Patent Publication Number: US-9887654-B2

Title: Apparatus employing coil inductance determination and method for operating the apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a U.S. National Phase Application pursuant to 35 U.S.C. § 371 of International Application No. PCT/EP2014/059153 filed May 6, 2014, which claims priority to European Patent Application No. 13166900.4 filed May 7, 2013. The entire disclosure contents of these applications are herewith incorporated by reference into the present application. 
     TECHNICAL FIELD 
     The invention relates to an apparatus comprising an electric motor with a stator, an armature, especially a rotor, and at least one coil. The invention further relates to a method for operating such an apparatus. 
     BACKGROUND 
     Electric motors, especially brushless DC motors are used as actuators in medical devices. For example, an electric motor may be provided in a liquid drug delivery device to actuate the drug delivery. The dose of the drug delivered to a patient may then be directly dependent on the motor rotation, so that a precise control of the motor rotation is crucial for these applications. The input signal for the motor control is usually the position of the armature, which in the art is often evaluated optically or magnetically with an additional sensor on the motor. Additional sensors, however, require additional components and therefore increase costs. They also may compromise the device robustness to malfunctions since extra components may cause additional functional failures. 
     There are known sensor-less motor control systems, which make use of electromotive force measurements. The measurement of the electromotive force works well for high speed (high rpm), but less for low speed (low rpm) motors. For some applications, such as drug delivery devices, it is however necessary to precisely control the motor also at low speed. 
     SUMMARY 
     It is therefore an object of the present invention to provide for a motor driven apparatus with a precise motor control also at low speed, that does not require additional sensors. 
     This object is at least in part solved by an apparatus comprising an electric motor with a stator, an armature, especially a rotor, and at least one coil, wherein the apparatus further comprises detection means configured to determine the inductance L of the coil by measuring at least one electrical quantity related to the coil during operation of the motor. By provision of such detection means, the coil inductance L is determinable during motor operation and operation parameters of the motor such as the current armature position may be calculated therefrom. 
     The object is furthermore at least in part solved by a method for operating such an apparatus, wherein the detection means of the apparatus determine the induction L of the coil and/or the position of the armature as a function of the inductance L of the coil by measuring at least one electrical quantity related to the coil during operation of the motor. 
     It was found that by determining coil inductance L during motor operation, the armature position may be determined precisely enough for applications in, for example, drug delivery devices. Moreover, the inductance L was found to be determinable during operations by measuring an electrical quantity related to the coil and without making use of additional sensing means like for example optical or magnetic sensors which are otherwise used to for example control the armature position. 
     The apparatus comprises an electric motor with a stator, an armature and at least one coil. The electric motor may be a rotary motor with a stator and a rotor, but also a linear motor with a stator and a linear moving armature. In particular, the motor may be a DC motor, especially a brushless DC motor, as often used in medical devices. The motor may be powered by line current or mobile power modules such as batteries and be controlled, for example, by pulse width modulation. The coil of the motor serves to generate a magnetic field within the motor and may be situated on the stator or on the armature. In case of a rotary motor, the coil may for example be situated on the rotor. 
     The motor is preferably configured to work at a speed of between 0.01 and 20000 rpm, preferably, of between 0.1 and 1000 rpm, more preferably of between 1 and 10 rpm. This motor speed is typically used for example in medical delivery devices. 
     The apparatus further comprises detection means. These detection means may for example comprise a circuitry connected to the circuitry for operating the motor. For example the detection means may comprise an integrated circuit or analog electronics or a combination thereof. The detection means are configured to determine the inductance L of the coil. The inductance L of the coil depends on the one hand on predetermined coil parameters such as the number of windings, the dimensions of the coil, the coil core or the like, and on the other hand on (time-dependent) magnetic characteristics of the coil environment such as especially the relative spatial orientation of the coil to armature, permanent magnets and/or other ferro-, para- or diamagnetic components of the apparatus, especially of the motor. The variation of inductance L over time therefore contains information about the armature position, i.e. about the relative spatial orientation of the coil to the armature (if the coil is on the stator) or about the relative spatial orientation of the coil to the stator (if the coil is on the armature). 
