Abstract:
There is described an inductive sensor for sensing a parameter such as position. The inductive sensor includes: receive aerial which is electro-magnetically coupled to a magnetic field generator via a resonant circuit with the electromagnetic coupling varying in dependence upon the sensed parameter so that a sense signal induced in the receive aerial is representative of the sensed parameter. The magnetic field generator generates a magnetic field including a first magnetic field component at a first frequency which is operable to induce resonance in the resonant circuit and a second magnetic field component at a second frequency which is not operable to induce resonance in the resonant circuit. The signal processor processes the sense signal to generate a signal component corresponding to a first component of the sense signal at the first frequency adjusted using a second component of the sense signal at the second frequency so that a noise component of the first component of the sense signal is reduced, and determines a value representative of the sensed parameter using the signal component.

Description:
This application claims priority to International Patent Application No. PCT/GB04/000597 filed on Feb. 17, 2004, which claims priority to GB Patent Application No. 0303627.4 filed on Feb. 17, 2003 in Great Britain. 
     This invention relates to a method of sensing the position or the speed of an object, and an apparatus therefor. The invention has particular relevance to inductive sensors in which a magnetic field induces a signal in a resonant circuit. 
     BACKGROUND OF THE INVENTION 
     UK Patent Application GB 23744A describes an inductive position sensor in which a transmit aerial and a receive aerial are formed on a first member, and a resonant circuit having an associated resonant frequency is formed on a second member which is movable relative to the first member. An excitation signal having a frequency component at or near the resonant frequency of the resonant circuit is applied to the transmit aerial resulting in the generation of a magnetic field having a magnetic field component at or near the resonant frequency of the resonant circuit. The generated magnetic field induces a resonant signal in the resonant circuit, which in turn induces a sense signal in the receive aerial that varies with the relative position of the first and second members. The sense signal is processed to determine a value representative of the relative position of the first and second members. 
     In the position sensor described in GB 2374424A, the resonant signal induced in the resonant circuit is generated as a result of an electromotive force which is proportional to the rate of change of the magnetic field component at or near the resonant frequency. As the impedance of the resonant circuit is substantially entirely real at the resonant frequency, the resonant signal is approximately in phase with the electromotive force and accordingly is approximately 90° out of phase with the frequency component of the excitation signal near the resonant frequency. The sense signal induced in the receive aerial is generally in phase with the resonant signal, and therefore the sense signal is also approximately 90° out of phase with the component of the excitation signal near the resonant frequency of the resonant circuit. 
     The sense signal is synchronously detected using a signal which has the same frequency as, but is in phase quadrature with, the frequency component of the excitation signal near the resonant frequency of the resonant circuit. By using such phase sensitive detection, noise which is at the same frequency as, and is in phase with, the frequency component of the excitation signal near the resonant frequency of the resonant circuit is substantially removed along with noise at frequencies away from the resonant frequency. 
     A problem with such an inductive sensor is that noise can occur in the sense signal having components which have the same frequency as, but are in phase quadrature with, the component of the excitation signal near the resonant frequency of the resonant circuit. These noise components are not removed by phase sensitive detection and therefore affect the accuracy of the position measurement. Such noise components can be generated through signal coupling between components of the inductive position sensor, either directly or indirectly via a magnetically permeable body which is in close proximity with the inductive position sensor. This problem also arises in inductive position sensors in which a transmit aerial on a first member is directly coupled to a receive aerial, which includes a resonant circuit, on a second member. 
     SUMMARY OF THE INVENTION 
     According to a first aspect of the present invention, there is provided an inductive sensor for sensing a parameter, the inductive sensor comprising a magnetic field generator operable to generate a magnetic field, an aerial electromagnetically coupled to the magnetic field generator via a resonant circuit, and a signal processor operable to process the sense signal induced in the aerial. The electromagnetic coupling varies with the sensed parameter so that the sense signal is indicative of the sensed parameter. The magnetic field generator is operable to generate a magnetic field having a first oscillating component at a first frequency, which is operable to induce a resonant signal in the resonant circuit, and a second oscillating component at a second frequency, which is not operable to induce resonance in the resonant circuit. The signal processor is operable determine the value representative of the sensed parameter by processing the sense signal to generate a signal component corresponding to a first component of the sense signal at the first frequency adjusted using a second component of the sense signal at the second frequency in order to reduce noise. 
     Preferably, the signal processor is operable to perform synchronous detection of the components within the sense signal at the same frequency as, but out of phase with, the first and second components of the excitation signals, and to process these components to form a detection signal from which a value representative of the sensed parameter is derived. 
