Abstract:
A position sensor includes a longitudinally extending permanent magnet member at least two longitudinally extending arc-shaped projecting elements respectively projecting from the opposite ends toward the inside space to confront each other at a distance and a pair of compatible main magnetic sensors disposed in the inside space along the longitudinal axis at an interval so as to generate a pair of output signals when the permanent magnet member shifts along the longitudinal axis. The opposite ends of the permanent magnet member are configured to surround a common inside space and polarized to have opposite magnetic poles so as to provide in the inside space a magnetic field whose magnetic flux density becomes a maximum at a longitudinal center of the inside space and gradually becomes smaller as a position of the inside space shifts from the longitudinal center along a longitudinal axis of the permanent magnet members. The arc-shaped projecting elements are arranged so that the magnetic flux density and each of the output signals can be expressed by a cosine of a shift value from the longitudinal center, and the interval is ¼ of the cycle of the cosine.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
       [0001]    The present application is based on and claims priority from Japanese Patent Applications: 2007-196948, filed Jul. 30, 2007; 2007-284924, filed Nov. 1, 2007 and 2008-45881, filed Feb. 27, 2008, the contents of which are incorporated herein by reference. 
       BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to a permanent magnet type position sensor for detecting position of a moving member of an automobile, such as a power roller position sensor of a toroidal CVT, a height sensor of a suspension control system, a cam stroke sensor, an EGR lift sensor, or an accelerator pedal position sensor. 
         [0004]    2. Description of the Related Art 
         [0005]    JP-A-2000-180114 or, its counterpart, U.S. Pat. No. 6,809,512 discloses such a permanent magnet type position sensor This sensor includes a movable permanent magnet member that provides a magnetic field and a stator that provides an electric signal by sensing a change in the magnetic field when the movable permanent magnet member moves. The movable permanent magnet member of the above disclosed sensor includes a pair of permanent magnets forming two magnetic fields that are opposite to each other to provide two output signals, which are also opposite to each other. The electric signals are given to an electric control unit (ECU) to control a certain device. 
         [0006]    However, the electric signals are likely to change as the temperature around the sensor changes. Hence, it is difficult to accurately detect the position of the object without taking the temperature change into account. 
       SUMMARY OF THE INVENTION 
       [0007]    An object of the invention is to provide an improved permanent magnet type position sensor that can detect an accurate position even if the temperature around the sensor changes. 
         [0008]    According to an aspect of the invention, a position sensor includes a longitudinally extending permanent magnet member having opposite ends polarized to have opposite magnetic poles, at least two longitudinally extending arc-shaped projecting magnetic elements respectively projecting from the opposite ends toward the inside space to confront each other at a distances a pair of main magnetic sensors disposed in the inside space along the longitudinal axis at an interval so as to generate a pair of output signals when the permanent magnet member shifts along the longitudinal axis. The opposite ends are configured to surround the common inside space so as to provide in the common inside space a magnetic field whose magnetic flux density becomes a maximum at a longitudinal center of the inside space and gradually becomes smaller as a position of the inside space shifts from the longitudinal center along a longitudinal axis of the permanent magnet members. The arc-shaped projecting elements are arranged so that each of the output signals can be expressed by a cosine of a shift value from the longitudinal center; and the interval is ¼ of the cycle of the cosine. 
         [0009]    In the above described position sensor: the permanent magnet member may include a pair of semi-cylindrical or prism-like permanent magnets that have a uniform side width along the longitudinal direction thereof and are disposed side by side in such that the tops of the projecting elements confront each other; on the other hand, the permanent magnet member may be a cylindrical permanent magnet; each of the arc-shaped projecting element may include a pair of magnetic yokes respectively extending from opposite ends of one of the permanent magnets. 
         [0010]    The above position sensor may include an offset adjusting circuit for subtracting a mean value of the maximum and minimum of output signals of the main magnetic sensors as an offset value from the output signals of the main magnetic sensors and an inverse trigonometric function processor for providing an inverse trigonometric value from an output signal of the offset adjusting circuit. Each of the magnetic sensor may be a Hall element. The offset adjusting circuit and the inverse trigonometric function processor may be integrally formed in a chip. 