     The detection means are configured to determine inductance L of the coil by measuring at least one electrical quantity related to the coil. The electrical quantity may in particular be the discharge current of the coil (coil current) and/or the voltage over the coil (coil voltage). For example the detection means may comprise an ammeter circuitry or a voltmeter circuitry for measuring a respective current or voltage. The at least one electrical quantity is to be measured during motor operation. Therefore, the detection means have to be configured such to allow a measurement during motor operation. In particular, the detection means comprise a control configured to perform the measurement during motor operation. Motor operation in this context especially means that the armature is in motion, for example that the rotor of a rotary motor rotates relative to the stator. 
     Further embodiments of the apparatus and of the method will be described in the following. The features and advantages of these embodiments are understood to apply for the apparatus and the method alike, even if they are described only for one of them. 
     According to an embodiment of the apparatus, the detection means are further configured to determine the position of the armature as a function of the inductance L of the coil during operation of the motor, especially when the armature is in motion. Since coil inductance L is especially a function of the coil&#39;s spatial relative position to armature, magnets and components in the coil environment, the armature position of the electric motor is determinable from time-dependent inductance L. In case of a rotary motor with the coil being situated on the stator, the rotor rotation for example changes the relative position of a magnet on the rotor to the coil on the stator, thereby influencing coil inductance L so that the rotor position is determinable by a time-dependent measurement of coil inductance L. 
     The specific relation between coil inductance L and armature position for a specific motor geometry may be determined by computer simulations, analytics, experimental measurement or any combination thereof. For example, the relation between coil inductance and armature position may be stored in a lookup table on storage means of the apparatus so that during operation the current armature position may be deduced by a comparison of the lookup table with the current coil inductance measurement. 
     It is understood that for determining the armature position as a function of coil inductance L it is not necessary to first explicitly calculate and/or output the actual value of inductance L by for example storing this value into a variable in a specific memory location. Rather, the determination of inductance L may be implicitly or explicitly incorporated into the determination of the armature position, such that the value of inductance L may only appear as part of a formula to determine the armature position. For example, the relation of inductance L as a function of the electrical quantity may be inserted into the relation of the armature position as a function of coil inductance L yielding a relation of the armature position as a function of the electrical quantity. 
     According to an embodiment of the apparatus, the apparatus further comprises a pulse width modulation (PWM) circuitry configured to control the electric motor, wherein the pulse width modulation circuitry is configured to connect the coil to a voltage supply during charge time periods T on  and to disconnect the coil from the voltage supply during discharge time periods T off , and wherein the detection means are configured to determine a discharge current from the coil during discharge time periods T off . 
     According to a corresponding embodiment of the method the electric motor is controlled by PWM and the detection means determine a discharge current from the coil during at least one discharged time period T off  of the PWM. 
     PWM is a widely used method for motor control, in which the average value of a voltage (and current) fed to the motor is controlled by turning one or more switches switch between a voltage supply and the motor on and off at a fast pace, so that the longer the switch-on periods T on  are compared to the switch-off periods T off , the higher is the power supplied to the motor. The PWM is relatively energy saving, allows a decent control of the motor and may be largely integrated in digital electronics. The electronic switches used for the PWM may be for example transistors, IGBTs or MOSFETs. 
     Due to the high frequency of the PWM, in which the PWM turns the switch or the switches from off to on or vice versa, it is however challenging to determine information about the electric motor during operation since measurements are interfered by the PWM frequency and its harmonics. The PWM period, i.e. the time period between two consecutive switching&#39;s from off to on (which equals the sum of one T on  and one T off  period), is preferably between 0.2 ms and 100 ms, more preferably between 0.4 ms and 10 ms, for example about one millisecond. 
     It was found, that a very precise measurement of coil inductance L is possible by determining a discharge current from the coil during the discharge time periods T off  of the PWM. 
     During the T on  time periods the coil is connected to a voltage supply so that the current through the coil gradually increases. When the PWM switches from T on  to T off , the voltage supply is disconnected from the coil and the coil is instead connected with a discharge circuitry having a total resistance R, so that the coil discharges and the current through the coil gradually decreases again. The increasing and decreasing current through the coil is referred to as charge current and discharge current, respectively. 
     According to an embodiment of the apparatus the detection means are configured to determine a length of time for a discharged current from the coil dropping from a first given current value to a second given current value. 
