Abstract:
A stepper motor driving apparatus, includes a stepper motor; a driven member interlocked with a rotation of a rotor of the stepper motor, a stopper stopping the driven member in a zero position, a controller controlling the excitation state of an excitation coil of the stepper motor, an induced voltage waveform detector detecting an induced voltage waveform generated on the basis of change of magnetic flux in accordance with the rotation of the rotor, and a zero position detector detecting whether the driven member is stopped in the zero position. The zero position detector includes a comparator which compares a time T 2  in which each induced voltage waveform exceeds a predetermined threshold value with a predetermined contact determining reference time Tref, and a determinant which determines whether the driven member is stopped in the zero position by the stopper based on a result of the comparison by the comparator.

Description:
BACKGROUND OF THE INVENTION 
   The present invention relates to a stepper motor driving apparatus and particularly to a stepper motor driving apparatus improved in a process of initializing a stepper motor used in an on-vehicle meter or the like. 
   For the reason of indication accuracy and cost, a stepper motor has been recently put into wide use in an on-vehicle meter such as a speed meter for indicating vehicle velocity or a tachometer for indicating the number of engine revolutions. 
   In a vehicle equipped with an on-vehicle meter using such a stepper motor, there is however a possibility that a difference between the required amount of movement of an indicating pointer interlocked with the rotation of the stepper motor and the actual amount of movement of the indicating pointer may be generated by a mistaken drive signal caused by vibration of the vehicle, noise, etc. 
   Therefore, in an on-vehicle meter using such a stepper motor, an initializing process is carried out so that the stepper motor is rotated backward in a stopper direction, for example, at switching-on timing of an ignition switch to restore the indicating pointer to a zero position decided by the stopper. 
   In the initializing process, whether the indicating pointer position-controlled by the stepper motor comes into contact with the stopper deciding the zero position of the indicating pointer is detected as follows. An induced voltage generated on the basis of change of magnetic flux in accordance with the rotation of a rotor of the stepper motor is detected. Zero position detection is performed so that when the detected induced voltage is not higher than a predetermined threshold, a decision is made that the indicating pointer has been stopped because of collision with the stopper disposed in the zero position. 
   For example, a stepper motor driving apparatus in which such zero position detection can be performed has been disclosed in International Patent Publication No. WO97/37425. 
     FIGS. 8 and 9  are block circuit diagrams of a related stepper motor driving apparatus disclosed in the WO97/37425. A stepper motor  10  includes four winding wires  1  to  4 , and four switches  5  to  8  connected in series to the winding wires respectively. These winding wires  1  to  4  are connected between a positive supply potential UB, for example, of a car battery and a ground potential  0  by the switches  5  to  8  respectively. Tap terminals  11  to  14  are provided between the winding wires and the switches, respectively. The tap terminals  11  to  14  are used for monitoring voltages of the winding wires  1  to  4  respectively in order to specify a stopper and blocking. When the switches  5  to  8  are controlled to be opened or closed, the winding wires  1  to  4  included in the stepper motor  10  are connected to or disconnected from the supply potential UB. That is, the winding wires  1  to  4  are in a current conduction state or in a current non-conduction state. 
   In the stepper motor including the switches  5  to  8  disposed between the ground potential  0  and the winding wires  1  to  4  respectively as shown in  FIG. 8 , there is formed a stepper motor control portion having ground switches or low side drivers. 
   Next, in  FIG. 9 , an evaluation circuit  20  detects voltage peaks  51  and  52  of a voltage chart  50  induced in each current non-conduction winding wire as shown in  FIG. 10 . When the voltage peaks  51  and  52  are larger than a predetermined threshold, the evaluation circuit  20  specifies elastic blocking and generates a suitable output signal. The output signal serves as an external interrupt signal supplied to a micro-controller provided in a not-shown control circuit for controlling the stepper motor  10 . 
   The voltage peaks  51  and  52  are different in polarity. This fact will be understood well when a zero line  53  shown in  FIG. 10  is used as a reference line. The polarity can be measured appropriately by the evaluation circuit  20 . More advantageously, detection can be executed even in the case where the stepper motor operates slowly because the stepper motor is out of order. The evaluation circuit need not have a high time sensitivity. Accordingly, inexpensive constituent elements can be used. 
