Device and method for determining the angle of a rotating shaft

Abstract

The invention relates to a device and a method for determining the angle of a rotating shaft. The device (100) comprises a permanent magnet (104) fixed on the shaft (102) and at least two magnetic sensor arrangements (110A; 110B) which are arranged with an angular offset in relation to a pole pair and which generate a differential output signal. A further device (200) comprises at least three magnetic field sensors (210) which are arranged at an equidistant angular distance, wherein an evaluation unit (220) derives a sine signal and a cosine signal by means of a transformation and calculates therefrom an angle information. Furthermore, an angle measuring system (300) and a corresponding computer program product are proposed.

Description

Technical Field

[0001] The present invention relates to an apparatus and method for determining the angle of a rotating shaft, and more particularly to an angle measuring system arranged outside the shaft (OoS). Background Technology

[0002] Off-axis angle measurement systems can be used to measure the angular position of rotating shafts, especially when the ends of the shaft are inaccessible. Existing technologies include magnetic rotary transformers and inductive sensors, which can be used, for example, in the automotive industry. In magnetic rotary transformers, a paramagnetic ring is fixed to the shaft in a specific manner and rotates within the space of a structural assembly consisting of two coil groups, requiring precise positioning. However, these systems can lead to corresponding installation and maintenance costs due to the necessary precise orientation of the components. Inductive systems, which can consist of multilayer circuit boards with coils and conductive rotors, also require precise orientation and a certain minimum size, which can increase structural space and associated costs. Another disadvantage is that rotary transformers and inductive systems are sensitive to mechanical tolerances, which can affect the accuracy of angle measurements.

[0003] Therefore, there is a need for a system that overcomes these limitations and enables accurate angle measurement with minimal space requirements and lower cost, while also providing high resistance to external disturbances such as stray fields. Summary of the Invention

[0004] This requirement is met by the apparatus and method according to the invention. Advantageous improvements are available from the description.

[0005] According to a first aspect of the invention, an apparatus for determining the angle of a rotation axis is provided. The apparatus includes a permanent magnet fixed to the rotation axis having at least one pair of magnetic poles and at least two mutually spaced magnetic sensor devices. The sensor devices are arranged around the axis with an angular offset relative to the magnetic pole pairs and each has at least two magnetic field-sensitive elements that generate differential output signals. An evaluation unit is further provided, configured to receive the differential output signals from the at least two sensor devices and thereby determine the angle information of the axis. This apparatus enables accurate (OoS) angle measurement using differential signals that ensure high accuracy even in the presence of interfering fields.

[0006] According to some embodiments, the permanent magnet is constructed as a bipolar magnet, wherein at least two magnetic sensor devices are arranged around an axis with an angular offset of 180° / 2 = 90° relative to each other. If the permanent magnet is constructed as a quadrupole magnet (two pole pairs), then the magnetic sensor devices can be arranged around an axis with an angular offset of 180° / 4 = 45° relative to each other. In magnetization along the diameter with only one pole pair (north and south poles), the optimal angular offset between the two magnetic sensor devices is 90°, as this corresponds to a 90° electrical angle. When the permanent magnet has two pole pairs (four poles in total), the optimal angular offset is correspondingly reduced to 45°, because the electrical angle is now smaller due to the higher number of poles. The advantage of this implementation with multiple pole pairs is that the sensor senses magnetic field changes more frequently with each mechanical turn, which improves angular resolution. Furthermore, the smaller angular offset enables a more compact and space-saving arrangement of the sensor. Simultaneously, high robustness to interference fields is maintained through differential measurements. The flexibility in the arrangement of sensor elements allows the device to be optimally adapted to specific structural requirements and different geometric frame conditions.

[0007] According to some implementations, permanent magnets can be constructed in the form of rings or disks. Ring-shaped or disk-shaped permanent magnets used for angle measurement can be magnetized along a diameter or with multiple poles, wherein the magnetic poles are arranged segmentally along the periphery or disk surface, such that field lines extend between opposing north and south poles. This produces a well-defined, locally varying magnetic field, ideally suited to determine the angular position of the axis by surrounding magnetic field-sensitive sensor elements. The advantage of both alternative structural forms is that they allow the device to be flexibly adapted to different mechanical requirements. Ring-shaped or disk-shaped implementations can reduce the required installation height, and thus facilitate more compact and space-saving integration into existing systems, for example, in applications with limited structural space and high requirements for overall system design. Additionally, the magnet shape can be selectively chosen based on the desired magnetic field distribution to obtain optimal measurement results in terms of accuracy and robustness against external disturbance fields.

