistive effect elements (MR elements), such as a TMR element, a GMR element or an AMR element, a Hall element and the like. It is particularly preferable to use TMR elements. The TMR element and the GMR element have a magnetic fixed layer where the magnetization direction is fixed, a free layer where its magnetization direction varies according to the direction of the magnetic field to be applied, and a nonmagnetic layer that is arranged between the magnetization fixed layer and the free layer. 
     Specifically, as shown in  FIG. 11 , the TMR element and the GMR element have a plurality of lower-side electrodes  61 , a plurality of MR films  50  and a plurality of upper-side electrodes  62 . The plurality of lower-side electrodes  61  are placed on a substrate (not shown). Each lower-side electrode  61  has a long and narrow shape. A crevice is formed between two lower-side electrodes  61  that are adjacent in the longitudinal direction of the lower-side electrode  61 . MR films  50  are placed in the vicinity of both ends in the longitudinal direction on the upper surface of the lower-side electrode  61 , respectively. The MR film  50  includes a free layer  51 , a nonmagnetic layer  52 , a magnetization fixed layer  53  and an antiferromagnetic layer  54  laminated in respective order from the lower-side electrode  61  side. The free layer  51  is electrically connected to the lower-side electrode  61 . The antiferromagnetic layer  54  is made of an antiferromagnetic material, and fulfills a role to pin the direction of magnetization of the magnetization fixed layer  53  by causing exchange coupling with the magnetization fixed layer  53 . The plurality of upper-side electrode  62  is placed on the plurality of MR films  50 . Each upper-side electrode  62  has a long and narrow shape, and is arranged on two lower-side electrodes  61  that are adjacent in the longitudinal direction of the lower-side electrode  61 , and electrically connect the antiferromagnetic layers  54  of the two adjacent MR films  50 . Furthermore, the MR films  50  may have a configuration where the free layer  51 , the nonmagnetic layer  52 , the magnetization fixed layer  53  and the antiferromagnetic layer  54  in respective order from the upper-side electrode  62  side. 
     In the TMR element, the nonmagnetic layer  52  is a tunnel bather layer. In the GMR element, the nonmagnetic layer  52  is a nonmagnetic conductive layer. In the TMR element and the GMR element, a resistance value varies according to an angle between the direction of magnetization of the free layer  51  and the direction of magnetization of the fixed layer  53 , and when this angle is 0° (the magnetization directions are parallel to each other), the resistance value becomes minimal, and when it is 180° (the magnetization directions are anti-parallel with each other), the resistance value becomes maximal. 
     In  FIG. 10A , the magnetization directions of the magnetization fixed layers in the magnetic detecting elements R 11  to R 14  are indicated with a solid arrow, respectively. In the first detecting circuit  31 , the magnetization direction of the magnetization fixed layers  53  in the magnetic detecting elements R 11  and R 14  and the magnetization direction of the magnetization fixed layers  53  in the magnetic detecting elements R 12  and R 13  are anti-parallel with each other, and are orthogonal to the radial direction of the magnet  2 . 
     In the first signal generating part  31 A, when the magnetic field intensity H r  in the radial direction is changed due to the rotation of the magnet  2 , the magnetization directions of the free layers  51  in the magnetic detecting elements R 11  and R 12  are changed accordingly, the potential of the connecting point J 11  is changed based upon a relative angle between the magnetization directions of the free layer  51  and those of the magnetization fixed layers  53 . Further, similarly in the second signal generating part  31 B, the potential of the connecting point J 14  is changed based upon a relative angle between the magnetization directions of the free layer  51  and those of the magnetization fixed layers  53  in the magnetic detecting elements R 13  and R 14 . Therefore, the first signal generating part  31 A generates a first signal S 1  corresponding to the magnetic field intensity H r  in the radial direction, and the first signal S 1  is output from the output port E 11 . The second signal generating part  31 B generates a second signal S 2  corresponding to the magnetic field intensity H r  in the radial direction, and the second signal S 2  is output from the output port E 12 . 
     Similarly, in  FIG. 10B , the magnetization directions of the magnetization fixed layers in the magnetic detecting elements R 21  to R 24  are indicated with a solid arrow, respectively. In the second detecting circuit  32 , the magnetization direction of the magnetization fixed layers  53  in the magnetic detecting elements R 21  and  214  and the magnetization direction of the magnetization fixed layers  53  in the magnetic detecting elements R 22  and R 23  are anti-parallel with each other, but are parallel to the magnetization direction of the magnet  2 . 