         [0011]    The above position sensor may include an angle correction magnetic sensor disposed in the inside space so as to detect an inclination of the pair of main magnetic sensors to a normal direction. In this aspect, the pair of main magnetic sensors has sensing surfaces facing to the longitudinal direction of the permanent magnet member, and the angle correction magnetic sensor has a sensing surface inclined perpendicular to the sensing surfaces of the main magnetic sensors. The angle correcting magnetic sensor may be disposed between the pair of main magnetic sensors. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    Other objects, features and characteristics of the present invention as well as the functions of related parts of the present invention will become clear from a study of the following detailed description, the appended claims and the drawings. In the drawings: 
           [0013]      FIGS. 1A and 1B  show a position sensor according to the first embodiment of the invention; 
           [0014]      FIG. 2  is a graph showing a relation between the longitudinal position of a permanent magnet used in the position sensor and the magnetic flux density thereof; 
           [0015]      FIG. 3  is a graph showing relations between the respective longitudinal positions of a pair of permanent magnets used in the position sensor and output signals of a pair of magnetic sensors; 
           [0016]      FIG. 4A  is a block diagram of a sensor assembly and  FIG. 4B  is a block diagram of a processor; 
           [0017]      FIG. 5  is a graph showing relations between the respective longitudinal positions of the pair of permanent magnets and the output signals after offset adjustment; 
           [0018]      FIG. 6  is a graph showing a relation between the longitudinal position of the permanent magnets and the output voltage level of the sensor assembly; 
           [0019]      FIG. 7  is a graph showing characteristic curves of magnetic flux density provided by permanent magnets having different shapes; 
           [0020]      FIG. 8  is a block diagram of a sensor assembly according to the second embodiment of the invention; 
           [0021]      FIGS. 9A and 9B  show a position sensor according to the third embodiment of the invention; 
           [0022]      FIGS. 10A ,  10 B and  10 C show a position sensor according to the fourth embodiment of the invention; 
           [0023]      FIG. 11  shows a position sensor according to the fifth embodiment of the invention; 
           [0024]      FIG. 12  shows a position sensor according to the sixth embodiment of the invention; 
           [0025]      FIG. 13  shows a position sensor according to the seventh embodiment of the invention; 
           [0026]      FIG. 14  shows a position sensor according to the eighth embodiment of the invention; and 
           [0027]      FIG. 15  shows a position sensor according to the ninth embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0028]    Several preferred embodiments according to the present invention will be described with reference to the appended drawings. 
         [0029]    A position sensor  1  according to the first embodiment of the invention will be described with reference to  FIGS. 1-7 . 
         [0030]    The position sensor  1  includes a permanent magnet member that is comprised of a pair of permanent magnets  2 ,  3  and a sensor assembly  19  that includes a pair of magnetic sensors  4 ,  5 . The pair of permanent magnets  2 ,  3  forms a magnetic field and moves along the horizontal axis Hax in response to a moving object whose position is to be detected. The pair of magnetic sensors  4 ,  5  senses a change in the magnetic field and provides a pair of digital electric signals. The position sensor  1  is mounted in a vehicle, and the digital electric signals are processed to form an inverse trigonometric function, which is inputted to an electronic control unit (ECU) to control various devices. 
         [0031]    Each of the permanent magnets  2 ,  3  has a prism-like rod portion  2   r  or  3   r  and an arc-shaped projecting portion  2   p  or  3   p  that projects from one side surface of the rod portion  2   r  or  3   r  between the opposite ends. Each of the permanent magnets  2 ,  3  is polarized in the longitudinal direction that is parallel to the horizontal axis Hax to have an S-pole at one end thereof and an N-pole at the other end. The pair of permanent magnets  2 ,  3  is disposed side by side in such that the tops  2   t,    3   t  of the projecting elements  2   p,    3   p  and the same magnetic poles confront each other, as shown in  FIG. 1A . Each of the pair of permanent magnets  2 ,  3  also has a uniform side width along the longitudinal axis Hax as shown in  FIG. 1B , thereby forming the permanent magnet member that provides a magnetic field in the inside space between the permanent magnets  2 ,  3 . In other words, the pair of permanent magnets is disposed in plane-symmetric with respect to a plane Sp that includes the horizontal axis Hax. In this magnetic field, magnetic flux density is the maximum at the center thereof in the longitudinal direction (magnetic center) and gradually decreases as the longitudinal position of the space leaves from the magnetic center, as shown in  FIG. 2 . Incidentally, a vertical axis Vax includes the magnetic center, whose longitudinal position L is 0. 