     According to a corresponding embodiment of the method the detection means determine a length of time for a discharge current from the coil dropping from a first given current value to a second given current value. 
     The current decrease during the T off  periods is generally given by the discharge current formula
 
 I ( t )= I   0 ·exp(− t·R/L ),  (1)
 
wherein I(t) is the time-dependent discharge current, I 0  is the coil current at the beginning of the respective interval T off , R is the resistance of the discharge circuitry via which the coil discharges, L is the coil inductance and t is the time passed since the coil is being discharged, i.e. since the coil is connected to the discharge circuit in particular at the beginning of the respective interval T off .
 
     With two given pairs of values (t 1 , I(t 1 )), (t 2 , I(t 2 )) inductance L may be calculated by means of the following formula: 
                     L   =       Δ   ⁢           ⁢     t   ·   R         ln   ⁡     (       I   1     /     I   2       )           ,           (   2   )               
wherein Δt=t 2 −t 1  and R is the resistance via which the coil discharges. Thus, L may be determined from the length of time interval Δt in which the discharge current drops from a first given current value I 1  to a second given current value I 2 .
 
     The first and second current values I 1  and I 2  may for example be given as a percentage of the maximum discharge current I 0  at the beginning of respective time period T on . For example the first and second current values may be selected to be 100% and 80% of I 0 , respectively. Of course it is also possible to set I 1  less than 100% of I 0  such as for example 90%. 
     According to an embodiment of the apparatus the detection means are configured to drain a discharge current from the coil through a variable electric resistance provided by a variable resistance circuitry comprising at least one resistor, wherein the variable resistance circuitry is adjustable to provide at least two different electric resistance values. In particular, the detection means may further be configured to determine a voltage over at least one resistor of the variable resistance circuitry for each one of the at least two different electric resistance value. 
     According to a corresponding embodiment of the method the detection means at least twice drain a discharge current from the coil through a variable electric resistance provided by a variable resistance circuitry comprising at least one resistor and measure a voltage over at least one resistor of the variable resistance circuitry, wherein at the first time the variable resistance circuitry provides the first electric resistance value and wherein at the second time the variable resistance circuitry provides a different second electric resistance value. 
     For a very precise determination of coil inductance L according to formula (2) the total resistance of the discharge circuit has to be known with high precision. This is sometimes a problem since this resistance may be unknown or not known precisely enough. The embodiments of the apparatus and the method described beforehand allow precise determination of inductance L even if the absolute value of total resistance R is not known. 
     Let R 1  be a first and R 2  be a second electric resistance value provided by the variable resistance circuitry. The respective total resistance value of the discharge circuit, over which the coil is discharged, is then given by R a =R+R 1  and R b =R+R 2 , wherein R is an unknown (or imprecisely known) additional resistance of the discharge circuit in series with the first or second resistance of the variable resistance circuitry. 
     According to formula (2), the following applies for a time measurement for each of the two electric resistance values of the variable resistance circuitry: 
     
       
         
           
             
               
                 
                   
                     
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     Under the assumption that L a ≈L b , which is fulfilled when L a  and L b  are both determined within a time period relatively short compared to the motor speed, the unknown or imprecisely known resistance R may be eliminated by combining formulas (3) and (4), so that L is determinable from the relative difference ΔR=R b −R a  by the following formula: 
     
       
         
           
             
               
                 
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     Thus, inductance L in formula 5 does not dependent on the unknown resistance R, but only on a known difference ΔR between the first and the second electrical resistance values of the variable resistance circuitry. 
     The variable resistance circuitry may for example comprise a potentiometer or two parallel sub-circuits with different resistances, wherein at each time one of the two sub-circuits is selectable by a switch. In particular, the variable resistance circuitry may comprise a series connection of at least two resistors, wherein one of these resistors may be short circuited by a switch. 
     The discharge current and time periods for the two different electric resistance values of the variable resistance circuitry may be measured in a single T off  period or in separate T off  periods, for example in two consecutive T off  periods. 
     According to an embodiment of the method the detection means determine a first length of time for a discharge current from the coil dropping from a first given current value to a second given current value, while the variable resistance circuitry provides the first electric resistance value, and the detection means determine a second length of time from a discharged current from the coil dropping from a third given current value to a fourth given current value, while the variable resistance circuitry provides the second electric resistance value, and the detection means determines the inductance L of the coil and/or the position of the armature as a function of the first and the second length of time. This embodiment allows for example performing the two time measurements during a single T off  period so that coil inductance L may be precisely determined in a very short time. 