     In an embodiment, the magnetic field generator is provided on a first member and the resonant circuit is provided on a second member, with relative movement between the first and second members resulting in a variation between the electromagnetic coupling between the magnetic field generator and the aerial. In this way, the relative position of the first and second members is determined by analysing the sense signal induced in the aerial. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various embodiments of the invention will now be described with reference to the attached Figures in which: 
         FIG. 1  schematically shows a perspective view of a position sensor according to a first embodiment of the invention, 
         FIG. 2A  schematically shows the main components of a sensor element which forms part of the position sensor illustrated in  FIG. 1 ; 
         FIG. 2B  schematically shows a plot of how the phase of a signal induced in the sensor element illustrated in  FIG. 2A  varies with the frequency of an applied magnetic field; 
         FIG. 2C  schematically shows a plot of how the magnitude of a signal induced in a sense coil forming part of the position sensor illustrated in  FIG. 1  varies with the frequency of an applied magnetic field; 
         FIG. 3  schematically shows the main signal generating and processing circuitry of the position sensor illustrated in  FIG. 1 ; 
         FIG. 4  schematically shows in more detail the form of a quadrature signal generator of the signal generating and processing circuitry illustrated in  FIG. 3 ; 
         FIG. 5  schematically shows in more detail a coil driver of the signal generating and processing circuitry illustrated in  FIG. 3 ; 
         FIG. 6  schematically shows in more detail a synchronous detector of the signal generating and processing circuitry illustrated in  FIG. 3 ; 
         FIG. 7  schematically shows the main signal generating and processing circuitry of a position sensor according to a second embodiment of the invention; 
         FIG. 8  schematically shows the main components of an alternative coil driver to the coil driver illustrated in  FIG. 5 ; and 
         FIG. 9  schematically shows the main components of an alternative synchronous detector to the synchronous detector illustrated in  FIG. 6 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     First Embodiment 
       FIG. 1  schematically shows a position sensor for detecting the position of a sensor element  1  which is slidably mounted to a support  3  to allow linear movement along a measurement direction (the direction x in  FIG. 1 ). A printed circuit board (PCB)  5  extends along the measurement direction adjacent to the support  3  and has printed thereon conductive tracks which form a sine coil  7 , a cosine coil  9  and a sense coil  11 , each of which are connected to a control unit  13 . A display  15  is also connected to the control unit  13  for displaying a number representative of the position of the sensor element  1  along the support  3 . 
     The layout of the sine coil  7  is such that current flowing through the sine coil  7  generates a first magnetic field having a magnetic field component B 1  perpendicular to the PCB  5  which varies along the measurement direction according to one period of the sine function over a distance L. Similarly, the layout of the cosine coil  9  is such that current flowing through the cosine coil  9  generates a second magnetic field having a magnetic field component B 2  perpendicular to the PCB  5  which varies along the measurement direction according to one period of the cosine function over the distance L. In particular, in this embodiment the layout of the sine coil  7 , the cosine coil  9  and the sense coil  11  on the PCB  5  is identical to the layout of the corresponding coils of the position sensor described in GB 2374424A, whose content is hereby incorporated by reference. 
     The control unit  13  includes excitation signal generating circuitry (not shown in  FIG. 1 ) for applying excitation signals to the sine coil  7  and the cosine coil  9 , and sense signal processing circuitry (not shown in  FIG. 1 ) for processing a sense signal in the sense coil  11 . In this way, the sine coil  7  and the cosine coil  9  form a transmit aerial and the sense coil  11  forms a receive aerial. In this embodiment the layout of the sine coil  7 , the cosine coil  9  and the sense coil  11  results in the electromotive forces directly induced in the sense coil  11  by current flowing through the sine coil  7  and/or the cosine coil  9  generally balance each other out. In other words, in the absence of the sensor element  1 , the sense signal directly generated in the sense coil  11  by current flowing through the sine coil  7  and/or the cosine coil  9  is small. Using the sine coil  7  and the cosine coil  9  for the transmit aerial has the further advantage that the electromagnetic emissions resulting from current flowing through the sine coil  7  and/or the cosine coil  9  diminish with distance at a faster rate than for a single conductive loop. This allows larger drive signals to be used while still satisfying regulatory requirements for electromagnetic emissions. 
     As shown in  FIG. 2A , the sensor element  1  includes a coil  21  whose ends are connected together via a capacitor  23 . As the coil  21  has an associated inductance, the coil  21  and the capacitor  23  together form a resonant circuit. In this embodiment, the resonant circuit has a nominal resonant frequency f res  of 2 MHz, although the actual resonant frequency varies slightly with variations in environmental factors such as temperature and humidity. 
     When an oscillating excitation signal having a frequency component at or near the resonant frequency of the resonant circuit is applied to the sine coil  7  and the cosine coil  9 , an oscillating resonant signal is induced in the resonant circuit. This oscillating resonant signal varies with the position of the sensor element  1  along the measurement direction because the proportions of the resonant signal induced by the sine coil  7  and the cosine coil  9  vary with the position of the sensor element  1 . The oscillating resonant signal in turn induces a signal in the sense coil  11 , which will hereafter be referred to as the signal component of the sense signal. 
