POSITION SENSOR

[0001] The present invention relates to position sensors and to apparatus for use in such sensors. The invention has particular, although not exclusive, relevance to inductive position sensors that can be used in linear or rotary applications and to excitation circuitry and processing circuitry used in such position sensors.

[0002] Position sensors are used in many industries. Optical encoders are used in many applications and offer the advantages of providing low latency measurements and high update rates. However, optical encoders are expensive and require a clean environment to work correctly.

[0003] Inductive position encoders are also well known and typically include a movable target, whose position is related to the machine about which position or motion information is desired, and stationary sensor coils which are inductively coupled to the moving target. The sensor coils provide electrical output signals which can be processed to provide an indication of the position, direction, speed and/or acceleration of the movable target and hence for those of the related machine. In some applications, the target may be stationary and the sensor coils move and in other applications both may move.

[0004] Some inductive position encoders employ a magnetic field generator as the target. The magnetic field generator and the sensor coils are arranged so that the magnetic coupling between them varies with the position of the movable member relative to the stationary member. As a result, an output signal is obtained from each sensor coil which varies with the position of the movable member. The magnetic field generator may be an active device such as a powered coil; or a passive device, such as a field concentrating member (e.g. a ferrite rod), a conductive screen or a resonator. When a passive device is used, the magnetic field generator is typically energised by an excitation coil which can be mounted on the stationary member.

[0005] Whilst inductive position encoders are much cheaper than optical encoders, they typically have a higher latency and a lower update rate compared to optical encoders which make them less reliable for use in applications where the moving object is moving quickly.

[0006] The present invention aims to provide alternative position encoders and to provide novel components therefor. Embodiments of the invention provide new processing circuitry and new excitation circuitry that can be used with, for example, an inductive position encoder to reduce its latency and improve its accuracy.

[0007] According to one aspect, the present invention provides processing circuitry for use in processing sensor signals, the processing circuitry comprising: a first measurement circuit configured to receive a first plurality of sensor signals from a plurality of sensor inputs and configured to pass the first plurality of sensor signals through the first measurement circuit in a time division manner in a sequence of time intervals to generate a first time division sequence of sensor measurements in response thereto; a second measurement circuit configured to receive at least one sensor signal from a sensor input and configured to pass the at least one sensor signal through the second measurement circuit to generate sensor measurements in response thereto; and measurement processing circuitry configured to process the sensor measurements generated by the first and second measurement circuits to determine and output sensor results; wherein the first and second measurement circuits are both configured to receive a sensor signal from at least one common sensor input and to output respective common sensor measurements in response thereto; and wherein the measurement processing circuitry is configured to determine and output sensor results using the common sensor measurements obtained from the first and second measurement circuits. By providing two (or more) measurement circuits in this way, where each measurement circuit can process a common sensor signal, the processing circuitry can detect errors in the measurements and can also continuously calibrate one or more of the measurement circuits.

[0008] The measurement processing circuitry can determine various different calibration data including:

• • [0009] calibration data that maps the signal amplitude measured in one measurement channel to the signal amplitude measured in another measurement channel in order to remove the difference in the gain and offset between measurement channels;
  • [0010] calibration data determined by measuring the amplitude and phase of a reference signal that is used for breakthrough offset correction in the sensor signals measured by electronics;
  • [0011] calibration data determined by measuring the phase of the reference signal to actively tune its value to a predetermined phase stored in the memory of the electronics;
  • [0012] calibration data corresponding to the phase shift introduced in the amplification and filtering circuitry in order to correct the measurement provided by the measurement circuit;
  • [0013] calibration data that removes any remaining differences between sensor results obtained from different measurement circuits so that substantially the same sensor result is output from either measurement circuit.

[0014] The measurement processing circuitry may determine and output a sensor result using the common sensor measurement obtained from the first measurement circuit and the common sensor measurement obtained from the second measurement circuit. In one embodiment, the measurement processing circuitry determines calibration data using the common sensor measurement from the first measurement circuit and determines a sensor result using the common sensor measurement from the second measurement circuit and the calibration data determined using the common sensor measurement from the first measurement circuit. The measurement processing circuitry may be arranged to determine mapping data that relates measurements made by the first measurement circuit to measurements made by the second measurement circuit using the common sensor measurements from the first and second measurement circuits.

[0015] In some embodiments, the measurement processing circuitry switches between determining sensor results using sensor measurements from the first measurement circuit and sensor measurements obtained from the second measurement circuit and determines calibration data to smooth changes in the sensor results when performing said switching using the common sensor measurement from the first measurement circuit and the common sensor measurement from the second measurement circuit.

[0016] Typically, each input sensor signal has a first frequency and the first and second measurement circuits are configured to receive and down convert the sensor signals to a sensor signal having a second frequency that is lower than the first frequency. In some embodiments, the measurement processing circuitry may control the switching of the sensor signals through said first measurement circuit in a time division multiplexed manner so that said common sensor signal passes through said first and second measurement circuits at different times. Preferably, the common sensor signal is switched through said first and second measurement circuits at a third frequency that is higher than said second frequency as this allows measurements of the common signal to be obtained at around the same point in time, without requiring any buffer amplifiers that would allow the common sensor signal to be input to both measurement circuits at the same time.

[0017] In one embodiment, the plurality of sensor inputs includes main sensor inputs and auxiliary sensor inputs and the first measurement circuit is configured to receive auxiliary sensor signals from the auxiliary sensor inputs and to output auxiliary sensor measurements and wherein said measurement processing circuitry is configured to process said auxiliary sensor measurements to determine calibration data for use in calibrating sensor results.

[0018] The plurality of sensor inputs typically includes at least one main sensor input and at least one auxiliary sensor input, wherein the first measurement circuit is configured to receive auxiliary sensor signals from the at least one auxiliary sensor input and to output auxiliary sensor measurements.

[0019] The measurement processing circuitry may be arranged to determine mapping data that relates measurements made by the first measurement circuit to measurements made by the second measurement circuit using the common sensor measurements from the first and second measurement circuits and may be arranged to determine a breakthrough correction for a sensor result using at least one auxiliary sensor measurement and the determined mapping data.

[0020] The second measurement circuit may also be configured to receive a plurality of sensor signals from a plurality of sensor inputs and to pass the plurality of sensor signals through the second measurement circuit in a time division manner in a sequence of time intervals to generate a second time division sequence of sensor measurements.

[0021] In this case, the plurality of sensor inputs may include at least one main sensor input and at least one auxiliary sensor input, wherein the first measurement circuit is configured to receive auxiliary sensor signals from the at least one auxiliary sensor input and to output auxiliary sensor measurements, wherein the second measurement circuit is configured to receive auxiliary sensor signals from the at least one auxiliary sensor input and to output auxiliary sensor measurements. The first and second measurement circuits may be configured: i) so that during time intervals when the first measurement circuit is passing the auxiliary sensor signals there through, the second measurement circuit is passing sensor signals from the at least one main sensor input there through; and ii) so that during time intervals when the second measurement circuit is passing the auxiliary sensor signals there through, the first measurement circuit is passing the sensor signals from the at least one main sensor input there through.

[0022] The measurement processing circuitry may be configured to determine a breakthrough correction for the first measurement circuit using an auxiliary sensor measurement obtained from the first measurement circuit and to determine a breakthrough correction for the second measurement circuit using an auxiliary sensor measurement obtained from the second measurement circuit and may be configured to correct main sensor measurements obtained from the first measurement circuit using the breakthrough correction for the first measurement circuit and to correct main sensor measurements obtained from the second measurement circuit using the breakthrough correction for the second measurement circuit.

[0023] In some embodiments, the first and second measurement circuits overlap the passing of the signals from the at least one main sensor input there through, so that during some time intervals, both the first and second measurement circuits generate sensor measurements of the sensor signals received from the at least one main sensor input.

[0024] The processing circuitry may further comprise excitation circuitry for generating an excitation signal for energising a target and the sensor signals are received from the sensor inputs in response to the energising of target. In this case, each measurement circuit may include demodulating circuitry for multiplying the sensor signal passing through the measurement circuit with a demodulation signal comprising a phase shifted version of the excitation signal and phase shift circuitry can be provided for varying the phase of the excitation signal or the phase shifted version of the excitation signal forming part of the demodulation signal. In this case, the plurality of sensor inputs may include an auxiliary sensor input, and the phase shift circuitry may vary the phase in dependence upon a control signal determined using a sensor measurement obtained from the sensor signal received at said auxiliary sensor input.

[0025] In one embodiment, each measurement circuit is arranged to output a first main sensor measurement corresponding to a sensor signal received from a first main sensor input and to output a second main sensor measurement corresponding to a sensor signal received from a second main sensor input and wherein the measurement processing circuitry is configured: i) to perform a ratiometric calculation of the first main sensor measurement and the second main sensor measurement obtained from the first measurement circuit, to determine a first ratiometric result; ii) to perform a ratiometric calculation of the first main sensor measurement and the second main sensor measurement obtained from the second measurement circuit, to determine a second ratiometric result; and iii) to determine and output sensor results using the first and second ratiometric results.

[0026] The measurement processing circuitry may be arranged to determine a difference between sensor results obtained using sensor measurements from the first measurement circuit and corresponding sensor results obtained using sensor measurements from the second measurement circuit and may determine a correction to be applied to the sensor measurements obtained from at least said first measurement circuit using said difference so that sensor results obtained using measurements from said first and second measurement circuits in relation to the same sensor signals are substantially the same. In this case, the measurement processing circuitry may also determine a correction to be applied to the sensor measurements obtained from said second measurement circuit using said difference.

[0027] A speed measure relating to a rate of change of the sensor results may also be determined and used to determine a compensation to be applied to the sensor results to compensate for motion of a sensor target. The compensation to be applied to a sensor result may depend on the value of the uncompensated sensor result. In a preferred embodiment, the measurement processing circuitry determines a sensor result using a first sensor measurement of a sensor signal obtained from a first main sensor input during a first time interval by the first measurement circuit and a second sensor measurement of a sensor signal obtained from a second main sensor input during a second time interval by the first measurement circuit; and the measurement processing circuitry applies a first compensation to the sensor result if the first time interval is before the second time interval and applies a second, different, compensation to the sensor result if the second time interval is before the first time interval. An acceleration measure may also be used to determine the compensation measure.

[0028] In one embodiment, the first and second measurement circuits are configured, during an overlap period, to overlap the passing of sensor signals from the at least one main sensor input there through, so that during some time intervals, both the first and second measurement circuits generate sensor measurements of the sensor signals received from the at least one main sensor input, wherein the measurement processing circuitry is arranged: i) to determine a first sensor result using sensor measurements obtained from the first measurement circuit during said overlap period; ii) to determine a second sensor result using sensor measurements obtained from the second measurement circuit during said overlap period; iii) to determine a difference between the first and second sensor results; and iv) to apply a compensation to subsequent sensor results using said difference to compensate for dynamic errors caused by motion of a sensor target.

[0029] In this case, the measurement processing circuitry may determine a sensor result using a first sensor measurement of a sensor signal obtained from a first main sensor input during a first time interval by the first measurement circuit and a second sensor measurement of a sensor signal obtained from a second main sensor input during a second time interval by the first measurement circuit, wherein the measurement processing circuitry is arranged may apply a first compensation using said difference to the sensor result if the first time interval is before the second time interval, and may apply a second, different, compensation using said difference to the sensor result if the second time interval is before the first time interval.

[0030] In one embodiment, each measurement circuit has an auxiliary mode of operation and a main sensor mode of operation, wherein when the first measurement circuit is configured to operate in the main sensor mode of operation, the second measurement circuit is configured to operate in the auxiliary mode of operation and vice versa. When operating in the main sensor mode of operation, a measurement circuit is configured to pass the sensor signals obtained from the at least one main sensor input there through without passing the sensor signals from the auxiliary sensor inputs there through and when operating in the auxiliary mode of operation, a measurement circuit is configured to pass the signals obtained from the auxiliary sensor inputs and sensor signals obtained from the at least one main sensor input there through in a time division manner. In this case, the measurement processing circuitry may determine calibration data for a measurement circuit using sensor measurements of the sensor signals obtained from the at least one main sensor input when the measurement circuit is operating in said auxiliary mode of operation and may apply the calibration data to sensor results obtained from the measurement circuit when operating in said main sensor mode of operation. Again, the calibration data determined for one measurement circuit may depend on a speed (an acceleration) measure determined from sensor results obtained using sensor measurements from the other measurement circuit. Typically, the determined calibration data for a measurement circuit is for cancelling a phase offset introduced into the sensor results by the measurement circuit.

[0031] In one embodiment, analogue to digital converter, ADC, circuitry is provided for converting sensor measurements obtained from the first measurement circuit to digital data and second analogue to digital converter circuitry is provided for converting sensor measurements obtained from the second measurement circuit, wherein the measurement processing circuitry dynamically adjusts a timing of a conversion performed by the first ADC circuitry in dependence upon a speed measure determined using sensor measurements obtained from the second measurement circuit. Similarly, the measurement processing circuitry may dynamically adjust a timing of a conversion performed by the second ADC circuitry in dependence upon a speed measure determined using sensor measurements obtained from the first measurement circuit.

[0032] In one embodiment, each measurement circuit is configured to multiplex a pair of sensor signals there through during each time interval to generate a sensor measurement signal whose phase varies with the ratio of the pair of sensor signals. In this case, the measurement processing circuitry may include a zero crossing detector for detecting zero crossings of the sensor measurement signal. The measurement circuitry may also include an analogue to digital converter, ADC, for obtaining an amplitude measure of an amplitude of the sensor measurement signal between a pair of adjacent detected zero crossing events and wherein the measurement processing circuitry is configured to use the amplitude measure to identify which of the pair of adjacent zero crossing events is a rising zero crossing event and which is a falling zero crossing event.

[0033] In one embodiment, the measurement processing circuitry is configured to report sensor results using the sensor measurements from the first measurement circuit during a first part of a detection cycle and is configured to report sensor results using the sensor measurements from the second measurement circuit in a second part of the detection cycle; and wherein the measurement processing circuitry is configured to ignore or add sensor results when switching between reporting using the sensor measurements obtained from the first measurement circuit and reporting using the sensor measurements from the second measurement circuit. For example, the measurement processing circuitry may ignore a first sensor result after switching to the sensor measurements obtained from the second measurement circuit in the event that a first sensor result obtained from the second measurement circuit is obtained within a defined time period of a last reported sensor result obtained using the sensor measurements of the first measurement circuit. Similarly, the measurement processing circuitry may add a sensor result after switching to the sensor measurements obtained from the second measurement circuit if a sensor result was determined using the sensor measurements from the second measurement circuit within a defined time period before switching over to reporting sensor results using the sensor measurements of the second measurement circuit. When adding a new sensor result, the measurement processing circuitry may extrapolate a sensor result made using sensor measurements obtained from the second measurement circuit in a previous time interval in accordance with a measure of a speed of motion of a sensor target (and optionally in accordance with a measure of the acceleration as well).

[0034] In one embodiment, the first measurement circuit comprises a first multiplexor for multiplexing a sensor signal with a modulation control signal having a fundamental frequency within a pass band of amplification and filtering circuitry forming part of the first measurement circuit, wherein the switching of the first multiplexor injects unwanted charge injection into the sensor signals at around said fundamental frequency, wherein an output from the first multiplexor is passed through a second multiplexor of the first measurement circuit and a chopper signal, having a frequency that is a multiple of said fundamental frequency, is used to enable and disable the second multiplexor in order to inject additional charge into the sensor signals, and wherein transition points of said chopper signal are time aligned with transition points of said modulation control signal so that the total charge injection into the sensor signals is at the higher frequency of said chopper signal, which higher frequency is outside the pass band of said amplification and filtering circuitry, whereby said charge injection is substantially attenuated in a sensor measurement signal output from the first measurement circuit.

[0035] The chopper signal and said modulation control signal may be generated from a common clock signal in order to time align the transition points of the chopper signal and the transition points of the modulation control signal. For example, control signal logic may be provided for generating said chopper signal and said modulation control signal from a master clock signal.

[0036] In one embodiment, one of the first and second measurement circuits provides sensor measurements for use in determining main sensor results and the other one of the first and second measurement circuits provides auxiliary measurements and wherein the roles of the first and second measurement circuits is reversed depending on a value of the sensor result.

[0037] In an embodiment, the measurement processing circuitry may use the sensor measurements from the first measurement circuit to determine first sensor results that vary with a sensor variable according to a first function and to use the sensor measurements from the second measurement circuit to determine second sensor results that vary with the sensor variable according to a second function that is different from the first function; and wherein the measurement processing circuitry is configured to determine a value of the sensor variable using the first and second sensor results. The measurement processing circuitry may use the first sensor results to determine the value of the sensor variable or may use the second sensor results to determine the value of the sensor variable depending on the value of the sensor variable. The measurement processing circuitry may to use the first sensor results to determine a first value of the sensor variable and to use the second sensor results to determine a second value of the sensor variable and may combine the first and second values in accordance with a weighting function. The weighting function used may depend on the value of the sensor variable.

[0038] In one embodiment, the plurality of sensor inputs include auxiliary sensor inputs, wherein the first and second measurement circuits are configured to obtain sensor measurements of the sensor signals from the at least one main sensor input more frequently than they obtain sensor measurements of the sensor signals from the auxiliary sensor inputs; and wherein sensor inputs that are defined as being main sensor inputs and sensor inputs that are defined as being the auxiliary sensor inputs change in dependence upon sensor results determined by the measurement processing circuitry. In this case, the measurement processing circuitry may use the sensor results to determine a value of a sensor variable and when the sensor variable falls within a first range of values the main sensor inputs correspond to a first set of the sensor inputs and the auxiliary sensor inputs correspond to a second set of the sensor inputs and when the sensor variable falls within a second range of values the main sensor inputs correspond to the second set of the sensor inputs and the auxiliary sensor inputs correspond to the first set of the sensor inputs.

[0039] According to another aspect, the present invention also provides a position sensor comprising: a plurality of detection elements and a target, at least one of: i) the detection elements; and ii) the target, being moveable relative to the other such that signals are generated in the detection elements that depend on the relative position of the target and the detection elements; and any of the processing circuitry described above for processing the signals from the detection elements and for determining and outputting position information relating to the relative position of the target and the detection elements. The position sensor may be, for example, a linear or rotary position sensor or a proximity sensor. The sensor may use inductive detection elements, capacitive detection elements or Hall effect detection elements.

[0040] According to another aspect, the present invention provides a sensor board carrying: an excitation coil comprising a first set of one or more substantially planar conductor loops and a second set of one or more substantially planar conductor loops, wherein the loops of the first set are substantially concentric and are connected in series and wound in the same sense, wherein the one or more conductor loops of the second set are connected in series and wound in the same sense, the one or more conductor loops of the first set being grouped together between a first inner diameter and a first outer diameter and the conductor loops of the second set being grouped together between a second inner diameter and a second outer diameter and wherein the second outer diameter is smaller than the first inner diameter; and a first detection coil comprising a third set of one or more substantially planar conductor loops and a fourth set of one or more substantially planar conductor loops, the conductor loops of the first detection coil being substantially concentric with each other and with the conductor loops of the excitation coil;

[0041] wherein the one or more conductor loops of the third set are connected in series and wound in the same sense, wherein the one or more conductor loops of the fourth set are connected in series and wound in the same sense, wherein the one or more conductor loops of the third set are connected in series and wound in the opposite sense with the one or more conductor loops of the fourth set; wherein the one or more conductor loops of the third set are grouped together between a third inner diameter and a third outer diameter; wherein the one or more conductor loops of the fourth set are grouped together between a fourth inner diameter and a fourth outer diameter, wherein the fourth outer diameter is less than the third inner diameter; wherein the number of conductor loops in, and the respective inner and outer diameters of, the third and fourth sets of conductor loops are selected so that the first detection coil is substantially insensitive to background electromagnetic signals; and wherein the number of conductor loops in, and the respective inner and outer diameters of, the first, and second conductor loops are selected so that the detection coil is substantially balanced with respect to the excitation coil.

[0042] In one embodiment, the one or more conductor loops of the third set are located in closer proximity to the one or more conductor loops of the first set than the proximity of the one or more conductor loops of the fourth set to the one or more conductor loops of the first set. Alternatively, the one or more conductor loops of the fourth may be located in closer proximity to the one or more conductor loops of the second set than the proximity of the one or more conductor loops of the third set to the one of more conductor loops of the first set. Alternatively still, the one or more conductor loops of the third set may be located in closer proximity to the one or more conductor loops of the second set than the proximity of the one or more conductor loops of the fourth set to the one of more conductor loops of the second set.

[0043] According to another aspect, the present invention provides processing circuitry for use in processing sensor signals, the processing circuitry comprising: a first measurement circuit configured to receive a plurality of sensor signals from a plurality of sensor inputs and configured to pass the plurality of sensor signals through the first measurement circuit in a time division manner in a sequence of time intervals to generate a first time division sequence of sensor measurements in response thereto; a second measurement circuit configured to receive at least one sensor signal and configured to pass the at least one sensor signal through the second measurement circuit to generate sensor measurements in response thereto; and measurement processing circuitry configured to process the sensor measurements generated by the first and second measurement circuits to determine and output sensor results; wherein the first and second measurement circuits are both configured to receive a sensor signal from at least one common sensor input and to output respective common sensor measurements in response thereto; and wherein the measurement processing circuitry is configured to use said common sensor measurements to determine first mapping data that relates sensor measurements obtained from said second measurement circuit to sensor measurements obtained from said first measurement circuit.

[0044] According to another aspect, the present invention provides processing circuitry for use in processing sensor signals, the processing circuitry comprising: a first measurement circuit configured to receive a plurality of sensor signals from a plurality of sensor inputs and configured to pass the plurality of sensor signals through the first measurement circuit in a time division manner in a sequence of time intervals to generate a first time division sequence of sensor measurements in response thereto; a second measurement circuit configured to receive a plurality of sensor signals from a plurality of sensor inputs and configured to pass the plurality of sensor signals through the second measurement circuit in a time division manner in a sequence of time intervals to generate a second time division sequence of sensor measurements in response thereto; and measurement processing circuitry configured to process the first and second time division sequences of sensor measurements to determine and output sensor results; wherein during first time periods, the measurement processing circuitry is arranged to determine sensor results using sensor measurements from the first measurement circuit and during second time periods, the measurement processing circuitry is arranged to determine sensor results using sensor measurements from the second measurement circuit; wherein during at least one first time period, the measurement processing circuitry is arranged to determine calibration data for use in determining the sensor results using the sensor measurements generated by the second measurement circuit.