   The evaluation circuit  20  shown in  FIG. 9  has four branch paths which are the same in configuration and which correspond to the four winding tap terminals  11  to  14  shown in  FIG. 8 . Comparators  21  corresponding to the winding wires are provided in the branch paths respectively so as to be independent of one another. Each of the comparators  21  has a noninverting input terminal designated by “+”, and an inverting input terminal designated by “−”. The inverting input terminal of each comparator  21  is connected to a predetermined potential through a voltage divider which is composed of resistors  22  and  23  and which is connected between the supply potential UB and the ground potential  0 . The noninverting input terminal of each comparator  21  is connected to a predetermined potential through a voltage divider which is composed of resistors  24  and  25  and which is connected between the supply potential UB and the ground potential  0 . A series circuit composed of a diode  26  and a capacitor  27  is connected between each of the input terminals  11  to  14  of the evaluation circuit  20  and the noninverting input terminal of corresponding one of the comparators  21 . The polarity of each diode  26  is decided as follows. That is, the polarity of each diode  26  is decided so that only a negative voltage, e.g. a voltage peak  52  shown in  FIG. 10  can reach the noninverting input terminal “+” of a corresponding comparator  21  through a corresponding capacitor  27 . 
   A threshold for the comparator  21  is decided in the inverting input terminal “−” by the voltage divider composed of the resistors  22  and  23 . The voltage divider composed of the resistors  24  and  25  is provided so that only the voltage peak  52  exceeding a predetermined potential can reach the noninverting input terminal. The voltage in the inverting input terminal of the comparator  21  is decided by the voltage divider composed of the resistors  22  and  23  so that the voltage is lower than the voltage in the noninverting input terminal. Only the negative voltage is input and coupled to the noninverting input terminal of the comparator  21  by the diode  26  while only the edge of the negative voltage is input and coupled to the noninverting input terminal by the capacitor  27 . The resistance ratio at a tap of the voltage divider composed of the resistors  22  and  23  is set to be equal to the resistance ratio at a tap of the voltage divider composed of the resistors  24  and  25 . Accordingly, even in the case where the supply potential UB fluctuates, a signal output from the comparator  21  does not depend on the fluctuation of the supply potential UB because the two voltage dividers can lead the fluctuation of the supply potential UB in the same ratio. 
   The comparators  21  have output terminals  28  respectively. The output terminals  28  are led to an output terminal  200  common to all the comparators  21  through negatively polarized diodes  29  respectively. The common output terminal  200  is further connected to a reference voltage source Uref through a resistor  201  and connected to the ground potential  0  through a capacitor  202 . As described above, when the voltage peak  52  of the voltage chart  50  induced in a current non-conduction winding wire exceeds a reference value, that is, when elastic blocking is specified, a signal is generated at the common output terminal  200 . The output signal generated at the common output terminal  200  for designating blocking is supplied as an external interrupt signal to the micro-controller in the control circuit of the stepper motor. In the micro-controller, the output signal is further processed appropriately. 
   The fact that a reversed phase voltage is induced in a current non-conduction winding wire when an armature rotates backward is used in the evaluation for specifying elastic blocking. This voltage in the noninverting input terminal of at least one of the comparators  21  is lower than the voltage in the inverting input terminal. As a result, the output of the comparator  21  is switched. Accordingly, an interrupt is triggered so that blocking of the stepper motor is specified. On the contrary, when the stepper motor is operating, the voltage in the noninverting input terminal of the comparator  21  is kept higher than the voltage in the inverting input terminal. 
   SUMMARY OF THE INVENTION 
   In the above related stepper motor driving apparatus, however, the fact that a reversed phase voltage is induced in a current non-conduction wiring wire when an armature rotates backward is used in the evaluation for specifying elastic blocking (i.e. detecting the zero position). 
   For this reason, when the stepper motor driving apparatus is applied to an on-vehicle meter, the indicating pointer attached to the rotation shaft of the stepper motor stops in a position far from the stopper because of the backward rotation of the armature after the indicating pointer comes into contact with the stopper. Accordingly, there is a problem of accuracy in the meter because the indicating pointer cannot be set in the zero position accurately. Moreover, the indicating pointer behaves intensively because of the retreat (backward rotation) of the indicating pointer, so that the behavior of the indicating pointer looks unattractive. It is therefore necessary to detect the induced voltage before the backward rotation. 
   Therefore, an object of the invention is to provide a stepper motor driving apparatus in which the zero position can be detected more accurately in consideration of the above problem in the background art.