     According to an embodiment of the apparatus the PWM circuitry comprises at least one electric switch to selectively connect the motor to a voltage source and the switch comprises an inverse series connection of two MOSFETs. 
     MOSFETs may be used as electric switches for a PWM control to connect and disconnect a coil to and from a voltage source. However, MOSFETs have a parasitic body diode behavior, so that during the discharge time periods T off  part of or the complete discharge current from the coil may flow over the open MOSFET switch instead of a designated discharge circuitry. Such a parasitic discharge current drain over the MOSFET switch is reduced or even prevented by providing an inverse series connection of two MOSFETs for one switch. In particular, an inverse series connection of two MOSFETs may be used for the low-side switches of a PWM H bridge. 
     An inverse series connection of two MOSFETs is understood to mean that two MOSFETs are connected in series, wherein either the respective sources/drains of two re-channel- or two p-channel-MOSFETs are connected to each other or wherein a source/drain of an n-channel-MOSFET is connected in series to a drain/source of a p-channel-MOSFET, respectively. This combination of two MOSFETs removes the parasitic diode behavior as due to the inverse series connection provides for an inverse pre junction in either direction when the MOSFETs are open, thus blocking the discharge current from the coil. 
     According to an embodiment of the apparatus the apparatus comprises processing means and storage means containing commands, the execution of which on the processing means causing a method according to the embodiments described above to be performed. 
     The processing means may for example comprise an integrated circuit, especially a processor, or analog or semi-analog electronics or any combination thereof. The storage means may comprise volatile, permanent or transient storage means such as RAMs, ROMs, hard disks, flash memory etc. 
     With the embodiment described in beforehand, the apparatus may be operated according to predefined methods, the advantages of which are described in the context of the method according to this disclosure and to its embodiments so that reference is made thereto. 
     According to an embodiment of the apparatus the apparatus is a medical device, especially a drug delivery device. Precise motor control is especially important for medical devices, and more especially for drug delivery devices, in which for example the amount of the drug delivered to a patient depends on the motor rotation. With the apparatus according to this embodiment it is possible to precisely control the motor speed by the armature position of the motor and therewith improve the reliability and precision of the delivered medicament. 
     According to an embodiment of the apparatus the apparatus is a hand-held device. Motors of hand-held devices are usually powered by batteries and use energy saving PWM control. Thus, the embodiments of the apparatus as described above are in particular suitable for such hand-held devices. 
     Further features and advantages of the apparatus and of the method will now be explained in connection with exemplary embodiments, wherein reference is made to the figures. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       In the figures 
         FIG. 1 a    shows a schematic diagram of an exemplary embodiment of an apparatus comprising a rotary motor with three pairs of stator coils, 
         FIG. 1 b    shows a schematic graph of the time-dependent inductance for three coils of the motor in  FIG. 1   a,    
         FIG. 2  shows a schematic circuitry diagram with a general circuitry according to an embodiment of the apparatus, 
         FIG. 3  shows a schematic circuitry diagram according to a more specific implementation of the general circuitry of  FIG. 2 , 
         FIG. 4 a - b    show graphs illustrating coil charge and discharge currents of a PWM controlled electric motor such as the motor in  FIG. 1 , 
         FIG. 5 a    shows a graph illustrating time length measurements over two PWM cycles for a coil discharge current decay over two different electrical resistances, 
         FIG. 5 b    shows a graph illustrating alternative time length measurements over one PWM cycle for a coil discharge current decay over two different electrical resistances, and 
         FIG. 6  shows a schematic circuitry diagram with an alternative implementation of the detection means according to the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1 a    shows a schematic diagram of an exemplary embodiment of an apparatus according to this disclosure. The apparatus  2  comprises an electric motor  4 , which in this example is a rotary motor with a stator  6  and a rotor  8  as armature. A first pair of coils  12   a +d, a second pair of coils  12   b - e  and a third pair of coils  12   c +f are situated on the stator  6 , and a permanent magnet  14  is situated on the rotor  8  of motor  4 . 