         [0032]    The arc-shaped projecting elements  2   p,    3   p  are formed so that the magnetic flux density characteristic curve changes along an approximate cosine curve S, as shown by a thick solid line in  FIG. 7 , where, a broken line indicates a magnetic flux density characteristic curve formed by a pair of rod-shaped permanent magnets having no arc-shaped projecting elements, and a thin solid line indicates a magnetic flux density characteristic curve formed by a pair of disk-like permanent magnets having no arc-shaped projecting elements. 
         [0033]    Each of the magnetic sensors  4 ,  5  is comprised of a Hall element and a processor, which are formed on an IC chip so as to provide the digital electric signals. The magnetic sensors  4 ,  5  are disposed spaced apart from each other at a distance d/2 along the horizontal axis Hax in the inside space between the permanent magnets  2 ,  3 . Incidentally, a distance d/2 corresponds to a quarter of the cycle of the cosine shown in  FIG. 3 . 
         [0034]    The magnetic sensors  4 ,  5  are the same in performance and size and compatible with each other. Therefore, the digital signals of the magnetic sensors  4 ,  5  draw approximate cosine curves α, β that respectively represent the magnetic flux density as the permanent magnets  2 ,  3  move along the horizontal axis Hax from the Vertical axis Vax where the longitudinal position L=0, as shown in  FIG. 3 . Incidentally, the amplitude of the characteristic curves α, β are adjusted to be same to each other. 
         [0035]    As shown in  FIG. 4A , the magnetic sensors  4 ,  5  are connected to a processor circuit  18  to form a sensor assembly  19 . The processor circuit  18  is comprised of a digital signal processor (DSP)  16  and a D/A converter  17 , as shown in  FIG. 4B . The DSP  16  includes an offset adjusting circuit  20 , an inverse trigonometric function processor  21  and a gain adjusting circuit  22 . The offset adjusting circuit  20  subtracts an offset value from the digital electric signals of the magnetic sensors  4 ,  5  to provide a pair of output signals α′ and β′ as shown in  FIG. 5 . The offset value corresponds to the mean value between the maximum signal level and the minimum signal level. The offset value may be a value that corresponds to a weighted average of the maximum and the minimum levels. The inverse trigonometric function processor  21  provides an inverse trigonometric value from the output signals of the offset adjusting circuit  20 . 
         [0036]    Thus, the characteristic curves α and β, which are shown in  FIG. 3 , are converted to cosine curves α′ and sine curve β′ shown in  FIG. 5 . That is, the sensor assembly provides the following digital output signals Va and Vb, wherein: E represents the amplitude; and L represents a shift value. The gain adjusting circuit  22  equalizes the amplitude E of the cosine and sine curves α′ and β′. 
         [0000]      Va=E cos L   (Ex. 1) 
         [0000]      Vb=E sin L   (Ex. 2) 
         [0000]      The amplitude  E  can be expressed by the magnetic flux density  B  and the Hall current as  E=K·I·B    (Ex. 3) 
         [0000]      Because  Vb/Va= tan  L    (Ex. 4) 
         [0000]        L =arc tan( Vb/Va )   (Ex. 5) 
         [0037]    Thus, L is calculated by the inverse trigonometric function processor  21 . 
         [0038]    Then, the inverse trigonometric function processor  21  outputs the following output value V, which is shown in  FIG. 6 . 
         [0039]    V=arctan(Vb/Va)·d/Π (6), wherein d/Π is a coefficient for converting the unit “radian” to the unit “millimeter”. 
         [0040]    Because the member (Vb/Va) almost eliminates temperature dependent variation, the output value V will not change even if the temperature around the sensor changes. 
         [0041]    The output value V, which is a digital value, is converted into an analog value by the D/A converter  17  and sent to an ECU to control some device. Hence, it is possible to accurately detect the position of the object without taking the temperature change into account. 
         [0042]    A position sensor according to the second embodiment of the invention will be described with reference to  FIG. 8 . 
         [0043]    Incidentally, the same reference numeral indicates the same or substantially the same member, portion, part or unit as the first or previous embodiment hereafter. 
         [0044]    As shown in  FIG. 8 , a sensor assembly  24  includes a pair of Hall elements  41 ,  51 , a pair of operational amplifiers  25 ,  26  and an A/D converter  27  instead of the pair of magnetic sensors  4 ,  5  that provides digital electric signals. This embodiment can detect the position of a shift value L between several micrometers and several tens of micrometers. 