     In the third signal generating part  32 A, if the magnetic field intensity H θ  in the circumferential direction is changed due to the rotation of the magnet  2 , the magnetization directions of the free layers  51  of the magnetic detecting elements R 21  and R 22  are changed accordingly, and the potential of the connecting point J 21  is changed based upon a relative angle between the magnetization direction of the free layers  51  and the magnetization direction of the magnetization fixed layers  53 . Further, similarly in the fourth signal generating part  32 B, the potential of the connecting point J 24  is changed based upon a relative angle between the magnetization direction of the free layers  51  and the magnetization direction of the magnetization fixed layers  53  in the magnetic detecting elements R 23  and R 24 . Therefore, the third signal generating part  32 A generates a third signal S 3  corresponding to the magnetic field intensity H θ  in the circumferential direction of the magnet  2 , and the third signal S 3  is output from the output port E 21 . The fourth signal generating part  32 B generates a fourth signal S 4  corresponding to the magnetic field intensity H θ  in the circumferential direction of the magnet  2 , and the fourth signal S 4  is output from the output port E 22 . 
     The rotation angle detecting part  4  in the present embodiment, as shown in  FIG. 12 , has a first arithmetic circuit  41 , a second arithmetic circuit  42  and a third arithmetic circuit  43 , and generates a rotation angle detection value θ s  based upon the first to fourth signals S 1  to S 4 . 
     The output ports E 11  and E 12  are connected to two input terminals of the first arithmetic circuit  41 , respectively. The output ports E 21  and E 22  are connected to two input terminals of the second arithmetic circuit  42 , respectively. Output terminals of the first and second arithmetic circuits  41  and  42  are connected to the two input terminal of the third arithmetic circuit  43 , respectively. 
     The first arithmetic circuit  41  generates a first post-operation signal Sa 1  based upon the first and second signals S 1  and S 2 . The second arithmetic circuit  42  generates a second post-operation signal Sa 2  based upon the third and fourth signals S 3  and S 4 . The third arithmetic circuit  43  generates a rotation angle detection value θ s  based upon the first and second post-operation signals Sa 1  and Sa 2 . 
     The first post-operation signal Sa 1  is generated by an operation to obtain a difference between the first signal S 1  and the second signal S 2  (S 1 -S 2 ). The second post-operation signal Sa 2  is generated by an operation to obtain a difference between the third signal S 3  and the fourth signal S 4  (S 3 -S 4 ). 
     The third arithmetic circuit  43  has normalization circuits N 1  to N 4 , an adder circuit  43 A, a subtraction circuit  43 B and an operation part  43 C. The normalization circuits N 1  to N 4  have an input terminal and an output terminal, respectively. The adder circuit  43 A, the subtraction circuit  43 B and the operation part 43 C have two input terminals and one output terminal, respectively. 
     An output terminal of the first arithmetic circuit  41  is connected to an input terminal of the normalization circuit N 1 . An output terminal of the second arithmetic circuit  42  is connected to an input terminal of the normalization circuit N 2 . Output terminals of the normalization circuits N 1  and N 2  are connected to two input terminals of the adder circuit  43 A, respectively. Output terminals of the normalization circuits N 1  and N 2  are connected to two input terminals of the subtraction circuit  43 B, respectively. An output terminal of the adder circuit  43 A is connected to an input terminal of the normalization circuit N 3 , and an output terminal of the subtraction circuit  43 B. Each output terminal of the normalization circuits N 3  and N 4  is connected to two input terminals of the operation part  43 C. 
     The normalization circuit N 1  outputs a value where the first post-operation signal Sa 1  is normalized to the adder circuit  43 A and the subtraction circuit  43 B. The normalization circuit N 2  outputs a value where the second post-operation signal Sa 2  is normalized to the adder circuit  43 A and the subtraction circuit  43 B. The normalization circuits N 1  and N 2  normalize the first and second post-operation signals Sa 1  and Sa 2 , for example, to adjust maximum values of the first and second post-operation signals Sa 1  and Sa 2  both to be 1 and to adjust minimum values both to be −1. In the present embodiment, a value where the first post-operation signal Sa 1  has been normalized becomes sin (θ+π/4), and a value where the second post-operation signal Sa 2  has been normalized becomes sin (θ−π/4). Furthermore, θ is an angle between a segment connecting the connecting points J 12  and J 14 , and, an external magnetic field. 
     The adder circuit  43 A performs an operation to obtain a sum of a value where the first post-operation signal Sa 1  has been normalized and a value where the second post-operational signal Sa 2  has been normalized, and generates an addition signal S 11 . The subtraction circuit  43 B performs an operation to obtain a difference of a value where the first post-operation signal Sa 1  has been normalized and a value where the second post-operational signal Sa 2  has been normalized and generates a subtraction signal S 12 . The addition signal S 11  and the subtraction signal S 12  are expressed with the formulae below. 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   = 
                     