       FIG. 2B  shows how the phase of the signal component of the sense signal varies with the frequency of the excitation signal. As shown, as the frequency of the excitation signal passes through the resonant frequency f res  of the resonant circuit, the phase difference between the signal component of the sensed signal and the excitation signal passes from 0° to 180°, with the phase difference being 90° at the resonant frequency. 
     The sense signal induced in the sense coil also includes noise formed by signal coupling between components of the position sensor, either directly (for example the signals directly induced in the sense coil  11  by current flowing through the sine coil  7  and the cosine coil  9 ) or indirectly via a body other than the resonant circuit of the sensor element  1 . As such, the noise is a systematic error signal. Even after synchronous detection, this noise results in a noise component in the detected signal.  FIG. 2C  schematically shows the variation in the magnitude of the sense signal after synchronous detection with the frequency of the excitation signal. In  FIG. 2C , the noise component forms a background noise level  33  which is substantially constant over the illustrated frequency range, and the signal component of the sense signal forms a peak  31  above the background noise level  33  which is centred at the resonant frequency f res . 
     According to the present invention, the excitation signal generated by excitation signal generating circuitry has a first frequency component at a frequency f 1  at or near the resonant frequency f res  of the resonant circuit and a second frequency component at a second frequency f 2  away from the resonant frequency f res . The sense signal processing circuitry synchronously detects the amplitude of components of the sense signal at the first frequency f 1  and the second frequency f 2 . The amplitude of the component at the second frequency f 2  provides a measure of the noise level, and the sense signal processing circuitry uses the measure of the noise level to adjust the detected component at the first frequency f 1  to improve the signal to noise ratio. 
     The excitation signal generating circuitry and the sense signal processing circuitry will now be described in more detail with reference to  FIG. 3 . As shown in  FIG. 3 , the excitation signal generating circuitry includes a first quadrature signal generator  41   a  which generates an in-phase signal I 1  and a quadrature signal Q 1  at the first frequency f 1 , which in this embodiment is 2 MHz (i.e. approximately equal to the nominal resonant frequency f res  of the resonant circuit of the sensor element  1 ). The excitation signal generating circuitry also includes a second quadrature signal generator  41   b  which generates an in-phase signal I 2  and an inverted quadrature signal −Q 2  at the second frequency f 2 , which in this embodiment is 1 MHz which is sufficiently far away from the nominal resonant frequency f res  that a signal at the second frequency f 2  does not induce resonance in the resonant circuit. 
       FIG. 4  shows the main components of a quadrature signal generator  41 . As shown in  FIG. 4 , each quadrature signal generator  41  is formed by a conventional arrangement in which the output of a square wave oscillator  63  is input to the clock input of a first D-type flip-flop  65   a , with the inverting output of the first D-type flip-flop being connected to the input of the first D-type flip-flop  65   a  to form a divide-by-two circuit. The output of the square wave oscillator  63  is also input, via an inverter  67 , to the clock input of a second D-type flip-flop  65   b , with the non-inverting output of the first D-type flip-flop  65   a  being connected to the input of the second D-type flip-flop  65   b . In this way, the non-inverting output of the second D-type flip-flop outputs a signal Q which is phase quadrature with the signal I output by the non-inverting output of the first D-type flip-flop  65   a.    
     Returning to  FIG. 3 , the excitation signal generating circuitry also includes a square wave oscillator  43  which generates a modulation square wave signal at a frequency f mod  of 2.5 kHz. The modulation square wave signal is input to a pulse width modulation (PWM) type pattern generator  45  which generates digital data streams, clocked at 2 MHz, representative of sinusoidal signals at the modulation frequency f mod . In particular, the PWM type pattern generator  45  has two outputs  46   a ,  46   b  with the first output  46   a  outputting either a signal +SIN representative of a sine signal at f mod  or a signal −SIN representative of an inverted sine signal at f mod , and the second output  46   b  outputting a signal COS which is representative of a cosine signal at f mod . 
     The sine signal ±SIN output by the first output  46   a  of the PWM type pattern generator  45  is applied to a first digital mixer  47   a  and a second digital mixer  47   b , and the cosine signal COS output by the second output  46   b  of the PWM type pattern generator  45  is applied to a third digital mixer  47   c  and a fourth digital mixer  47   d . The first digital mixer  47   a  and the third digital mixer  47   c  mix the sine signal ±SIN and the cosine signal COS respectively with the in-phase carrier signal I 1  at the first frequency f 1 . Similarly, the second digital mixer  47   b  and the fourth digital mixer  47   d  respectively mix the sine signal ±SIN and the cosine COS with the in-phase carrier signal I 2  at the second frequency f 2 . In this embodiment, each digital mixer  47  is formed by a NOR gate. 
     The outputs of the first digital mixer  47   a  and the second digital mixer  47   b  are input to a first coil driver  49   a  which adds and amplifies the outputs to form a drive signal which is applied to the sine coil  7 . The drive signal applied to the sine coil  7  therefore has a term I(t) of the form:
 