         [0045]    A position sensor according to the third embodiment of the invention will be described with reference to  FIGS. 9A and 9B . 
         [0046]    The pair of permanent magnets  2 ,  3  of the first embodiment is replaced by a single, generally cylindrical permanent magnet  30 , which has an inwardly projecting inside surface  40 . In other words, the longitudinal cross section of the permanent magnet has an arc-shaped projecting element having a top  30   t  at the center thereof. The longitudinal cross section of the inside surface corresponds to the arc-shaped projecting elements  2   p  and  3   p  of the first embodiment, which confronts each other. The permanent magnet  30  also forms a ring on a plane perpendicular to the longitudinal direction, as shown in  FIG. 9A . 
         [0047]    The permanent magnet  30  is polarized in the longitudinal direction to have an S-pole at one end thereof and an N-pole at the other end. The magnetic sensors  4 ,  5  are disposed spaced apart from each other at a distance d/2 in the longitudinal direction inside the permanent magnet  30 . Therefore, the digital signals of the magnetic sensors  4 ,  5  draw approximate cosine characteristic curves α, β as the permanent magnet  30  moves along the horizontal axis thereof from the longitudinal position L=0 of the inside space, as shown in  FIG. 3 . As a result, the output signal V of the position sensor  1 , which is expressed by Ex. (6) and shown in  FIG. 6  can be provided. 
         [0048]    Because the generally cylindrical shape of the permanent magnet  30  forms a smooth and regular magnetic field, the output signal V can be detected accurately even if the position of the magnetic sensors  4 ,  5  is shifted in a direction perpendicular to the longitudinal direction a little from a designated position. 
         [0049]    A position sensor according to the fourth embodiment of the invention will be described with reference to  FIGS. 10A ,  10 B and  10 C. 
         [0050]    The pair of permanent magnets  2 ,  3  of the first embodiment is replaced by a pair of semi-cylindrical permanent magnets  32 ,  33 , each of which is a fraction of the cylindrical permanent magnet  30  shown in  FIGS. 9A and 9B . In other words, the inside surface corresponds to the arc-shaped projecting element  2   p  or  3   p  of the permanent magnet  2  or  3  of the first embodiment. The outside surface may form differently according to a mounting circumstance. 
         [0051]    The arcs are generally concentric with the horizontal axis Hax. In other words, the pair of permanent magnets  32 ,  33  is disposed in a plane symmetric with respect to a symmetry plane that includes the horizontal axis Hax. 
         [0052]    Each of the permanent magnets  2 ,  3  is polarized in the longitudinal direction to have an S-pole at one end thereof and an N-pole at the other end. The pair of permanent magnets  32 ,  33  is disposed side by side in such that the tops of the projecting elements  32   t,    33   t  confront each other at the center thereof in the longitudinal direction and, also, in such that the same magnetic poles confront each other at the ends thereof, as shown in  FIG. 10B . Each of the pair of permanent magnets  32 ,  33  has an arc-length, or a uniform side width in the circumferential direction along the longitudinal direction as shown in  FIG. 10C , thereby forming the permanent magnet member that provides a magnetic field at the inside space onside the permanent magnets  32 ,  33 . 
         [0053]    In this magnetic field, magnetic flux density is the maximum at the magnetic center thereof and gradually decreases as the longitudinal position of the space leaves from the magnetic center, as shown in  FIG. 2 . That is, the arc-shaped projecting elements are formed so that the magnetic flux density characteristic curve changes along a cosine curve S, as shown by a thick solid line in  FIG. 7 . 
         [0054]    The magnetic sensors  4 ,  5  are disposed spaced apart from each other at a distance d/2 in the longitudinal direction inside the permanent magnets  32 ,  33 . Therefore, the digital signals of the magnetic sensors  4 ,  5  draw approximate cosine characteristic curves α, β as the permanent magnet  30  moves along the horizontal axis H ax  thereof from the Vertical axis V ax , as shown in  FIG. 3 . 
         [0055]    Because the generally semi-cylindrical shape of the permanent magnets  32 ,  33  form a smooth and regular magnetic field, the output signal V can be detected accurately even if the position of the magnetic sensors  4 ,  5  is shifted in a direction perpendicular to the longitudinal direction a little from a designated position. 