                   ⁢ 
                   
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           θ 
                           - 
                           
                             π 
                             / 
                             4 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           θ 
                           + 
                           
                             π 
                             / 
                             4 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       θ 
                       · 
                       cos 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           - 
                           π 
                         
                         / 
                         4 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     1.41 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     θ 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   = 
                     
                   ⁢ 
                   
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           θ 
                           + 
                           
                             π 
                             / 
                             4 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           θ 
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                             π 
                             / 
                             4 
                           
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     2 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       θ 
                       · 
                       sin 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       
                         π 
                         / 
                         4 
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     1.41 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     θ 
                   
                 
               
             
           
         
       
     
     The normalization circuit N 3  outputs the value S 21  where the addition signal S 11  has been normalized to the operation part  43 C. The normalization circuit N 4  outputs the value S 22  where the subtraction signal S 12  has been normalized to the operation part  43 C. The normalization circuits N 3  and N 4  normalize the addition signal S 11  and the subtraction signal S 12 , for example, to adjust maximum values of the addition signal S 11  and the subtraction signal S 12  both to be 1, and to adjust minimum values both to be −1. In the present embodiment, the value S 21  where the addition signal S 11  has been normalized becomes  sin  θ, and the value S 22  where the subtraction signal S 12  has been normalized becomes  cos  θ. 
     The operation part  43 C calculates a rotation angle detection value θs having a correspondence relationship with the angle θ based upon the values S 21  and S 22 . For example, the operation part  43 C calculates the rotation angle detection value θ s  using the formula below.
 
θ s =arctan( S 21/ S 22)
 