 I ( t )= A  sin 2 πf   mod   t (sin 2 πf   1   t +sin 2 πf   2   t )
 
where A is a constant.
 
     The outputs of the third digital mixer  47   c  and the fourth digital mixer  47   d  are input to a second coil driver  49   b , which adds and amplifies the outputs to form a drive signal which is applied to the cosine coil  9 . The drive signal applied to the cosine coil  9  therefore has a term Q(t) of the form:
 
 Q ( t )= A  cos 2 πf   mod   t (sin 2 πf   1   t +sin 2 πf   2   t )
 
       FIG. 5  shows the main components of each coil driver  49 . As shown, the signals output by the corresponding digital mixers  47  are input, via respective resistors having resistance R 1 , to the inverting input of an operational amplifier  71 . The non-inverting input of the operational amplifier  71  is connected to ground, and a resistor having a resistance R 2  is connected between the inverting input of the operational amplifier  71  and the output of the operational amplifier  71  so that the operational amplifier  71  acts as an inverting amplifier. The coil being driven is connected between the output of the operational amplifier  71  and ground. 
     The magnetic fields generated by the drive signals flowing through the sine coil  7  and the cosine coil  9  induce a sense signal S(t) in the sense coil  11  of the form: 
                 S   ⁡     (   t   )       ⁢     α   ⁡     [       C   ⁢           ⁢     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢     f   mod     ⁢   t     -       2   ⁢   π   ⁢           ⁢   X     L       )         +       ξ   1     ⁡     (   t   )         ]       ⁢   cos   ⁢           ⁢   2   ⁢           ⁢   π   ⁢           ⁢     f   1     ⁢   t     +         ξ   2     ⁡     (   t   )       ⁢   cos   ⁢           ⁢   2   ⁢   π   ⁢           ⁢     f   2     ⁢   t     +     other   ⁢           ⁢   terms           
where C is a constant, X is the position of the sensor element  1  relative to the PCB  5  along the X-direction, ξ 1 (t) and ξ 2 (t) are the amplitudes of the part of the noise component in phase quadrature with the components of the drive signals at the first frequency f 1  and the second frequency f 2  respectively. The other terms relate to terms at frequencies away from f 1  and f 2  and terms at the frequencies f 1  and f 2  which are in phase with the components of the drive signals at f 1  and f 2 . The noise component amplitudes ξ 1 (t) and ξ 2 (t) at the modulation frequency f mod  and frequencies which are comparatively slow with respect to the modulation frequency f mod , due to changes in environmental factors such as movement of a nearby conductive object.
 
     The sense signal S(t) is input to a first synchronous detector  51   a  together with the quadrature signal Q 1  at the first frequency f 1 . The first synchronous detector  51   a  performs synchronous detection of the sense signal S(t) using the quadrature signal Q 1  as the reference signal to generate a first detection signal D 1 (t) having the form: 
     
       
         
           
             
               
                 D 
                 1 
               
               ⁡ 
               
                 ( 
                 t 
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             = 
             
               
                 C 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   cos 
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                     ( 
                     
                       
                         2 
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                         π 
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                         ⁢ 
                         
                           f 
                           mod 
                         
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                         t 
                       
                       - 
                       
                         
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     The sense signal S(t) is also input to a second synchronous detector  51   b  together with the inverse quadrature signal −Q 2  at the second frequency f 2 . The second synchronous detector  51   b  performs synchronous detection of the sense signal S(t) using the inverse quadrature signal −Q 2  as the reference signal to generate a second detection signal D 2 (t) of the form:
 