         [0056]    A position sensor  1  according to the fifth embodiment of the invention will be described with reference to  FIG. 11 . 
         [0057]    A position sensor  1  includes a permanent magnet member that is comprised of a pair of magnet members  50 ,  51  and a sensor assembly that includes a pair of magnetic sensors  4 ,  5 . The pair of magnet members  50 ,  51  forms a magnetic field and moves in response to a moving object whose position is to be detected. 
         [0058]    The pair of magnetic sensors  4 ,  5  senses a change in the magnetic field and provides a pair of digital electric signals. 
         [0059]    Each of the magnet members  50 ,  51  has a prism-like permanent magnet  2 A or  3 A and a pair of arc-shaped projecting members  2 B,  2 C or  3 B,  3 C that projects from opposite ends of the permanent magnets  2 A or  3 A. Each of the permanent magnets  2 A or  3 A is polarized in the longitudinal direction to have an S-pole at one end thereof and an N-pole at the other end. The pair of magnet members  50 ,  51  is disposed side by side in such that the ends of the pair of arc-shaped projecting members  2 B,  2 C or  3 B,  3 C of one magnet member  50  or  51  approaches and confronts the ends of the other pair and, also, in such that the same magnetic poles confront each other. Each of the pair of magnet members  50 ,  51  also has a uniform side width along the longitudinal direction, thereby forming the permanent magnet member that provides a magnetic field at the space between the magnet members  50 ,  51 . In other words, the pair of magnet members  50 ,  51  is disposed in plane symmetric with respect to a symmetry plane that includes a horizontal axis Hax. In this magnetic field, magnetic flux density is the maximum at the center thereof in the longitudinal direction and gradually decreases as the longitudinal position of the space leaves from the magnetic center that is included in a vertical axis Vax. That is, the arc-shaped projecting members  2 B,  2 C,  3 B,  3 C are formed so that the magnetic flux density characteristic curve changes along a cosine curve S, as shown in  FIG. 7 . 
         [0060]    A position sensor  1  according to the sixth embodiment of the invention will be described with reference to  FIGS. 12 and 13 . 
         [0061]    The position sensor  1  includes a permanent magnet member that is comprised of a pair of permanent magnets  2 ,  3  and a sensor assembly that includes an angle correction magnetic sensor  55  in addition to a pair of main magnetic sensors  4 ,  5 . That is, the position sensor  1  according to the sixth embodiment is substantially the same as the first embodiment except for the angle correction sensor  55  and an angle correcting program. The angle correction magnetic sensor  55  is the same in performance and size as each of the pair of main magnetic sensors  4 ,  5  and compatible with each other. The angle correction magnetic sensor  55  is disposed at the middle of the space between the main magnetic sensors  4 ,  5  so that the sensing surface of the angle correction magnetic sensor  55  inclines to a direction of an angle α to the sensing surface of the main magnetic sensors  4 ,  5 , as shown in  FIG. 12 . The angle correction magnetic sensor  55  can be integrated with the main magnetic sensors  4 ,  5 . 
         [0062]    The angle correction magnetic sensor  55  is effective for the position sensor  1  to provide accurate output signals even if the pair of the permanent magnets  2 , 3  inclines to a direction of an angle θ to the horizontal axis by accident. 
         [0063]    When the permanent magnet member that includes the pair of permanent magnets  2 ,  3  moves along the horizontal axis, the output signal Va of one of the main magnetic sensor and the output signal Vc of the angle correction magnetic sensor  55  are respectively expressed as follows. 
         [0000]        Va=K·I·B  cos θ  (Ex 7) 
         [0000]        Vc=K·I·B  cos(θ+α)   (Ex 8) 
         [0000]      Accordingly: 
         [0000]      ( Va−Vc )/( Va+Vc )=tan {(2θ+α)/2}·tan(α/2)   (Ex 9) 
         [0000]      θ=arctan {( Va−Vc )/( Va+Vc )·cot(α/2)}·180°/Π−α/2   (Ex 10) 
         [0000]    Then, the corrected output voltages Va′ and Vb′ and the shift value L can be expressed as follows. 
         [0000]        Va′=Va  cos θ+ Vc  cos(α−θ)   (Ex 11) 
         [0000]        Vb′=Vb  cos θ+ Vc  cos(α−θ)   (Ex 12) 
         [0000]        L= arctan( Va′/Vb′ )· d/Π ·cos θ  (Ex 13) 
         [0064]    This correction can be made even if the angle correction magnetic sensor  55  is different in performance from the main magnetic sensors  4 ,  5 . 