[0045] According to another aspect, the present invention provides processing circuitry for use in processing sensor signals, the processing circuitry comprising: a first measurement circuit configured to receive and down convert an input sensor signal having a first frequency to a sensor signal having a second frequency that is lower than the first frequency and to generate therefrom sensor measurements; a second measurement circuit configured to receive and down convert an input sensor signal having said first frequency to a sensor signal having said second frequency and to generate therefrom sensor measurements; wherein the first and second measurement circuits are both configured to receive a common sensor signal from at least one common sensor input; control circuitry for causing said common sensor signal to be switched through said first and second measurement circuits in a time division multiplexed manner so that said common sensor signal passes through said first and second measurement circuits at different times; wherein said control circuitry is arranged to cause said common sensor signal to be switched through said first and second measurement circuits at a third frequency that is higher than said second frequency; and measurement processing circuitry configured to process the sensor measurements obtained from said first and second measurement circuits to determine sensor results.

[0046] According to another aspect, the present invention provides processing circuitry for use in processing sensor signals, the processing circuitry comprising: a first measurement circuit configured to receive a plurality of sensor signals from a plurality of sensor inputs, including at least one main sensor input and at least one auxiliary sensor input, and configured to pass the plurality of sensor signals through the first measurement circuit in a time division manner in a sequence of time intervals to generate a first time division sequence of sensor measurements in response thereto; a second measurement circuit configured to receive a plurality of sensor signals from a plurality of sensor inputs, including said at least one main sensor input and said at least one auxiliary sensor input, and configured to pass the plurality of sensor signals through the second measurement circuit in a time division manner in a sequence of time intervals to generate a second time division sequence of sensor measurements in response thereto; and measurement processing circuitry configured to process the first and second time division sequences of sensor measurements to determine and output sensor results; wherein each measurement circuit has an auxiliary mode of operation and a main sensor mode of operation; wherein when the first measurement circuit is configured to operate in the main sensor mode of operation, the second measurement circuit is configured to operate in the auxiliary mode of operation and when the second measurement circuit is configured to operate in the main sensor mode of operation, the first measurement circuit is configured to operate in the auxiliary mode of operation; wherein when operating in the main sensor mode of operation, a measurement circuit is configured to pass the sensor signals obtained from the at least one main sensor input there through and when operating in the auxiliary mode of operation, a measurement circuit is configured to pass the signals obtained from the at least one auxiliary sensor input there through; and wherein said measurement processing unit is configured: i) to determine sensor results using sensor measurements obtained from a measurement circuit when operating in said main sensor mode of operation; ii) to determine calibration data for a measurement circuit using sensor measurements obtained from the measurement circuit when the measurement circuit is operating in said auxiliary mode of operation; and iii) to use the calibration data for a measurement circuit when determining the sensor results using the sensor measurements obtained from that measurement circuit when operating in said main sensor mode of operation.

[0047] According to another aspect, the present invention provides processing circuitry for use in processing sensor signals, the processing circuitry comprising: measurement circuitry configured to receive a first plurality of sensor signals from a first plurality of sensor inputs, including a first main sensor input and a second main sensor input and configured to pass the first plurality of sensor signals through the measurement circuitry in a time division manner in a sequence of time intervals to generate at least one time division sequence of sensor measurements in response thereto; and measurement processing circuitry configured to process the sensor measurements generated by the measurement circuitry to determine and output sensor results; wherein the measurement processing circuitry is configured to determine a sensor result using a first sensor measurement of a sensor signal obtained from said first main sensor input during a first time interval and a second sensor measurement of a sensor signal obtained from said second main sensor input during a second time interval, and is arranged to apply a first compensation when determining the sensor result if the first time interval is before the second time interval and is arranged to apply a second, different, compensation when determining the sensor result if the second time interval is before the first time interval.

[0048] According to another aspect, the present invention provides processing circuitry for use in a position sensor, the processing circuitry comprising: an input for receiving a sensor signal from a sensor input, the sensor signal being generated in response an excitation signal being applied to an excitation element; wherein the excitation signal has an excitation frequency and an excitation signal phase that can vary during use and wherein the sensor signal has the excitation frequency and a sensor signal phase that depends on the excitation signal phase; a demodulator for multiplying the sensor signal with a demodulating clock signal having said excitation frequency and a demodulating clock signal phase, to generate a demodulated sensor signal; control circuitry for processing the demodulated sensor signal to determine position information for a sensor target; and phase tracking circuitry for maintaining a desired phase relationship between the excitation phase and the demodulating clock phase, the phase tracking circuitry comprising: logic circuitry for generating a first square wave clock signal having a fundamental frequency that is a multiple of the excitation frequency; a filter circuit for filtering the square wave clock signal to produce a filtered signal having the fundamental frequency; a comparator circuit for comparing the filtered signal with a reference value to generate a digital signal at the fundamental frequency, with a duty ratio of the digital signal depending on the reference value; and a frequency divider circuit for receiving the digital signal output from the comparator circuit and for dividing the frequency of the digital signal to generate a square wave clock signal having the excitation frequency and a phase that depends on the reference value; and wherein the square wave clock signal generated by the frequency divider circuit is for use in generating said excitation signal or the demodulating clock signal; and wherein the control circuitry is configured to vary the reference value used by said comparator to adjust the phase of the square wave clock signal generated by the frequency divider circuit to maintain the desired phase relationship between the excitation signal phase and the demodulating clock signal phase.

[0049] The frequency divider circuit may be arranged to generate first and second demodulating clock signals that are separated in phase by substantially 90 degrees and wherein the demodulator is configured to multiply the sensor signal with the first and second demodulating clock signals in a time interleaved manner. The control circuitry may vary the reference value in dependence upon a sensor signal received from an auxiliary sensor input.

[0050] According to another aspect, the present invention provides processing circuitry for use in a position sensor, the processing circuitry comprising first and second measurement circuits that each process at least one common sensor signal and provide corresponding measurements; and measurement processing circuitry that is arranged to use the measurements from each measurement circuit, in a time interleaved and cyclic manner, to determine sensor results so that whilst the measurement processing circuitry is using the measurements from one measurement circuit to determine sensor results, measurements obtained from the other measurement circuit are used to determine correction data that is used to correct subsequent measurements obtained from that measurement circuit. Typically, the measurement processing circuitry will repeatedly update the correction data for a measurement circuit each time the measurement processing circuitry is using measurements from the other measurement circuit to determine sensor results.

[0051] As those skilled in the art will appreciate, these various aspects of the invention may be provided separately or they may be combined together in one embodiment. Similarly, the modifications and alternatives described above are applicable to each aspect of the invention and they have not been repeated here for expediency.

[0115] FIG. 1 is a schematic block diagram illustrating the main components of a position sensor 1 used in this embodiment to sense the position of a target (not shown). The position sensor 1 has a connector 3 for connection to sensor coils (not shown). As will be described in more detail below with reference to FIG. 2, in this embodiment the sensor coils include an excitation coil and coarse and fine detection coils. The connector 3 is connected to a microcontroller 9 that controls the application of excitation signals to the excitation coil and that processes the signals obtained from the detection coils. As shown in FIG. 1, the microcontroller 9 includes excitation and control signal logic 11 that generates the control signals used to control the excitation and processing of the excitation and sensor coils. In particular, the excitation and control signal logic 11 controls excitation circuitry 23 to apply an excitation signal to the excitation coil via the connector 3 and controls measurement circuitry 25 to measure the signals obtained from the detection coils via the connector 3. The microcontroller 9 also includes an analogue to digital converter (ADC) 13 which converts analogue measurements into digital values which are then stored in memory 17. The microcontroller 9 also includes a measurement processing unit 19 which processes the digital measurements stored in memory 17 to determine the position of the target relative to the sensor coils and which then reports this position to a host device (not shown) via a host interface unit 21. Breakthrough calibration data 29 is provided that is used to reduce errors caused by direct inductive coupling between the excitation coil and the detection coils; and dynamic correction data 31 is maintained and used dynamically to correct for systematic errors introduced because measurements are being calculated using different measurement circuits and/or because of target movement during the measurement process.

[0116] As will be explained in more detail below, the fine detection coils provide more accurate (but ambiguous) position information and the coarse detection coils provide less accurate (but non-ambiguous) position information that can be used to disambiguate the accurate position information from the fine detection coils. Further, the measurement circuitry 25 has two measurement circuits that are used to process the signals obtained from the fine detection coils in an overlapped time division multiplexed manner to maximise the rate at which accurate position information can be obtained from the position sensor 1 whilst also allowing measurements to be obtained from the coarse detection coils.

[0117] The circuitry shown in FIG. 1 can be used with a wide range of different sensor coils, such as those described in WO95/31696, WO97/14935, WO2005/085763 or WO2009/115764, the contents of which are hereby incorporated by reference. FIG. 2 schematically illustrates the different sensor coils used in this embodiment for sensing the position of the target 5 along the X direction illustrated. In particular, FIG. 2a shows an excitation coil 2, a coarse sine detection coil 4-1 and a coarse cosine detection coil 4-2. FIG. 2a also shows a fine sine detection coil 6-1 and a fine cosine detection coil 6-2. Although FIG. 2a illustrates the sensor coils in a side by side arrangement (for ease of illustration), they are all mounted (superimposed) on top of each other on a sensor board 8. In this embodiment, the sensor board 8 is a printed circuit board, with the conductors forming the sensor coils being defined by conductive tracks on different layers of the printed circuit board 8 so that the different sensor coils are electrically insulated from each other. FIG. 2a also shows the target 5 that is arranged to move along the X direction relative to the sensor coils. A number of different types of target 5 may be used. Typically the target 5 will be a short circuit coil, a conductive screen (for example made of a piece of aluminium or steel) or, as illustrated in FIG. 2a, an electromagnetic resonator 12 that is formed by a coil 14 and a capacitor 16. The excitation coil 2 and the target 5 are arranged so that when the excitation circuitry 23 applies an excitation signal to the excitation coil 2, the excitation magnetic field generates a signal in the target 5 that creates its own electromagnetic field. In the case of a resonant target 5, the signal is a current flowing in the resonator coil 14 and in the case of a metallic screen, the signal is in the form of Eddy currents flowing on the surface of the metallic screen. The detection coils 4 and 6 are geometrically patterned along the X direction (the measurement path) as a result of which, the electromagnetic coupling between each detection coil 4 and 6 and the target 5 varies as a function of position along the measurement path. Therefore, the signal generated by the target 5 in each of the detection coils will vary with position along the measurement path. As will be explained in further detail below, since the geometric patterning of each of the detection coils is slightly different, the signal obtained from each detection coil will vary in a slightly different manner with the position of the target 5.

[0118] In this embodiment, the excitation and detection coils are geometrically arranged on the PCB 8 so that, in the absence of the target 5, there is substantially no electromagnetic (inductive) coupling between them. In other words, in the absence of the target 5, when an AC excitation current is applied to the excitation coil 2, substantially no signal is induced in each of the detection coils 4, 6. This is not however essential.

[0119] As shown, the coarse sine detection coil 4-1 is formed from a conductor that defines two loops which are connected together in the opposite sense in a figure of eight configuration. As a result of the figure of eight connection EMFs (electromotive forces) induced in the first loop by a common background magnetic field will oppose the EMFs induced in the second loop by the same common background magnetic field. The coarse sine detection conductor 4-1 has a pitch (L_c) that approximately corresponds to the measurement range over which the target 5 can move. As those skilled in the art will appreciate, the coarse cosine detection coil 4-2 is effectively formed by shifting the coarse sine detection coil 4-1 by a quarter of the pitch (L_c) along the X direction. As shown, the coarse cosine detection coil 4-2 has three loops, with the first and third loops being wound in the same direction as each other but opposite to the winding direction of the second (middle) loop. The fine sine and cosine detection coils 6-1 and 6-2 are similar to the coarse detection coils 4, except that they have a smaller pitch (L_f) so that, in this embodiment, there are four repeats or periods along the measurement range over which the target 5 can move.

[0120] The excitation coil 2 is wound around the outside of the detection coils 4 and 6 and is arranged so that (in the absence of the target 5) it generates a magnetic field which is substantially symmetric along an axis which is parallel to the Y axis and which passes through the middle of the excitation coil 2. This axis of symmetry is also an axis of symmetry for the detection coils 4 and 6. Therefore, as a result of the figure of eight arrangement of the detection coils 4 and 6 and as a result of the common symmetry between the excitation coil 2 and the detection coils 4 and 6, there is minimal direct inductive coupling between the excitation coil 2 and the detection coils 4 and 6. Further, as a result of the figure of eight configuration of the detection coils 4 and 6, the coupling between each detection coil 4, 6 and the target 5 is approximately sinusoidal, with the period of the sinusoidal variation being defined by (L_c) for the coarse detection coils 4 and with the period of the sinusoidal variation being defined by (L_f) for the fine detection coils 6. The EMFs induced in the detection coils 4 and 6 by the target 5 may therefore be represented by the following:

$\begin{array}{cc}{V}^{\mathrm{CS}}=A_C\sin \left[\frac{2\pi d_c}{L_c}\right]\cos \omega t& \left(1\right)\\ V^{\mathrm{CC}}=A_C\cos \left[\frac{2\pi d_c}{L_c}\right]\cos \omega t& \left(2\right)\\ V^{\mathrm{FS}}=A_F\sin \left[\frac{2\pi d_f}{L_f}\right]\cos \omega t& \left(3\right)\\ V^{\mathrm{FC}}=A_F\cos \left[\frac{2\pi d_f}{L_f}\right]\cos \omega t& \left(4\right)\end{array}$

where d_C is the coarse position of the target 5 along the measurement direction, d_f is the fine position of the target 5 along the measurement direction, A_C and A_F are amplitude terms and ω represents the angular frequency of the excitation signal applied to the excitation coil 2. As those skilled in the art will appreciate, the equations above are approximate in that the peak amplitudes of the signals obtained from the detection coils do not vary exactly sinusoidally with the position of the target 5. This is an approximation to the actual variation, which will depend upon edge effects, positions of via holes on the printed circuit board and other effects that introduce non-linearities into the system. If the detection coils 4 and 6 were ideal, then d_c and d_f would be the same value. After demodulation and filtering to remove the excitation frequency component, the coarse position (d_C) of the target 5 can be determined from:

$\begin{array}{cc}{\varphi }^C=\left[\frac{2\pi d_c}{L_c}\right]=\arctan \left(\frac{V^{\mathrm{CS}}}{V^{\mathrm{CC}}}\right)& \left(5\right)\end{array}$

and the fine position (d_f) of the target 5 can be determined from:

$\begin{array}{cc}{\varphi }^F=\left[\frac{2\pi d_f}{L_f}\right]=\arctan \left(\frac{V^{\mathrm{FS}}}{V^{\mathrm{FC}}}\right)& \left(6\right)\end{array}$

[0121] The determination of the position of the target 5 as a function of the ratio of the peak amplitudes of the signals induced in the detection coils makes the system less sensitive to variations in the amplitude of the excitation current and variations in the distance between the target 5 and the sensor coils.

[0122] FIG. 2b illustrates the way in which the phases φ^F and φ^C vary with the position of the target 5 along the measurement path (X). As can be seen, the coarse measurement (φ^C) varies monotonically with the position of the target along the measurement range, whilst the fine measurement (φ^F) repeats four times along the measurement range. Thus whilst the fine position measurement is more accurate, it is ambiguous. However, the coarse position information can be used to resolve the period ambiguity associated with the fine position measurement.

[0123] FIG. 3 illustrates in more detail the way in which the excitation circuitry 23 connects to the excitation coil 2 at the connections labelled ex+ and ex− of the connector 3. FIG. 3 also shows that the coarse sine detection coil 4-1 is connected to the measurement circuitry 25 at the connections labelled C_sin+ and C_sin− of the connector 3; that the coarse cosine detection coil 4-2 is connected to the measurement circuitry 25 at the connections labelled C_cos+ and C_cos− of the connector 3; that the fine sine detection coil 6-1 is connected to the measurement circuitry 25 at the connections labelled F_sin+ and F_sin− of the connector 3; and that the fine cosine detection coil 6-2 is connected to the measurement circuitry 25 at the connections labelled F_cos+ and F_cos− of the connector 3.

[0124] FIG. 3 also shows in more detail the excitation circuitry 23 used in this embodiment which is most suited for use with sensors that use non-resonant targets 5, such as targets formed from a short circuit coil or from a piece of metal (as systems that use non-resonant targets 5 are more susceptible to the effects of direct breakthrough from the excitation coil 2 to the detection coils 4 and 6). As shown, the excitation circuitry has a symmetrical drive circuit formed by multiplexor 41 that applies VCC to ex+ and ground to ex− or that applies VCC to ex− and ground to ex+ in accordance with the control signal ex_clock (supplied from the excitation and control signal logic 11). Such a symmetric drive is useful to reduce the amplitude of any common mode current which can be established via capacitive coupling from the excitation coil 2 into conductive objects in the vicinity of the sensor coils. The excitation signal output from the multiplexor 41 is filtered by R-C low pass filters 43-1 and 43-2 to remove higher frequency harmonics from the excitation signal.

[0125] FIG. 3 also shows a simple resistor divider 45 that is used to provide a fraction of the excitation voltage to the Ref+ and Ref− inputs of the measurement circuitry 25. As will be explained in more detail below, this reference signal is used to reduce the amount of direct breakthrough noise in the measurement resu Its.

[0126] FIG. 4 is a block diagram illustrating the way in which the inputs to the measurement circuitry 25 are connected to the inputs of two separate measurement circuits labelled measurement circuit N 51-1 and measurement circuit M 51-2. As can be seen from FIG. 4, each sensor coil connection and each reference signal connection is connected to the following inputs of both measurement circuits 51-1 and 51-2 as follows:

• • [0127] Input 1+=F_sin+
  • [0128] Input 1−=F_sin−
  • [0129] Input 2+=F_cos+
  • [0130] Input 2−=F_cos−
  • [0131] Input 3+=C_sin+
  • [0132] Input 3−=C_sin−
  • [0133] Input 4+=C_cos+
  • [0134] Input 4−=C_cos−
  • [0135] Input 5+=Ref+
  • [0136] Input 5−=Ref−

[0137] As will be explained in more detail below, this allows each measurement circuit 51 to be able to process the signal from each detection coil or to process the reference signal. As shown in FIG. 4, measurement circuit N 51-1 outputs processed signal AF^N_out and measurement circuit M 51-2 outputs processed signal AF^M_out to the ADC 13 of the microcontroller 9. Therefore, the microcontroller 9 can obtain signal measurements relating to any of the detection coils or relating to the reference input from each of the two measurement circuits 51.

[0138] The resistors 59-0 to 59-7 and capacitors 63-0 to 63-9 are provided to reduce noise and to reduce electromagnetic emissions from the sensor coils. The capacitors 65-0 and 65-2 provide a DC decoupling of the excitation circuitry 23 and the measurement circuitry 25. Finally, the resistors 61-0 to 61-9 are used to condition the DC level on each conductor to the mid-rail voltage.

[0139] Each of the measurement circuits 51 has the same structure, although they are controlled by different control signals to ensure that at any point in time the two measurement circuits 51 are processing different input signals. FIG. 5 is a block diagram illustrating the components of each of the measurement circuits 51. As shown, the positive inputs 1+ to 4+ are applied to multiplexor 55-1 and the negative inputs 1− to 4− are applied to multiplexor 55-2. Multiplexors 55 are used to select the ends of one of the detection coils 4 or 6 and connect them through to a demodulating switch 56. Thus when the 1+ input is selected by multiplexor 55-1 the 1− input is selected by multiplexor 55-2 and therefore the signal induced in detector coil 6-1 is passed through to the demodulating switch 56. This is similarly true for the selection of the signals from the other detection coils. The particular input that is selected by each of the two multiplexors 55 is defined by the control signals in1 and in2 which are generated by the excitation and control signal logic 11. In this embodiment, the control of the connection through each multiplexor 55 is defined by the following truth table:

	in1	in2	Selected o/p
	0	0	±1
	0	1	±3
	1	0	±2
	1	1	±4

[0140] The reference signal inputs are applied to the multiplexor 57 and an enable signal in3 is used to ensure that multiplexor 57 is disabled when multiplexors 55 are enabled and vice versa. When multiplexor 57 is enabled, the reference signal applied to inputs 5+ and 5− are passed directly through to the demodulating switch 56.

[0141] The output labelled A from the multiplexor 55-1 or from the multiplexor 57, is input to terminals 1 and 4 of the demodulating switch 56 and the output labelled B from the multiplexor 55-2 or from the multiplexor 57, is input to terminals 2 and 3 of the demodulating switch 56. The demodulating switch 56 acts to multiply a “demod” signal with the input signal applied to the demodulating switch 56. As shown in FIG. 5, the demod signal is obtained by combining (in this example using an exclusive OR (XOR) gate 100) a polarity control signal and an ex_shifted control signal, both of which are generated by the excitation and control signal logic 11. The ex_shifted control signal is a phase shifted version of ex_clock and thus acts to effectively demodulate the incoming signal to a “baseband” (quasi DC) signal whose amplitude depends on the position of the target 5. The polarity control signal is used to periodically change the polarity of the ex_shifted clock so that the signal being processed by the measurement circuit 51 during the current detection interval is demodulated an equal amount of time with a positive polarity of ex_shifted and with a negative polarity of ex_clock. This results in the signal that is applied to the amplification and filtering circuit 83 having a zero DC component. This allows a high pass filter to be used in the amplification and filtering circuit 83 which helps to remove DC offsets caused by the amplifiers as well as lower frequency noise associated with such DC offsets.