     When the rotation angle detection value θ s  is within the range 0° or greater but less than 360°, there are two different values by 180° in solutions of the rotation angle detection value θ s . However, the true value of the rotation angle detection value θ s  can be determined to be either one of the two solutions according to a combination of positive and negative of the values S 21  and S 22 . In other words, when the value S 21  is a positive value, the rotation angle detection value θ s  is greater than 0° but smaller than 180°. When the value S 21  is a negative value, the rotation angle detection value θ s  is greater than 180° but smaller than 360°. When the value S 22  is a positive value, the rotation angle detection value θ s  is within a range of 0° or greater but less than 90° and greater than 270° and 360° or less. When the value S 22  is a negative value, the rotation angle detection value θ s  is greater than 90° but smaller than 270°. The operation part  43 C can acquire a true value for the rotation angle detection value θ s  within the range of 0° or greater but less than 360° according to a combination of the positive and negative of the values S 21  and S 22 . 
     As described above, in the rotation angle sensing device  1  relating to the present embodiment, because the magnet  2  has the base portion  21  having the second surface  2 B, and, the convex portion  22  that has the first surface  2 A and protrudes toward the first surface  2 A side from the base portion  21 , a region (magnetic sensor arrangeable region  5 ) where the amplitudes of the magnetic field intensities H r  and H θ  in the radial direction and the circumferential direction is created beneath the second surface  2 B. Then, since the magnetic sensor part  3  is placed in this magnetic sensor arrangeable region  5 , a detection error of the rotation angle can be reduced. Further, since it is configured to calculate a rotation angle according to the magnetic field intensity a in the radial direction and the magnetic field intensity H θ  in the circumferential direction and the magnetic sensor arrangeable region  5  is sufficiently larger than the magnetic sensor parts  3 , generation of a detection error of the rotation angle due to deviation of the shaft S can be suppressed. In addition, the magnet  2  has the base portion  21  having the second surface  2 B, and, the convex portion  22  that has the first surface  2 A and protrudes toward the first surface  2 A side from the base portion  21 , and because the rotation angle detection value θ s  can be calculated according to the magnetic field intensity H r  in the radial direction and the magnetic field intensity H θ  in the circumferential direction, it becomes possible to reduce the volume of the magnet  2 . 
     The embodiment explained above was described to facilitate the understanding of the present invention, but not described to restrict the present invention. Therefore, each element disclosed in the embodiment is a concept including all design around and equivalents belonging to the technical scope of the present invention. 
     For example, in the embodiment, the magnetic sensor part  3  may detect either one of the magnetic field intensity H r  in the radial direction and the magnetic field intensity H r0  in the circumferential direction, and, the magnetic field intensity H z in the direction along the rotation axis C of the shaft S, and the rotation angle detection value θ s  can be calculated by the rotation angle detecting part  4  based upon either one of the magnetic field intensity H r  in the radial direction and the magnetic field intensity H r  in the circumferential direction, and, the magnetic field intensity H z , in a direction along the rotation axis C of the shaft S. 
     EXAMPLE 
     Hereafter, the present invention will be explained in further detail with reference to examples and the like, but the present invention shall not limited to the examples below. 
     Example 1 
     In the magnet having the configuration shown in  FIG. 1  and  FIG. 2 , a magnetic field distribution of the magnet  2  and an angle error distribution based upon it were obtained by simulation using a finite element method (FEM). Furthermore, the thickness T 21  of the base portion  21  of the magnet  2  was set to 2.25 mm; the thickness T 22  of the convex portion  22  was set to 2.75 mm; the length L from the side surface  2 C to a rising position P was set to 2.0 mm; the diameter D 2A  of the first surface  2 A was set to 12 mm; the diameter D 2B  of the second surface  2 B was set to 28 mm; the inclination angle θ 2D  of the inclined side surface  2 D was set to 25°; and the volume was set to 1.86 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:0.46). The results are shown in  FIG. 13 . 
     Example 2 
     As similar to Example 1 except for using the magnet  2  having the configuration shown in  FIG. 3 , the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by simulation. Furthermore, the thickness T 21  of the base portion  21  of the magnet  2  was set to 1.1 mm; the thickness T 22  of the convex portion  22  was set to 3.9 mm; the diameter D 2A  of the first surface  2 A was set to 14.4 mm; the diameter D 2B  of the second surface  2 B was set to 28 mm; the inclination angle θ 2D  of the inclined side surface  2 D was set to 30°; and the volume was set to 1.75 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:1.75). The results are shown in  FIG. 14 . 
     Example 3 
     As similar to Example 2 except for setting the thickness T 21  of the base portion  21  of the magnet  2  to 1.8 mm; the thickness T 22  of the convex portion  22  to 3.2 mm; the volume to 2.08 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:0.95), the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by simulation. The results are shown in  FIG. 15 . 
     Example 4 