 D   2 ( t )=−ξ 2 ( t )
 
       FIG. 6  shows the sense coil  11  and the main components of one of the synchronous detectors  51 . As shown, a first end  81  and a second end  83  of the sense coil  11  are connected to respective inputs of a switching arrangement  85 , which multiplies the sense signal by the input reference signal (i.e. the quadrature signal Q 1  for the first synchronous detector  51   a  and the inverse quadrature signal −Q 2  for the second synchronous detector  51   b ). The two outputs of the switching arrangement  85  are connected to respective inputs of a differential amplifier  87 , and the output of the differential amplifier  87  is passed through a low pass filter  89  which removes frequency components which are above the modulation frequency f mod . 
     Returning to  FIG. 3 , the first detection signal D 1 (t) and the second detection signal D 2 (t) are then input to a summing amplifier  53 , which adds the first detection signal D 1 (t) and second detection signal D 2 (t) together. In this embodiment it is assumed, for ease of explanation, that the noise components ξ 1 (t) and ξ 2 (t) are so similar in magnitude that when the first detection signal D 1 (t) and the second detection signal D 2 (t) are added together the noise components ξ 1 (t) and ξ 2 (t) cancel each other out. The summed signal output by the summing amplifier  53  is then input to a bandpass filter  55  centred on the modulation frequency f mod . The filtered signal F(t) output by the filter  55  is of the form: 
     
       
         
           
             
               F 
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             ⁢ 
             α 
             ⁢ 
             
                 
             
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                     2 
                     ⁢ 
                     
                         
                     
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                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       f 
                       mod 
                     