[0142] When the demod signal has a value of one, the input labelled A passes through multiplexor terminal 1 to the A* input of the amplification and filtering circuit 83; and the input labelled B passes through the multiplexor terminal 3 to the B* input of the amplification and filtering circuit 83. When the demod signal is zero the demodulating switch 56 changes position such that the input labelled A passes through multiplexor terminal 4 to the B* input of the amplification and filtering circuit 83; and the input labelled B passes through the multiplexor terminal 2 to the A* input of the amplification and filtering circuit 83. As will be explained in more detail below, the amplification and filtering circuit 83 amplifies the difference between A* and B*. Thus, the demodulating switch 56 and the amplification and filtering circuit 83 act to demodulate and amplify A-B or B-A, depending on the value (1 or 0) of the polarity control signal. Hence positive and negative measurements can be obtained from each individual detection coil.

[0143] FIG. 6 is a timing diagram illustrating the way in which the signals from the different inputs of a measurement circuit 51 can be selected in a time division manner using the control signals in1, in2 and in3. FIG. 6 also shows ex_shifted and the polarity control signal and the resulting demod signal that is applied to the demodulating switch 56. FIG. 6 shows that during detection interval Δt₁ the signals from the 1+/1− inputs (fine sine detection coil 6-1) are selected and processed by the measurement circuit 51; that during detection interval Δt₂ the signals from the 2+/2− inputs (fine cosine detection coil 6-2) are selected and processed by the measurement circuit 51; that during detection interval Δt₃ the signals from the 3+/3− inputs (coarse sine detection coil 4-1) are selected and processed by the measurement circuit 51; that during detection interval Δt₂ the signals from the 4+/4− inputs (coarse cosine detection coil 4-2) are selected and processed by the measurement circuit 51; and that during detection interval Δt₅ the signals from the 5+/5− inputs (reference signal) are selected and processed by the measurement circuit 51.

[0144] As can be seen from FIG. 6, if the signals from the different inputs are multiplexed through the measurement circuit 51 in this consecutive manner, then the update rate (the time between measurements of the same signal) is five times the period of the polarity control signal. Using the two measurement circuits this update rate can easily be increased to 2.5 times the period of the polarity control signal. Further, as will be described in more detail later, it is possible to increase this update rate further through a more complex interleaving of the measurements through the two measurement circuits 51.

[0145] The amplification and filtering circuit 83 amplifies and filters the signals output from the demodulating switch 56, to remove high frequency demodulation signals and to remove the low frequency DC offsets. As shown in FIG. 7a, the amplification and filtering circuit 83 has differential amplification circuitry 85 that amplifies the difference between A* and B*. As discussed above, this results in amplifying A-B or B-A, depending on the value (1 or 0) of the polarity control signal. The output from the differential amplification circuitry 85 is filtered by a bandpass filter 87 to remove the unwanted frequency components from the amplified signal.

[0146] FIG. 7b illustrates the spectrum of the signal output from the differential amplification circuitry 85. Most of the desired signal components are around the frequency corresponding to the polarity control signal. The higher frequency components correspond to the high frequency demodulation harmonics generated by the demodulating switch 56.

[0147] FIG. 7c illustrates the desired frequency response of the bandpass filter 87 shown in FIG. 7a to filter the signals output from the differential amplification circuitry 85. As shown, the high corner frequency of the filter 87 can be kept quite close to the frequency of the polarity control signal. In this embodiment, the high corner frequency has been set at 4 times the frequency of the polarity signal. This allows the amplification and filtering circuit 83 to filter out almost all the high frequency harmonics generated by the demodulating switch 56. The low corner frequency of the filter 87 cannot be set very close to the frequency of the polarity signal. This is evident from the spectrum of the input signal shown in FIG. 7b, which contains quite a long tail at the low frequency end; and filtering out this part of the spectrum will alter substantially the measured signal output by introducing low frequency transients in the response of the amplification and filtering circuit 83. In this embodiment, the low corner frequency of the amplification and filtering circuit 83 has been set at 100 times lower than the high corner frequency. This still allows the amplification and filtering circuit 83 to filter out the DC offsets of the differential amplification circuitry 85 as well as most of the unwanted low frequency noise caused by the measurement circuitry 25 and allows for a well defined gain for the measured signals within the pass band of the filter 87.

[0148] FIG. 8 illustrates the way in which the output (AF_out) from measurement circuit 51 varies during the five detection intervals illustrated in FIG. 6. This AF_out signal is passed to the ADC 13, where it is converted into a digital value. As shown, during each detection interval Δt_k the AF_out signal settles to a quasi DC level towards the end of each half period of the polarity control signal. The ADC 13 is triggered to sample AF_out during each detection interval at each of the two quasi DC levels and the difference in the levels is determined to provide a peak to peak voltage level (marked Δ₁, Δ₂, Δ₃, Δ₄ and Δ₅ in FIG. 8) as the measurement for the currently selected detection coil (or reference signal). FIG. 9 shows in more detail the control signals used to trigger the ADC conversion and to trigger the processing of the raw data by the measurement processing unit 19 (shown in FIG. 1). In particular, the ADC 13 is triggered by the control signal ADC_trigger. The frequency of the ADC_trigger signal is exactly two times the frequency of the polarity control signal. The ADC 13 is triggered to perform a conversion on the rising edge of the ADC_trigger control signal so that each of the two quasi DC levels reached during a detection interval is converted into a digital value and stored in memory 17.

[0149] Another control signal, CALC_trigger, is used to interrupt the microcontroller 9 so that the digital values can be read from memory 17 into the measurement processing unit 19. As shown, the CALC_trigger control signal has the same frequency as the polarity signal but is slightly delayed from the edges of the ADC_trigger signal to ensure that the results of the ADC conversion are already stored in memory 17 before the CALC_trigger signal forces the microcontroller 9 to read the values obtained from a detection interval from memory 17 into the measurement processing unit 19.

[0150] Each peak to peak voltage measurement calculated by the measurement processing unit 19 corresponds either to a measurement of the reference signal or to the signal from one of the detection coils and in order to calculate a position measurement, an arctangent function is calculated using the measurements from a sine and a cosine detection coil. If adjacent detection intervals are arranged to measure the signal from a sine detection coil and a cosine detection coil, then a position calculation can be determined after the second detection interval. This is illustrated in FIG. 9, which shows that if one measurement is calculated for detection interval Δt_k and another one is measured for detection interval Δt_k+1 then position information can be calculated using those measurements during detection interval Δt_k+2. This results in a measurement latency of just over two times the period of the polarity control signal.

[0151] An optimised switching scheme for switching the different signals from the detection coils (and the reference signal) through the two measurement circuits 51 will now be described. This switching scheme allows an improved update rate for position measurements. FIG. 10 shows the timeline of the control signals used to switch the measurement circuit inputs±1, ±2, ±3, ±4, and ±5 through measurement circuit N 51-1 and measurement circuit M 51-2. The detection cycle is periodic with a period (T_dc) corresponding to ten detection intervals Δt_i (for index i=1 to 10). FIG. 10 also shows a periodic mode_ref control signal that is generated by the excitation and control signal logic 11 and used to define the start of a detection cycle. As shown in FIG. 10, the measurement circuit inputs selected during each of these ten detection intervals is given in the following table:

	Measurement	Measurement
Index (i)	Circuit N	Circuit M
1	±1 (FS)	±4 (CC)
2	±2 (FC)	±5 (Ref)
3	±1 (FS)	±2 (FC)
4	±2 (FC)	±1 (FS)
5	±3 (CS)	±2 (FC)
6	±4 (CC)	±1 (FS)
7	±5 (Ref)	±2 (FC)
8	±2 (FC)	±1 (FS)
9	±1 (FS)	±2 (FC)
10	±2 (FC)	±3 (CS)

Where FS is the fine sine detection coil 6-1; FC is the fine cosine detection coil 6-2; CS is the coarse sine detection coil 4-1; CC is the coarse cosine detection coil 4-2 and Ref is the excitation reference signal.

[0152] As can be seen from the above table and from FIG. 10, during each detection interval the two measurement circuits 51 are processing different input signals. FIG. 10 also shows that during each detection interval at least one of the two measurement circuits 51 is processing a signal from one of the fine detection coils. Additionally, the fine sine and the fine cosine signals are processed in a time interleaved manner in each of the two measurement circuits and in an overlapping manner between the two measurement circuits. During each detection cycle, each measurement circuit 51 also processes the signals from the coarse detection coils 4 and the reference signal. Whilst one measurement circuit is processing the signals from the coarse detection coils and the reference signal, the other measurement circuit 51 is processing the signals from the fine detection coils. With this arrangement, an updated fine position measurement can be obtained at least every second detection interval.

[0153] As shown in FIG. 10, the interleaved manner of selecting signals through the two measurement circuits 51 is achieved by applying opposite polarity control signals in1_N and in1_M to the respective multiplexors 55 in the measurement circuit N and the measurement circuit M; and by phase shifting control signal in2_M and in3_M relative to in2_N and in3_N (by half the detection cycle) that are applied to the respective multiplexors 55 in the measurement circuit N and the measurement circuit M. As a result, during the detection interval Δtk when channel 1+ and 1− is selected by the measurement circuit N, channel 2+ and 2− is selected by measurement circuit M. During the next detection interval Δtk+1, channel 2+ and 2− is selected by measurement circuit N and channel 1+ and 1− is selected by measurement circuit M. This avoids unwanted collisions in which the same input (channel) is selected simultaneously by measurement circuit N and measurement circuit M.

[0154] FIG. 11 is a flow chart illustrating the processing performed by the measurement processing unit 19. As shown, in step s1, the measurement processing unit 19 waits until it receives the next mode_ref signal (rising edge of the mode_ref signal shown in FIG. 10). In response to receiving this rising edge (interrupt), the measurement processing unit 19 sets, in step s3, the index (i) to the value 1. In step s5-1, the measurement processing unit 19 reads the ADC data related to measurement circuit N from memory 17 and in step s7-1 the measurement processing unit 19 processes the retrieved data according to the current value of the index (i). In particular (and as will be described in more detail below), the processing that the measurement processing unit 19 does on the retrieved data depends on what that data relates to—whether it relates to a signal from a fine detection coil, a signal from a coarse detection coil or if it relates to the reference signal. Similarly, in step s5-2, the measurement processing unit 19 reads the ADC data related to measurement circuit M from memory 17 and in step s7-2 the measurement processing unit 19 processes the retrieved data according to the current value of the index (i). In this embodiment, the ADC data from the two measurement circuits 51 is written into separate portions of the memory 17 in a sequential manner—so that the ADC data from measurement circuit N for detection interval Δt_k+1 is written into the corresponding portion of memory 17 after the ADC data from measurement circuit N obtained for detection interval Δt_k.

[0155] After step s5-2, the processing continues to step s9, where the measurement processing unit 19 checks to see if the index (i) has a value greater than nine. If it does not, then the processing proceeds to step s11, where the index value (i) is incremented by one. The processing then proceeds to step s13, where the measurement processing unit 19 waits for the next rising edge of the CALC_trigger signal (from the excitation and control signal logic 11) indicating that the ADC values for the next detection interval will have been written into the relevant part of the memory 17. The processing then returns to step s5-1 so that these next ADC values can be read from memory and processed by the measurement processing unit 19. Once step s9 determines that the index value (i) is greater than nine, the processing returns to the start where the measurement processing unit 19 waits for the next mode_ref interrupt signal and the process is repeated.

[0156] As those skilled in the art will appreciate, the measurement processing unit 19 is operating independently and asynchronously relative to the excitation and control signal logic 11, only receiving the control signals mode_ref and CALC_trigger from the excitation and control signal logic 11 to ensure that it processes the data arriving into the memory 17 at the appropriate timing.

[0157] FIG. 12a is a timing diagram illustrating what inputs are being passed through each of the measurement circuits 51 and the calculations that the measurement processing unit 19 performs in steps s7 shown in FIG. 11 when processing the signals obtained from the fine detection coils 6. The processing of the signals from the coarse detection coils 4 and the processing of the reference signal is not illustrated in FIG. 12a to reduce the complexity of the figure. As shown in FIG. 12a when the index i=1, the signal on the fine sine detection coil 4-1 (FS) is passed through measurement circuit N. During this detection interval, the measurement processing unit 19 reads the ADC data obtained from measurement circuit N during the previous two detection intervals (when i=9 and 10 in the previous detection cycle) and calculates the above described peak to peak voltage levels (Δk) for the previous two detection intervals. As shown in FIG. 12a, during the detection interval corresponding to i=9, the signal from the fine sine detection coil (FS) was passed through measurement circuit N; and during the detection interval corresponding to i=10, the signal from the fine cosine detection coil (FC) was passed through measurement circuit N. These raw peak to peak values are then processed to reduce breakthrough noise (described in more detail later) and then the breakthrough corrected values are applied to an arctangent function that converts the peak to peak measures into fine position information (φ^F) which is then processed to balance phase offsets introduced by the measurement circuits 51-1 and 51-2 (described in more detail later).

[0158] As can be seen from FIG. 12a, the measurement processing unit 19 determines such fine position information using signals obtained from measurement circuit N during detection intervals corresponding to index values i=1, 3 and 5. Similarly, the measurement processing unit 19 determines such fine position information using signals from measurement circuit M during detection intervals corresponding to index values i=6, 8 and 10. Thus, during the detection interval corresponding to index value i=1, the measurement processing unit 19 switches over from using the data obtained from measurement circuit M to using the data from measurement circuit N to calculate the fine position information. Similarly, during the detection interval corresponding to index value i=6, the measurement processing unit 19 switches over from using the data obtained from measurement circuit N to using the data from measurement circuit M to calculate the fine position information. Therefore, with this switching arrangement, the measurement processing unit 19 can provide updated fine position measurements at an update rate of six times per ten detection intervals.

[0159] Although the signal (FC) from the fine cosine detection coil 6-2 is passed through measurement circuit N during the detection interval corresponding to index i=8, the measurement processing unit 19 does not use this data to determine any position information—as it has fine position data from measurement channel M. Similarly, although the signal (FC) from the fine cosine detection coil 6-2 is passed through measurement circuit M during the detection interval corresponding to index i=3, the measurement processing unit 19 does not use this data to determine any position information—as it has fine position data from measurement channel N. Having these extra measurements of the fine cosine signal makes it easier to generate the control signals used to select the signals through the measurement circuits M and N.

[0160] Although not illustrated in FIG. 12a, the measurement processing unit 19 also updates the coarse position information for measurement circuit N during the detection interval corresponding to index value i=7 using the ADC values obtained from measurement circuit N during detection intervals corresponding to i=5 and 6. Similarly, the measurement processing unit 19 updates the coarse position information for measurement circuit M during the detection interval corresponding to index value i=2 using the ADC values obtained from measurement circuit M during detection intervals corresponding to i=10 and 1. During the detection interval corresponding to index value i=8, the measurement processing unit 19 updates the breakthrough calibration data 29 stored for measurement circuit N using the ADC data obtained from measurement circuit N during the detection interval corresponding to index value i=7 (i.e. using the excitation reference signal as measured by measurement circuit N). Similarly, during the detection interval corresponding to index value i=3, the measurement processing unit 19 updates breakthrough calibration data 29 stored for measurement circuit M using the ADC data obtained from measurement circuit M during the detection interval corresponding to index value i=2 (i.e. using the excitation reference signal as measured by measurement circuit M). Thus whilst the measurement processing unit 19 is using the data from measurement circuit N for fine position measurements, the measurement processing unit 19 is using the data from measurement circuit M for obtaining coarse position measurements and for measuring the excitation reference signal (Ref); and whilst the measurement processing unit 19 is using the data from measurement circuit M for fine position measurements, the measurement processing unit 19 is using the data from measurement circuit N for obtaining coarse position measurements and for measuring the excitation reference signal (Ref).

[0161] As discussed above, the peak to peak voltages calculated by the measurement processing unit 19 are corrected for any direct breakthrough between the excitation coil 2 and the corresponding detection coil using the stored breakthrough calibration data 29 and the latest measurement for the reference signal (corresponding to the fraction of the excitation signal applied at input 5 of the measurement circuits).

[0162] The equations below illustrate the breakthrough corrections that are performed in this embodiment on the peak to peak voltage measurement (V^FS_N) calculated for the signal obtained from the fine sine detection coil 6-1 that is passed through measurement circuit N and on the peak to peak voltage measurement (V^FC_N) calculated for the signal obtained from the fine cosine detection coil 6-2 that is passed through measurement circuit N:

V_Ncorr^FS=V_N^FS−O_N^FS×V_N^EX  (7)

V_Ncorr^FC=V_N^FC−O_N^FC×V_N^EX  (8)

Where O^FS_N is offset calibration data 29 (stored in non-volatile memory) associated with measurement circuit N and the fine sine detection coil 6-1; O^FC_N is offset calibration data 29 associated with measurement circuit N and the fine cosine detection coil 6-2; and V^EX_N is the latest measurement for the excitation reference signal (corresponding to the fraction of the excitation signal applied at input 5 of measurement circuit N). Similar breakthrough calibrations are performed on the measurements obtained from measurement circuit M as follows:

V_Mcorr^FS=V_M^FS−O_M^FS×V_M^EX  (9)

V_Mcorr^FC=V_M^FC−O_M^FC×V_M^EX  (10)

[0163] These breakthrough corrected measurements from each measurement circuit N and M for the fine sine and fine cosine detection coils 4 can then be used to calculate the fine position information using an arctangent function as follows:

$\begin{array}{cc}{\varphi }_N^F=\arctan \left(\frac{V_{\mathrm{Ncorr}}^{\mathrm{FS}}}{V_{\mathrm{Ncorr}}^{\mathrm{FC}}}\right)& \left(11\right)\\ {\varphi }_M^F=\arctan \left(\frac{V_{\mathrm{Mcorr}}^{\mathrm{FS}}}{V_{\mathrm{Mcorr}}^{\mathrm{FC}}}\right)& \left(12\right)\end{array}$

[0164] This arctangent function can also be calculated approximately using the following arithmetic approach:

if V^FS_corr>0 and V^FC_corr≦0

if |V^FS_corr|<|V^FC_corr|φ^F=π+π/4*V^FS_corr/V^FC_corr

else φ^F=π/2−π/4*V^FC_corr/V^FS_corr

if V^FS_corr≧0 and V^FC_corr≧0

if |V^FS_corr|<|V^FC_corr|φ^F=π+π/4*V^FS_corr/V^FC_corr

else φ^F=π/2−π/4*V^FC_corr/V^FC_corr

if V^FS_corr≦0 and V^FC_corr≦0

if |V^FS_corr|<|V^FC_corr|φ^F=π+π/4*V^FS_corr/V_FC_corr

else φ^F=3π/2−π/4*V^FC_corr/V^FS_corr

if V^FS_corr≦0 and V^FC_corr>0

if |V^FS_corr<V^FC_corr|φ^F=2π+π/4*V^FS_corr/V^FC_corr

else φ^F=3π/2−π/4*V^FC_corr/V^FC_corr  (13)

[0165] The results of such arithmetic calculations will deviate from the true arctangent function by about 1% and this deviation can be further compensated by using look-up table correction. The phase ambiguity associated with the fine position information (φ^F) can then be resolved using the coarse position information (φ^C) calculated in a similar manner using the signals obtained from the coarse detection coils 4. Optionally, the breakthrough correction of the coarse signal measurements can be omitted as the coarse position information is only being used to resolve the period ambiguity problem associated with the fine position measurements. However, when the period of the fine scale detection coils 6 is rather dissimilar to the period of the coarse scale detection coils 4, a much better accuracy might be required for the coarse scale output. In this case, therefore, a similar breakthrough correction can be applied to the signals measured in the coarse scale coils 4 in order to improve the accuracy of the coarse position information.

[0166] The direct breakthrough offset from the excitation coil 2 into the detection coils 4 and 6 can vary from sensor to sensor and also can depend on the installation environment—especially to the location of various metallic objects in the close vicinity of the sensor coils. The set of offset calibration data O^FS_N, O^FC_N, O^CS_N, O^CC_N, O^FS_M, O^FC_M, O^CS_M and O^CC_M, should be determined after the sensor is packaged and preferably after the sensor is installed in the final application but prior to the target 5 being mounted near the sensor coils.

[0167] When performing the calibration, typically the host interface unit 21 will provide a signal to the measurement processing unit 19 to inform it that the subsequent measurements are for calibration purposes. The measurement processing unit 19 is configured in such case to measure differences between consecutive results of the conversions performed by the ADC 13, as peak-to-peak voltages:

V^FS_N, V^FC_N, V^CS_N, V^CC_N, V^EX_N
and
V^FS_M, V^FC_M, V^CS_M, V^CC_M, V^EX_M
and to accumulate the running average for each voltage without trying to calculate any ratiometric functions. This calibration measurement cycle is finished by a command from the host interface unit 21. At this time, the measured values of the averaged voltages above are used to calculate the offset calibration data 29:

$\begin{array}{cc}{O}_N^{\mathrm{FS}}=\left(\frac{V_N^{\mathrm{FS}}}{V_N^{\mathrm{EX}}}\right)& \left(14\right)\\ O_N^{\mathrm{FC}}=\left(\frac{V_N^{\mathrm{FC}}}{V_N^{\mathrm{EX}}}\right)& \left(15\right)\\ O_N^{\mathrm{CS}}=\left(\frac{V_N^{\mathrm{CS}}}{V_N^{\mathrm{EX}}}\right)& \left(16\right)\\ O_N^{\mathrm{CC}}=\left(\frac{V_N^{\mathrm{CC}}}{V_N^{\mathrm{EX}}}\right)\mathrm{and}& \left(17\right)\\ O_M^{\mathrm{FS}}=\left(\frac{V_M^{\mathrm{FS}}}{V_M^{\mathrm{EX}}}\right)& \left(18\right)\\ O_M^{\mathrm{FC}}=\left(\frac{V_M^{\mathrm{FC}}}{V_M^{\mathrm{EX}}}\right)& \left(19\right)\\ O_M^{\mathrm{CS}}=\left(\frac{V_M^{\mathrm{CS}}}{V_M^{\mathrm{EX}}}\right)& \left(20\right)\\ O_M^{\mathrm{CC}}=\left(\frac{V_M^{\mathrm{CC}}}{V_M^{\mathrm{EX}}}\right)& \left(21\right)\end{array}$

[0168] This offset calibration data 29 is then written to the non-volatile memory of the microcontroller 9 and is used in the manner described above to correct the raw data for direct breakthrough between the excitation coil 2 and the detection coils 4 and 6.