     (1) The invention provides a stepper motor driving apparatus including:
       a stepper motor, which includes an excitation coil, and a rotor rotating in accordance with change of excitation state of the excitation coil;   a driven member, which is interlocked with the rotation of the rotor;   a stopper, which mechanically stops the driven member in a zero position;   a controller, which controls the excitation state of the excitation coil;   an induced voltage waveform detector, which detects an induced voltage waveform generated on the basis of change of magnetic flux in accordance with the rotation of the rotor; and   a zero position detector, which detects whether the driven member is stopped in the zero position by the stopper or not, on the basis of the induced voltage waveform detected by the induced voltage waveform detector,   wherein the zero position detector includes:
           a comparator, which compares a time T 2  in which each induced voltage waveform exceeds a predetermined threshold value with a predetermined contact determining reference time Tref; and   a determinant, which determines whether or not the driven member is stopped in the zero position by the stopper based on a result of the comparison by the comparator.   
           
       (2) The invention provides a stepper motor driving apparatus described in the paragraph (1), wherein the threshold value is set so that change of the time T 2  in which the induced voltage waveform exceeds the predetermined threshold value is minimized with respect to temperature change in a specific temperature range.   (3) The invention provides a stepper motor driving apparatus including:
       a stepper motor, which includes an excitation coil, and a rotor rotating in accordance with change of excitation state of the excitation coil;   a driven member, which is interlocked with the rotation of the rotor;   a stopper, which mechanically stops the driven member in a zero position;   a controller, which controls the excitation state of the excitation coil;   an induced voltage waveform detector, which detects an induced voltage waveform generated on the basis of change of magnetic flux in accordance with the rotation of the rotor; and   a zero position detector, which detects whether the driven member is stopped in the zero position by the stopper or not, on the basis of the induced voltage waveform detected by the induced voltage waveform detector,   wherein the zero position detector includes:
           a comparator, which compares the number of sampling cycles in which each induced voltage waveform sampled in predetermined sampling timing in a predetermined sampling time exceeds a predetermined threshold value with a predetermined contact determining reference number; and   a determinant, which determines whether or not the driven member is stopped in the zero position by the stopper based on a result of the comparison by the comparator.   
           
       (4) The invention provides a stepper motor driving apparatus described in the paragraph (3), wherein the threshold value is set so that change of the number of sampling cycles in which the induced voltage waveform sampled in predetermined sampling timing in a predetermined sampling time exceeds the predetermined threshold value is minimized with respect to temperature change in a specific temperature range.   

   According to the invention as in the paragraph (1), the zero position can be detected more accurately because the time in which the induced voltage waveform exceeds a threshold is monitored without use of the fact that a reversed phase voltage is induced in a current non-conduction winding wire when an armature rotates backward as in the related art. 
   According to the invention as in the paragraph (2), the zero position can be detected surely because the influence of temperature change can be avoided. 
   According to the invention as in the paragraph (3), the zero position can be detected more accurately because the number of sampling cycles in which the induced voltage waveform sampled in predetermined sampling timing in a predetermined sampling time exceeds a predetermined threshold is monitored without use of the fact that a reversed phase voltage is induced in a current non-conduction winding wire when an armature rotates backward as in the related art. 
   According to the invention as in the paragraph (4), the zero position can be detected surely because the influence of temperature change can be avoided. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above objects and advantages of the present invention will become more apparent by describing in detail preferred exemplary embodiments thereof with reference to the accompanying drawings, wherein: 
       FIG. 1  is a configuration view of an on-vehicle meter using an embodiment of a stepper motor driving apparatus according to the invention; 
       FIG. 2  is a diagram showing the configuration of the driving apparatus in the on-vehicle meter depicted in  FIG. 1 ; 
       FIG. 3  is a current vector graph of an excitation signal in an ordinary operating mode; 
       FIG. 4  is a waveform graph showing time-series current vectors of an excitation signal supplied to each excitation coil in a micro-stepping drive method in an ordinary operating mode; 
       FIG. 5  is a flow chart showing a procedure of processing executed by a CPU of the drive circuit; 
       FIGS. 6A and 6B  are views for explaining a principle of judgment as to whether an indicating pointer is in contact with a stopper or not; 
       FIG. 7  is a view for explaining another method for setting the threshold; 
       FIG. 8  is a block circuit diagram of a related stepper motor driving apparatus; 
       FIG. 9  is a block circuit diagram of an evaluation circuit in the driving apparatus depicted in  FIG. 8 ; and 
       FIG. 10  is a graph showing voltage change in a current non-conduction winding wire in the driving apparatus depicted in  FIGS. 8 and 9 . 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1  is a configuration view of an on-vehicle meter using an embodiment of a stepper motor driving apparatus according to the invention. For example, the on-vehicle meter is a speed meter which has a stepper motor  1 , and a drive circuit  4  for performing the drive control of the stepper motor  1 . The stepper motor  1  includes two excitation coils  1   a   1  and  1   a   2  disposed on a stator (not shown) so as to be perpendicular to each other, and a rotor  1   b  which is magnetized so that three N poles and three S poles are arranged alternately and which rotates in accordance with change in excitation state of the excitation coils  1   a   1  and  1   a   2 . 