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                     t 
                   
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     The filtered signal F(t) is therefore an oscillating signal at the modulation frequency f mod  whose phase varies with the relative position of the sensor element  1  and the PCB  5 . 
     The filtered signal F(t) is input to a phase detector  57  which measures the phase difference between the filtered signal F(t) and the square wave modulation signal output by the square wave oscillator  43 , and outputs a signal indicative of the measured phase difference to a position calculator  59  which calculates the position of the sensor element  1  relative to the PCB  5  using the measured phase difference. 
     The modulation of the signal at the first frequency f 1  by the +SIN signal and the COS signal, any difference between the first frequency f 1  and the actual resonant frequency of the resonant circuit, the low pass filter  89  of the synchronous detector  51  and the filter  55  introduce a phase shift Δ F  in the filtered signal F(t) which needs to be corrected for in order to obtain high accuracy position measurement. In this embodiment, this correction is performed by the PWM type pattern generator  45  alternately outputting the +SIN signal and the −SIN signal and the position calculator  59  averaging the resultant measured phase differences, in the same manner as described in GB 2374424A. 
     Second Embodiment 
     In the first embodiment, the amplitude of the noise components ξ 1 (t) and ξ 2 (t) at the frequencies f 1  and f 2  respectively are assumed to be equal. In practice, however, there will be a variation in the amplitude of the noise component ξ(t) with frequency, although the variation of the noise component ξ(t) with frequency is slower than the variation with frequency of the amplitude of the signal component resulting from resonance in the resonant circuit of the sensor element  1 . Nevertheless, the arrangements described in the first embodiment do give a reduction in noise, and therefore an improvement in the accuracy of position measurement. 
     A second embodiment will now be described with reference to  FIG. 7  in which, in order to achieve a more accurate estimate of the noise component ξ 1 (t) at the first frequency f 1 , the excitation signal generating circuitry generates components of the excitation signal at two frequencies away from the resonant frequency f res , and the sense signal processing circuitry measures the strength of the noise components at these frequencies and interpolates the noise component ξ 1 (t) at the first frequency f 1 . In  FIG. 7 , components which are identical with corresponding components of the first embodiment have been referenced by the same numerals and will not be described in detail again. 
     As shown in  FIG. 8 , in this embodiment a third quadrature signal generator  41   c  generates an in-phase signal I 3  and an inverse quadrature signal −Q 3  at a third frequency f 3 , which does not induce resonance in the resonant circuit. In this embodiment, the third frequency f 3  is 3 MHz so that the second and third frequencies are evenly spaced on either side of the first frequency f 1 . The in-phase signal I 3  is input to a fifth digital mixer  47   e  together with the sine signal ±SIN output by the first output  46   a  of the PWM type pattern generator  45 , and the resultant output of the fifth digital mixer  47   e  is input to a first coil driver  111   a  together with the outputs of the first digital mixer  47   a  and the second digital mixer  47   b . Similarly, the in-phase signal I 3  is input to a sixth digital mixer  47   f  together with the cosine signal COS output by the second output  46   b  of the PWM type pattern generator  45 , and the resultant output of the sixth digital mixer  47   f  is input to a second coil driver  111   b  together with the outputs of the third digital mixer  47   c  and the fourth digital mixer  47   d.    
     Each of the first and second coil drivers  111  is similar to the coil drivers  49  of the first embodiment, as shown in  FIG. 5 , but with three input signals instead of two being directed to the non-inverting input of the operational amplifier via respective resistors. The output of the first coil driver  111   a  drives the sine coil  7 , and the output of the second coil driver  111   b  drives the cosine coil  9 . 
     The sense signal S(t) induced in the sense coil  11  is input to: i) a first synchronous detector  51   a  together with the quadrature signal Q 1  at the first frequency f 1 ; ii) a second synchronous detector  51   b  together with the inverse quadrature signal −Q 2  at the second frequency f 2 ; and iii) a third synchronous detector together with the inverse quadrature signal −Q 3  at the third frequency f 3 . The outputs of the second synchronous detector  51   b  and the third synchronous detector  51   c , which are respectively representative of the noise component ξ 2 (t) at the second frequency and the nose component ξ 3 (t) at the third frequency, are input to an interpolator  153  which derives a value for the noise component ξ 1 (t) at the first frequency f 1 . In this embodiment, the interpolator  153  performs a linear interpolation by averaging the magnitudes of the signals output by the second synchronous detector  51   b  and the third synchronous detector  51   c.    
     The signal output by the interpolator is input to a summing amplifier  53  together with the output of the first synchronous detector  51   a , and the sense signal processing then proceeds in the same manner as the first embodiment. 
     Modifications and Further Embodiments 
     In the second embodiment, the interpolator  153  performs a linear interpolation of the noise component at the carrier frequency near the resonant frequency f res  using the noise components at two frequencies which do not induce resonance in the resonant circuit. It will be appreciated that the excitation signals applied to the sine coil  7  and the cosine coil  9  could include components at more than two frequencies which do not induce resonance in the resonant circuit, with the noise components at these frequencies being measured by respective synchronous detectors and input to an interpolator. Further, the interpolator  153  could perform the interpolation in accordance with a more complicated function which more closely matches the variation of the noise component ξ(t) with frequency. 