[0169] The fine position information (φ^F) thus calculated still has an error associated with slightly different properties of each measurement circuit N and M. This means that for the same target position, the fine position information (φ^F_N) obtained using the data measured with measurement circuit N will be slightly different from the fine position information (φ^F_M) obtained using the data measured with measurement circuit M. As the measurement processing unit 19 is calculating fine position measurements from each measurement circuit M and N three times per detection cycle (T_dc), this will cause the appearance of micro-oscillations in the position calculations which will reduce the effective resolution of the measurement set-up below its actual accuracy capabilities. In order to reduce such micro-oscillations, the measurement processing unit 19 performs a phase correction to compensate for the difference in the systematic error between the two measurement circuits N and M. FIG. 12b illustrates the problem. In particular, FIG. 12b is a plot showing the way in which the measured fine position (φ^F) changes over time between the detection interval corresponding to index i=8 in one detection cycle and the detection interval corresponding to index i=3 in the next detection cycle. As shown, between detection intervals corresponding to index i=8 to i=10, the fine position measurement (φ^F_M) is calculated by measurement circuit M and it changes in value by Δφ1. As the two measurements calculated during these detection intervals are determined from signals passed through the same measurement circuit M, the change in fine position will be due to motion of the target 5. When the measurement processing unit 19 starts to determine fine position measurements using the signals obtained from measurement circuit N (in detection interval i=1), there is a change in the measured fine position due to the motion of the target 5 but also because the measurements are being determined using signals that have been processed by a different measurement circuit N. To compensate, the position measurement obtained at index i=10 is extrapolated to detection time interval at index i=1; this extrapolated value is then used to determine a suitable correction value that should be applied to the fine position measurements from the two measurement circuits. More specifically, the following procedure is used:

[0170] The difference between the fine position measurements (φ^F) calculated during the detection intervals Δti with index 10 and 8 is assigned to Δφ1:

Δφ1=φ^F₁₀−φ^F₈  (22)

[0171] The difference between the fine position measurements (φ^F) calculated during the detection intervals Δti with index 1 and 3 is assigned to Δφ2:

Δφ2=φ^F₃−φ^F₁  (23)

[0172] The value of the fine position measurement φ^F₁₀ is extrapolated to detection interval Δti with index i=1:

φ^F_10new=φ^F₁₀+1/4*(Δφ1+Δφ2)  (24)

[0173] This extrapolated value φ^F_10new should be very close to the measured fine position φ^F₁. The difference between these two values represents the systematic error caused by differences between the measurement circuits (M and N) used to determine the different fine position measurements. A correction value is then defined by dividing this difference by two:

Δφ_corr=(φ^F_10new−φ^F₁)/2  (25)

This dynamic correction value is determined during the detection interval corresponding to index value i=3.

[0174] A similar switch over in using the signals obtained from the two measurement circuits M and N is performed during detection interval Δti with index i=6 and a similar correction value is determined during detection interval corresponding to i=8 as follows:

Δφ1=φ^F₅−φ^F₃  (26)

Δφ2=φ^F₈−φ^F₆  (27)

φ^F_5new=φ^F₅+1/4*(Δφ1+Δφ2)  (28)

Δφ_corr=(φ^F₆−φ^F_5new)/2  (29)

[0175] The value of Δφ_corr can be averaged over several detection cycles (T_dc) to reduce noise levels and is used by the microcontroller 9 as part of the dynamic correction. The last line of FIG. 12a illustrates the detection intervals when this dynamic correction value is updated. Then for all data points calculated for channel N the φ^F values are corrected by:

φ^F_corr=φ^F_N+Δφ_corr  (30)

And for all data points calculated for channel M the φ^F values are corrected by

φ^F_corr=φ^F_M−Δφ_corr  (30)

[0176] Whilst the fine position measurements corrected in this way may still contain some degree of systematic error, the fine position measurements will now be practically free from the micro-oscillations at the moments of switching the ratiometric calculations using the signals obtained from measurement circuit N to using the signals obtained from measurement circuit M and vice versa. As those skilled in the art will appreciate, other extrapolations and other correction values could be calculated. For example, a single correction could be applied to the output from just one of the measurement circuits, with no correction being applied to the output from the other measurement circuit.

[0177] As illustrated in FIG. 12b, the phase measurements obtained during consecutive detection intervals change due to motion of the target 5. This causes a systematic error in the position measurements because all four measurements made by the ADC controller 13 that are used to calculate the ratiometric answer φ^F are measurements taken at consecutive moments in time in which the instantaneous value of φ^F is changing. One way to dynamically correct for such motion, is to calculate a mean rate of change of φ^F as a running average Δ_mean of the following differences:

Δφ^F_3-1=φ^F₃−φ^F₁

Δφ^F_5-3=φ^F₅−φ^F₃

Δφ^F_8-6=φ^F₈−φ^F₆

Δφ^F_10-8=φ^F₁₀−φ^F₈

[0178] Assuming that the value of φ^F is changing by a constant amount between each measurement, then the shift in phase measurement between adjacent measurements output by the ADC 13 is equal to the following speed parameter:

$\begin{array}{cc}s=\frac{{\Delta }_{\mathrm{mean}}}{4}& \left(31\right)\end{array}$

[0179] This speed parameter is not exactly equal to the speed of movement of the target 5, as it represents the average rate of change of the measured phase. However, as the measured phase is substantially linearly related to the position of the target 5 (see FIG. 2), the rate of change of the measured phase will be substantially proportional to the rate of change of the target position (=speed).

[0180] As illustrated in FIG. 12a, in this embodiment, position information is determined using measurements that are taken of the signals from the fine sine detection coil 6-1 and then from the fine cosine detection coil 6-2. Therefore, accounting for the motion of the target 5, the peak to peak voltage measurements determined by the measurement processing unit 19 using the raw data obtained from the ADC 13 can be written as:

{circumflex over (V)}^FS=A_F sin [(φ^F−3s]+A_F sin [φ^F−2s]  (32)

{circumflex over (V)}^FC=A_F cos [φ^F−s]+A_F cos [φ^F]  (33)

and from this we can determine the following compensation to be applied to φ^F_corr:

φ_comp^F=φ_corr^F+s(3/2+cos(2φ_corr^F)  (34)

[0181] As can be seen, the compensation that is applied to φ_corr^F depends itself on the value of φ^F_corr and thus different compensations are performed depending on the position of the target 5 relative to the sensor coils. This compensation is performed on either the fine position measurement using the data from measurement circuit M or using the data from measurement circuit N and can significantly reduce (by as much as 50 times) the dynamic error in the determined position of the target 5 due to using measurements taken at consecutive times. There is no need to perform this dynamic compensation on the coarse position measurements as they are only being used to resolve the period ambiguity of the fine position measurements.

[0182] The above compensation is specific to the situation where the signals from the fine sine detection coil 6-1 are measured before the signals from the fine cosine detection coil 6-2. If the signals from the fine cosine detection coil 6-2 are measured before the signals from the fine sine detection coil 6-1, then, accounting for the motion of the target 5, the peak to peak voltage measurements determined by the measurement processing unit 19 using the raw data obtained from the ADC 13 can be written as:

{circumflex over (V)}^FC=A_F cos [φ^F−3s]+A_F cos [φ^F−2s]  (35)

{circumflex over (V)}^FS=A_F sin [φ^F−s]+A_F sin [φ^F]  (36)

from which we can determine the following compensation to be applied to φ^F_corr:

φ_comp^F=φ_corr^F+s(3/2−cos(2φ_corr^F))  (37)

[0183] Thus different compensations are performed depending on the order in which the signals from the two fine detection coils are measured by the measurement circuit.

[0184] This movement compensation can be calculated arithmetically or, in order to speed-up the calculations, can be determined in advance and stored in a look-up table. For instance, compensation can be written as

φ_comp^F=φ_corr^F+K0(φ_corr^F)*s

φ_comp^F=φ_corr^F+K1(φ_corr^F)*s  (38)

in which either coefficient K0 or K1 is used for the dynamic correction according to which sine or cosine detection coil was measured first; the values of K0 and K1 are determined from the look-up table using φ^F_corr to determine the index to the table, for example as follows:

$\begin{array}{cc}\mathrm{index}=\mathrm{round}\left(\frac{{\varphi }_{\mathrm{corr}}^F\times 1024}{2\pi }\right)& \left(39\right)\end{array}$

where the look-up table has a length of 1024 with coefficients K0 in a first column and coefficients K1 in a 15 second column. This look-up-table would be stored in the non-volatile memory of the microcontroller 9 as part of the dynamic correction data 31. The values of K0 and K1 for the different entries in the look-up-table can be determined in advance from the following:

$\begin{array}{cc}K0\left(j\right)=\frac{3}{2}+\cos \left(\frac{4\pi j}{1024}\right)& \left(40\right)\\ K1\left(j\right)=\frac{3}{2}-\cos \left(\frac{4\pi j}{1024}\right)& \left(41\right)\end{array}$

[0185] As a further possibility, the values of K0 and K1 in the look-up-table can be determined experimentally. For example a set of experimental measurements from the sensor are collected together with the readings from a much faster sensor (e.g. from a fast incremental optical encoder) at different speeds of the target 5. The look-up table correction coefficients K0 and K1 can be found for each value of φ^F_corr as the best parameters for the parabolic fit to the experimental data (φ^opt−φ^F_corr) measured for different speeds of the target 5. Different correction coefficients K0 and K1 are determined depending on whether the signals from the fine sine detection coil 6-1 are measured before the signals from the fine cosine detection coil 6-2 or if the signals from the fine cosine detection coil 6-2 are measured before the signals from the fine sine detection coil 6-1. The above compensation assumes that the target is moving with constant speed. Even better accuracy for the dynamic compensation for the consecutive nature of the measurements can be obtained if the acceleration of the target 5 is taken into account. In this case instantaneous measures of the speed and acceleration can be determined at each calculation time as follows:

For detection interval corresponding to i=3

s=(Δφ^F_3-1)/4=(φ^F₃−φ^F₁)/4  (43)

Acc=(Δφ^F_3-1−Δφ^F_10-8)/6;  (44)

For detection interval corresponding to i=5

s=(Δφ^F_5-3)/4=(φ^F₅−φ^F₃)/4  (45)

Acc=(Δφ^F_5-3−Δφ^F_3-1)/4;  (46)

For detection interval corresponding to i=8

s=(Δφ^F_8-6)/4=(φ^F₈−φ^F₆)/4  (47)

Acc=(Δφ^F_8-6−Δφ^F_5-3)/6;  (48)

For detection interval corresponding to i=10

s=(Δφ^F_10-8)/4=(φ^F₁₀−φ^F₈)/4  (49)

Acc=(Δφ^F_10-8−Δφ^F_8-6)/4;  (50)

[0186] As there is a switch over of the measurement circuit (from measuring circuit M to measuring circuit N and vice versa) at detection intervals corresponding to i=1 and 6, and as calculations are performed in adjacent detection intervals at the switch over time, instantaneous speed and acceleration values are not calculated during detection intervals corresponding to i=1 and 6 (as different equations would need to be used). Instead, the speed measurement and the acceleration measurement determined for the detection interval corresponding to i=10 is also used during detection interval corresponding to i=1; and the speed measurement and the acceleration measurement determined for the detection interval corresponding to i=5 is also used during detection interval corresponding to i=6.

[0187] When determining the speed measurement and the acceleration measurement, the phase values φ^F may be used (as per the equations above) or the phase values (φ^F_corr) after correction for oscillations may be used instead.

[0188] The speed value (s) determined at the given calculation time point can then be adjusted based on the corresponding acceleration value (Acc); for example as follows:

s_adj=s−⅔Acc  (51)

[0189] This adjusted speed value can then be used in place of speed (s) in the above calculations for dynamically compensating φ^F_corr. Experiments have shown that there is very little to be gained by taking into account even higher derivatives.

[0190] In the case when the compensation coefficients are determined from a large set of experimental data measured at different positions, speeds and accelerations of the target 5, compensation can be achieved using the following:

φ_comp^F=φ_corr^F+K0×s+K0^Acc×(Acc)

φ_comp^F=φ_corr^F+K1×s+K1^Acc×(Acc)  (52)

where the values of K0, K1, K0^Acc, and K1^Acc are determined from the relevant look-up-table using φ^F_corr in the manner discussed above.

[0191] For many types of ratiometric sensors the phase of the measured signal from the target 5 and the phase of the breakthrough offset voltage from the excitation coil are equal to each other (or 180 degrees out of phase with each other). This happens for example when the target 5 is not resonant and is, for example formed from a short circuit coil or a conductive (metallic) plate in which Eddy currents caused by the excitation coil 2 induce voltages in the detection coils via an electromagnetic coupling. Simultaneously the non-exact balance between the excitation coil and the detection coils causes direct breakthrough coupling due to the electromagnetic field created by the excitation current flowing in the excitation coil. In such sensors the exact phase difference between the excitation current and the demodulation control signal ex_shifted is not particularly important, as long as this phase difference does not lead to a significant reduction in the measured signal amplitudes.

[0192] However, with a resonant target 5 as illustrated in FIG. 2a, there is approximately a 90 degree phase shift between the signals induced in the detection coils 4 and 6 caused by the magnetic field generated by the resonator 12 when it is energised by the excitation coil 2 and the direct breakthrough signal induced in the detection coils 4 and 6 directly from the excitation coil 2. The 90 degree phase shift is achieved by choosing the ex-clock signal to have a fundamental frequency corresponding in frequency to the resonant frequency of the resonator 12. In order to obtain the best possible performance out of such resonant target 5 sensors, a precise phase tuning of the measurement circuit is required. In particular, as will be explained below, it is possible to precisely phase tune the sensor to align the demodulation control signal ex_shifted so that it becomes orthogonal (90 degrees phase shifted) to the direct breakthrough signal from the excitation coil 2.

[0193] FIG. 13 illustrates the excitation circuitry 23 that is used in this second embodiment with a resonant target 5. The other components of this embodiment are the same as those in the first embodiment described above except as discussed below. The reference voltage in this embodiment is measured by the measurement circuitry 25 by passing the excitation current via a complex impedance Z. In practical applications the complex impedance Z is constructed as either a parallel or serial combination of a resistor and a capacitor whose values are chosen in order that there is a desired phase relationship between the phase of the measured excitation reference signal and the phase of the direct breakthrough signals induced in the detection coils 4 and 6 by the excitation coil 2. In the preferred embodiment, the impedance Z is chosen (at the design stage of the sensor) so that the phase of the measured excitation reference signal is close to the phase of the direct breakthrough signal induced from the excitation coil 2 into the detection coils 4 and 6 and thus is about 90 degrees out of phase with the signals induced in the detection coils 4 and 6 by the resonator 12. As a result of the chosen phase of ex_shifted applied to the incoming signal at the demodulation switch 56, the measured excitation reference value should, in theory, be close to zero. However, during sensor operation, the phase characteristics of the sensor will change (for example due to changing impedance values caused by temperature changes of the circuit components etc) and as a result, the phase of the ex_shifted control signal will not be 90 degrees out of phase with the direct breakthrough signal and so more of the direct breakthrough signal will pass through the amplification and filtering circuit 83. By arranging the impedance Z so that the phase of the measured excitation reference signal is close to that of the direct breakthrough signal, the microcontroller 9 can use a simple zero tuning approach to vary the phase of the excitation signal applied to the excitation coil 2 in order to keep the measured excitation reference value close to zero (and thereby also minimising the direct breakthrough signal).

[0194] As will be explained below, the phase of the excitation signal ex_clock applied to the excitation coil 2 is controlled by the comparator 91. The input control signal ex_double is at twice the desired excitation frequency. This double frequency signal is low pass filtered by the R-C filter 93 to smooth its edges. Then the rising and falling edges of ex_double are compared, by the comparator 91, with a DAC voltage level generated by the microcontroller 9. The signal at the output of the comparator 91 will have a variable duty cycle depending on the exact level of the DAC voltage. In order to generate a desired 50% duty cycle for the ex_clock signal, the output of the comparator 91 is passed through a latch circuit 95, which also halves the frequency of the input signal and provides an output which has rising or falling edges at the rising edges of the comparator output, as shown in FIG. 14a. In particular, as can be seen from FIG. 14a, by changing the DAC voltage, the microcontroller 9 changes the phase of the excitation signal ex_clock without modifying the 50% duty cycle. The excitation circuitry 23 shown in FIG. 13 has the advantage of being able to tune the phase of the excitation signal (ex_clock) with very high resolution exceeding 10 ps using an ordinary microcontroller 9 having a clock speed of tens of MHz.

[0195] FIG. 14b is a flow chart illustrating the procedure used by the microcontroller 9 to determine the DAC voltage to apply to the comparator 91. As shown, in step s21, the microcontroller 9 determines that phase adjustments should be made. The microcontroller 9 makes this determination when new excitation reference voltages (V^EX_N and V^EX_M) become available. In step s23, the microcontroller 9 updates the mean excitation reference value using the latest excitation reference values that have just been determined in the current detection cycle. In step s25, the microcontroller 9 determines if the updated mean excitation reference value is outside defined boundaries. As the impedance Z shown in FIG. 13 has been chosen to minimise the excitation reference signal in line with minimising the direct breakthrough signal in the detection coils 4 and 6, the mean value for the measured excitation reference value should be around zero. By increasing or decreasing the DAC value generated by the microcontroller 9, it is possible to maintain the measured excitation value close to the zero level. Thus, if the measured mean value of the measured excitation reference signal exceeds a positive or negative threshold, then the microcontroller 9 increments or decrements, in step s27, the DAC value output to the comparator 91. The continual adjustment of the DAC value in this way ensures a fixed relationship between the demodulation clock signal ex_shifted and the phase of the signals being sensed in the measurement circuits N and M. As those skilled in the art will appreciate, in this case where the excitation reference signal is being reduced to zero it is not essential to perform the direct breakthrough corrections discussed above.

[0196] In most sensing applications the ability to automatically tune continuously to zero the value of the measured reference excitation voltage (measured from the Z-impedance) allows the microcontroller 9 to minimise the direct breakthrough in the signals obtained from the detection coils 4 and 6 and no further breakthrough corrections are required. However in the case of sensors designed for the most accurate measurements, the remaining level of the direct breakthrough offset should be compensated by the microcontroller 9. In this case measurements are taken with the sensor when the target 5 is removed far away from the sensor coils. The microcontroller 9 actively controls the level of the measured reference excitation signal and keeps it close to zero (in the manner discussed above). The signals induced in each detection coil 4 and 6 are measured, averaged and stored in the non-volatile memory of the microcontroller 9 as breakthrough calibration data 29:

$\begin{array}{cc}{B}_N^{\mathrm{FS}}=\frac{1}{P}\sum _{r=1}^PV_N^{\mathrm{FS}}\left(r\right)& \left(53\right)\\ B_N^{\mathrm{FC}}=\frac{1}{P}\sum _{r=1}^PV_N^{\mathrm{FC}}\left(r\right)& \left(54\right)\\ B_N^{\mathrm{CS}}=\frac{1}{P}\sum _{r=1}^PV_N^{\mathrm{CS}}\left(r\right)& \left(55\right)\\ B_N^{\mathrm{CC}}=\frac{1}{P}\sum _{r=1}^PV_N^{\mathrm{CC}}\left(r\right)\mathrm{and}& \left(56\right)\\ B_M^{\mathrm{FS}}=\frac{1}{P}\sum _{r=1}^PV_M^{\mathrm{FS}}\left(r\right)& \left(57\right)\\ B_M^{\mathrm{FC}}=\frac{1}{P}\sum _{r=1}^PV_M^{\mathrm{FC}}\left(r\right)& \left(58\right)\\ B_M^{\mathrm{CS}}=\frac{1}{P}\sum _{r=1}^PV_M^{\mathrm{CS}}\left(r\right)& \left(58\right)\\ B_M^{\mathrm{CC}}=\frac{1}{P}\sum _{r=1}^PV_M^{\mathrm{CC}}\left(r\right)& \left(60\right)\end{array}$

where P is the number of measurements of each signal that are averaged.

[0197] This breakthrough calibration data 29 can then be applied to actual measurements obtained when the target 5 is being sensed as follows:

V_Ncorr^FS=V_N^FS−B_N^FS  (61)

V_Ncorr^FC=V_N^FC−B_N^FC  (62)

V_Ncorr^CS=V_N^CS−B_N^CS  (63)

V_Ncorr^CC=V_N^CC−B_N^CC  (64)

V_Mcorr^FS=V_M^FS−B_M^FS  (65)

V_Mcorr^FC=V_M^FC−B_M^FC  (66)

V_Mcorr^CS=V_M^CS−B_M^CS  (67)

V_Mcorr^CC=V_M^CC−B_M^CC  (68)

[0198] In the first and second embodiments, the measurement processing unit 19 obtained position information approximately once every two periods of the polarity control signal. In this third embodiment, the measurement processing unit 19 is arranged to update the fine position measurement during each detection interval. This is illustrated in FIG. 15, which shows that a fine position measurement is obtained during each detection interval (Δtk) either using measurements from measurement circuit M or using measurements from measurement circuit N. As illustrated in FIG. 15, during the detection interval corresponding to the index value i=1, the position information is calculated using fine sine and fine cosine measurements when the fine sine measurement is obtained before the fine cosine measurement. During the detection interval corresponding to the index value i=2, the position information is obtained using fine sine and fine cosine measurements when the fine cosine measurement is obtained before the fine sine measurement. As explained above, in order to compensate for the movement of the target 5 between the times that the measurements are taken, different compensations should be used depending on whether the sine measurement or the cosine measurement is measured first. This is illustrated in FIG. 15 by the shading used in the boxes showing the calculations that are performed, to illustrate that different compensations are being applied to these measurements compared with the non-shaded boxes. The compensation to the φ^F_corr value will have a positive sign when the signals from the fine sine detection coil 6-1 are measured before the signals from the fine cosine detection coil 6-2. More specifically, during detection intervals corresponding to index values i=1, 3, 5, 6, 8 and 10 the measurement processing unit 19 performs the dynamic compensation for movement of the target 5 using:

φ_comp^F=φ_corr^F+s(3/2+cos(2φ_corr^F))  (69)

[0199] The compensation to the φ^F_corr value will have a negative sign when the signals from the fine cosine detection coil 6-2 are measured before the signals from the fine sine detection coil 6-1. More specifically, during detection intervals corresponding to index values i=2, 4, 7 and 9 the measurement processing unit 19 performs the dynamic compensation for movement of the target 5 using:

φ_comp^F=φ_corr^F+s(3/2−cos(2φ_corr^F))  (70)

[0200] As explained above in the first embodiment, instead of using such arithmetic compensations, the measurement processing unit 19 may use different look-up-tables instead to store the relevant correction coefficients (K0, K1 etc) for the two types of compensation.