     The inductances L a-f  of coils  12   a - f  are a function of the relative spatial position to magnet  14  and therewith functions of the angular position of the rotor  8  relative to the stator  6 , which is denoted by angle φ as depicted in  FIG. 1   a.    
       FIG. 1 b    shows schematic graphs of the angle-dependent inductance L a-c  for the three adjacent coils  12   a - c . The inductance of a coil is highest when the magnetic field of the coil is directly opposite to the magnetic field of magnet  14 , i.e. when magnet  14  is in line with the coil and has opposite polarity, so that either two magnetic north poles or two magnetic south poles face each other. For coil  12   a  this is the case for an angle φ of 0°, 180° and 360°, so that  FIG. 1 b    shows an inductance maximum of L a  at these angles. The inductance maxima of L b  and L c  are shifted by 60° and 120° due to the corresponding position of coils  12   c  and  12   e  on the stator  6   
     Apparatus  2  comprises detection means  16  with first, second and third inductance detection means  18   a - c  configured to determine these angle-dependent inductances L a-c  of coils  12   a ,  12   c  and  12   e  during operation, i.e. when the rotor  8  is in motion. Due to the angle dependence of the coil inductances, the current rotor position φ may be calculated as a function of one or more of the measured coil inductances. For this purpose, apparatus  2  further comprises processing means  20  and storage means  22 , wherein information about the angular dependence of the inductances L a-c  are stored in the storage means  22  in the form of a look-up table and wherein the processing means  20  are configured to compare the inductances L a-c  determined by inductance detection means  18   a - c  with the look-up table to determine the angular position of rotor  8 . 
     The thus determined current angular position φ of the rotor  8  may then be used, for example, to control the speed of motor  4 . 
     A possible implementation of the inductance detection means  18   a - c  will now be illustrated with reference to  FIG. 2 . 
       FIG. 2  shows a schematic diagram of a general circuitry  32  for determining the inductance L of a coil. The left sub-circuitry  34  of circuitry  32  represents part of the motor control and the right sub-circuitry  36  of circuitry  32  represents inductance detection means like the inductance detection means  18   a - c  in  FIG. 1 . 
     Sub-circuitry  34  comprises as voltage supply a DC voltage source  38  connectable to a coil  40  of an electric motor by means of an electronic switch  42 . Coil  40  may be situated on the armature or on the stator of the motor, for example like one of stator coils  12   a - f  in  FIG. 1   a.    
     The motor is controlled by a PWM circuitry (not shown) operating switch  42  such, that coil  40  is connected to voltage source  38  during charge time periods T on  and is disconnected from voltage source  38  during discharge time periods T off . 
     At least during discharge time periods T off , coil  40  is connectable to sub-circuitry  36  so that the inductance of coil  40  may be determined during these periods by measuring with sub-circuitry  36  an electric quantity related to the coil. 
     In the example illustrated in  FIG. 2 , sub-circuitry  36  is configured to determine the discharge current draining from coil  40  over switch  42  to sub-circuitry  36  as electrical quantity related to the coil. For that purpose, sub-circuitry  36  comprises a resistance circuitry, which preferably is a variable resistance circuitry  44  that can provide at least two different electrical resistance values, and a voltage measurement circuitry  46  to determine the voltage over resistance circuitry  44  (as illustrated in  FIG. 2 ) or over at least one resistor of the resistance circuitry  44 . With a voltage measurement by means of voltage measurement circuitry  46  the discharge current draining through resistance circuitry  44  can then be determined according to Ohm&#39;s law I=U/R, wherein I is the discharge current, U is the measured voltage and R is the resistance of resistance circuitry  44  or of the at least one resistor of the resistance circuitry  44 , respectively. 
     During operation, when switch  42  is in the on-position during time periods T on  (as shown in  FIG. 2 ), coil  40  is connected to voltage source  38 , so that a gradually increasing charge current flows from voltage source  38  to coil  40 . When switch  42  is in the off-position during time periods T off , a gradually decreasing discharge current flows from coil  40  over resistance circuitry  44 . The time-dependence of the discharge current I(t) corresponds to formula (1) as described above. 
     By measuring time length Δt, in which the discharge current I(t) falls from a first given value I 1  to a second given value I 2 , the current inductance L of coil  40  is determinable with formula (2) as described above. 