         [0065]    In that case, the following expressions can be used. 
         [0000]        Va=m·K·I·B  cos θ  (Ex 14) 
         [0000]        Vc=n·Kc·Ic·B  cos(θ+α)   (Ex 15) 
         [0066]    In the above expressions, n and m are set so that m·K·I·B and n·Kc·Ic·B can be equalized. 
         [0067]    The angle correction magnetic sensor  55  can be disposed so that the sensing surface of thereof can be perpendicular to the sensing surface of the main magnetic sensors  4 ,  5 , as shown in  FIG. 15 . 
         [0068]    In this case, the expressions (Ex 10), (Ex 11) and (Ex 12) are expressed as follows. 
         [0000]      θ=arctan {( Va−Vc )/( Va+Vc )·180°/Π  (Ex 16) 
         [0000]        Va′=Va  cos θ+ Vc  sin θ  (Ex 17) 
         [0000]        Vb′=Vb  cos θ+ Vc  sin θ  (Ex 18) 
         [0069]    A position sensor  1  according to the seventh embodiment of the invention will be described with reference to  FIGS. 14 and 15 . 
         [0070]    The position sensor  1  includes a permanent magnet member that is comprised of a pair of permanent magnets  2 ,  3  and a sensor assembly that includes a pair of angle correction magnetic sensors  55 ,  56  in addition to a pair of main magnetic sensors  4 ,  5 . That is, the position sensor  1  according to the seventh embodiment is substantially the same as the sixth embodiment except for the angle correction sensor  56  and the angle correcting program. The pair of angle correction magnetic sensors  55 ,  56  is the same in performance and size as each of the pair of main magnetic sensors  4 ,  5  and compatible with each other. The angle correction magnetic sensors  55 ,  56  are respectively disposed at the sides of the main magnetic sensors  5 ,  4  so that the sensing surfaces of the angle correction magnetic sensors  55 ,  56  face perpendicular to the sensing surface of the main magnetic sensors  5 ,  4 , as shown in  FIG. 14 . The angle correction magnetic sensors  55 ,  56  can be integrated with the main magnetic sensors  4 ,  5 . 
         [0071]    The angle correction magnetic sensors  55 ,  56  are effective for the position sensor  1  to provide accurate output signals even if the pair of the permanent magnets  2 ,  3  inclines to a direction of an angle θ to the horizontal axis by accident, as described previously. 
         [0072]    When the permanent magnet member that includes the pair of permanent magnets  2 ,  3  moves along the horizontal axis Hax, the output signals Va, Vb of the main magnetic sensors  4 ,  5  and the output signals Vc, Vd of the angle correction sensors  55 ,  56  are respectively provided. 
         [0073]    The corrected output voltage Vb′ of the main magnetic sensor  5  is expressed as follows. 
         [0000]        Vb′=Vb  cos θ+ Vd  sine θ  (Ex 19) 
         [0074]    Because the corrected output voltage Va′ is expressed previously in the expression (Ex 11), the shift value L can be obtained by the expression (Ex 13). 
         [0075]    If the angles between the sensing surfaces of the main magnetic sensors  4 ,  5  and each of the permanent magnets  2 ,  3  are respectively θ 1  and θ 2 , these angles can be expressed as follows. 
         [0000]      θ1=arctan( Vc/Va )·180°/Π  (20) 
         [0000]      θ2=arctan( Vd/Vb )·180°/Π  (21) 
         [0076]    The corrected output voltages Va′, Vb′ can be expressed as follows. 
         [0000]        Va′=Va  cos θ1 +Vc  sine θ1   (Ex 22) 
         [0000]        Vb′=Vb  cos θ2 +Vd  sine θ2   (Ex 23) 
         [0077]    Then, the shift value can be expressed as follows. 
         [0000]        L =arctan( Va′/Vb′ )· d/Π· cos {(θ1+θ2)/2}  (Ex 24) 
         [0078]    In the foregoing description of the present invention, the invention has been disclosed with reference to specific embodiments thereof It will, however, be evident that various modifications and changes may be made to the specific embodiments of the present invention without departing from the scope of the invention as set forth in the appended claims. Accordingly, the description of the present invention is to be regarded in an illustrative, rather than a restrictive, sense.