   The on-vehicle meter further has an indicating pointer  2  provided as a driven member interlocked with the rotation drive of the rotor  1   b , gears  3  for transmitting the rotation drive of the rotor  1   b  to the indicating pointer  2 , and a stopper  5  for stopping the indicating pointer  2  in a zero position by contacting the indicating pointer  2  mechanically. Incidentally, the zero position setting based on contact between the stopper  5  and the indicating pointer  2  may be replaced by a zero position setting based on contact between a stopper piece  6  as a driven member protruded from one of the gears  3  and a stopper  5 ′ provided separately in a position corresponding to the zero position. 
   As shown in  FIG. 2 , the drive circuit  4  includes a micro-computer  41  as a controller. The micro-computer  41  has a central processing unit (CPU)  41   a  for performing various kinds of processes in accordance with programs, a memory  41   b , a motor drive circuit  41   c , and a zero position detection circuit  41   d.    
   An angular data signal D 1  calculated on the basis of velocity information given from a vehicle velocity sensor (not shown) and an initialization command signal Son of a high level based on an ignition-on operation of an ignition switch (not shown) are input to the CPU  41   a . Excitation signals S 1 , S 2 , S 3  and S 4  are output from the motor drive circuit  41   c  so as to be supplied to respective opposite ends a and b of the excitation coils  1   a   1  and  1   a   2 . 
   Induced voltage waveforms V 1 , V 2 , V 3  and V 4  are input to the zero position detection circuit  41   d  through interface (I/F) circuits  42   a ,  42   b ,  42   c  and  42   d  respectively. The I/F circuits  42   a  to  42   d  are connected to the respective ends a and b of the excitation coils  1   a   1  and  1   a   2 . The zero position detection circuit  41   d  supplies a zero position judgment signal to the CPU  41   a.    
   In an ordinary operating mode, the CPU  41   a  generates a first excitation pattern in accordance with the angular data signal D 1  by a micro-stepping drive method so that one electrical cycle is formed by a plurality of excitation steps for rotating the rotor  1   b  forward and backward, and supplies the first excitation pattern to the excitation coils  1   a   1  and  1   a   2  to control the excitation state of the excitation coils  1   a   1  and  1   a   2  to thereby drive the stepper motor  1  to rotate the rotor  1   b  in a forward direction (Y 2 ) or a backward direction (Y 1 ) in accordance with the angular data signal D 1 . During the initializing process, the CPU  41   a  generates a second excitation pattern in accordance with the initialization command signal S 1  in such manner that the plurality of excitation steps in the first excitation pattern are partially converted into excitation steps for detecting induced voltage waveforms, and supplies the second excitation pattern to the excitation coils  1   a   1  and  1   a   2  to thereby drive the stepper motor  1  to rotate the rotor  1   b  in the backward direction (i.e. Y 1  direction) in which the indicating pointer  2  moves toward the stopper  5 . 
   The micro-stepping drive method uses 1/n(n≧3) micro-stepping. For example, in this embodiment, micro-stepping for dividing one electrical cycle into 64 steps is used so that an electrical angle of 90 degrees is divided into 16 steps. 
     FIG. 3  is a current vector graph of an excitation signal in an ordinary operating mode.  FIG. 3  shows an example of current vectors in an angle of 90 degrees corresponding to excitation steps  0  to  16  in one electrical cycle. 
     FIG. 4  is a waveform graph showing time-series current vectors of an excitation signal supplied to the excitation coils  1   a   1  and  1   a   2  in the micro-stepping drive method in an ordinary operating mode. As shown in  FIG. 4 , in the ordinary operating mode, an excitation signal PWM-controlled so that the duty ratio increases or decreases stepwise in a range of from 0% to 100% is supplied to each of the excitation coils  1   a   1  and  1   a   2 . 
