DETERMINATION OF AXIAL AND ROTARY POSITION OF A BODY

Abstract

A sensor device for determining an axial position of a body (10) along a longitudinal axis (A) comprises an excitation coil (23) that extends around the longitudinal axis, one or more first detection coils (21) arranged in the vicinity of the excitation coil in a first detection plane (P1), and one or more second detection coils (22) arranged in the vicinity of the excitation coil in a second detection plane (P2). Excitation circuitry supplies the excitation coil (23) with current at an excitation frequency to create an excitation magnetic field distribution. Detection circuitry determines the axial position of the body based on signals from the first and second detection coils at the excitation frequency. The detection circuitry bases the determination of the axial position on at least one difference between the signals from the first detection coils and the signals from the second detection coils. A rotary position of the body can be determined by detecting a stray magnetic field of a magnet carried by the body, using at least two magnetic field sensors (24). The magnetic field sensors are arranged on a common printed circuit board (25) with the excitation and detection coils.

Claims

1. A sensor device for determining an axial position of a body along a longitudinal axis, the sensor device comprising: at least one excitation coil that extends around the longitudinal axis; at least one first detection coil arranged in the vicinity of the excitation coil essentially in a first detection plane perpendicular to the longitudinal axis; at least one second detection coil arranged in the vicinity of the excitation coil essentially in a second detection plane perpendicular to the longitudinal axis, the second detection plane being arranged at an axial distance to the first detection plane; excitation circuitry configured to supply the excitation coil with current at an excitation frequency to create an excitation magnetic field distribution; and detection circuitry configured to determine the axial position of the body based on at least one difference between signals from the first and second detection coils at the excitation frequency.

2. The sensor device of claim 1, comprising a plurality of first detection coils arranged essentially in the first detection plane at a plurality of different angular positions around the longitudinal axis, and a plurality of second detection coils arranged essentially in the second detection plane perpendicular to the longitudinal axis at a plurality of different angular positions around the longitudinal axis.

3. The sensor device of claim 2, wherein the detection circuitry is configured to determine, in addition to the axial position of the body, at least one of the following: a radial position of the body along at least one radial direction, based on at least one sum of signals that are detected by the first detection coils and signals that are detected by the second detection coils; and a tilt position of the body around at least one radial tilt axis, based on comparing at least two differences between signals that are detected by the first detection coils and signals that are detected by the second detection coils, each difference being formed from signals for a different angular position around the longitudinal axis.

4. The sensor device of claim 1, wherein the excitation coil is arranged essentially in an excitation plane extending perpendicular to the longitudinal axis and being arranged between the first and second detection planes.

5. The sensor device of claim 1, further comprising an electrically conductive target on the body, the target having, on its outer circumference, a radial dimension that varies along the longitudinal axis, wherein the excitation coil and the target are configured and arranged in such a manner that the excitation magnetic field distribution excites eddy currents in the target, the eddy currents essentially preventing the excitation magnetic field distribution from entering the target.

6. The sensor device of claim 5, comprises a radially protruding ring on a circumferential surface of the body or an annular notch in the circumferential surface, the ring or notch extending around the longitudinal axis.

7. The sensor device of claim 5, wherein the target is not ferromagnetic.

8. The sensor device of claim 1, wherein the excitation frequency is in the range from 100 kHz to 100 MHz.

9. The sensor device of claim 1, wherein the excitation coil and the first and second detection coils are printed coils formed on at least one printed circuit board.

10. The sensor device of claim 9, further comprising at least one magnetic field sensor, the at least one magnetic field sensor being arranged on the at least one printed circuit board at different angular positions around the longitudinal axis, the at least one magnetic field sensor being configured to detect a stray magnetic field of a magnet carried by the body; wherein the detection circuitry is configured to operate the at least one magnetic field sensor to determine a rotary position of the body around the longitudinal axis, based on signals from the at least one magnetic field sensor.

11. A sensor device for determining positions of a body along multiple degrees of freedom, the body defining a longitudinal axis, the sensor device comprising: at least one printed circuit board; at least one excitation coil that extends around the longitudinal axis; a plurality of detection coils arranged in the vicinity of the excitation coil, the excitation and detection coils being formed as printed coils on the at least one printed circuit board; excitation circuitry configured to supply the excitation coil with current at an excitation frequency to create an excitation magnetic field distribution; at least one magnetic field sensor, the at least one magnetic field sensor being arranged on the at least one printed circuit board together with the excitation coil and/or detection coils, the at least one magnetic field sensor being configured to detect a stray magnetic field of a magnet carried by the body and detection circuitry configured to determine at least one of an axial position, a radial position and a tilt position of the body, based on signals received from the detection coils at the excitation frequency, and to determine a rotary position of the body around the longitudinal axis, based on signals from the at least one magnetic field sensor.