[0008] According to some implementations, each magnetic sensor device includes two magnetic field sensing elements, configured as either xMR or VHall sensor elements. xMR stands for magnetoresistive sensor technology, which responds to changes in the resistance of a material when exposed to an external magnetic field. Different types of magnetoresistive effects exist for use in sensors, including anisotropic magnetoresistive (AMR), giant magnetoresistive (GMR), tunneling magnetoresistive (TMR), and anomalous magnetoresistive (EMR). These technologies provide accurate magnetic field measurements and can be used in applications involving angle and position measurements. VHall stands for Vertical Hall effect sensor. The Hall effect describes a phenomenon where a magnetic field in a conductor through which a current flows generates a voltage perpendicular to both the current and the magnetic field. VHall sensors are specifically designed Hall effect sensors that provide sensitivity to magnetic fields in a vertical configuration, rather than a traditional horizontal configuration. This type of sensor can be used in applications where accurate detection of magnetic fields in a specific orientation is crucial. Both sensor technologies offer robust and accurate magnetic field detection possibilities.

[0009] According to some embodiments, at least two magnetic sensor devices have the same radial distance from the permanent magnet. This means that at least two magnetic sensor devices are positioned at the same distance from the center of the permanent magnet, i.e., at the same distance from the axis of rotation of the shaft. Therefore, the two sensors are located on a common ring, the center point of which forms the axis of the permanent magnet or shaft. The advantage of this symmetrical arrangement is that the two sensor devices are affected by the magnetic field in the same way. Therefore, the sensor devices experience almost identical changes in the influence of external disturbances, such as a uniform magnetic stray field, which are effectively compensated for by the differential formation of the output signal. Thus, the robustness of angle measurement relative to external disturbances can be significantly improved, which in turn improves the accuracy and reliability of the system. Additionally, this symmetrical positioning can reduce possible offset effects and signal distortion, which can further improve the accuracy and reproducibility of the measurement results.

[0010] According to some embodiments, at least two magnetic field sensing elements within a magnetic sensor device are respectively arranged in planes extending parallel to or perpendicular to the axis. This means that the magnetic field sensing elements can be spatially positioned in two different ways. They can be arranged in a plane parallel to the axis of rotation (axial arrangement) or in a plane extending perpendicular to the axis (radial or tangential arrangement). In the orientation parallel to the axis (axial arrangement), the sensor elements primarily detect the axial magnetic field generated along the axis of rotation. This arrangement has the advantage that the sensor elements, due to their symmetrical positioning relative to the axis, can provide particularly high robustness against uniform magnetic stray fields. Here, the external magnetic field acts on both sensor elements in the same manner, thereby effectively eliminating these interference effects by creating signal differences. In contrast, the arrangement of the sensor elements in a plane extending perpendicular to the axis (radial or tangential arrangement) means that the elements measure the magnetic field peripherally or radially relative to the axis. This orientation enables particularly compact integration, for example, when axial structural space is limited. However, in this arrangement, interference field suppression may be slightly lower because the sensor elements may be exposed to magnetic fields or external stray fields of varying strengths depending on the radial or tangential distance. Therefore, choosing between these two orientations offers the possibility of flexibly adapting the device to different mechanical edge conditions, space requirements, and requirements regarding robustness to interference fields.

[0011] Therefore, according to some embodiments, at least two magnetic field sensing elements within a magnetic sensor device are arranged axially spaced apart in a plane extending parallel to the axis. This means that at least two magnetic field sensing elements are positioned in a plane oriented parallel to the axis of rotation, with an axial distance between the elements along the axis. In other words, the sensor elements are located side-by-side in a plane extending along the axis, but not exactly at the same axial position, but rather axially offset from each other. The advantage of this axially offset arrangement is that the two sensor elements are exposed to similar magnetic field strengths, thereby producing a symmetrical field distribution. Due to this symmetry, the two elements are exposed to the same external disturbance field, which results in the efficient calculation of a uniform disturbance field when forming a differential signal. Therefore, this axial arrangement can significantly improve the robustness and accuracy of angle measurements relative to the external magnetic field. Additionally, this symmetrical arrangement simplifies signal evaluation because, ideally, no additional correction is required, which might be necessary in an asymmetrical arrangement. This can result in higher accuracy, better reproducibility of measurement results, and simplified calibration and maintenance.