     With a variable resistance circuitry  44  (as illustrated in  FIG. 2 ) the inductance L may be precisely determined even if the absolute electric resistance value of the discharge circuitry is not known or not known precisely enough. For this purpose, variable resistance circuitry  44  is controlled to provide one after another two different electric resistance values R a  and R b  and for each case the according time length Δt a  and Δt b  is measured, in which the discharge current falls from a first given value I 1  to a second given value I 2 . The inductance L of coil  40  is then determinable with formula (5) as described above. 
     Experiments have shown that in this way the coil inductance L may be determined with an error margin of about 1%. For an inductance L=500 μH and a sub-circuitry  36  configured such that ΔR=1Ω and I 2 /I 1 =1.1, time measurements of the discharge current falling from I 1  to I 2  for each resistance value R 1 , R 2  yielded the following results: Δt a =17.04 μs, Δt b =12.52 μs. Application of formula (5) yields an inductance of about 495.2 μH which is less than 1% error from the real inductance value of 500 μm. 
       FIG. 3  shows a schematic circuitry diagram of a more specific implementation of a circuitry  52  for determining the inductance L of a coil. 
     The left sub-circuitry  54  of circuitry  52  again represents part of the motor control and the right sub-circuitry  56  of circuitry  52  represents inductance detection means like the inductance detection means  18   a - c  in  FIG. 1 . 
     Sub-circuitry  54  comprises a coil  58  of an electric motor which is connectable to a DC voltage source  60  via an H bridge  62  comprising two upper electronic switches  64   a - b  and two lower electronic switches  64   c - d . By means of the H bridge  62  the coil  58  may be connected to DC voltage source  60  in either direction. 
     By closing for example switches  64   a  and  64   d  and opening switches  64   c  and  64   b , a voltage from voltage source  60  may be supplied to coil  58  so that a charge current flows through coil  58 . A voltage with opposite polarity may be supplied to coil  58  by opening switches  64   a  and  64   d  and closing switches  64   c  and  64   b . Coil  58  may also be disconnected from voltage source  60  by opening both upper switches  64   a  and  64   b.    
     The motor is controlled by a PWM circuitry (not shown) that may operate switches  64   a - d . In particular, the PWM circuitry operates switch  64   a  such, that coil  58  is connected to voltage source  60  during charge time periods T on  and is disconnected from voltage source  60  during discharge time periods T off  while coil  58  is connected to ground via switch  64   d  in each case. For reverse direction of motor rotation, the PWM circuitry may alternatively operate switch  64   b  such, that coil  58  is connected to voltage source  60  during charge time periods T on  and is disconnected from voltage source  60  during discharge time periods T off  while coil  58  is connected to ground via switch  64   c  in each case. 
     Both terminals of coil  58  are connected to sub-circuitry  56  over two diodes  68   a - b , which may be for example Schottky PN-diodes, and a detection line  66 . During discharge time periods T off  (when both upper electronic switches  64   a - b  are open) a discharge current flows from one terminal of coil  58  over one of diodes  68   a - b  in forward direction to sub-circuitry  56 . The high-side switches  64   a - b  and the low-side switch  64   c  or  64   d  on the side of this particular diode are controlled to be open, while the other low-side switch  64   d  or  64   c  is closed to connect the opposite terminal of coil  58  to ground potential. In this way, the discharge current of coil  58  may be drained to sub-circuitry  56  independent of the coil polarity. Low-side switches  64   c - d  are configured not to have a parasitic diode, so that coil is not short-circuited over ground. For example switches  64   c - d  may each be implemented as an inverse series connection of two MOSFETs. 
     Sub-circuitry  56  is configured to determine inductance L of coil  58  according to formula (5) as described above. For this purpose, sub-circuitry  56  comprises a variable resistance circuitry  70 , which can provide two different electrical resistance values R a  and R b , and an inductance determination circuitry  80 . This inductance determination circuitry  80  is configured to measure the time lengths Δt a  and Δt b , which the respective discharge currents draining over R a  or R b , respectively, take to fall from a first given value I 1  to a second given value I 2 . 