12. The sensor device of claim 11, wherein each magnetic field sensor is arranged at an angular position that is located between adjacent detection coils.

13. The sensor device of claim 11, wherein the at least one magnetic field sensor has an operating bandwidth that is below the excitation frequency of the excitation magnetic field distribution; and/or wherein the detection circuitry comprises at least one frequency filter for filtering out the excitation frequency from the signals detected by the at least one magnetic field sensor.

14. A method of determining an axial position of a body along a longitudinal axis, the method comprising: arranging at least one excitation coil around the body, the excitation coil extending around the longitudinal axis; arranging at least one first detection coil in the vicinity of the excitation coil essentially in a first detection plane perpendicular to the longitudinal axis; arranging at least one second detection coil in the vicinity of the excitation coil essentially in a second detection plane perpendicular to the longitudinal axis, the second detection plane being arranged at an axial distance to the first detection plane; supplying the excitation coil with current at an excitation frequency to create an excitation magnetic field distribution; and determining the axial position of the body based on at least one difference between signals that are detected by the at least one first detection coil and signals that are detected by the at least one second detection coil.

15. A method of determining positions of a body along multiple degrees of freedom, the body defining a longitudinal axis, the method comprising: arranging at least one excitation coil around the body, the excitation coil extending around the longitudinal axis; arranging a plurality of detection coils in the vicinity of the excitation coil, the excitation and detection coils being formed as printed coils on a common printed circuit board; supplying the excitation coil with current at an excitation frequency to create an excitation magnetic field distribution; determining at least one of an axial position, a radial position and a tilt position of the body, based on signals received from the detection coils at the excitation frequency; detecting a stray magnetic field of a magnet carried by the body using at least two magnetic field sensors, the magnetic field sensors being arranged on the printed circuit board at different angular positions around the longitudinal axis; and determining a rotary position of the body around the longitudinal axis, based on the stray magnetic field.

16. The sensor device of claim 1, comprising a plurality of third detection coils arranged in the vicinity of the excitation coil at a plurality of different angular positions around the longitudinal axis.

17. The sensor device of claim 16, wherein the detection circuitry is configured to determine, in addition to the axial position of the body, a radial position of the body along at least one radial direction based on the signals that are detected by the third detection coils.

18. The sensor device of claim 1, wherein the excitation coil comprises first and second windings, the first winding being arranged essentially in the first detection plane, and the second winding being arranged essentially in the second detection plane.

19. The sensor device of claim 4, wherein the excitation plane is arranged equidistantly from the first and second detection planes.

20. The sensor device of claim 5, wherein the excitation coil and the first and second detection coils, in a projection along the longitudinal direction, do not overlap with those portions of the target in which the eddy currents are excited.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Preferred embodiments of the invention are described in the following with reference to the drawings, which are for the purpose of illustrating the present preferred embodiments of the invention and not for the purpose of limiting the same. In the drawings,

[0060] FIG. 1 shows, in a highly schematic manner, parts of a rotary electric machine that comprises a sensor device according to an embodiment of the invention in a perspective view;

[0061] FIG. 2 shows, in a highly schematic manner, a central longitudinal section through a sensor device according to the first embodiment;

[0062] FIG. 3 shows, in a highly schematic manner, a central longitudinal section through a sensor device according to a second embodiment;

[0063] FIG. 4 shows, in a highly schematic manner, a central longitudinal section through a sensor device according to a third embodiment;

[0064] FIG. 5 shows, in a highly schematic manner, a top view of a sensor device according to the second embodiment;

[0065] FIG. 6 shows, in a highly schematic manner, a top view of a sensor device according to a fourth embodiment; and

[0066] FIG. 7 shows an exemplary block diagram of excitation and detection circuitry, illustrating operation of a sensor according to the present invention.

DESCRIPTION OF PREFERRED EMBODIMENTS

[0067] FIG. 1 shows, in a highly schematic manner, parts of a rotary electric machine that comprises a sensor device according to an embodiment of the invention. It is to be understood that FIG. 1 is not to scale.