[0012] According to some embodiments, at least two magnetic field sensing elements within a magnetic sensor device are arranged radially spaced apart in a plane extending perpendicular to the axis of rotation of the shaft. This means that at least two magnetic field sensing elements in the magnetic sensor device are positioned in a plane extending perpendicular to the axis of rotation of the shaft, wherein the magnetic field sensing elements have different radial distances from the center of the shaft or the permanent magnet. In other words, the magnetic field sensing elements are located in the same horizontal plane around the shaft, but not in the same radius, but in different radii. A possible advantage of this arrangement is that it creates additional degrees of freedom in terms of the mechanical structure and positioning of the sensor elements. Therefore, the system can be more flexibly adapted to different mechanical edge conditions and space requirements. For example, the magnetic field sensing elements can be placed near the shaft to detect stronger magnetic field components. Other magnetic field sensing elements are positioned further away to detect other field components or field intensities. This enables targeted measurement of radial magnetic field gradients, but it can also be challenging because the elements are exposed to different magnetic field intensities based on different radial distances. To compensate for the resulting differences or potential offsets in signal amplitude, it may be necessary to evaluate the signal in the unit through subsequent normalization or calibration. Compared to an axial arrangement (where elements are positioned radially equidistant and symmetrically relative to the axis), a radially different arrangement can provide less protection against external disturbance fields because it results in an asymmetrical field distribution. This implementation still allows for greater flexibility in the device's structural design and adaptability to specific measurement conditions.

[0013] In axial arrangements, subsequent normalization or calibration may also be required. Even in ideally symmetrical magnetic fields, differences in signal amplitude between two sensor devices can occur, for example, due to variations in the sensitivity of xMR (e.g., TMR) elements caused by manufacturing processes.

[0014] According to some embodiments, the magnetic field sensing elements within a magnetic sensor device are arranged tangentially spaced apart in a plane extending perpendicular to the axis. This describes an arrangement in which the magnetic field sensing elements of the sensor are located in a plane positioned perpendicular to the axis of rotation. Here, the sensor elements are tangentially spaced apart from each other, i.e., staggered at a specific angle along the periphery of the circle surrounding the axis and the permanent magnet. This means that while two sensor elements may have the same distance from the axis in the radial direction, they are spatially separated from each other along the periphery of the circle, i.e., along the tangential direction. The advantage of this tangential arrangement is that the sensor detects changes in the magnetic field from different tangential positions. This results in the detection of a phase shift in the magnetic field component, which can then be used to determine the angular position. This tangential placement allows for targeted measurement of field changes that may appear particularly pronounced along the periphery. This provides an advantage especially when axial arrangement is impossible or undesirable due to structural limitations. However, similar to radial arrangement, tangential positioning may be more susceptible to external magnetic interference, especially when ferromagnetic components enhance the external magnetic field. Despite this potential drawback, the tangential arrangement allows for flexible integration of sensors within limited axial structural space, enabling the device to be used more versatilely in different structural and technical environments.

[0015] According to some implementations, the shaft of the device is constructed non-ferromagnetically. This means that the shaft is made of a material that lacks ferromagnetic properties and is therefore non-magnetic. Typical materials for this purpose include, for example, aluminum, stainless steel, or other non-magnetic metals and alloys. The advantage of this material choice is that the shaft does not enhance or affect the magnetic field because there is no concentration or distortion of magnetic flux. Therefore, the magnetic field detected by the magnetic sensor element remains uniform and undistorted, which improves the accuracy and stability of angle measurements. Furthermore, a non-ferromagnetic shaft facilitates sensor calibration because less compensation is required based on the interference of magnetic influences. This ultimately improves measurement accuracy and reduces the calibration and maintenance costs of the device.