   During the initializing process, induced voltage waveforms V 1 , V 2 , V 3  and V 4  generated at the respective opposite ends of the excitation coils  1   a   1  and  1   a   2  in a non-excitation state in which one end is opened are input to the zero position detection circuit  41   d  through the I/F circuits respectively in accordance with the detection timing signal. When the time or the number of sampling cycles in which any one of the input induced voltage waveforms V 1 , V 2 , V 3  and V 4  is not larger than a threshold is not larger than a predetermined value, the zero position detection circuit  41   d  generates a zero position judgment signal for judging that the indicating pointer  2  has come into contact with the stopper  5  in the zero position, and supplies the zero position judgment signal to the CPU  41   a . That is, when one end of each of the excitation coils  1   a   1  and  1   a   2  is opened, the excitation coils  1   a   1  and  1   a   2  serve as elements for detecting induced voltage waveforms. 
   Next, the operation of the on-vehicle meter configured as described above will be described below with reference to  FIG. 5  which is a flow chart showing a procedure for the zero position detection process executed by the CPU  41   a  and the zero position detection circuit  41   d . When the initializing process starts, the excitation step is updated at regular update intervals (step S 1 ). Then, a judgment is made as to whether backward rotation has reached the induced voltage waveform detection excitation inversion step or not (step S 2 ). When backward rotation has reached the excitation inversion step, the induced voltage waveform detection process starts (step S 3 ). 
   Then, the induced voltage waveform measuring coils are changed from a drive output to a Hi-Z output (high impedance output) in accordance with the detection timing signal (step S 4 ). The term “Hi-Z output” means a state in which one end of each of excitation coils equivalent to the induced voltage waveform measuring coils is opened during a sampling time (e.g. 3 ms in this embodiment) based on the induced voltage waveform detection excitation step so that the excitation coils are not excited so that induced voltages are output from the excitation coils during the sampling time. 
   The waveforms of the induced voltages generated from the induced voltage waveform measuring coils during the sampling time (T 1 ) based on the induced voltage waveform detection excitation step are sampled by several times at predetermined sampling timing intervals (step S 5 ). That is, the induced voltage waveforms V 1 , V 2 , V 3  and V 4  generated at the respective opposite ends of the excitation coils  1   a   1  and  1   a   2  are sampled through the I/F circuits respectively and input to the zero position detection circuit  41   d.    
   Then, a judgment is made as to whether a time (T 2 ) in which each induced voltage waveform sampled during the sampling time T 1  exceeds a threshold is shorter than a predetermined reference time (Tref) (i.e. T 2 &lt;Tref) or not (step S 6 ). 
   That is, when the time T 2  in which each induced voltage waveform sampled during the sampling time T 1  exceeds a threshold (Vref) is not shorter than the reference time Tref, a decision is made that the indicating pointer  2  has not come into contact with the stopper  5  yet and is rotating. When the time T 2  is shorter than the reference time Tref, a decision is made that the indicating pointer  2  has already come into contact with the stopper  5 . 
     FIGS. 6A and 6B  are views for explaining a principle of the judgment as to whether the indicating pointer  2  has come into contact with the stopper  5  or not.  FIGS. 6A and 6B  show the relations among the induced voltage, the result of comparison between the induced voltage value and the threshold Vref and the sampling timing in the sampling time T 1  in the case where the sampling time T 1  is long.  FIG. 6A  shows a state in which the indicating pointer  2  is rotating.  FIG. 6B  shows a state in which the indicating pointer  2  has come into contact with the stopper  5 . 
   In the rotating state shown in  FIG. 6A , sampling is performed by 15 times at predetermined sampling timing intervals during the sampling time T 1 . As a result of comparison between the induced voltage value and the threshold Vref, it is found that, in 7 sampling cycles among the 15 sampling cycles, the induced voltage value exceeds the threshold Vref. That is, in the third to seventh sampling cycles and the twelfth and thirteenth sampling cycles, that is, in 7 sampling cycles in total, in a period of from the start of the sampling time T 1  to the end of the sampling time T 1 , the induced voltage value exceeds the threshold Vref. A result of comparison between the induced voltage value and the threshold Vref is expressed as a high level signal having two pulses with time widths T 2   1  and T 2   2 . The time T 2  in which the sampled induced voltage value exceeds the threshold Vref is given as the sum of the time widths T 2   1  and T 2   2  of the high level signal (T 2 =T 2   1 +T 2   2 ). 