[0068] The rotary electric machine comprises a rotor body 10. The rotor body 10 is supported in a stator (not shown) for rotation about a rotation axis A, corresponding to a longitudinal axis of the rotor body 10. The rotor body 10 is supported in the stator by bearings (not shown). The bearings can be magnetic bearings, in particular, active magnetic bearings.

[0069] A permanent magnet 11 having a north pole N and a south pole S is mounted on the rotor body 10 for interaction with stator windings (not shown) on the stator. The stator windings and the permanent magnet 11 together form an electric motor or generator. The direction of magnetization of the permanent magnet 11 is transverse to the rotation axis A.

[0070] The following directions are defined in FIG. 1: The Z direction designates the nominal direction of the rotation axis A, i.e., the rotation axis A extends along the Z direction in an equilibrium position of the rotor body 10. Deviations of the rotation axis A from the Z direction are called a “tilt” of the rotor body 10. In the present example, the Z direction is a vertical direction; however, the Z direction can have arbitrary orientation in space. The X and Y directions are called radial directions. In the present example, they are horizontal directions. The X, Y and Z directions are mutually perpendicular. The rotary position of the rotor about the A axis is designated as the rotation angle φ.

[0071] The rotary machine comprises a sensor device 20 for determining the radial, axial, tilt and rotary positions of the rotor body relative to the stator at the location of the sensor device. The sensor device 20 comprises a multi-layer printed circuit board (PCB) 25. The printed circuit board 25 has annular shape, defining a central opening. The rotor 10 passes through the opening. Instead of a single printed circuit board, it is also conceivable that a stack of two or more separate printed circuit boards is provided, and that the printed circuit boards in the stack are connected together and optionally axially spaced by spacers.

[0072] The printed circuit board 25 carries a plurality of kidney-shaped first detection coils 21. In the present example, there are four first detection coils 21. However, in other embodiments, there can also be three, five, six or more first detection coils. The first detection coils 21 are arranged essentially in a common first detection plane. They can be formed, e.g., in a top layer of the printed circuit board 25 or in two or more of the topmost layers. Each first detection coil 21 does not enclose the rotor body 10. The first detection coils 21 are arranged at different angular positions along the circumference of the rotor body 10, preferably at equal angular distances from one another. While in the present example adjacent first detection coils do not overlap in the angular direction, it is also possible that there is some degree of overlap in this direction. In this case adjacent first detection coils would have to be provided in different layers. If these layers are sufficiently closely spaced, the first detection coils can still be considered to be disposed essentially in a common first detection plane.

[0073] The printed circuit board 25 furthermore carries a plurality of second detection coils, which are disposed essentially in a second detection plane at an axial distance below the first detection plane. For instance, the second detection coils can be disposed in a bottom layer of the printed circuit board 25 or in two or more of the bottommost layers. The second detection coils are not visible in FIG. 1. The second detection coils are of similar configuration and are similarly arranged as the first detection coils 21. There is exactly one second detection coil in the second detection plane for each first detection coil 21 in the first detection plane. In a projection along the Z axis, each second detection coil in the second detection plane is essentially congruent with its corresponding first detection coil 21 in the first detection plane. In other words, the sensor device 20 comprises a plurality of pairs of mutually congruent first and second detection coils in two different detection planes. In the present example, there are four such pairs.

[0074] The printed circuit board 25 also carries an excitation coil. In the present example, the excitation coil is disposed in one or more central layers of the printed circuit board 25 between the first and second detection planes and is not visible in FIG. 1. The excitation coil extends around the rotor body 10, i.e., its turns encircle the rotation axis A.

[0075] Finally, the printed circuit board 25 carries a plurality of magnetic field sensors 24. In the present example, the magnetic field sensors 24 are disposed on the top layer of the printed circuit board 25 in which also turns of the first detection coils 21 are formed; however, it is also conceivable to dispose the magnetic field sensors 24 on the bottom layer of the printed circuit board 25. The magnetic field sensors 24 are arranged at different positions and preferably at equal angular distances along the circumference of the rotor 10. In the present example, there are four such magnetic field sensors 24. Each magnetic field sensor 24 is arranged between two adjacent first detection coils 21 along the circumference of the rotor 10.