[0201] Like in the first embodiment, instead of assuming a fixed speed of the target 5, the measurement processing unit 19 may also consider acceleration of the target 5. In this case, instantaneous speed and acceleration values for the different detection intervals can be determined as follows:

For detection interval corresponding to i=1

s=(Δφ^F_1-10)/2=(φ^F₁−φ^F₁₀)/2  (71)

Acc=(Δφ^F_1-10−Δφ^F_10-8)/3;  (72)

For detection interval corresponding to i=3

s=(Δφ^F_3-1)/4=(φ^F₃−φ^F₁)/4  (73)

Acc=(Δφ^F_3-1−Δφ^F_1-10)/3;  (74)

For detection interval corresponding to i=4

s=(Δφ^F_4-2)/4=(φ^F₄−φ^F₂)/4  (75)

Acc=(Δφ^F_4-2−Δφ^F_3-1)/2;  (76)

For detection interval corresponding to i=5

s=(Δφ^F_5-3)/4=(φ^F₅−φ^F₃)/4  (77)

Acc=(Δφ^F_5-3−Δφ^F_4-2)/2;  (78)

For detection interval corresponding to i=6

s=(Δφ^F_6-5)/2=(φ^F₆−φ^F₅)/2  (79)

Acc=(Δφ^F_6-5−Δφ^F_5-3)/3;  (80)

For detection interval corresponding to i=8

s=(Δφ^F_8-6)/4=(φ^F₈−φ^F₆)/4  (81)

Acc=(Δφ^F_8-6−Δφ^F_6-5)/3;  (82)

For detection interval corresponding to i=9

s=(Δφ^F_9-7)/4=(φ^F₉−φ^F₇)/4  (83)

Acc=(Δφ^F_9-7−ΔφF_8-6)/2;  (84)

For detection interval corresponding to i=10

s=(Δφ^F_10-8)/4=(φ^F₁₀−φ^F₈)/4  (85)

Acc=(Δφ^F_10-8−Δφ^F_9-7)/2;  (86)

(As before, φ^F_corr values may be used instead of the φ^F values in the above calculations for speed and acceleration.)

[0202] As can be seen from the above equations and FIG. 15, the speed and acceleration values are determined using consecutive values of φ^F from earlier detection intervals where the same order of processing the sine and cosine signals is performed. Thus, for example, in detection time interval corresponding to i=3, the measurement processing unit 19 calculates target position when the sine measurement is obtained before the cosine measurement and therefore uses the position measurement from earlier detection intervals where the sine measurement is obtained before the cosine measurement to calculate the instantaneous speed. As can be seen from FIG. 15, the closest earlier detection interval where the sine measurement is obtained before the cosine measurement, is the detection interval corresponding to i=1. Consequently, the instantaneous speed is determined from the difference in position between the measurements in these two detection intervals (Δφ^F_3-1). The acceleration measure is also determined using signals obtained when the sine measurement are measured before the cosine measurement.

[0203] As there is a switch over of the measurement circuit (from measuring circuit M to measuring circuit N and vice versa) at detection intervals corresponding to i=1 and 6, and in order not to overcomplicate the calculations of the speed and acceleration measures during detection time intervals corresponding to i=2 and 7, the acceleration measurement determined for the detection interval corresponding to i=1 is also used during the detection interval corresponding to i=2; and the speed measurement and the acceleration measurement determined for the detection interval corresponding to i=6 is also used during the detection interval corresponding to i=7.

[0204] Like in the first embodiment, each speed value is then adjusted in view of the corresponding acceleration value:

s_adj=s−⅔Acc  (87)

[0205] This adjusted speed value can then be used in place of speed (s)(in the above calculations to dynamically compensate φ^F_corr. The thus compensated phase values can then be mapped to a position of the target 5 through an appropriate look-up-table correction and the period ambiguity associated with the fine position measurements can be corrected using the latest coarse position measurement. The final position is then sent to the host Interface unit 21 for reporting to the host. As shown in FIG. 15, in this embodiment, the fine position information is updated once per period of the polarity control signal, i.e. once per detection interval.

[0206] In the third embodiment, a fine position measurement was obtained during every detection interval. Signals from the fine detection coils are processed in two measurement circuits M and N in an overlapping manner. As a result of the overlapping, it is possible to calculate two position measurements using the data obtained from the two measurement circuits. For example, during the detection interval corresponding to i=10, the third embodiment calculated a position measurement using the fine sine data from measurement circuit M obtained in detection interval corresponding to i=8 and the fine cosine data from measurement circuit M obtained in detection interval corresponding to i=9. However, during detection interval corresponding to i=10 another position measurement can be calculated using the fine cosine data from measurement circuit N obtained in detection interval corresponding to i=8 and the fine sine data from measurement circuit N obtained in detection interval corresponding to i=9.

[0207] These two position measurements would be calculated as follows:

$\begin{array}{cc}{V}_{\mathrm{Ncorr}}^{\mathrm{FS}}=V_N^{\mathrm{FS}}-O_N^{\mathrm{FS}}\times V_N^{\mathrm{EX}}& \left(88\right)\\ V_{\mathrm{Ncorr}}^{\mathrm{FC}}=V_N^{\mathrm{FC}}-O_N^{\mathrm{FC}}\times V_N^{\mathrm{EX}}& \left(89\right)\\ {\varphi }_N^F=\arctan \left(\frac{V_{\mathrm{Ncorr}}^{\mathrm{FS}}}{V_{\mathrm{Ncorr}}^{\mathrm{FC}}}\right)& \left(90\right)\\ {\varphi }_{\mathrm{Ncorr}}^F={\varphi }_N^F+\Delta {\varphi }_{\mathrm{corr}}\mathrm{and}& \left(91\right)\\ V_{\mathrm{Mcorr}}^{\mathrm{FS}}=V_M^{\mathrm{FS}}-O_M^{\mathrm{FS}}\times V_M^{\mathrm{EX}}& \left(92\right)\\ V_{\mathrm{Mcorr}}^{\mathrm{FC}}=V_M^{\mathrm{FC}}-O_M^{\mathrm{FC}}\times V_M^{\mathrm{EX}}& \left(93\right)\\ {\varphi }_M^F=\arctan \left(\frac{V_{\mathrm{Mcorr}}^{\mathrm{FS}}}{V_{\mathrm{Mcorr}}^{\mathrm{FC}}}\right)& \left(94\right)\\ {\varphi }_{\mathrm{Mcorr}}^F={\varphi }_M^F+\Delta {\varphi }_{\mathrm{corr}}& \left(95\right)\end{array}$

[0208] The resulting position measurements (φ^F_Mcorr and φ^F_Ncorr) will deviate from each other due to the dynamic error terms related to the speed of the target movement, as discussed above. However, the mean value of these two position measurements

φ^F_mean=(φ^F_Mcorr+φ^F_Ncorr)/2  (96)

will have much smaller dynamic error and any remaining dynamic error will have very little, if any, dependence on the determined position measurement. Thus, by calculating during the detection interval with i=10 the instantaneous value of the parameter:

Δφ^F_comp=φ^F_Mcorr−φ^Fmean=(φ^F_Mcorr−φ^F_Ncorr)/2  (97)

we can remove a significant part of the dynamic error caused by the movement of the target in the measurements performed during detection intervals with i=1, 3 and 5 (fine sine measured before fine cosine) using formula:

φ^F_Ncorr=φ^F_N+Δφ_corr−Δφ^F_comp  (98)

and during detection intervals with i=2 and 4 (fine sine is measured after fine cosine) using formula:

φ^F_Ncorr=φ^F_N+Δφ_corr+Δφ^F_comp  (99)

[0209] During the detection time interval with i=5, the instantaneous value of the parameter Δφ^F_comp can be updated using the two position measurements obtained using the data measured simultaneously in measurement circuits N and M. Namely, the position measurement obtained using the fine sine data from measurement circuit N obtained in detection interval corresponding to i=3 and the fine cosine data from measurement circuit N obtained in detection interval corresponding to i=4; and the position measurement using the fine cosine data from measurement circuit M obtained in detection interval corresponding to i=3 and the fine sine data from measurement circuit M obtained in detection interval corresponding to i=4. This updated value of Δφ^F_comp can then be used to compensate for movement of the target as follows during the position calculations performed in detection intervals with i=6, 8 and 10 (fine sine is measured before fine cosine) using formula:

φ^F_Mcorr=φ^F_M−Δφ_corr−Δφ^F_comp  (100)

and during detection intervals with i=7 and 9 (fine sine is measured after fine cosine) using formula:

φ^F_Mcorr=φ^F_M−Δφ_corr+Δφ^F_comp  (101)

[0210] The sign with which the velocity compensation factor (Δφ^F_comp) is applied to the position measurement changes depending on which of the two signals fine sine or fine cosine was measured first. This compensation technique will cause the position measurements to change smoothly between adjacent measurements. As discussed above, this speed compensation removes the dependence on the position measurement itself and so any remaining dynamic error can be compensated using a simple formula like:

$\begin{array}{cc}{\varphi }_{\mathrm{comp}}^F={\varphi }_{\mathrm{corr}}^F+\frac{3s}{2}& \left(102\right)\end{array}$

[0211] In the above embodiments, the measurement circuits 51 were arranged to demodulate the signals obtained from the selected detection coil 4, 6. The measurement circuits 51 also multiplied the incoming signal with a polarity control signal that allowed a positive and a negative measure of the amplitude of the demodulated signal from each detection coil to be obtained. In the first embodiment, the update rate can be improved by increasing the frequency of the polarity control signal. However, if there is a limit on the excitation frequency (for example because the excitation coil has high inductance), then this will limit the available update rate. Also, even if the excitation frequency can be significantly increased, there is a practical upper limit on the frequency of the polarity control signal the signals must be filtered to remove external noise, but also the signals being measured must be allowed to settle to the quasi dc level before the ADC 13 converts the voltage into a corresponding digital value. This means that in practice, the upper limit on the frequency of the polarity control signal is about 150 kHz.

[0212] In the fifth embodiment that is described below, the measurement architecture is based on the fast multiplexing of voltages from two detection coils through the same measurement circuit 51 multiple times during the same polarity modulation period, so that a ratiometric measurement of the signals from the two detection coils is achieved with minimum latency. In particular, in this embodiment, the measurement circuits 51 demodulate and combine the signals from the fine sine and the fine cosine detection coils 6 with a polarity modulation signal to produce a signal whose phase varies with the target position (φ^F) to be measured. The measurement circuits 51 also perform a similar processing of the signals from the coarse sine and cosine detection coils 4. The position of the target 5 is then determined from zero crossing positions of the filtered output signal from the measurement circuits 51.

[0213] This embodiment is ideally suited to sensors where the excitation frequency can be much higher than the desired update rate of the sensor which is applicable to sensors having low impedance sensor coils. As will be demonstrated below, the update rate of the fifth embodiment is equal to half of the period of the polarity modulation signal. Further, the requirement of the high corner frequency of the band pass filter 87 can be reduced by about four times for the same period of the polarity modulation signal. This is because in the fifth embodiment, the output from the amplification and filtering circuit 83 does not need to settle to a quasi dc level for conversion by the ADC 13. This helps to reduce significantly the level of the internal and external noise in the results of the measurements. Additionally, the latency of the fifth embodiment is defined by the filtering time and the calculation time of the microcontroller 9, which is less than half the period of the polarity modulation signal. So this represents a four-fold improvement in the latency.

[0214] FIG. 16 is a block diagram of the main components used in this fifth embodiment. As shown, the implementation of this embodiment is similar to the embodiments described above using a general purpose microcontroller and measurement circuitry 25. The same reference numerals have been used to designate similar components. The main difference with this embodiment is that it requires a more complex measurement process and the generation of more complex control signals to control the measurement process. The new components include digital switching circuitry 101, which is shown here as being outside the microcontroller 9, although it may form part of the excitation and control signal logic 11. In addition to the digital switching circuitry 101, this embodiment also has phase detectors 103 and timers 105 both of which are implemented inside the microcontroller 9. The phase detectors 103 detect zero crossings of the signals output from the measurement circuitry 51 and the timers 105 provide control signals which trigger the ADC 13 and provide an interrupt for the microcontroller 9 to start processing the converted data by the measurement processing unit 19. The phase of the timers 105 is controlled by the measurement processing unit 19.

[0215] The measurement circuitry 25 that is used in this embodiment has the same two measurement circuits 51 that were used in the first embodiment and shown in FIG. 5. However, the timeline of the control signals (in1, in2) used for selecting the signals from the different detection coils 4, 6 through to the demodulation switch 56; and the timeline of the polarity modulation signal are very different. FIG. 17 shows example control signals that can be used in this embodiment and illustrates the effect of the two control signals Int and polarity on the selection of the signals from the 1+/1− input (corresponding to the fine sine detection coil 6-1) and on the selection of the signals from the 2+/2− input (corresponding to the fine cosine detection coil 6-2). As shown, when the polarity modulation signal is low and in1 is low, the signal from the 1+/1 input is passed through to the amplification and filtering circuitry 83. When the polarity modulation signal is low and in1 is high, the signal from the 2+/2− input is passed through to the amplification and filtering circuitry 83. When the polarity modulation signal is high and in1 is low, the signal from the 1+/1− input is inverted and passed through to the amplification and filtering circuitry 83. Finally, when the polarity modulation signal is high and in1 is high, the signal from the 2+/2− input is inverted and passed through to the amplification and filtering circuitry 83. The in1 and polarity signals are periodic and have a repeat period of T_mod. As shown in FIG. 17, the effect of using these in1 and polarity signals is to multiply the signal from the 1+/1− input with the following periodic sequence of 32 numbers (although other numbers could be used):

1 1 0 1 0 1 0 0 0 0 −1 0 −1 0 −1 −1 −1 −1 0 −1 0 −1 0 0 0 0 1 0 1 0 1 1
and to multiply the signal from the 2+/2− input with the following periodic sequence of 32 numbers:
0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 −1 0 −1 0 −1 −1 −1 −1 0 −1 0 −1 0 0

[0216] These two periodic sequences of 32 numbers are related in that one is a phase shifted version of the other. In particular, one is shifted by a quarter of the period (T_mod). Therefore, the output from the demodulating switch 56 when the signal from the 1+/1− input (corresponding to the signal from the fine sine detection coil 6-1) is selected can be represented as:

$\begin{array}{cc}{A}_F\sin {\varphi }^F\cos \left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\mathrm{harmonics}& \left(103\right)\end{array}$

and the output from the demodulating switch 56 when the signal from the 2+/2− input (corresponding to the signal from the fine cosine detection coil 6-2) is selected can be represented as:

$\begin{array}{cc}{A}_F\sin {\varphi }^F\sin \left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\mathrm{harmonics}& \left(104\right)\end{array}$

[0217] The two sequences of 32 numbers are also organized in a time division multiplexed manner, so that whenever one of them corresponds to zero the other one corresponds to either one or minus one. The time division multiplexing of the two inputs achieved with this approach leads to the interposing of the signals from the two detection coils which, after passing through the amplification and filtering circuit 83 for filtering out the harmonics, can be represented as a combined signal of the form:

$\begin{array}{cc}{\mathrm{AF}}_{\mathrm{out}}={\mathrm{GA}}_F\sin {\varphi }^F\cos \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi \right)+{\mathrm{GA}}_F\cos {\varphi }^F\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi \right)& \left(105\right)\end{array}$

where G represents the gain of the amplification and filtering circuit 83, φ^F is the phase to be determined that corresponds to the desired target position information, and φ is an unknown phase shift introduced by the processing circuitry (mainly the bandpass filter 87 in the amplification and filtering circuit 83). This expression can be rewritten as:

$\begin{array}{cc}{\mathrm{AF}}_{\mathrm{out}}=V_0\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi +{\varphi }^F\right)& \left(106\right)\end{array}$

[0218] Thus the phase of the AF_out signal varies with the target position information (φ^F). The time points or phases when AF_out crosses zero can be determined by comparing AF_out with zero in a comparator. Thus, the signal AF_out will cross zero at the rising edge when

$\begin{array}{cc}\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+{\varphi }_1& \left(107\right)\end{array}$

as measured from the beginning of the modulation period T_mod. Therefore,

φ₁+φ_rising+φ^F=2π∴φ₁=2π−φ_rising−φ^F  (108)

Similarly, the signal AF_out will cross zero at the falling edge when

$\begin{array}{cc}\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t={\varphi }_2& \left(109\right)\end{array}$

as measured from the beginning of the modulation period T_mod. Therefore,

φ₂+φ_falling+φ^F=π∴φ₂=π−φ_falling−φ^F  (110)

[0219] In practice the phase shift introduced by the measurement circuits (φ) will be different for the rising and the falling edges for various reasons, for instance due to the hysteresis in the comparator used to detect the zero crossing. The above equations represent these different measurement circuit phase shifts as φ_rising and φ_falling. These measurement circuit phase shifts are relatively stable parameters, although they can slowly drift, for example with temperature. It is possible to measure and then remove these unwanted phase shifts by obtaining a new measurement with a new polarity modulation signal that, when combined with the in1 control signal, results in the polarity reversal of one of the sequences of 32 numbers whilst leaving the other sequence of 32 numbers unchanged. For example, the signal from the 1+/1− input can be multiplied with the following periodic sequence of 32 numbers:

−1 −1 0 −1 0 −1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 −1 0 −1 0 −1 −1
and the signal from the 2+/2− input can be multiplied with the same periodic sequence of 32 numbers as before:
0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 −1 0−1 0−1−1−1−1 0−1 0−1 0 0

[0220] FIG. 18 shows an example of the new polarity modulation signal that can achieve this result when combined with the in1 control signal. FIG. 18 also shows the AF_out signal that is obtained as a result of using this new polarity modulation signal. FIG. 18 also shows (in phantom) the AF_out signal obtained with the polarity modulation signal shown in FIG. 17. In order to distinguish the two polarity modulation signals, the polarity modulation signal used in FIG. 17 is labelled polarity+ and in FIG. 18 it is labelled polarity−. The other control signals remain the same. In this case, the AF_out signal can be represented as:

$\begin{array}{cc}{\mathrm{AF}}_{\mathrm{out}}=-{\mathrm{GA}}_F\sin {\varphi }^F\cos \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi \right)+{\mathrm{GA}}_F{\mathrm{cos\varphi }}^F\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi \right)& \left(111\right)\\ {\mathrm{AF}}_{\mathrm{out}}=V_0\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi -{\varphi }^F\right)& \left(112\right)\end{array}$

[0221] This new signal AF_out will cross zero at the rising edge when

$\begin{array}{cc}\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t={\varphi }_3& \left(113\right)\end{array}$

as measured from the beginning of the modulation period T_mod. Therefore,

φ₃+φ_rising−φ^F=0 ∴φ₃=φ^F−φ_rising  (114)

Similarly, the signal AF_out will cross zero at the falling edge when

$\begin{array}{cc}\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t={\varphi }_4& \left(115\right)\end{array}$

as measured from the beginning of the modulation period T_mod. Therefore,

φ₄+φ_falling−φ^F=π∴φ₄=π−φ_falling+φ_F  (116)

[0222] Consequently, if the measured phases φ₁ and φ₃ are added together, we can obtain a measure of φ_rising as follows:

$\begin{array}{cc}{\varphi }_1+{\varphi }_3=\left(2\pi -{\varphi }_{\mathrm{ri}\mathrm{sing}}-{\varphi }^F\right)+\left({\varphi }^F-{\varphi }_{\mathrm{rise}}\right)& \left(117\right)\\ {\varphi }_{\mathrm{ri}\mathrm{sing}}=\pi -\left(\frac{{\varphi }_1+{\varphi }_3}{2}\right)& \left(118\right)\end{array}$

[0223] Similarly, by adding the measured phases φ₂ and φ₄ together, we can obtain a measure of φ_falling as follows:

$\begin{array}{cc}{\varphi }_{\mathrm{falling}}=\pi -\left(\frac{{\varphi }_2+{\varphi }_4}{2}\right)& \left(119\right)\end{array}$

However, the phases φ₁ and φ₃ are defined only from 0 to 2π and so (as can be seen from FIG. 19a), φ_rising can also be equal to:

$\begin{array}{cc}{\varphi }_{\mathrm{ri}\mathrm{sing}}=2\pi -\left(\frac{{\varphi }_1+{\varphi }_3}{2}\right)& \left(120\right)\end{array}$

and similarly (as can be seen from FIG. 19c), φ_falling can also be equal to:

$\begin{array}{cc}{\varphi }_{\mathrm{falling}}=2\pi -\left(\frac{{\varphi }_2+{\varphi }_4}{2}\right)& \left(121\right)\end{array}$

[0224] In particular, FIG. 19a is a phase plot showing the way in which the phases φ₁ and φ₃ vary with the target position phase φ^F and show (with the horizontal lines) the values that (φ₁+φ₃)/2 can take. FIG. 19c illustrates the corresponding phase plots for phases φ₂ and φ₄ and showing (with the horizontal lines) the values that (φ₂+φ₄)/2 can take.

It is easy to deal with two possible answers for φ_rising—in particular, the microcontroller 9 can determine:

$\begin{array}{cc}{\varphi }_{\mathrm{ri}\mathrm{sing}}=\pi -\left(\frac{{\varphi }_1+{\varphi }_3}{2}\right)& \left(122\right)\end{array}$

and if the answer is negative then the microcontroller 9 can add π to the answer. A similar calculation can be performed in respect of φ_falling.