   In the contact state shown in  FIG. 6B , the amplitude of the induced voltage becomes smaller than that in the rotating state. Accordingly, as a result of comparison between the induced voltage value and the threshold Vref during the sampling time T 1 , it is found that, in 3 sampling cycles among the 15 sampling cycles, the induced voltage value exceeds the threshold Vref. That is, in the second to fourth sampling cycles, that is, in 3 sampling cycles in total, in a period of from the start of the sampling time T 1  to the end of the sampling time T 1 , the induced voltage value exceeds the threshold Vref. A result of comparison between the induced voltage value and the threshold Vref is expressed as a high level signal having one pulse with a time width T 2   3 . The time T 2  in which the sampled induced voltage value exceeds the threshold Vref is given as the time width T 2   3  of the high level signal (T 2 =T 2   3 ). 
   Therefore, when, for example, the criterional reference time Tref is set to have a value corresponding to four sampling cycles in advance, the time T 2  based on the comparison result shown in  FIG. 6A  is longer than the criterional reference time Tref to make it possible to decide that the indicating pointer  2  has not come into contact with the stopper  5  and is rotating whereas the time T 2  based on the comparison result shown in  FIG. 6B  is shorter than the criterional reference time Tref to make it possible to decide that the indicating pointer  2  has already come into contact with the stopper  5 . 
   Referring back to the flow chart of  FIG. 5 , when the step S 6  results in “YES”, the output excitation phase is kept for a predetermined time (step S 8 ) and then the initializing process is terminated normally. 
   On the other hand, when the step S 6  results in “NO”, a judgment is made as to whether the rotor  1   b  has rotated by a predetermined angle or not (step S 9 ). When the step S 9  results in “YES”, the output excitation phase is kept for a predetermined time (step S 10 ) and then the initializing process is terminated abnormally. When the step S 9  results in “NO”, the backward rotation process is executed up to the next detection excitation step in a micro-stepping manner (step S 11 ) and then the current position of the routine goes back to the step S 4 . 
   As described above, unlike the related apparatus, the fact that a reversed phase voltage is induced in a current non-conduction winding wire when an armature rotates backward is not used in the invention. In the invention, a judgment is made as to whether the time T 2  in which the sampled induced voltage waveform exceeds the threshold Vref is shorter than the predetermined criterional reference time Tref or not. When the time T 2  in which the sampled induced voltage waveform exceeds the threshold Vref is not shorter than the criterional reference time Tref, a decision is made that the indicating pointer  2  has not come into contact with the stopper  5  yet and is rotating. When the time T 2  is shorter than the criterional reference time Tref, a decision is made that the indicating pointer  2  has already come into contact with the stopper  5 . Accordingly, the zero position can be detected more accurately. 
   Although an embodiment of the invention has been described above, the invention is not limited thereto and various changes and modifications may be made. 
   For example, the threshold Vref in the above embodiment may be set so that the influence of temperature change can be eliminated as sufficiently as possible. 
     FIG. 7  is a view for explaining change of an induced voltage waveform in accordance with temperature change. In  FIG. 7 , the curves A, B and C show induced voltage waveform characteristics at temperatures of −40° C., 25° C. and 85° C. respectively. It is obvious from these curves that the characteristic of the induced voltage waveform is sharpened to exhibit a high peak value and a short time between zero-cross points as the temperature decreases, and that the characteristic of the induced voltage waveform is softened to exhibit a low peak value and a long time between zero-cross points as the temperature increases. 
   Therefore, from these characteristics, the threshold Vref is set in advance so that change of the time T 2  in which the induced voltage waveform exceeds the threshold Vref is minimized with respect to temperature change in a specific temperature range. That is, the threshold Vref is set in advance so that time widths T 2   A , T 2 B and T 2   C  in which the induced voltage waveform exceeds the threshold Vref are substantially equal to one another. 
   In other words, the threshold Vref is set in advance so that change of the number of sampling cycles in which the induced voltage waveform sampled in predetermined sampling timing in a predetermined sampling time exceeds the threshold Vref is minimized with respect to temperature change in a specific temperature range. 
   When the threshold Vref is set as described above, the time T 2  or the number of sampling cycles in which the induced voltage waveform exceeds the threshold Vref can be kept substantially constant even in the case where the value of the induced voltage waveform varies according to temperature change in a specific temperature range. Accordingly, the zero position can be detected accurately without any influence of temperature change.