     As similar to Example 3 except for setting the inclined angle θ 2D  of the inclined side surface  2 D of the magnet  2  to 45°; and the volume was set to 2.41 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:1.44), the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by simulation. The results are shown in  FIG. 16 . 
     Example 5 
     As similar to Example 4 except for setting the thickness T 21  of the base portion  21  of the magnet  2  to 0.6 mm; the thickness T 22  of the convex portion  22  to 4.4 mm; and the volume to 2.04 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:6.24), the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by the simulation. The results are shown in  FIG. 17 . 
     Example 6 
     As similar to Example 1 except for using the magnet having the configuration shown in  FIG. 4 , the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by simulation. Furthermore, the thickness of the magnet  2  (the thickness T 22  of the convex portion  22 ) was set to 5 mm; the diameter D 2A  of the first surface  2 A was set to 12 mm; the diameter D 2B  of the second surface  2 B was set to 28 mm; the inclination angle θ 2D  of the inclined side surface  2 D was set to 32°; and the volume was set to 14.03 cm 3 . The results is are shown in  FIG. 18 . 
     Example 7 
     As similar to Example 1 except for using the magnet  2  having the configuration shown in  FIG. 5 , the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by simulation. Furthermore, the thickness T 21  of the base portion  21  of the magnet  2  was set to 2.0 mm; the thickness T 22  of the convex portion  22  was set to 2.0 mm; the length from the side surface  2 C to the rising position P in the radial direction to 4 mm; the diameter D 2A  of the first surface  2 A was set to 20 mm; the diameter D 2B  of the second  2 B was set to 28 mm; and the volume to 1.66 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:0.47). The results are shown in  FIG. 19 . 
     Example 8 
     As similar to Example 1 except for setting the thickness T 21  of the base portion  21  of the magnet  2  to 3.25 mm; the volume to 2.45 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:0.32), the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by simulation. The results are shown in  FIG. 20 . 
     Example 9 
     As similar to Example 1 except for setting the thickness T 21  of the base portion  21  of the magnet  2  to 4.25 mm; and the volume to 2.99 cm 3  (volume ratio of the base portion  21  to the convex portion  22  (V 21 :V 22 )=1:0.24), the magnetic field distribution of the magnet  2  and the angle error distribution were obtained by simulation. The results are shown in  FIG. 21 . 
     Comparative Example 1 
     As similar to Example 1 except for using the magnet  200  having the configuration shown in  FIGS. 23A and 23B , the magnetic field distribution of the magnet  200  and the angle error distribution were obtained by simulation. Furthermore, thickness of the magnet  200  was set to 3 mm; the diameter was set to 28 mm; and the volume was set to 16.96 cm 3 . The results are shown in  FIG. 22 . 
       FIGS. 13 to 22  show the angle error distribution in the vicinity of the outer circumference part of the magnets  2  and  200  obtained by simulations of Examples 1 to 9 and Comparative Example 1, respectively. In  FIGS. 13 to 22 , regions where their brightness is the lowest around the circumference of the magnets  2  and  200  (regions with hatching of dots) are regions where the magnetic field intensities H r  and H θ  in the radial direction and the circumferential direction are less than 15 mT; regions where their brightness is the highest (regions with hatching of dashed lines) are regions where the magnetic field intensities H r  and H θ  in the radial direction and the circumferential direction are 20 mT or greater; and regions where their brightness is intermediate (regions with hatching of continuous lines) are regions where the magnetic field intensities H r  and H θ  in the radial direction and the circumferential direction are 15 mT or greater but less than 20 mT. Regions surrounded with a broken line are regions where an angle error is improved; regions having magnetic field intensities that are detectable by the magnetic sensor part or parts  3  (magnetic field intensities H r  and H θ =20 to 80 mT); and regions that can be the magnetic sensor arrangeable region. 
     According to the results shown in  FIGS. 13 to 22 , in Examples 1 to 9, it was determined that the rotation angle would be accurately detectable based upon the magnetic field intensities H r  and H θ  in the radial direction and/or the circumferential direction at a predetermined position on a circular virtual plane Vf. Further, according to the results shown in  FIGS. 14 to 16 , it was determined that a position of the region where the rotation angle would be accurately detectable (magnetic sensor arrangeable region  5 ) would not fluctuate even if the inclination angle of the inclined side surface  2 C was changed. In addition, according to the results shown in  FIGS. 13 to 11 , in Examples 1 to 9, it t was determined hat a position of the region where the rotation angle would be accurately detectable (magnetic sensor arrangeable region  5 ) would not fluctuate regardless of the shape or the like of the magnet  2 . Further, according to the results shown in  FIGS. 13 to 21 , it was determined that a detection error of the rotation angle could be reduced because the convex portion  22  of the magnet  2  protrudes toward the first surface  2 A from a position internally in the radial direction from the side surface  2 C. In addition, according to the results shown in  FIGS. 13, 20 and 21 , it was determined that the size of the magnetic sensor arrangeable region  5  would increase as the volume ratio of the base portion  21  in the magnet  2  increases. 
     DESCRIPTION OF SYMBOLS 
     
         
           1  . . . rotation angle sensing device 
           2  . . . magnet 
           2 A . . . first surface 
           2 B . . . second surface 
           3  . . . magnetic sensor part 
           4  . . . rotation angle sensing part