[0225] Now that φ_rising has been calculated, the microcontroller 9 can add this to φ₃ in order to determine φ^F. FIG. 19b is a plot showing that φ₃+φ_rising varies linearly with the target position phase (φ^F). Similarly, now that φ_falling has been calculated, the microcontroller 9 can add this to φ₄ in order to determine φ^F. FIG. 19d is a plot showing that φ₄+φ_falling−π varies linearly with the target position phase (φ^F). In this way, the microcontroller 9 can determine two measurements of the target position phase (φ^F).

[0226] The description above deals with the measurements made in a single measurement circuit 51. However, as discussed above, the measurement circuitry 25 has two parallel measurement circuits 51-1 and 51-2 (M and N). To avoid the situation where the same measurement inputs (detection coil) are selected simultaneously in both measurement circuits N and M, the control signal in1_N applied to the multiplexers 55-1 and 55-2 of measurement circuit N is inverted and used as the control signal in1_M applied to the multiplexors 55-1 and 55-2 of the measurement circuit M. In the following description the suffix “_N” or “_M” will be added to the reference numbers of the components to signify in which measurement circuit (M or N) the corresponding component belongs. FIG. 20 illustrates the way in which the fine sine detection coil (connected to inputs 1+/1−) and the fine cosine detection coil (connected to inputs 2+/2−) can be switched through both measurement circuits N and M in the above manner. As shown, during the moment in time when the fine sine detection coil 6-1 is selected by the multiplexers 55_N in measurement circuit N, the fine cosine detection coil 6-2 is selected by the multiplexers 55_M in the measurement circuit M. Similarly, during the moment in time when the fine cosine detection coil 6-2 is selected by the multiplexers 55_N in measurement circuit N, the fine sine detection coil 6-1 is selected by the multiplexers 55_M in the measurement circuit M.

[0227] The value of the target position phase (φ^F) measured in measurement circuit M will deviate (by π/2) from the value of the target position phase (φ^F) measured in measurement circuit N because the order of the selected measurement inputs is interchanged. This change of phase can be seen from the AF^M_out signal and the AF^N_out signal which are given by:

$\begin{array}{cc}{\mathrm{AF}}_{\mathrm{out}}^N=V_0\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+{\varphi }_N+{\varphi }^F\right)& \left(123\right)\\ {\mathrm{AF}}_{\mathrm{out}}^M={\mathrm{GA}}_F\cos {\varphi }^F\cos \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi \right)+{\mathrm{GA}}_F\sin {\varphi }^F\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi \right)& \left(124\right)\\ {\mathrm{AF}}_{\mathrm{out}}^M=V_0\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+{\varphi }_m+\frac{\pi }{2}-{\varphi }^F\right)& \left(125\right)\end{array}$

[0228] These equations also show that the phases of the AF_out signals output from the two measurement circuits move in different directions for a changing position of the target 5. Therefore, the microcontroller 9 can determine the value of the target position phase (φ^F) from each measurement circuit N and M and, by measuring both the rising zero crossing and the falling zero crossing, the microcontroller 9 can obtain four independent results for the same measurement (φ^F). Of course the microcontroller 9 only needs to use one of these measurements at any given time.

[0229] FIG. 21 is a block diagram illustrating the operation of the phase detector 103_N and the timers 105_1N and 105_2N used to process the AF^N_out signal from measurement circuit N. The components marked with the subscripts _N indicate that the circuit component is associated with measurement circuit N and that a corresponding circuit component (not shown) is provided separately for measurement circuit M. It should be understood that whilst the following description of FIG. 21 concentrates on the processing of the signal AF^N_out, similar processing will be performed on the AF^M_out signal output from the other measurement circuit M. As shown, the AF^N_out signal from measurement circuit N is input to a comparator 113_N where it is compared with the mid-rail voltage (zero level). The digital signal output from the comparator 113 is used to trigger capture/compare timers 115_1N and 115_2N. Both of these capture/compare timers 115_N are reset (for example to zero) on the rising edge of a period_ref control signal that is generated by the excitation and control signal logic 11. The period_ref control signal is periodic having period T_mod and its rising edge is time aligned with the start of the T_mod period. Thus at the start of each T_mod period, the capture/compare timers 115_N are reset and they then start to count up (or down) until they are stopped by the appropriate trigger output from the comparator 113_N. The rising edge of the digital signal output from the comparator 113 stops the capture/compare timer 115_1N and the falling edge of the digital signal output from the comparator 113_N stops the capture/compare timer 115_2N. The numeric values held by the capture/compare timers 115_N are stored in the memory 17_1N (as the above described values φ₁ and φ₂ if the polarity+ modulation signal is being used in the current modulation period or as the above described values φ₃ and φ₄ if the polarity− modulation signal is being used in the current modulation period) and used by the measurement processing circuitry 19 to determine the desired target position information φ^F in the manner described above. The values held by the capture/compare timers 115_N are stored into the memory 17_1N as soon as the capture/compare timer 115_N is stopped by the output of the comparator 113_N. The resolution of such phase detection measurement is determined by the analogue noise and by the number of the counts in the capture/compare timers 115 which correspond to the period of modulation T_mod. Typically the capture/compare timers 115_N will use about 11 bits, but in some embodiments may use more than 15 bits.

[0230] When using the counts that are stored in the memory 17_1N to calculate the target position information φ^F, the counts must first be converted into phases. This is achieved by dividing the stored count value by the number of counts corresponding to the period of modulation T_mod and by multiplying the result by 2π.

[0231] The measurement processing unit 19 uses the last two determined counts (φ_last and φ_last-1) from the timers 115_N that are stored in memory 17_1N to update the phase of the control signal (ADC_triggerN) used to trigger the ADC 13_N to convert the amplitude of the AF^N_out signal. In particular, the last two determined counts stored in memory 17_1N will correspond to a rising edge zero crossing and a falling edge zero crossing. Therefore, the phase half way between these two phases will correspond to the maximum or the minimum of the AF^N_out signal. This is illustrated in FIG. 22, which shows the signal AF^N_out and the measured phases φ₁ and φ₂ that are measured by the timers 115_N. Half way between φ₁ and φ₂ corresponds to the minimum peak amplitude of AF^N_out, which is the optimum time to convert the amplitude of AF^N_out. As can be seen, the control signal ADC_triggerN has its rising edge aligned with the peak of the AF^N_out signal. This is achieved by the measurement processing unit 19 determining the value of shift_ADCN that is used to shift the phase of the timer 105_1N used to generate the ADC_triggerN control signal. As, half way between the last two phase measurements corresponds to the optimum time to trigger the ADC 113N, the measurement processing unit 19 can determine this optimum time from:

$\begin{array}{cc}{\varphi }_{\mathrm{mean}}=\left(\frac{{\varphi }_{\mathrm{last}}+{\varphi }_{\mathrm{last}-1}}{2}\right)& \left(126\right)\\ \mathrm{If}{\varphi }_{\mathrm{mean}}>\pi ,\mathrm{then}{\varphi }_{\mathrm{mean}}={\varphi }_{\mathrm{mean}}-\pi & \left(127\right)\end{array}$

[0232] As the ADC 13_N is arranged to sample the positive peak and the negative peak of AF^N_out, the ADC_triggerN control signal has twice the frequency of the period_ref control signal. Thus, the value of φ_mean is doubled before writing it to the timer 105_1N to reflect the fact that the period of the ADC_triggerN control signal is two times smaller than the period of T_mod:

shift_ADCN=2φ_mean  (128)

[0233] The sampled and ADC converted amplitude values are stored into memory 17_2N. An interrupt at the end of the modulation period T_mod is used for moving available data from memory 17-2N to the measurement processing unit 19. However, a precaution is taken to avoid the situation where the ADC 13_N is triggered just before the end of the modulation period T_mod such that the conversion result is not ready at the end of the modulation period T_mod. Similarly, a precaution is taken to ensure that when the interrupt at the end of the modulation period T_mod forces the measurement processing unit 19 to read the last set of data from the memory 17-2N, the ADC 13_N is not triggered at the very beginning of the next modulation period T_mod. To achieve this, a forbidden band is introduced at the start and end of the modulation period T_mod so that the ADC 13_N is not triggered during the time T_mod*φ_threshold1/2π before the end of the modulation period and also is not triggered during a shorter time T_mod*φ_threshold2/2π just after the start of the next modulation period T_mod. This dead zone with a total width of:

φ_forbidden=φ_threshold1+φ_threshold2  (129)

should be small enough compared to π in order to avoid introducing a significant error in the measurement of the peak-to-peak amplitude performed by the ADC 13_N. For instance, φ_forbidden should be less than 6% of π to provide peak-to-peak amplitude measurements with an error below 2%; φ_forbidden should be less than 4.5% of π to provide peak-to-peak amplitude measurements with an error below 1%. This forbidden zone 121 is illustrated in FIG. 22 and can be defined through the operation of the measurement processing unit 19 when determining shift_ADCN as follows:

If φ_mean<φ_threshold2 then φ_mean=φ_threshold2

If φ_mean>π−½(φ_threshold1−φ_threshold2), then φ_mean=φ_threshold2

If φ_mean>π−φ_threshold1, then φ_mean=π−φ_threshold1  (130)

[0234] The ADC conversion is always triggered two times per modulation period T_mod and by introducing the dead zone (φ_forbidden) for the ADC_triggerN control signal, it can be assured that both data for the minimum and the maximum values of AF^N_out converted by the ADC 13_N are available in the memory 17_2N by the end of the modulation period T_mod. The signal amplitudes converted by the ADC 13_N can be used to identify, in the sequence of phases stored in the memory 17-1N, the set of phases corresponding to the rising zero crossing values (φ1 or φ3) and the set of phases corresponding to the falling zero crossing values (φ2 or φ4). In particular, when the measurement processing unit 19 reads the memories 17_1N and 17_2N at the interrupt aligned with the end of the modulation cycle T_mod, one of the two last phases read by the measurement processing unit 19 from the memory 17_1N will have its phase close to:

φ=φ_mean+π/4  (131)

[0235] This measurement (for instance, the measurement marked as φ₂ in FIG. 22) corresponds to the zero crossing which happens between the two consecutive amplitude measurements which the ADC 13_N converted during the last modulation period T_mod. If the last reading from the ADC 13_N (ADC_last) is larger than the last but one reading (ADC_last-1), then the signal AF^N_out was rising, and thus the measurement point with the value close to φ_mean+π/4 corresponds to the φ1 or φ3 measurement. However, if the last reading by the ADC 13 (ADC_last) is smaller than the last but one reading (ADC_last-1) (as shown in FIG. 22), then the signal AF^N_out was falling, and thus the measurement point with the value close to φ_mean+π/4 corresponds to either the φ2 or φ4 measurement.

The peak-to-peak amplitude of the signal AF^N_out is calculated as follows:

A_F^N=|ADC_last−ADC_last-1|  (132)

[0236] The CALC_trigger control signal interrupts the measurement processing unit 19 and causes it to process the last phase measurement written into memory 17_1N and the last two amplitude measurements written into memory 17_2N. The last two amplitude measurements are processed to update the value of A_F^N and the phase measurement is processed after each zero crossing event (i.e. on the falling and rising edges of the CALC_trigger control signal) in order to update the value of φ^F. As shown in FIGS. 21 and 22, the CALC_trigger control signal is generated by the timer 105_2 and it has the same frequency as the period_ref control signal, but is phase shifted relative to period_ref by a phase shift (shift_CALC). The phase shift is determined by the measurement processing unit 19 to ensure that the rising and falling edges of CALC_trigger occur a short time period after the zero crossing events to be measured. The duration of this short time period is chosen to ensure that there is sufficient time for the measurements to be written into memory 17_N. As discussed above, the subscripts _N shown in FIG. 21 indicate that the circuit component is associated with measurement circuit N and that a corresponding circuit component is provided separately for measurement circuit M. As can be seen, timer 105_2 does not have this subscript—as there is only one CALC_trigger control signal.

[0237] The interrupt at each rising and falling edge of the CALC_trigger signal is used by the measurement processing unit 19 to reload the phase shift values into the timers 105 (shift_CALC into timer 105_2 and shift_ADCN into timer 105_1N (and the corresponding shift_ADCM value into the timer 105_1M used for measurement circuit M)), and then to run the required calculations to update the target position information to the host interface unit 21. When the microcontroller 9 receives an interrupt from the rising edge of the CALC_trigger control signal, it reloads its configuration so that the next interrupt will be triggered by the falling edge of the CALC_trigger control signal. Similarly, when the microcontroller 9 receives an interrupt from the falling edge of the CALC_trigger control signal, it reloads its configuration so that the next interrupt will be triggered by the rising edge of the CALC_trigger control signal. Such an interchanging role of the rising and falling edges of the CALC_trigger control signal, to generate an interrupt event in the microcontroller 9, is important as it allows continuous tuning of the phase of the CALC_trigger control signal without introducing additional false trigger events.

[0238] The CALC_trigger adjustment algorithm uses an additional parameter φ_shift—a small phase shift (equivalent to the above short time period) which provides a safety zone to ensure that the data related to the position of the zero crossing will be available in the memory 17-1N at the moment of the interrupt generated by the corresponding edge of the CALC_trigger control signal. The value of shift_CALC can be calculated as follows:

if φ3>φ4 (or φ1>φ2)

shift_CALC=(φ_last+φ_last-1)/2+π/4+φ_shift  (133)

if φ3<φ4 (or φ1<φ2)

shift_CALC=(φ_last+φ_last-1)/2−π/4+φ_shift  (134)

[0239] FIG. 23 is a timing diagram illustrating the way in which, in this embodiment, the measurement circuitry 25 selects the different detection coils and the reference signal through the two measurement circuits during one detection cycle (T_dc). FIG. 23 also shows many of the different control signals used in this embodiment to control the operation of the sensor electronics. As shown at the bottom of FIG. 23, the detection cycle is split into two parts a first part having three detection intervals Δtk (k=1 to 3); and a second part having three detection intervals Δtk (k=4 to 6). In this embodiment, each detection interval Δtk is formed from four modulation periods T_mod, with the polarity modulation signal being the same at least during the first two modulation periods and during the second two modulation periods. (If desired, each detection interval may have more than four modulation periods.) During the first part of the detection cycle, the in2_M and in3_M selection control signals ensure that the signals from the fine detection coils 6 (corresponding to inputs 1+/1− & 2+/2−) are passed through measurement circuit M and used to update the fine position measurements. (Control signal in1_M and in1_N are not shown in FIG. 23 for clarity due to the time scale of the figure.) FIG. 23 also shows the pol_swM signal used in this embodiment to switch the polarity modulation signal used in measurement circuit M. As shown, during the first part of the detection cycle, the pol_swM signal is always at a low value and therefore the polarity− modulation signal (as shown in FIG. 18) is applied continuously to the selected signals passed through measurement channel M. This is represented by the “−” sign in each box corresponding to measurement circuit M during the first part of the detection cycle. Thus during the first part of the detection cycle, measurement circuit M is only calculating fine position measurements from the determined phase shifts φ3M and φ4M).

[0240] During this first part of the detection cycle, measurement circuit N is configured: i) to obtain measurements of the reference signal during detection interval Δt1—using the polarity+ modulation signal (FIG. 17) and then the polarity− modulation signal (FIG. 18); ii) to obtain measurements from the coarse detection coils 4 during detection interval Δt2—using the polarity+ modulation signal (FIG. 17) and then the polarity− modulation signal (FIG. 18); and iii) to obtain measurements from the fine detection coils 6 during detection interval Δt3—using the polarity+ modulation signal (FIG. 17) and then the polarity− modulation signal (FIG. 18). The pol_swN control signal controls which polarity modulation signal is used in measurement circuit N during each half of each detection interval. The signals measured in the measurement circuit N during the first part of the detection cycle are used to update breakthrough parameters, the coarse position information φ^C_N, and to update the phase offsets φ_fallingN and φ_risingN.

[0241] During the second part of the detection cycle, the roles of the two measurement circuits N and M are reversed, so that during the second part, the in2_N and in3_N selection control signals ensure that the signals from the fine detection coils 6 (corresponding to inputs 1+/1− & 2+/2−) are passed through measurement circuit N and used to update the fine position measurements; and so that measurement circuit M is configured: i) to obtain measurements of the reference signal during detection interval Δt4—using the polarity+ modulation signal (FIG. 17) and then the polarity− modulation signal (FIG. 18); ii) to obtain measurements from the coarse detection coils 4 during detection interval Δt5—using the polarity+ modulation signal (FIG. 17) and then the polarity− modulation signal (FIG. 18); and iii) to obtain measurements from the fine detection coils 6 during detection interval Δt6—using the polarity+ modulation signal (FIG. 17) and then the polarity− modulation signal (FIG. 18). The signals measured in the measurement circuit M during the second part of the detection cycle are used to update breakthrough parameters, the coarse position information φ^C_M, and to update the phase offsets φ_fallingM and φ_risingM.

[0242] Thus as can be seen from the shaded boxes “main data” in FIG. 23, the measurement processing unit 19 will update the fine position information during the first part of the detection cycle using the measurements from measurement circuit M and will update the fine position information during the second part of the detection cycle using the measurements from measurement circuit N. Configuring the two measurement circuits N and M in this way provides the fastest possible update rate of the fine position information to the host interface 21—whilst allowing each measurement circuit M and N to obtain measurements from ancillary channels (such as the reference signal and the coarse detection coils).

[0243] The reason for this is illustrated in FIG. 24 which shows in more detail example signals obtained at the end of detection interval Δt3 and the beginning of detection interval Δt4. As shown in FIG. 23, during the time interval corresponding to i=5, measurement circuit N is arranged to obtain measurements (φ1N and φ2N) from the fine detection coils 6 using the polarity+ modulation signal. Then during the time interval corresponding to i=6, measurement circuit N is arranged to obtain measurements (φ3N and φ4N) from the fine detection coils 6 using the polarity− modulation signal. However, because of the change of the polarity modulation signal that is used, the AF^N_out signal is perturbed just after the transition from i=5 to i=6 (as shown in FIG. 24); and takes a short time to settle to its new cyclic form. As shown in FIG. 24, after the transition from i=5 to i=6, the AF^N_out signal only crosses the zero crossing level once during the first modulation period with the new polarity modulation signal. Therefore, in this embodiment, the measurement processing unit 19 only considers the last two zero crossing events (φ3N and φ4N) of AF^N_out at the end of the time interval corresponding to i=6. In contrast, since the polarity modulation signal used in measurement circuit M does not change during detection interval Δt3, the AF^M_out signal is stable and the measurement processing unit 19 can use all of the detected zero crossing events to update the fine position information for the target 5 during each of the four modulation periods (T_mod) corresponding to detection interval Δt3. The measurement processing unit 19 is triggered to do this using the CALC_trigger control signal that is aligned with the zero crossing events φ3M and φ4M to allow interrupts to the measurement processing unit 19 with relatively low latency to the actual zero crossing events detected in the phase detector 103_M.

[0244] At the start of the next detection interval (Δt4), measurement circuit M is configured for obtaining measurements of the excitation reference signal firstly using the polarity+ modulation signal (during i=7) and then using the polarity− modulation signal (during i=8). Thus at the end of time interval with i=7, the measurement processing unit 19 obtains the last two zero crossing events of AF^M_out to obtain phase measurements for the excitation reference signal φ1^R_M and φ2^R_M; and at the end of time interval with i=8 (which also correspond to the end of detection interval Δt4), the measurement processing unit 19 obtains the last two the zero crossing events of AF^M_out to obtain phase measurements for the excitation reference signal φ3^R_M and φ4^R_M. During detection interval Δt4, the fine position measurements are obtained using measurement circuit N—and so the CALC_trigger control signal is realigned with the zero crossings of AF^N_out. This realignment is achieved using the phase measurements φ3_N and φ4_N obtained at the end of detection interval Δt3 from measurement circuit N.

[0245] As the measurement processing unit 19 reads the measurements from the two measurement circuits at different rates, in this embodiment, two interrupt signals are used to interrupt the measurement processing unit 19 to perform the read operations—the CALC_trigger control signal and the polarity switch control signal (pol_sw).

[0246] The edges of the pol_sw signal are aligned with the edges of consecutive pairs of modulation periods T_mod. The interrupt started by either the rising or the falling edge of the pol_sw control signal is used to move the last two phase measurements and the last two amplitude measurements from the memories 17-1 and 17-2 (associated with the measurement circuit N or M in which the ancillary measurements are currently being made) to the measurement processing unit 19. This interrupt generated by the pol_sw control signal has the highest priority of all other interrupts and so can interrupt active calculations in the measurement processing unit 19 or even the process of moving data from another measurement circuit (started by the CALC_trigger interrupt signal). The measurement processing unit uses the last two phase measurements to update the optimum timing for sampling the amplitude of the incoming signal in that time interval—which it stores in memory for use in the next detection cycle; and then loads a new value into shift_ADCN for use in controlling when the ADC 13_N will make the amplitude measurements during the next time interval. Of course, the same value of shift_ADCN used in the current time interval cannot be used again in the next time interval because the phase of the incoming signal will be very different (due to the use of a different polarity modulation signal and in some cases because the signal being measured is different).