[0076] On its circumferential surface, the rotor body 10 carries a target ring 12 of electrically conductive, non-ferromagnetic material, e.g., made of copper or aluminum. The target ring 12 forms a target for the excitation and detection coils of the sensor device 20. The target ring 12 may be made separately from the rotor body 10, or it may be an integral part of the rotor body 10. In the latter case the entire rotor body would be electrically conductive. Instead of being ring-shaped, the target can have a different shape; in particular, it can be disk-shaped. The target ring 12 is disposed radially inside the central opening of the printed circuit board 25. An annular radial gap 13 is present between the target ring 12 and the inner circumference of the annular printed circuit board 25. The target ring 12 is axially spaced from the permanent magnet 11.

[0077] Processing circuitry 30 is connected to the excitation coil, to the detection coils, and to the magnetic field sensors. Operation of the processing circuitry will be discussed in more detail below.

[0078] A possible arrangement of the excitation coil and the detection coils will now be described with reference to FIG. 2.

[0079] In FIG. 2, the printed circuit board 25 defines three different planes. Each of these planes extends perpendicular to the Z direction. The first detection coils 21 are arranged in a first detection plane P1. The second detection coils 22 are arranged in a second detection plane P2. The first and second detection planes P1, P2 are axially spaced by a non-zero distance D. The excitation coil 23 is arranged in an excitation plane PE. The excitation plane is axially located in the center between the detection planes P1 and P2. The excitation coil 23 overlaps with the first and second detection coils 21, 22 in a projection along the Z axis. In this example, additional third detection coils 26 are arranged in the excitation plane PE radially outside from the excitation coil. The purpose of the additional coils will be explained further below.

[0080] The excitation and detection planes do not necessarily coincide with a particular conductive layer of the printed circuit board. If each of the excitation and/or detection coils has turns in more two or more adjacent conductive layers, each of the planes PE, P1 and P2 may be defined by two or more such adjacent layers of the printed circuit board, e.g., the first detection plane P1 may be defined by the two uppermost layers of the printed circuit board and in this case may be considered to be located between these two layers.

[0081] The target ring 12 has a length L along the rotational direction A that essentially corresponds to the distance D between the first and second detection planes P1, P2 along the Z direction. At its outer circumference, the target ring 12 has two oppositely oriented circumferential edge structures: A first (upper) circumferential edge 15 is present where the outer circumferential surface of the target ring 12 meets the upper axial end face of the target ring 12. A second (lower) circumferential edge 16 is present where the outer circumferential surface of the target ring 12 meets the lower axial end face of the target ring 12. These edges have opposite orientations along the rotation axis A.

[0082] In operation, the processing circuitry 30 supplies the excitation coil with a high-frequency current at an excitation frequency, which is typically in the range of 100 kHz to 100 MHz.

[0083] The current creates a high-frequency excitation magnetic field distribution. The magnetic field distribution excites eddy currents in the target ring. The eddy currents prevent the magnetic field distribution from entering the bulk of the target ring. This leads to a concentration of the magnetic field distribution in the radial gap 13 between the excitation coil 23 and the circumferential surface of the target ring 12.

[0084] Radial displacements of the rotor body 10 along some radial direction decrease the gap size on one radial side and increase the gap size on the opposite radial side of the target ring 12. This leads to a displacement of the magnetic field distribution in a direction opposite to the direction of movement of the target ring 12. As a result, the first and second detection coils 21, 22 on the one radial side receive a smaller signal than the first and second detection coils 21, 22 on the other radial side. The radial displacement can be determined based on this difference.

[0085] Axial displacements of the rotor body 10 change the axial position of the target ring 12 inside the printed circuit board 25. An upward displacement of the rotor body 10 along the positive Z direction causes the target ring 12 to move upward as well. Thereby the lower circumferential edge 16 moves up to an axial position between the detection planes P1 and P2, while the upper circumferential edge 15 moves up to an axial position that is above the first (upper) detection plane P1. Thereby the magnetic field distribution will change, such that the magnetic field at the position of any one of the first (upper) detection coils 21 will be different from the magnetic field at the position of the corresponding second (lower) detection coil 22. The overall axial displacement of the rotor body 10 can be determined based on this signal difference. In particular, the difference can be summed up over all pairs of detection coils along the circumference of the target ring 12.

[0086] Tilt displacements of the rotor body 10 can be determined by comparing the signal difference of a pair of detection coils on one radial side of the rotor body to the signal difference of a pair of detection coils on the opposite radial side.

[0087] FIG. 3 illustrates a second embodiment. The excitation coil 23 has two windings 231, 232. The first winding 231 is disposed in the first detection plane P1, radially inside of the first detection coils 21. The second winding 232 is disposed in the second detection plane P2, radially inside of the second detection coils 22. The windings 231, 232 have the same numbers of turns. They are connected in series.