     Variable resistance circuitry  70  comprises a series connection of two resistors  72 ,  74 , wherein a switch  76  is connected in parallel to resistor  72 . When switch  76  is open, the total resistance value R a  of variable resistance circuitry  70  is given by R a =R 1 +R 2 , and when switch  76  is closed the total resistance value R b  of variable resistance circuitry  70  is given by R b =R 2 . As can be seen from formula (1), the lower is the resistance of the discharge circuit the faster the discharge current decreases. Therefore, discharge current from coil  58  decreases faster when switch  76  is closed. 
     Inductance determination circuitry  80  is connected to the connection point  78  of the two resistors  72 ,  74  and switch  76 , wherein the voltage at this connection point  78  is related to the discharge current by Ohm&#39;s law I=U/R 2  (inductance determination circuitry  80  is in particular configured to have a high internal resistance so that the discharge current I(t) drains basically completely through resistor R 2 ). 
     The inductance determination circuitry  80  comprises a comparator  88  for providing start and stop signals to a clock  90  to subsequently measure time lengths Δt a  and Δt b  for both resistance values R a  and R b  of variable resistance circuitry  70 . 
     In the example shown in  FIG. 3 , comparator  88  is configured to trigger clock  90  to start a time measurement once a discharge current drains through sub-circuitry  56  at the beginning of a time period T off . Thus, the first current value I 1  in this example equals the maximum discharge current value I 0 . The second current value I 2  is defined by means of a voltage divider  82  comprising a series connection of two resistors  84   a - b , the connecting point  86  of which being connectable to the comparator  88  over switch  90 . Switch  90  and a capacitor  92  provide a sample-and-hold functionality to bias comparator  88  with a fixed ratio by resistors  84   a  and  84   b  to define a voltage threshold corresponding to discharge current I 2 . 
     The operation of circuitry  52  illustrated in  FIG. 3  will now be described in detail with references to  FIGS. 4 a - b    and  FIG. 5 . 
     During operation of the motor comprising coil  58 , the PWM control connects coil  58  to voltage source  60  during time periods T on , so that the current flowing through coil  58  gradually increases (charge current), and disconnects coil  58  from voltage source  60  during time periods T off , so that the current flowing through coil  58  flows over variable resistance circuitry  70  and thereby gradually decreases (discharge current). In  FIGS. 4 a - b   , the rectangular signals corresponding to the right ordinate of the graph illustrate the PWM switching between time periods T on  and T off .  FIG. 4 a    shows a PWM duty cycle of 20% and  FIG. 4 b    shows a PWM duty cycle of 90%, in which the lengths of T on  are 20% or 90%, respectively, of one full PWM cycle, which corresponds to T on +T off . Generally, the higher is the proportion of T on  of the full PWM cycle, the higher is the power transferred to the motor. 
       FIGS. 4 a - b    also show the charge and discharge currents of the coil. During T on , the coil is connected to a voltage source and a gradually increasing charge current flows through the coil. During T off , the coil is instead connected to a discharge circuitry, so that the discharge currents gradually decrease again. For the PWM duty cycle of 90% illustrated in  FIG. 4 b    the time period T off  is too short for a complete discharging of the coil, so that the next T on  period starts with a current offset and the maximum current value I 0  at the beginning of T off  gradually increases from one PWM cycle to another. 
     The time periods T off  are used to determine the inductance L of coil  58  by means of sub-circuitry  56 . During a first time period T off,a  switch  76  is controlled to be open, so that the discharge current discharges over the sum resistance R a =R 1 +R 2  of the variable resistance circuitry. During a subsequent second time period T off,b  switch  76  is controlled to be closed, so that the discharge current discharges over sum resistance R b =0+R 2 .  FIG. 5 a    shows the discharge current during the two consecutive time periods T off,a  (left in  FIG. 5 a   ) and T off,b . (right in  FIG. 5 a   ). Since R b &lt;R a  the discharge current decays faster during the second time period T off,b  compared to the first time period T off,a . 
     At the beginning of each time period T off,a  and T off,b , clock  90  is triggered to start a time measurement Δt a  and Δt b , respectively, so that the first given current value I 1  for the time measurements is set equal to the maximum discharge current I 0  in this example. 