     In the first embodiment, as shown in  FIG. 5  the coil driver  49  includes a summing amplifier which performs an analogue summation of the two input signals.  FIG. 8  shows an alternative coil driver to the coil driver used in the first embodiment. As shown, the two input signals are input to a NAND gate  121  and an OR gate  123 . The coil driver comprises a first amplification circuit  125   a  and a second amplification circuit  125   b  which are connected in parallel between the supply voltage V cc  and ground. The first amplification circuit  125   a  comprises a p-channel MOSFET switch P 1  and an n-channel MOSFET switch N 1  with the drain of P 1  connected to the drain of N 1  and the gates of P 1  and N 1  connected to each other. The signal output by the NAND gate  121  is input to an input terminal located at the common gate of P 1  and N 1 . Similarly, the second amplification circuit  125   b  is formed in an identical manner to the first amplification circuit  125   a  using a p-channel MOSFET switch P 2  and an n-channel MOSFET switch N 2  and the output of the OR gate  123  is applied to an input terminal located at the common gate of P 2  and N 2 . The coil being driven is connected between an output terminal of the first amplification circuit  125   a  located at the connection between the drain of P 1  and the drain of N 1  and an output terminal of the second amplification circuit  125   b  located at the connection between the drain of P 2  and the drain of N 2 . 
     In this way, if the signals input to the NAND gate  121  and the OR gate  123  are both at the LOW level, current flows in a first direction through the coil being driven; if the signals input to the NAND gate  121  and the OR gate  123  are both in a HIGH level, then current flows through the coil being driven in a second direction which is opposite to the first direction. If one of the signals input to the NAND gate  121  and the OR gate  123  is in a HIGH level and the other signal is in a LO level, then no current flows thought the coil being driven. In this way, digital switching allows three different states of driving of the coil being driven and therefore summation using digital signals is possible. 
     In the first embodiment, separate synchronous detectors are used to detect the signal components at the frequencies f 1  and f 2 . However, a single synchronous detection operation may be performed by multiplying the sense signal by a reference signal having frequency components at f 1  and f 2 .  FIG. 9  shows a synchronous detector implementing such an arrangement, together with the sense coil  11 . As shown, the sense coil  11  is connected to a switching arrangement  131  having two independently controlled signal-pole signal-throw switches  133   a  and  133   b . Each of the switches  133  has two input terminals connected to respective ends of the sense coil  11 . The control signal for the switches  133  are generated by inputting the quadrature signal Q 1  at f 1  and the inverse quadrature signal −Q 2  to an AND gate  135  and an OR gate  137 . The output of the AND gate  135  is connected to the first switch  133   a  and the output of the OR gate  137  is connected to the second switch  133   b.    
     The output terminals of each switch  13  is connected to a respective input of a differential amplifier  139 , and the output of the differential amplifier is input to a low pass filter  141  which removes frequency components above the modulation frequency f mod . 
     In the described embodiments, a transmit aerial is formed by two excitation windings and a receive aerial is formed by a single sensor winding. It will be appreciated that many other arrangements of transmit aerial and receive aerial in which the electromagnetic coupling between the transmit aerial and the receive aerial varies along a measurement path could be used. For example, the transmit aerial could be formed by a single excitation winding and the receive aerial could be formed by a pair of sensor windings, with the respective strengths of signals induced in the two sensor windings being indicative of the location of the sensor element. In such an arrangement, the sense signal induced in each sensor winding is adjusted using a noise component at a frequency away from the resonant frequency in order to reduce noise. 
     It will also be appreciated that the position sensor described in the first embodiment could be adapted to measure a linear position along a curved line, for example a circle (i.e. a rotary position sensor) by varying the layout of the sine coil and the cosine coil in a manner which would be apparent to persons skilled in the art. The position sensor could also be used to detect speed by periodically detecting the position of the sensor element as the sensor element moves along the measurement path, and then calculating the rate of change of position. 
     As described in the first embodiment, the phase shift Δ F  introduced in the filtered signal F(t) is removed by effectively taking two measurements of the position with the phase of the signal applied to the sine coil  7  being reversed between measurements. It will be appreciated that in alternative embodiments, the reverse measurement need only be performed intermittently to determine a value for the phase shift Δ F  which has the advantage of increasing the measurement update rate. Alternatively, a predetermined value for the phase shift Δ F , determined by a factory calibration, could be subtracted from a single phase measurement. However, this is not preferred because it cannot allow for environmental factors which affect the resonant frequency f res  and quality factor of the resonant circuit and therefore vary the phase shift Δ F . 
     It will be appreciated that if the phase angle measured using the −SIN signal is subtracted from, rather than added to, the phase angle measured using the +SIN signal then the position-dependent phase shift would be removed to leave a value equal to twice the phase shift Δ F . In an embodiment, the resonant circuit is manufactured using components having a high sensitivity to environmental factors so that the variation of resonant frequency with environmental factors is the dominant cause of the phase shift Δ F . In this way, a measurement of the phase shift Δ F  can be indicative of an environmental factor, for example temperature in a constant humidity environment or humidity in a constant temperature environment. Typically, this would involve storing in the control circuitry of the inductive sensor a factory calibration between the measured phase shift Δ F  and the corresponding value of the environmental factor. 
     In the described embodiments, the sine coil  7  and the cosine coil  9  are arranged so that their relative contributions to the total magnetic field component perpendicular to the PCB  5  vary in accordance with position along the measurement direction. In particular, the sine and cosine coils have an alternate twisted loop structure. However, it would be apparent to a person skilled in the art that an enormous variety of different excitation winding geometries could be employed to form transmit aerials which achieve the objective of causing the relative proportions of the first and second transmit signals appearing in the ultimately detected combined signal to depend upon the position of the sensor element in the measurement direction. 
     While in the described embodiments, the excitation windings are formed by conductive tracks on a printed circuit board, they could also be provided on a different planar substrate or, if sufficiently rigid, could even be free standing. Further, it is not essential that the excitation windings are planar because, for example, cylindrical windings could also be used with the sensor element moving along the cylindrical axis of the cylindrical winding. 