[0088] FIG. 4 illustrates a third embodiment. The excitation and detection coils are arranged as in the first embodiment. However, instead of a target ring 12, a notch 14 is provided in the rotor body 10. The portion of the rotor body 10 that is near the notch 14 forms the target for the excitation and detection coils. In the equilibrium position of FIG. 4, the magnetic field distribution will be concentrated in the notch 14. When the rotor body 10 is displaced, the magnetic field distribution will move together with the rotor body. This again will lead to different signals in the first and second detection coils 21, 22.

[0089] In all these embodiments, instead of using the first and second detection coils 21, 22 for detecting both radial and axial displacements, third detection coils 26 can be used for detecting radial displacements, while the first and second detection coils 21, 22 are used only for detecting axial displacements and possibly tilt displacements. This may simplify signal processing. In particular, each pair of first and second detection coils 21, 22 may be directly connected in an anti-series configuration to directly obtain a difference signal from each pair without the need of electronics for forming such differences.

[0090] Instead of providing a plurality of first detection coils 21 distributed along the circumference of the excitation coil 23 and corresponding second detection coils 22, it is also possible to provide just a single first detection coil 21 and a single second detection coil 22, each of these coils extending around the longitudinal axis A (or, equivalently, around the body 10). These two coils may be connected in an anti-series configuration to directly obtain a difference signal from these coils. The axial position of the body 10 can be determined in this manner in a particularly simple manner. In this case, third detection coils 26 arranged at different positions along the circumference of the excitation coil can be provided for determining radial displacements of the body.

[0091] Of course, many other configurations of the excitation and detection coils are possible. Likewise, many other configurations of the target are possible. For instance, the target does not necessarily need to have sharp edge structures.

[0092] FIG. 5 illustrates the arrangement of the excitation and detection coils and of the magnetic field sensors according to the second embodiment in a view from above onto the first detection plane P1. Four first detection coils 21a, 21b, 21c and 21d are evenly distributed over the circumference of the target ring 12 in the first detection plane P1. Below each first detection coil, a corresponding congruent second detection coil is arranged in the second detection plane P2. Radially offset from the detection coils towards the rotation axis A, the upper winding 231 of the excitation coil 231 is visible. The magnetic field sensors 24 are disposed between adjacent first detection coils 21a-21d along the circumference of the excitation coil 23.

[0093] In this embodiment, the detection of radial, axial and tilt displacements can be exemplified as follows: For detecting radial displacements, the signals received from each first detection coil 21a, 21b, 21c and 21d and the corresponding second detection coil are added. This results in four sum signals Σa, Σb, Σc, and Σd, one sum signal for each pair of first and second detection coils. Radial displacements along the X direction are determined based on the difference Sx=Σa−Σc between such sum signals, while radial displacements along the Y direction are determined based on the difference Sy=Σb−Σd.

[0094] For detecting axial displacements, the signals received from each pair of first and second detection coils are subtracted. This results in four difference signals Δa, Δb, Δc, and Δd, one difference signal for each pair. Axial displacements of the rotor body 10 are determined based on the sum Sz=Δa+Δb+Δc+Δd of these difference signals.

[0095] Tilt displacements in the X-Z plane are determined based on the difference Tx=Δa−Δc between the difference signals on opposite sides of the rotor body along the X direction. Likewise, tilt displacements in the Y-Z plane are determined based on the difference Ty=Δb−Δd between the difference signals on opposite sides of the rotor body along the Y direction.

[0096] A determination of tilt displacements can be carried out with particularly high sensitivity if the diameter of the target is large compared to the axial distance D of the detection planes P1 and P2, as it is often the case with so-called disk rotors. For instance, if the diameter of the target is 10 cm, a tilt by 1° about the center of the target ring 12 will cause an axial displacement of the outer circumference at one radial side of the target ring 12 by approximately 0.9 mm and an axial displacement of equal magnitude, but different direction at the opposite radial side, which is readily detectable if the detection planes P1, P2 are spaced by not more than a few millimeters. Preferably the ratio of the diameter of the target to the axial distance between the first and second detection planes P1, P2 is at least 5, in particular at least 10, more preferably at least 20.