[0247] For example, in FIG. 24, at the boundary between intervals marked as i=5 and i=6, the measurement processing unit 19 will read the last two phase measurements stored in memory 17-1N and the last two amplitude measurements stored in memory 17-2N. The measurement processing unit 19 uses the two phase measurements to determine the optimum timing for ADC converting the signal during the time interval corresponding to i=5 which it stores as shift_ADC5 for use in the next detection cycle. The measurement processing unit 19 then retrieves the value of shift_ADC6 that was calculated at the end of the time interval corresponding to i=6 in the previous detection cycle T_dc. However, the signal that is being processed by measurement circuit N in the time interval corresponding to i=6 is the signal from the fine detection coils (see FIG. 23) and so its phase may have changed since the last detection cycle. Therefore, the measurement processing unit 19 determines the value of shift_ADCN to be used during the time interval corresponding to i=6 in the current detection cycle also taking into account the difference between the fine phase measurement value (φ^F_Mend6) recorded at the end of the time interval with i=6 in the previous detection cycle using the data from the other measurement circuit (i.e. from measurement circuit M) and the latest fine phase measurement (φ^F_M) determined using the data also from measurement circuit M obtained at the end of the time interval with i=5 of the current detection cycle (φ^F_Mend5) In particular, the following shift value is calculated:

shift_ADCN=shift_ADC6+(φ^F_Mend5−φ^F_Mend6)  (135)

[0248] In the more general form we can write:

shift_ADCN=shift_ADC_i−(φ^F_Mendi-1−φ^F_Mendi)  (136)

when the value shift_ADCN is updated for channel N utilizing the polarity+ modulation signal; and:

shift_ADCN=shift_ADC_i+(φ^F_Mendi-1−φ^F_Mendi)  (137)

when the value shift_ADCN is updated for channel N utilizing the polarity− modulation signal. The generalized form takes into account the fact that the phases φ2 and φ1 are moving in the opposite direction compared to φ^F (see FIG. 19a and FIG. 19c) which accounts for the opposite sign in the calculation.

[0249] Similarly, when measurement circuit M is processing the ancillary data (during detection intervals Δt4, Δt5 and Δt6), the measurement processing unit 19 determines the value of shift_ADCM to write into the timer 105_1M as follows:

shift_ADCM=shift_ADC_i+(φ^F_Nendi-1−φ^F_Nendi)  (138)

when the value shift_ADCM is updated for channel M utilizing the polarity+ modulation signal; and:

shift_ADCM=shift_ADC_i−(φ^F_Nendi-1−φ^F_Nendi)  (139)

when the value shift_ADCN is updated for channel M utilizing the polarity− modulation signal. In this case, φ^F_Nendi-1 is the fine phase measurement obtained using the data from measurement circuit N during the previous time interval (i−1); and φ^F_Nendi is the fine phase measurement obtained using the data from measurement circuit N during the time interval i in the current detection cycle. The change of the sign of the correction applied to shift_ADCM compared to shift_ADCN is related to the different direction of movement of φ1M and φ2M in measurement circuit M compared to the direction of movement of φ1N and φ2N in measurement circuit N.

[0250] Such new values of shift_ADC are also corrected to keep the forbidden zone for ADC triggering very near the boundaries of adjacent modulation periods T_mod as described above.

[0251] After storing the value φ_endi=φ^F and writing the value shift_ADCN in the timer 105_1N or shift_ADCM in the timer 105_1M (depending on which measurement circuit is involved in the ancillary measurements) the measurement processing unit 19 sets a flag which identifies the need to carry out processing of the new ancillary data. Such calculations have the lowest priority and are performed after the calculations (that are performed in response to the interrupt caused by the CALC_trigger control signal), release the required resources of the microcontroller 9.

[0252] A more detailed description of the processing performed by the measurement processing unit 19 will now be given for the different time intervals illustrated in FIG. 23. As discussed above, during detection intervals Δt1, Δt2, and Δt3 the measurement circuit N is used in the ancillary measurement mode.

At pol_sw Interrupt between i=12 and i=1:

[0253] At this interrupt, the measurement circuit N selects the reference signal to be measured and the polarity+ modulation signal is selected. At this interrupt, the value of shift_ADC12 is updated and stored in memory 17 for use in the next detection cycle (in the manner described above). At this interrupt the phase value of φ^F_N calculated with the data measured in the measurement circuit N during the time interval with index i=12 is stored as:

φ^F_Nend12=φ^F_N  (140)

Then shift_ADCN is updated in the timer 105_1N by using the parameter shift_ADCN1 (which is the value of shift_ADCN calculated at the end of the processing of the data obtained in detection interval Δt1 during the previous detection cycle) that is stored in the memory 17:

shift_ADCN=shift_ADC1  (141)

Note that in this case as the signal that is being measured in this time interval (i=1) is the excitation reference signal, its value does not change with the position of the target and therefore, there is no need to consider changes to the phase of the measured signal from one detection cycle to the next.
At pol_sw Interrupt between i=1 and i=2:

[0254] At this interrupt, the measurement circuit N selects the reference signal (on inputs 5+/5−) and uses the polarity− modulation signal. At this interrupt the data measured during the time interval with the index i=1 are moved from the memories 17_1N and 17_2N into the measurement processing unit 19 and then the value of shift_ADCN is updated in the timer 105_1N by using the parameter shift_ADC2 (which is the value of shift_ADCN calculated at the end of the processing of the data obtained in time interval with i=2 during the previous detection cycle) that is stored in the memory 17:

shift_ADCN=shift_ADC2  (142)

At pol_sw Interrupt between i=2 and i=3:

[0255] At this interrupt, the measurement circuit N selects the coarse detection coils 4 (inputs 3+/3− and 4+/4−) and uses the polarity+ modulation signal. At this interrupt the data measured during the time interval with index i=2 are moved from the memories 17_1N and 17_2N and the value of φ^F_M calculated with the data φ3M or φ4M measured by the measurement circuit M during time interval with index i=2 is stored as:

φ^F_Mend2=φ^F_M  (143)

[0256] Then the value of shift_ADCN is updated in timer 105_1N by using the parameter shift_ADC3 that was stored in memory 17 during the previous detection cycle:

shift_ADCN=shift_ADC3−(φ^F_Mend2−φ^F_Mend3)/NP  (144)

As can be seen from this calculation, the measurement processing unit 19 adjusts the value of shift_ADCN value calculated using data measured in the previous detection cycle using the change in the measured fine phase between the corresponding point in time of the previous detection cycle and the latest fine phase measurement obtained from the measurement circuit M. As measurement circuit N will be measuring the coarse phase during the time interval corresponding to i=3, the change in the fine phase is scaled down by the value NP, which equals the number of periods of the fine detection coils 6 in one period of the coarse detection coils 4.

[0257] After updating the shift_ADCN value at the boundary between time intervals with i=2 and i=3, the measurement processing unit 19 sets a flag to identify that the data measured for the excitation reference signal during detection interval Δt1 are ready for further processing. The measurement processing unit 19 then returns back from the pol_sw interrupt to continue with other tasks related to serving interrupts with a lower priority introduced by the CALC_trigger control signal, which is used in order to process the φ3M or φ4M data measured during the First part of the detection cycle by the measurement circuit M. After the end of each interrupt induced by the edges of the CALC_trigger control signal, the measurement processing unit 19 checks whether the flag for the further processing of the ancillary measurement data is set. If the flag is set, the measurement processing unit 19 starts the further processing of the stored ancillary data and after the further processing is finished, it clears the value of the flag.

Further Processing of Ancillary Data obtained during detection interval Δt1

[0258] During the further processing of the ancillary data obtained during detection interval Δt1, the new best value for the shift_ADCN is calculated using values of φ1N and φ2N detected during the time interval with index i=1 and the parameter shift_ADC1 is updated and saved to the operation memory 17_N. Then the new best value for the shift_ADCN is calculated using values of φ3N and φ4N detected during the time interval with index i=2 and the parameter shift_ADC2 is updated and saved to the operation memory 17_N. The data for φ^N_rising and φ^N_falling are updated and if necessary averaged together with the previous data for detection interval Δt1 from the previous detection cycle T_dc. Then the value of φ_N^Ref is calculated and compared with the value of π/4. Indeed, when the reference signal is being switched through the measurement circuit N or M, it is only the reference signal that is being switched through the demodulating switch 56 and so the value of φ_N^Ref is given by:

$\begin{array}{cc}{\varphi }_N^{\mathrm{Re}f}=\arctan \left(\frac{V_M^{\mathrm{Re}f}}{V_M^{\mathrm{Re}f}}\right)=\frac{\pi }{4}& \left(145\right)\end{array}$

[0259] If a substantial deviation from the value of π/4 is found, the measurement processing unit 19 outputs an error message to the host interface 21 and stops updating the fine phase measurements to the host interface 21 until the next detection cycle when this error is cleared if the measurement returns back to being close to π/4. At the end of this data processing, the last two amplitude values obtained from ADC 13_N (ADC_last and ADC_last-1) during each of the time intervals with i=1 and i=2 are used to calculate the average value of the peak-to-peak reference amplitude (V^EX).

At pol_sw Interrupt between i=3 and i=4:

[0260] At this interrupt, the measurement circuit N starts mixing the signals from the coarse detection coils (on inputs 3+/3− and 4+/4−) using the polarity− modulation signal. At this interrupt the data measured during the time interval with index i=3 are moved from the memory 17_1N and 17_2N and the value of φ^F_M calculated with the data φ3M or φ4M measured in the measurement circuit M during time interval with i=3 is stored as:

φ^F_Mend3=φ^F_M  (146)

Then the value of shift_ADCN is updated in timer 105_1N by using the parameter shift_ADC4 stored in the memory:

shift_ADCN=shift_ADC4+(φ^F_Mend3−φ^F_Mend4)/NP  (147)

At pol_sw Interrupt between i=4 and i=5:

[0261] At this interrupt, the measurement circuit N starts mixing the signals from the fine detection coils (on inputs 1+/1− and 2+/2−) using the polarity+ modulation signal. At this interrupt the data measured during the time interval with the index i=4 are moved from the memory 17_1N and 17_2N and the value of φ^F_M calculated with the data φ3M or φ4M measured in the measurement circuit M during time interval with i=4 is stored as:

φ^F_Mend4=φ^F_M  (148)

Then the value shift_ADCN is updated in the timer 105_1N by using the parameter shift_ADC5 stored in the memory:

shift_ADCN=shift_ADC5−(φ^F_Mend4−φ^F_Mend5)  (149)

[0262] After updating the shift_ADCN value, the measurement processing unit 19 sets the flag to indicate that the data measured for the coarse scale channels during the detection interval Δt2 are ready for further processing. The measurement processing unit 19 then returns back from the pol_sw interrupt to continue with other tasks related to serving interrupts with a lower priority introduced by the CALC_trigger control signal, which is used in order to process the φ3M or φ4M data measured during the First part of the detection cycle in the measurement circuit M. After the end of each interrupt induced by the edges of the CALC_trigger control signal, the measurement processing unit 19 checks whether the flag for the further processing of the ancillary measurement data is set. If the flag is set, the measurement processing unit 19 starts the further processing of the ancillary data and after the processing is finished, it clears the value of the flag.

[0263] During the further processing of the ancillary data obtained during detection interval Δt2 the new best value for the shift_ADCN is calculated using values of φ1N and φ2N detected during the time interval with index i=3 and the parameter shift_ADC3 is updated and saved to the operation memory 17. Then the new best value for the shift_ADCN is calculated using values of φ3N and φ4N detected during the time interval with index i=4 and the parameter shift_ADC4 is updated and saved to the operation memory 17. The data for φ^N_rising and φ^N_falling are updated and if necessary averaged together with the previous data for the time interval Δt2 from previous detection periods T_dc. Then the coarse target position information (φ^C) is calculated using the φ3N and the φ4N phase measurements obtained during time interval i=4. The last two amplitude measurements from the ADC 13_N (ADC^N_last and ADC^N_last-1) obtained for each time interval with i=3 and i=4 are used to calculate the average value of the peak-to-peak amplitude of AF^N_out when the coarse detection coils are selected (A_C^N). The obtained values are then used to correct the coarse phase measurements for breakthrough offset and to update the coarse position measurement of the target 5 relative to the coarse detection coils 4 and, together with the latest fine position measurement (φ^F_M), confirm the current absolute position of the target 5.

At Pol_sw Interrupt Between i=5 and i=6:

[0264] At this interrupt, the measurement circuit N starts mixing the signals from the fine detection coils (on inputs 1+/1− and 2+/2−) using the polarity− modulation signal. At this interrupt the data measured during the time interval with index i=5 are moved from the memory 17-1N and 17_2N and the value of φ^F_M calculated with the data φ3M or φ4M measured in the measurement circuit M during time interval with i=5 is stored as:

φ^F_Mend5=φ^F_M  (150)

[0265] Then the value shift_ADCN is updated in timer 105_1N by using the parameter shift_ADC6 stored in the memory:

shift_ADCN=shift_ADC6+(φ^F_Mend5−φ^F_Mend6)  (151)

At Pol_sw Interrupt Between i=6 and i=7

[0266] At this interrupt, the measurement circuit N continues mixing the signals from the fine detection coils (on inputs 1+/1− and 2+/2−) again using the polarity− modulation signal. At this interrupt the data measured during the time interval with the index i=6 are moved from the memory 17-1N and 17_2N and the value of φ^F_M calculated with the data φ3M or φ4M measured in the measurement circuit M during time interval with i=6 is stored as:

φ^F_Mend6=φ^F_M  (152)

As discussed above, in detection interval Δt4, measurement circuit M starts to obtain the ancillary measurements and measurement circuit N starts to obtain the fine position measurements. Therefore, at this time point, the measurement processing unit 19 updates the value of shift_ADCM applied to timer 105_1M by using the parameter shift_ADC7 stored in the memory.

shift_ADCM=shift_ADC7  (153)

[0267] Again as measurement circuit M will measure the excitation reference signal during the time interval corresponding to i=7, the phase of the incoming signal will not have changed with the position of the target 5 and so, at this point, there is no need to modify shift_ADCM to account for movement of the target. After updating the shift_ADCM value, the measurement processing unit 19 sets the flag to identify that the data measured from the fine detection coils by measurement circuit N during the detection interval Δt3 are ready for the further processing.

[0268] During this interrupt, as a result of the switch over of the roles of the two measurement circuits, an additional adjustment of the shift_CALC parameter is made to align the edges of the CAL_trigger control signal near (just after) the zero crossing events of the AF^N_out signal obtained from measurement circuit N. Indeed, in order to lock the CALC_trigger control signal to the zero events in the measurement circuitry N, the timer 105_2 has to be reloaded with a new value of shift_CALC calculated from the phase data φ3N and φ4N measured during the time interval with index i=6 that have just been read from the memory 17-1N into the measurement processing unit 19 at the pol_sw signal interrupt event. As a result of this change to the CALC_trigger control signal, it will jump and thus an additional edge can be introduced in the CALC_trigger control signal at this particular moment in time. In order to ignore any such extra edge of the CALC_trigger control signal, the interrupt events associated with the edges of the CALC_trigger control signal are disabled during the reloading of the timer 105_2 and are then enabled again once the timer 105_2 has been reloaded.

[0269] The measurement processing unit 19 then returns back from the pol_sw interrupt to continue with other tasks related to serving interrupts with a lower priority introduced by the CALC_trigger control signal, which from this time interval (until the end of the detection cycle) will now be used in order to process the φ3N or φ4N data obtained from measurement circuit N during the Second part of the detection cycle T_dc. As discussed above, after the end of each interrupt caused by the CALC_trigger control signal, the measurement processing unit 19 checks whether the flag for the further processing of the ancillary measurement data is set. If the flag is set, the measurement processing unit 19 starts the further processing of the ancillary data and after the processing is finished, it clears the value of the flag.

[0270] During the further processing of the ancillary data obtained during detection interval Δt3, the new best value for shift_ADCN is calculated using the values of φ1N and φ2N detected during the time interval with index i=5 and the parameter shift_ADC5 is updated and saved to the operation memory 17. Then the new best value for the shift_ADCN is calculated using the values of φ3N and φ4N detected during the time interval with index i=6 and the parameter shift_ADC6 is updated and saved to the operation memory 17. The data for φ^N_rising and φ^N_falling are updated and if necessary averaged together with previous data obtained for time interval Δt3 from previous detection periods T_dc. The last two amplitude measurements from the ADC 13_N (ADC^N_last and ADC^N_last-1) obtained in each of the time intervals with i=5 and i=6 are used to calculate the average value of the peak-to-peak amplitude of AF^N_out when the fine detection coils are selected (A_F^N).

[0271] After switching over between measurement circuits N and M for fine position measurements, the procedure discussed above for obtaining and processing the ancillary data is repeated for measurement circuit M with a shift of the index i by 6 positions (index i=1 is replaced with index i=7, index i=2 is replaced with an index i=8, etc.). All dynamic corrections described above for the value of the shift_ADCN are applied with an opposite sign to the shift_ADCM, reflecting the fact that the zero crossing values φ1N, φ2N are moving in the opposite direction to the φ1M, φ2M values with the change of target position, and the zero crossing values φ3N, φ4N are moving in the opposite direction to the φ3M, φ4M with the change of target position.

[0272] As discussed above, the CALC_trigger control signal interrupts the measurement processing unit 19 and causes it to process the last phase measurement written into memory 17_1 and the last two amplitude measurements written into memory 17_2. The last two amplitude measurements are processed to update the peak to peak measure of the AF_out signal value of (A_F^N or A_F^M) and the phase measurement is processed after each zero crossing event (i.e. on the falling and rising edges of the CALC_trigger control signal) in order to update the value of φ^F. During the first part of the detection cycle, the measurement processing unit 19 uses the signals from measurement circuit M to update the phase and amplitude measures (φ^F_M and A_F^M); and during the second part of the detection cycle, the measurement processing unit 19 uses the signals from measurement circuit N to update the phase and amplitude measures (φ^F_N and A_F^N). In the first part of the detection cycle the phase of the CALC_trigger control signal and the phase of the ADC_triggerM signal are constantly fine tuned after each interrupt generated by the CALC_trigger control signal. The fine position information φ^F_M is then recalculated to an absolute position of the target 5 using various adjustments including applying look-up table corrections, and by shifting the fine position measurement in accordance with the latest coarse position measurement. In the second part of the detection cycle the phase of the CALC_trigger control signal and the phase of the ADC_triggerN signal are constantly fine tuned after each interrupt generated by the CALC_trigger control signal. The fine position information φ^F_N is then recalculated to an absolute position of the target 5.

[0273] During the transition from continuous measurement of φ3M and φ4M in measurement circuit M to the same type of continuous measurement of φ3N and φ4N in measurement circuit N, the update events to the host interface, which are typically separated by about half of the modulation period T_mod, might experience a jump by about ±half of the modulation period T_mod. So, while the system on average will provide a small latency which is not going to be affected by the switching between measurement circuits N and M, the actual update events are affected and might show a sudden slip in the update time between adjacent measurements. For some switching events the separation between them can become close to zero instead of (T_mod)/2, and for other switching events the separation between adjacent update events can become as large as T_mod instead of (T_mod)/2. All other update events will be spaced equidistantly by about (T_mod)/2.

[0274] Most ratiometric sensors work on the assumption that the detection coils are well balanced with respect to the excitation coil—so that there is no coupling between them. In such ratiometric sensors the signals generated in the detection coils are mainly caused by the presence of the moving target 5 and therefore the accurate position of the target 5 can be obtained from two ratiometric channels if they show different dependencies of the induced signals against the actual position of the target. In real systems, however, the strength of the signal induced by the target 5 in the detection coils can be relatively small, so that even a small amount of direct breakthrough from the excitation coil can affect the accuracy of the ratiometric output. It is desirable to provide a sensor that has the capability to correct, in software, the output of the ratiometric sensor to account for the breakthrough between the excitation coil and the detection coil in order to improve the accuracy achievable by the sensor. Such breakthrough correction was described above in the first embodiment and a similar breakthrough correction is performed in this embodiment.

[0275] The correction of the data measured by the sensor can be achieved if the breakthrough offset coefficients are measured in a separate calibration step and stored in the memory 29 of the microcontroller 9. Below we show the required calculations which can be used to correct the raw measured data for the breakthrough offset from the excitation coil using calibrated coefficients O^FS and O^FC describing the breakthrough offset signal in the fine sine detection coil 6-1 and in the fine cosine detection coil 6-2 respectively. From equations (3), (4) and (6) above, the amplitude of the signals induced in each fine detection coil 6 by the target 5 is ideally given by:

V^FS=A_F sin(φ^F)  (154)

V^FC=A_F cos(φ^F)  (155)

However, the actual voltages that are measured contain both the desired signal due to the position of the target 5 in close proximity to the fine detection coils 6 as well as the direct breakthrough offset signal from the excitation coil 2; and can therefore be corrected by using:

V^FS_corr=A_F sin(φ^F)−O^FS×V^EX  (156)

V^FC_corr=A^F cos(φ^F)−O^FS×V^EX  (157)

where V^EX—is the peak-to-peak amplitude of the AF_out signal obtained when the reference signal is selected by the multiplexer 57 in the measurement circuit 51 (detection interval Δt1 for measurement circuit N and detection interval Δt4 for measurement circuit M). Thus, the breakthrough corrected fine position of the target 5 can be determined from:

$\begin{array}{cc}{\varphi }_{\mathrm{corr}}^F=\arctan \left(\frac{V_{\mathrm{corr}}^{\mathrm{FS}}}{V_{\mathrm{corr}}^{\mathrm{FC}}}\right)=\arctan \left(\frac{\left(\sin \left({\varphi }^F\right)-\frac{O^{\mathrm{FS}}\times V^{\mathrm{EX}}}{A_F}\right)}{\left(\cos \left({\varphi }^F\right)-\frac{O^{\mathrm{FC}}\times V^{\mathrm{EX}}}{A_F}\right)}\right)& \left(158\right)\end{array}$

Where φ^F is the raw fine position measurement obtained by processing the phases determined from the timers 115 (shown in FIG. 21), OFS and OFC are the stored calibration breakthrough offset coefficients 29, V^EX is the current value of the peak-to-peak amplitude of the reference signal, and A_F is the peak-to-peak amplitude of the signals used to determine φ^F. Similar breakthrough corrections can be performed on the coarse position measurements using coarse breakthrough offsets O^CS and O^CC.

[0276] The above formula (equation 158) for the corrected value of φ^F_corr has two correction terms which are proportional to the ratio between V^EX and A_F and thus the correction for breakthrough offset is independent of the actual gain of the measurement circuit N or M as well as the exact phase tuning of the demodulation performed by the demodulating switch 56. What is important is that both peak-to-peak amplitudes V^EX and A_F have been measured via the same analogue measurement circuitry 25 and have been converted using the same ADC 13. In this fifth embodiment, this is achieved by measuring the reference signal, which is a fraction of the excitation voltage, through each of the two measurement circuits N and M which are also used to measure the signals from the fine sine and the fine cosine detection coils 6 and the signals from the coarse sine and the coarse cosine detection coils 4.