     If the inductive sensor is used to measure only an environmental factor such as temperature or humidity, only one transmit aerial could be used as there is no requirement for the phase of the magnetic field to vary with position. 
     In the first embodiment, the modulating signals are described as digital representations of sinusoidal signals. This is not strictly necessary and it is often convenient to use modulating signals that can be more easily generated using simple electronics. For example, the modulating signals could be digital representations of triangular waveforms. The phase of the modulation can be decoded in the usual way by only looking at the fundamental frequency of the modulated signals, i.e. by filtering out the higher harmonics present in the triangular waveform. Note that some filtering will be performed as a result of the physical and electrical properties of, and the electromagnetic coupling between, the transmit and receive aerials. Alternatively, if no filtering is used, the zero crossing point of the demodulated waveform will still vary with the target position in some predictable, albeit non-linear, manner which could be converted to a linear measurement of position by using look-up table or a similar technique. 
     In the first and second embodiments, a quadrature pair of modulation signals are applied to carrier signals to generate first and second excitation signals which are applied to the sine coil  7  and cosine coil  9  respectively. However, the use of a quadrature pair of modulation signals is not essential because it is merely required that the information carrying components of the excitation signals are distinct in some way so that the relative contributions from the first and second excitation signals can be derived by processing the combined signal. For example, the modulation signals could have the same frequency and a phase which differs by an amount other than 90 degrees. Alternatively, the modulation signals could have slightly different frequencies thus giving rise to a continuously varying phase difference between the two signals. 
     In the above described embodiment, a passive resonator is used. However, in some circumstances it may be advantageous to use a powered resonator so that the signal induced in the resonator is considerably amplified, thus reducing the requirements on the signal processing circuitry. 
     Instead of detecting the phase of the information carrying components of the combined signal, it is also possible to perform parallel synchronous detection of the combined signal, one synchronous detection using an in-phase modulation signal and the other synchronous detection using a quadrature modulation signal, and then to perform an arctangent operation on the ratio of the detected magnitudes of the demodulated signals. In such an embodiment, by using excitation signals which comprise a carrier frequency signal and a modulation signal so that the modulation signals can have a relatively low frequency, the detection of the magnitude of the modulation signals and the ensuing arctangent calculation (or reference to a look-up table) can be performed in the digital domain after down-conversion from the carrier frequency. An alternative method of detection of the information carrying part of the signal after down-conversion from the carrier frequency signal to baseband would be to perform a fast Fourier transform detection. As will be appreciated, this could be done either using some additional specialised dedicated hardware (e.g. an application specific integrated circuit) or by suitably programming the microprocessor. Such a method of detection would be particularly convenient in an arrangement in which more than one degree of freedom of movement of a target is to be detected. 
     Although synchronous detection is preferred because the phase sensitive nature of the synchronous detection removes noise, alternatively a filtering arrangement could be used to isolate the signals at each carrier frequency. For example, the sense signal induced in the sense coil could be input to a parallel arrangement of bandpass filters, with each bandpass filter centred at a respective different carrier frequency. The signal strengths at each frequency can then be compared in order to determine the noise component at the carrier frequency close to the resonant frequency f res . 
     In the above described embodiment, the measurement path extends only over a single period of the spatial variation of the two transmit coils (i.e. the sine coil  7  and the cosine coil  9 ). However, this need not be the case and the measurement path could extend over more or less than a single period of the spatial variation of the transmit coils. In such a case, it is preferable to include a mechanism for resolving period ambiguity (i.e. the fact that the basic phase of the information carrying component of the combined signal will be identical for the same corresponding position in different spatial periods of the transmit coils). Mechanisms for overcoming spatial period ambiguity which can be employed include providing a single reference position detected, for example, by a single location position sensor (e.g. by having a single localised transmit coil transmitting a third transmit signal at a different modulation frequency to add with the first and second transmit aerials, or by using an opto-switch) and thereafter counting the periods from the reference position, and maintaining a record in a register within the microprocessor of the particular period within which the sensor element is currently located. Alternatively, an additional set of transmit coils transmitting at a different modulation frequency (or transmitting in a time multiplexed manner), could be used with either a slightly varying spatial frequency to provide a Vernier scale effect, or with a widely varying spatial frequency to provide coarse position detection using a large scale set of transmit coils and fine scale position detection using small scale transmission coils. 
     In the described embodiment, a modulation frequency of 2.5 kHz is used because it is well suited to digital processing techniques. This generally applies to frequencies in the range 100 Hz to 100 kHz. Preferably, frequencies in the range of 1–10 kHz are used, for example 3.9 kHz or 5 kHz. 
     Although in the first embodiment the PWM type pattern generator is clocked at 2 MHz, other clocking frequencies could be used. Further, the clocking frequency need not be equal to one of the carrier frequencies. 
     In the described embodiment, a carrier frequency of 2 MHz is used. Using a carrier frequency above 1 MHz facilitates making the sensor element small. However, in some applications it may be desirable to use a carrier frequency below 100 kHz, for example if a sheet of non-magnetic stainless steel separates the sensor element from the excitation and sensor windings, because the skin depth of the non-magnetic stainless steel is greater at lower frequencies.