[0097] The magnetic field sensors 24 are operated independently of the excitation and detection coils. These sensors detect the stray magnetic field from the magnet 11 of the motor or generator. In the example of FIG. 5, four magnetic field sensor signals are obtained. The signals from each pair of diametrically opposed magnetic field sensors may be subtracted to minimize the influence of radial displacements of the rotor body 10. This results in two difference signals along two mutually orthogonal directions, from which the rotary position of the rotor body 10 can be readily determined using methods well known in the art.

[0098] FIG. 6 illustrates a fourth embodiment, in which only three first detection coils 21, three second detection coils 22 (not visible in FIG. 6) and three magnetic field sensors 24 are provided. Again, sums and differences of the signals from each pair of first and second detection coils 21, 22 are formed. By forming appropriately weighted linear combinations of these sums and differences, it is readily possible to again determine radial, axial and tilt displacements of the rotor body in the same spirit as explained in conjunction with FIG. 5. By forming linear combinations of the signals of the three magnetic field sensors, signals along two mutually orthogonal directions are obtained. The rotary position of the rotor body 10 can be readily determined from these signals.

[0099] It is also possible to provide only two magnetic field sensors at two different angular positions at an angular distance that is different from 180°, or even only a single multi-axis magnetic field sensor. In this case, the signals from the magnetic field sensors will be influenced by radial displacements of the rotor body 10, and the influence cannot be compensated by forming linear combinations any more. However, this influence can still be corrected based on the radial displacement signals obtained from the detection coils 21, 22 and/or 26.

[0100] FIG. 7 illustrates a possible embodiment of the processing circuitry 30. In this embodiment, the processing circuitry comprises excitation circuitry 31 and detection circuitry 32. The excitation circuitry 31 comprises an oscillator that supplies a high-frequency current to the excitation coil 23 at the excitation frequency. Voltages are induced in first and second detection coils 21, 22. The detection circuitry comprises a subtractor 33 that subtracts the voltage signals received from the first and second detection coils 21, 22 from one another, followed by a bandpass filter 34 having a center frequency at the excitation frequency to filter out any undesired disturbances. The output from the bandpass filter is fed to a demodulator/ADC 35 that demodulates the high-frequency signal to obtain a low-frequency signal that is a measure of the amplitude of the output from subtractor 33 at the excitation frequency. This signal is digitized and outputted. The output is indicative of an axial displacement of a target portion near the pair of detection coils 21, 22. Similarly, an adder 36 adds the voltage signals received from the first and second detection coils 21, 22. The output from the adder is again passed through a bandpass filter 37 and demodulated and digitized in a demodulator/ADC 38. The output is indicative of a radial position of a target portion near the pair of detection coils 21, 22. Only one pair of detection coils with the corresponding processing circuitry is shown in FIG. 7. The processing circuitry for the other pairs of detections coils is identical. The outputs of the processing circuitry for the different pairs of detection coils can then be combined and subjected to further treatment in software.

[0101] The signals from each magnetic field sensor 24 are passed through a low pass filter 39 having a cutoff frequency well below the excitation frequency and digitized in an ADC. From the output, the rotary position of the rotor body 10 can be determined. Since the bandwidth of the circuitry for determining the stray magnetic field of magnet 11 is far below the excitation frequency for the excitation and detection coils, there is negligible cross talk between the corresponding signal pathways.

[0102] It is to be understood that FIG. 7 is provided only by way of example, and that the excitation and detection circuitry can be configured in many different manners. For instance, the signal from each detection coil can be processed and digitized separately, and all further processing can be carried out fully digitally. In other embodiments, further sums and differences can be formed by analog hardware before digitization of the signals. In yet other embodiments, the detection coils can even be hardwired in a configuration that directly provides the desired sums or differences.

[0103] Many other modifications can be made without leaving the scope of the present invention.

TABLE-US-00001 LIST OF REFERENCE SIGNS 10 rotor body 11 permanent magnet 12 target ring 13 radial gap 14 notch 15 circumferential edge 16 circumferential edge 20 sensor device 21 first detection coil 21a-21d first detection coil 22 second detection coil 23 excitation coil 231 first winding 232 second winding 24 magnetic field sensor 25 printed circuit board 26 third detection coil 30 processing circuitry 31 excitation circuitry 32 detection circuitry 33 subtractor 34 bandpass filter 35 demodulator/ADC 36 adder 37 bandpass filter 38 demodulator/ADC 39 lowpass filter/ADC A rotation axis Z axial direction X, Y radial directions P1 first detection plane P2 second detection plane PE excitation plane D axial distance L length of target ring N north pole S south pole