[0277] In order to speed-up calculations in the microcontroller 9 for the purpose of calculations of sine, cosine, and arc-tangent functions, a set of look-up tables can be used. The size of the required memory 29 for such look-up tables is not excessive because only a 45 degree look-up table section is required for the arc-tangent calculations and only a 90 degree look-up table section is required for calculations of both sine and cosine functions.

[0278] It is also worth noting that the measured amplitude V^EX is equal to:

V^EX=√{square root over (2)}×V₀^Ref  (159)

[0279] The coefficient √{square root over (2)} is related to the fact that when the reference signal is selected by the multiplexor 57, the excitation reference signal is applied to both inputs of the demodulating switch 56 and therefore the composite signal obtained during the reference channel measurement can be represented as:

$\begin{array}{cc}V=V^{\mathrm{Re}f}\sin \left[\frac{2\pi }{T_{\mathrm{mod}}}\right]t+V^{\mathrm{Re}f}\cos \left[\frac{2\pi }{T_{\mathrm{mod}}}\right]t=\sqrt{2}V^{\mathrm{Re}f}\sin \left(\left[\frac{2\pi }{T_{\mathrm{mod}}}\right]t+\frac{\pi }{4}\right)& \left(160\right)\end{array}$

After the amplification and filtering circuitry 83 the signal in the measurement circuit becomes equal to:

$\begin{array}{cc}{\mathrm{AF}}_{\mathrm{out}}=\mathrm{Gain}\times \sqrt{2}V^{\mathrm{Re}f}\sin \left(\left[\frac{2\pi }{T_{\mathrm{mod}}}\right]t+\frac{\pi }{4}+\varphi \right)=\sqrt{2}V_0^{\mathrm{Re}f}\sin \left(\left[\frac{2\pi }{T_{\mathrm{mod}}}\right]t+\frac{\pi }{4}+\varphi \right)& \left(161\right)\end{array}$

[0280] Thus, the coefficients O^FS and O^FC can be written in terms of the breakthrough between the excitation coil 2 and the corresponding sine and cosine detection coil as follows:

$\begin{array}{cc}{O}^{\mathrm{FS}}=\frac{B^{\mathrm{FS}}}{\sqrt{2}V_0^{\mathrm{Re}f}}& \left(162\right)\\ O^{\mathrm{FC}}=\frac{B^{\mathrm{FC}}}{\sqrt{2}V_0^{\mathrm{Re}f}}& \left(163\right)\end{array}$

Similarly for the coarse breakthrough offset coefficients:

$\begin{array}{cc}{O}^{\mathrm{CS}}=\frac{B^{\mathrm{CS}}}{\sqrt{2}V_0^{\mathrm{Re}f}}& \left(164\right)\\ O^{\mathrm{CC}}=\frac{B^{\mathrm{CC}}}{\sqrt{2}V_0^{\mathrm{Re}f}}& \left(165\right)\end{array}$

[0281] Before breakthrough corrections can be applied, a calibration mode must be performed to determine the values of the coefficients O^FS, O^FC, O^CS and O^CC. This can be achieved by physically removing the target 5 from the vicinity of the detection coils 4, 6 and then measuring the signal induced in the fine sine and the fine cosine coils 6 when the excitation signal is applied to the excitation coil 2 (and similarly by measuring the signal induced in the coarse sine and the coarse cosine detection coils 4 when the excitation signal is applied to the excitation coil 2). Such measurements can be performed during production of the sensor or after the sensor has been installed in the final application.

[0282] Unfortunately, it is not practical to mix the B^FS and the B^FC (or the B^CS and the B^CC) signals together through the measurement circuits N or M as such signals are typically relatively small and the composite signal created by mixing these signals through the measurement circuit 51 will result in an AC amplitude of AF_out that is too small to be detected by the comparator 113 of the phase detector 103 (shown in FIG. 21). The ratiometric electronics of this embodiment, however, will work well if each of the breakthrough signals is intermixed with a relatively large signal such as the reference signal. Thus, by intermixing each breakthrough signal (on input 1+/1− or 2+/2−) with the reference signal (from input 5+/5−), it is possible to measure the ratiometric value of B^FS/V^ref₀ and B^FC/V^ref₀ with good resolution and accuracy.

[0283] FIG. 25 is a timing diagram illustrating the control signals used to select the different inputs to be intermixed by the demodulating switch 56 during this breakthrough calibration mode. As shown, during the first detection interval Δt1 the signal from the fine sine detection coil and the reference signal (inputs 1+/1− and 5+/5−) are selected simultaneously in measurement circuits N and M. In the first half of the detection interval Δt1 the intermixing in the measurement circuit N and in measurement circuit M is performed using the polarity+ modulation signal. FIG. 26 shows the time line for the time division multiplexing of these two signals into the measurement circuits N and M during one modulation period of the first half of the detection interval. As can be seen, while both input signals are intermixed in measurement circuits N and M, there are no collisions when both measurement circuits N and M are selecting the same input signal at exactly the same moment in time. This is achieved by using the opposite polarity for the in3_N and in3_M control signals. By comparing FIGS. 26 and 20, it can be seen that the same waveform used for the control signals in1_N and in1_M in the main measurement mode presented in the FIG. 20 is used now for the control signals in3_N and in3_M in this calibration mode. As a result of this time division multiplexing, when the signal from the fine sine detection coil is selected by the measurement circuit N, the reference signal is selected in the same moment in time by measurement circuit M, and vice versa.

[0284] As a result of intermixing the breakthrough signal and the reference signal in this particular manner, the φ_N value measured using the data from measurement circuit N can then be related to the desired ratio of the breakthrough signal to the reference signal as follows:

$\begin{array}{cc}\frac{B_N^{\mathrm{FS}}}{V_{0N}^{\mathrm{Re}f}}=\tan \left({\varphi }_N\right)& \left(166\right)\end{array}$

And the φ_M value measured using the data from measurement circuit M can be related to the desired ratio of the breakthrough signal to the reference signal as follows:

$\begin{array}{cc}\frac{B_M^{\mathrm{FS}}}{V_{0M}^{\mathrm{Re}f}}=\tan \left(\frac{\pi }{2}-{\varphi }_M\right)& \left(167\right)\end{array}$

[0285] However, as explained above, the phase measurements obtained by the timers 115 include a phase shift introduced by the measurement circuitry 25 and so phase measurements obtained when the polarity− modulation signal is applied must also be obtained and combined with those obtained when the polarity+ modulation signal is used, in order to determine φ_N and φ_M. As shown in FIG. 25, in the next half of detection interval Δt1 the intermixing in measurement circuits N and M is performed using the polarity− modulation signal. Therefore the phase measurements obtained during detection interval Δt1 can be used to determine φ_N and φ_M, from which the above ratios can be calculated.

[0286] In the next detection interval Δt2 the same measurements are obtained in respect of the signal from the fine cosine detection coil and the reference signal (inputs 2+/2− and 5+/5−) to allow calculation of:

$\begin{array}{cc}\frac{B_N^{\mathrm{FC}}}{V_{0N}^{\mathrm{Re}f}}=\tan \left({\varphi }_N\right)& \left(168\right)\\ \frac{B_M^{\mathrm{FC}}}{V_{0M}^{\mathrm{Re}f}}=\tan \left(\frac{\pi }{2}-{\varphi }_M\right)& \left(169\right)\end{array}$

[0287] In the next detection interval Δt3 the same measurements are obtained in respect of the signal from the coarse sine detection coil and the reference signal (inputs 3+/3− and 5+/5−) to allow calculation of:

$\begin{array}{cc}\frac{B_N^{\mathrm{CS}}}{V_{0N}^{\mathrm{Re}f}}=\tan \left({\varphi }_N\right)& \left(170\right)\\ \frac{B_M^{\mathrm{CS}}}{V_{0M}^{\mathrm{Re}f}}=\tan \left(\frac{\pi }{2}-{\varphi }_M\right)& \left(171\right)\end{array}$

[0288] In the final detection interval Δt4 the same measurements are obtained in respect of the signal from the coarse sine detection coil and the reference signal (inputs 4+/4− and 5+/5−) to allow calculation of:

$\begin{array}{cc}\frac{B_N^{\mathrm{CC}}}{V_{0N}^{\mathrm{Re}f}}=\tan \left({\varphi }_N\right)& \left(172\right)\\ \frac{B_M^{\mathrm{CC}}}{V_{0M}^{\mathrm{Re}f}}=\tan \left(\frac{\pi }{2}-{\varphi }_M\right)& \left(173\right)\end{array}$

[0289] Such measurements are continuously obtained whilst the sensor is in the breakthrough offset measurement mode and a running average of each of the above ratios is determined to reduce the noise in the actual measurements. Once the breakthrough offset measurement mode is stopped, the set of calibration coefficients:

$\begin{array}{cc}\begin{array}{cc}{O}_N^{\mathrm{FS}}=\frac{1}{\sqrt{2}}\frac{B_N^{\mathrm{FS}}}{V_{0N}^{\mathrm{Re}f}}& O_M^{\mathrm{FS}}=\frac{1}{\sqrt{2}}\frac{B_M^{\mathrm{FS}}}{V_{0M}^{\mathrm{Re}f}}\\ O_N^{\mathrm{FC}}=\frac{1}{\sqrt{2}}\frac{B_N^{\mathrm{FC}}}{V_{0N}^{\mathrm{Re}f}}& O_M^{\mathrm{FC}}=\frac{1}{\sqrt{2}}\frac{B_M^{\mathrm{FC}}}{V_{0M}^{\mathrm{Re}f}}\\ O_N^{\mathrm{CS}}=\frac{1}{\sqrt{2}}\frac{B_N^{\mathrm{CS}}}{V_{0N}^{\mathrm{Re}f}}& O_M^{\mathrm{CS}}=\frac{1}{\sqrt{2}}\frac{B_M^{\mathrm{CS}}}{V_{0M}^{\mathrm{Re}f}}\\ O_N^{\mathrm{CC}}=\frac{1}{\sqrt{2}}\frac{B_N^{\mathrm{CC}}}{V_{0N}^{\mathrm{Re}f}}& O_M^{\mathrm{CC}}=\frac{1}{\sqrt{2}}\frac{B_M^{\mathrm{CC}}}{V_{0M}^{\mathrm{Re}f}}\end{array}& \left(174\right)\end{array}$

is calculated and stored in the non-volatile memory of the microcontroller 9 as the breakthrough calibration data 29.

[0290] This calibration data 29 is then used in the main measurement mode illustrated in the FIG. 23 for correcting the raw data measured in the presence of the target 5 in order to reduce the breakthrough error and therefore improve the accuracy of the ratiometric sensor output.

[0291] Like in the first embodiment, some of the measurements obtained in this embodiment combine phases measured in different time intervals—for example, combining the phase measurements obtained when the polarity+ modulation signal is used with the corresponding phase measurements obtained when the polarity− modulation signal is used. As a result, if the target 5 is moving, then this will introduce errors into the measurements that are obtained. As can be seen from FIG. 23, this is only a problem for the ancillary measurements that are being calculated using data from measurement circuit N during detection intervals Δt1, Δt2 and Δt3 and for the ancillary measurements that are being calculated using data from measurement circuit M during detection intervals Δt4, Δt5 and Δt6. The other measurements (fine position measurements) are calculated using instantaneous data for either φ3 or φ4—and so they are not subject to this movement error. The error to the final answer φ^F is determined mainly by the dynamic error in the value of φ_rising and φ_falling calculated from the ancillary measurement data. To calculate a measure of the speed of the target 5, we can look at how much the measured (raw) phases change during one time interval. For example, referring to FIG. 24, during the time interval corresponding to i=6, the timers 115_M will measure four phases—φ3M and φ4M in each of the two modulation periods corresponding to this time interval. If we label these measurements: φM_previous, φ4M_previous, φ3M_new and φ4M_new, then we can calculate a change in measured phase between φ3M_previous and φ3M_new and a change in measured phase between φ4M_previous and φ4M_new as follows:

Δφ3M=φ3M_new−φ3M_previous  (175)

Δφ4M=φ4M_new−φ4M_previous  (176)

[0292] Both of these phase differences represent the change in position of the target 5 over one modulation period (T_mod). In most cases φ3M_previous and φ3M_new should be relatively close together and therefore this change in phase should be relatively small. However, it is possible that, φ3M_previous is determined to be close to zero and that φ3M_new is close to 2π and vice versa. This is similarly true for φ4M_previous and φ4M_new. This is not because the target 5 has moved by a whole period of the fine detection coils (L_F in FIG. 2), but because the measured phases are bound between zero and 2π and so when the phase is measured close to the value 2π, the next phase measurement may well result in a jump back to a phase close to zero. This can be compensated as follows:

If Δφ3M>π, then Δφ3M=Δφ3M−2π

If Δφ3M<−π, then Δφ3M=Δφ3M+2π  (177)

[0293] Similarly for Δφ4M:

If Δφ4M>π, then Δφ4M=Δφ4M−2π

If Δφ4M<−π, then Δφ4M=Δφ4M+2π  (178)

We can then work out an average change in measured phase during one modulation period as:

$\begin{array}{cc}{\mathrm{\Delta \varphi }}_{\mathrm{mean}}=\frac{\left(\mathrm{\Delta \varphi }3M+\mathrm{\Delta \varphi }4M\right)}{2}& \left(179\right)\end{array}$

Therefore the rate of change of the measured phase (which is a measure of the speed of the target 5) can be calculated as:

$\begin{array}{cc}s=\frac{\left({\mathrm{\Delta \varphi }}_{\mathrm{mean}}\right)}{2\pi }& \left(180\right)\end{array}$

[0294] This speed parameter can be updated each time zero crossing measurements are made. As the fine position is being updated about twice every modulation period, the position of the target 5 will change by about π*s between each measurement.

[0295] We can also obtain a measure of the acceleration of the target 5 by considering the change of speed between adjacent updates as follows:

$\begin{array}{cc}\mathrm{Acc}=\frac{\left(s_{\mathrm{new}}-s_{\mathrm{previous}}\right)}{\pi }& \left(181\right)\end{array}$

[0296] The acceleration value (Acc) can also be averaged between several updates of the speed to reduce the noise. In this embodiment the speed and acceleration parameters are measured and continuously updated using the measurements from the measurement circuit N or M that is currently being used for fine position measurements. These values are then used to compensate the measurements made by the other measurement circuit M or N—i.e. to compensate the measurements being made by the measurement circuit that is currently in the “auxiliary” mode. For example, during detection interval Δt3, measurement circuit N is in the auxiliary mode and the signals from the fine detection coils 6 are selected by measurement circuit N and the polarity modulation signal is switched between polarity+ and polarity− so that the phase offsets φ_falling and φ_rising can be updated for subsequent use in calculating fine position information using the measurements from measurement circuit N during detection intervals Δt4, Δt5 and Δt6.

[0297] As shown in FIG. 24, in this embodiment the polarity+ modulation signal is applied first during the time interval corresponding to i=5 and then the polarity− modulation signal is applied during time interval i=6. In this embodiment, each time interval corresponds to two modulation periods, but in the general case each time interval may correspond to 1+L modulation periods (where L is a non-zero integer). As discussed above, when processing the data from the measurement circuit that is currently in the “ancillary” mode of operation, the measurement processing unit 19 only processes the last two zero crossing events obtained at the end of each time interval. Therefore, the measurement circuit N will obtain phase values φ1N and φ2N at the end of time interval corresponding to i=5; and will obtain phase values φ3N and φ4N at the end of time interval corresponding to i=6. The zero crossing measurements of φ3N and φ4N have been obtained in a period of modulation that is not immediately adjacent the period of modulation from which the phase measurements φ1N and φ2N have been obtained. In the general case when there are 1+L modulation periods in each time interval (i) the zero crossing measurements for φ1N and φ3N are separated in time by:

$\begin{array}{cc}\Delta T_{\mathrm{rising}}=\left(1+L\right)T_{\mathrm{mod}}-\left(\frac{\varphi 1N-\varphi 3N}{2\pi }\right)T_{\mathrm{mod}}& \left(182\right)\end{array}$

Or, writing this in terms of a phase:

Δφ^T_rising=(1+L)2π−φ1N+φ3N  (183)

[0298] However, the measurement processing unit 19 should also take into account the possibility that the zero crossing corresponding to φ1N does not occur in the last period of the time interval corresponding to i=5 and/or the possibility that the zero crossing corresponding to φ3N does not occur in the last period of the time interval corresponding to i=6. If this happens, then the above formula for the separation between the φ1N and φ3N phase measurements becomes incorrect. This is possible because when the target 5 is moving quickly the period of the signal AF^N_out will deviate from the modulation period (T_mod). Recall that during the time interval when the polarity+ modulation signal is applied to the demodulation switch 56, AF^N_out is given by:

$\begin{array}{cc}{\mathrm{AF}}_{\mathrm{out}}=V_0\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi +{\varphi }^F\right)& \left(184\right)\end{array}$

and during the time interval when the polarity− modulation signal is applied to the demodulation switch 56, AF^N_out is given by:

$\begin{array}{cc}{\mathrm{AF}}_{\mathrm{out}}=V_0\sin \left(\left(\frac{2\pi }{T_{\mathrm{mod}}}\right)t+\varphi -{\varphi }^F\right)& \left(185\right)\end{array}$

[0299] Therefore, if φ^F is changing with time, then depending on the direction of the target movement, the actual period of AF^N_out can become slightly shorter than T_mod or slightly longer than T_mod. For instance, when the period of AF^N_out is slightly shorter than T_mod when the polarity+ modulation signal is applied, then the period of AF^N_out becomes slightly longer than T_mod when the polarity− modulation signal is applied. Similarly, when the period of AF^N_out is slightly longer than T_mod when the polarity+ modulation signal is applied, then the period of AF^N_out becomes slightly shorter than T_mod when the polarity− modulation signal is applied. When the period of AF^N_out is slightly longer than T_mod, only one zero crossing might be detected during the last period of the interval (i) if the phases of AF^N_out and the modulation period become nearly aligned to each other.

[0300] The measurement processing unit 19 can detect when this happens and make the appropriate corrections. In particular, as discussed above, the phase measurements obtained by the timers 115_N are written into memory 17_1N in the order in which they are measured and when processing the measurements, the measurement processing unit 19 retrieves the last two phase measurements from the memory 17_1N. Under normal circumstances, the first phase measurement will be smaller than the second phase measurement (as both are counted from the start of the modulation period). However, if the second phase measurement is smaller than the first phase measurement, then this means that the first (larger) phase measurement was recorded in the last but one modulation period. For instance this can happen if this second (larger) phase measurement is very close to 2π in the last but one modulation period and so was not detected as a small value close to zero in the next modulation period. A similar analysis is performed for the sequence of φ3N and φ4N measurements written in to memory 17_1N to determine if the zero crossing corresponding to φ3N measurement does not occur in the last period of the time interval corresponding to i=6.

[0301] If the measurement processing unit 19 determines that last value for φ1N is detected in the last but one modulation period, then the formula for determining the separation between the zero crossing measurements for φ1N and φ3N, should be modified to:

Δφ^T_rising=(2+L)2π−φ1N+φ3N  (186)

[0302] Similarly, if the measurement processing unit 19 determines that last value for φ3N is detected in the last but one modulation period, then the formula for determining the separation between the zero crossing measurements for φ1N and φ3N, should be modified to:

Δφ^T_rising=L×2π−φ1N+φ3N  (187)

[0303] If the measurement processing unit 19 determines that both the last value for φ1N and φ3N are detected in the last but one modulation period, then the formula for determining the separation between the zero crossing measurements for φ1N and φ3N, should remain as originally defined:

Δφ^T_rising=(1+L)2π−φ1N+φ3N  (188)

[0304] Whatever value of Δφ^T_rising is determined, it can then be used to determine the actual change of the target position between the zero crossing corresponding to the last value of φ1N and the zero crossing corresponding to the last value of φ3N from:

Δφ_rising^F=(s−½Acc×Δφ^T_rising)×Δφ^T_rising  (189)

where s and Acc are the speed and acceleration values determined using the data from the other measurement circuit (in this case measurement circuit M). This value can then be used to correct for changing values of φ^F_N that are used to determine φ^N_rising Recall that:

φ1N=2π−φ^N_rising−φ_N^F  (190)

and

φ3N=φ_N^F−φ^N_rising  (191)

[0305] Therefore, to account for the delay in the measurement of φ3N compared to the measurement of φ1N, this becomes:

φ1N=2π−φ^N_rising−φ_N^F  (192)

and

φ3N=φ_N^F+Δφ_rising^F)−φ^N_rising  (193)

[0306] However, there is a further complication the inventors have found that the value of φ_rising when the polarity+ modulation signal is used is not the same as φ_rising when the polarity− modulation signal is used. This is because, as explained above, the apparent frequency of the AF^N_out signal in both cases will be slightly different; and the phase shift introduced by the amplification and filtering circuitry 83 will depend on the frequency. More specifically, as the frequency of AF^N_out increases the phase shift reduces and as the frequency of AF^N_out reduces the phase shift increases. Consequently, this dependence near the working frequency ω₀ corresponding to the period of modulation T_mod can be expressed using the dimensionless parameter:

$\begin{array}{cc}q=-\frac{\left(\frac{\mathrm{\Delta \varphi }}{\pi }\right)}{\Delta \frac{\omega }{{\omega }_0}}& \left(194\right)\end{array}$

[0307] In typical electronic circuits this parameter q will be close to the value of one and is related to the effective quality factor (Q) of the filters designed for the amplification and filtering circuitry 83. This parameter q can be calculated exactly for a given design of the amplification and filtering circuit 83 or measured experimentally.

[0308] Therefore, assuming that the target 5 is moving with constant speed, we can define the corresponding target phase shift (φ^F(t)) as:

$\begin{array}{cc}{\varphi }_N^F\left(t\right)={\varphi }_{0,N}^F+s\times \left(\frac{2\pi t}{T_{\mathrm{mod}}}\right)={\varphi }_{0,N}^F+s\times {\omega }_0t& \left(195\right)\end{array}$