[0016] According to another aspect of the invention, a method for determining the angle of a rotating shaft is proposed, the method comprising fixing a permanent magnet having at least one pair of magnetic poles to the rotating shaft, and arranging at least two magnetic sensor devices with an angular offset associated with the magnetic pole pairs. The method includes detecting differential output signals by the at least two magnetic sensor devices and evaluating these signals to determine the angle, thus providing an effective possibility for achieving accurate and continuous angle tracking of rotating components in various industrial applications.

[0017] According to another aspect, the present invention provides an apparatus for determining the angle of a rotation axis. The apparatus includes a permanent magnet fixed to the rotation axis, having at least one pair of magnetic poles. The apparatus also includes at least three magnetic field sensors arranged at equidistant angular distances around the permanent magnet. Each magnetic field sensor is configured to detect the magnetic field generated by the permanent magnet and output a corresponding sensor signal. The apparatus further includes an evaluation unit. The evaluation unit is configured to receive the sensor signals from the at least three magnetic field sensors. Using a transformation, the evaluation unit derives sine and cosine signals from the sensor signals. The evaluation unit calculates the angle information of the axis based on the sine and cosine signals.

[0018] Therefore, multiple magnetic field sensors, evenly distributed around a rotating magnet, collectively measure the magnetic field generated by the magnet. A computational unit uses mathematical transformations to convert the resulting measurements into sine and cosine signals, from which the precise rotation angle of the shaft can be derived. This arrangement enables angle detection without the need for mechanically complex orientation of individual sensors. The proposed device achieves accurate 360° absolute angle measurements. The equidistant arrangement of at least three magnetic field sensors reduces errors caused by the magnetic field, which are present in arrangements with fewer sensors. The device also achieves more robust measurements relative to interfering and stray fields.

[0019] According to some embodiments, each magnetic field sensor is configured to detect the radial component of the magnetic field generated by the permanent magnet. Therefore, each sensor does not measure the entire magnetic field, but rather selectively measures the component pointing outwards along the axis perpendicular to the axis, i.e., in the radial direction. This targeted detection ensures selective evaluation of magnetic field information relevant to angle calculations. Detecting the radial magnetic field component improves angular accuracy because it suppresses the effects of magnetic interference in other spatial directions. Consequently, measurements become more stable and less susceptible to axial or tangential stray fields.

[0020] In some embodiments, the permanent magnet is magnetized along its diameter. This means that the magnetization direction of the permanent magnet extends laterally through the entire magnet, such that the north and south poles are aligned along the diameter. As the magnet rotates, the resulting magnetic field also rotates, producing a sinusoidal signal variation at each measurement point. Diameter-based magnetization produces uniform and well-predictable magnetic field characteristics. This improves the quality of the derived sinusoidal and cosine signals, and thus increases the accuracy of angle calculations.

[0021] In some embodiments, the transformation is the Clarke transform. The Clarke transform is a mathematical method that transfers signals from a three-phase system to a two-dimensional coordinate system, directly generating orthogonal sine-cosine pairs. Using the Clarke transform enables the efficient derivation of angle information from sensor signals. It can also help filter out common-mode shares and in-phase interference signals from filtered sensor signals.

[0022] According to some embodiments, the magnetic field sensor is constructed as a TMR sensor. The use of a TMR sensor enables accurate and low-noise magnetic field detection. This contributes to higher angular resolution and better measurement accuracy even in weak magnetic fields, such as those with large air gaps.

[0023] According to some embodiments, each magnetic field sensor is constructed as a differential sensor with two magnetic field-sensitive measuring elements. Each magnetic field sensor is configured to form a differential signal from the measurement signals of its two measuring elements. This means that the two measuring elements within the sensor detect the magnetic field at two adjacent points. The difference between these two measurement signals forms the sensor's output signal. Differential signal evaluation can help effectively suppress in-phase interference signals, such as those caused by external stray fields or temperature drift. Measurement sensitivity relative to the useful signal can be maintained, while the signal-to-noise ratio can be improved.