     At the same time, switch  90  is closed but for a moment to provide the comparator with a voltage bias which due to the voltage divider  82  equals a defined proportion of the voltage at connection point  78  at the beginning of the respective time period T off . The voltage at connection point  78  at the beginning of the respective time period T off  corresponds to the maximum discharge current I 0 . The voltage bias provided at comparator  88  corresponds to an according proportion I 2  of the maximum discharge current I 0 . For example, if the electrical resistance value of resistor  84   a  is set 25% of the electrical resistance value of resistor  84   b , the voltage bias at comparator  88  is set 80% of the respective voltage at connection point  78  which then corresponds to a discharge current value I 2  of 80% of the maximum discharge current I 0 . 
     It is preferred to set I 1  and I 2  to proportions of I 0  of the current PWM cycle rather than using fixed current values since this accounts for a possible increase of I 0  at high PWM duty cycles from one PWM cycle to another as for example shown in  FIG. 4   b.    
     Once the discharge current and therewith the voltage at connection point  78  drops below the threshold given by the voltage bias at the comparator  88 , the comparator  88  triggers the clock  90  to stop the time measurement. 
     After determination of the two time lengths Δt a  and Δt b  the inductance L of coil  58  may then be calculated according to formula (5) by means of processing means (not shown). Since formula (5) does not depend on the absolute total resistance values of the discharge circuitry, but only on the difference ΔR=R b −R a =−R 1 , coil inductance L may be calculated with high precision even if the total resistance of the discharge circuitry is unknown or imprecisely known. 
       FIG. 5 b    shows a graph illustrating an alternative measurement of time lengths Δt a  and Δt b  over a single PWM cycle. During the time period T off  of the PWM cycle, the variable resistance circuitry  70  first is set to provide electric resistance value R a  and a time measurement of Δt a  for the discharge current decreasing from given current values I 1,a  to I 2,a  is performed. After the end of this time measurement, variable resistance circuitry  70  is switched to provide electric resistance value R b  and a second time measurement of Δt b  is performed for the discharge current further decreasing from given current values I 1,b  to I 2,b . 
     By selecting I 1,a  I 2,a , I 1,b  and I 2,b  such that I 1,a /I 2,a =I 1,b /I 2,b  the coil inductance L may still be calculated according to formula (5). 
       FIG. 6  shows a schematic circuitry diagram with an alternative implementation of the detection means according to the present disclosure. Circuitry  102  comprises a coil  104  of an electric motor, wherein coil  104  is connectable to a DC voltage source  106  by means of an H bridge  108  with two high-side electronic switches  110   a - b  and two low-side electronic switches  110   c - d . The electronic switches  110   a - d  are controlled by a PWM circuitry (not shown). 
     Low-side switches  110   c - d  are bridged by resistors  112   a - b  and the lower side of the H bridge  108  is connected to detection means  114  comprising a detection circuitry  116  which is controlled by a micro controller  118 . 
     Detection circuitry  116  may for example comprise a shunt, i.e. a resistor with a resistance value of less than 100 mOhm, to connect the lower sides of switch  110   c  and resistors  112   a - b  to ground. The discharge current may than be determined by means of the shunt, for example by determining the voltage drop over the shunt. Alternatively, detection circuitry  116  may comprise two tracks or wires on a printed circuit board (PCB) which are positioned very close to each other. The discharge current may then be determined by inductive coupling of these tracks or wires. 
     During PWM time periods T on , two diagonally opposed switches ( 110   a +d or  110   b +c) are closed, the remaining switches being open, and detection circuitry  116  is controlled to only impose a small resistance or even a direct connection between the low-side of the H bridge  108  and ground. In this way, coil  104  is connected to voltage source  106  during time periods T on . 
     During PWM time periods T off , the upper side switches  110   a - b  and at least one of the lower side switches  110   c  or  110   d  are open, so that coil  104  is disconnected from voltage source  106  and the discharge current from coil  104  drains through at least one resistor  112   a  or  112   b  and through detection circuitry  116 . Detection circuitry  116  is then controlled by micro controller  118  to determine the discharge current, and the inductance L of coil  104  may be determined as a function of the discharge current as described before, for example as described in the context of formulas (2) and (5). In particular, AD channels of the microcontroller  118  may be used to perform time measurements Δt a  and Δt b  and to calculate the inductance L of coil  104  or the position of the armature of a motor, coil  104  may be provided on.