[0024] According to some embodiments, the two magnetic field-sensitive measuring elements of each magnetic field sensor are arranged such that the axial component of the magnetic field generated by the permanent magnet is detected differentially, wherein the chip plane of each magnetic field sensor is oriented substantially parallel to the shaft or the surface of the permanent magnet, or the tangential component of the magnetic field generated by the permanent magnet is detected differentially, wherein the magnetic field-sensitive measuring elements are spaced apart from each other tangentially around the periphery of the shaft and arranged at the same radial distance as the axis of the shaft. Therefore, depending on the geometric arrangement of the measuring elements, either the axial or tangential magnetic field components can be detected selectively and differentially. This allows the sensor configuration to be flexibly adapted to different mounting conditions and magnet geometries. This flexibility in the sensor arrangement can improve the system's adaptability to different mechanical structures. Differential detection of the defined magnetic field direction can further improve robustness against stray fields.

[0025] In some embodiments, exactly three magnetic field sensors are arranged around the permanent magnet at angular distances of 120°. The three uniformly distributed sensors form a symmetrical three-phase system, to which the Clarke transform can be directly applied. This three-sensor arrangement represents a good compromise between system complexity and measurement accuracy. Angular errors are reduced compared to a two-sensor arrangement.

[0026] According to some embodiments, exactly six magnetic field sensors are arranged around the permanent magnet at angular distances of 60° from each other. This arrangement of six sensors represents an extension of the three-sensor arrangement and can further improve angular accuracy through redundancy and averaging. The six-sensor arrangement can further reduce angular errors compared to the three-sensor arrangement. Spatially distributed detection of the magnetic field can effectively compensate for the inhomogeneities of the permanent magnet caused by the magnetic field.

[0027] According to some embodiments, the evaluation unit is also configured to calculate three intermediate signals, each formed by the difference between the sensor signals of two opposing magnetic field sensors. A transform is applied to these three intermediate signals. In a six-sensor arrangement, the signals of two opposing sensors are subtracted separately before applying the Clarke transform. This prior differential formation enables additional suppression of common-mode interference signals. It also increases the signal amplitude and thus improves the dynamic range of the downstream transform.

[0028] According to some embodiments, the permanent magnet is constructed as a ferrite magnet. Ferrite magnets are composed of iron oxide-based ceramic materials and are low-cost, corrosion-resistant, and temperature-stable. The use of ferrite magnets can reduce the manufacturing cost of the system. Ferrite magnets can be used in industrial environments requiring temperature resistance and chemical robustness. The lower remanence of ferrite magnets compared to rare-earth magnets can be compensated for through appropriate sensor selection and system design.

[0029] According to some embodiments, the permanent magnet is constructed in the form of a ring or a disk. These two shapes enable coaxial, mechanically simple fixation on the axis of rotation and are well-suited for magnetization along a diameter. The ring or disk-shaped magnet geometry can facilitate a uniform distribution of the magnetic field in the outer region. This magnet geometry also allows for simple and space-saving integration into existing shaft structures.

[0030] According to some embodiments, the magnetic field sensors are arranged radially outside the permanent magnet. Therefore, these sensors are not located above or below the magnet, but rather at a uniform angular distance around the axis on the outer periphery of the magnet. This radially external sensor arrangement allows for mechanically flexible mounting on a circuit board surrounding the axis. Furthermore, this arrangement provides easy access to the sensors for maintenance and calibration.

[0031] In some embodiments, the air gap between the permanent magnet and the magnetic field sensor is greater than 3 mm. The air gap refers to the unused distance between the outer surface of the permanent magnet and the activation surface of the magnetic field sensor. A sufficiently large air gap can help the magnetic field sensor operate within its linear measurement region. An excessively strong magnetic field can saturate the sensor and lead to an increase in angular error.

[0032] According to some embodiments, the evaluation unit is also configured to perform calibration. Calibration may include normalizing the sensor signal through offset and amplitude correction. Alternatively or additionally, calibration may include elliptic fitting to extract correction factors. In elliptic fitting, sine and cosine signals are analyzed, and deviations from an ideal circle are corrected to reduce systematic angular errors. The calibration function can improve the measurement accuracy of the system. Manufacturing tolerances and mounting errors can be compensated for by correcting offset and amplitude errors. Elliptic fitting can be particularly helpful in correcting nonlinear magnetic field characteristics and sensor mismatch.

[0033] According to some embodiments, the evaluation unit is configured to calculate angle information from sine and cosine signals using the atan2 function. The atan2 function is a variant of the arctangent function that clearly covers the entire angle range from 0° to 360° and takes into account the signs of both input signals. The use of the atan2 function ensures clear 360° absolute angle detection. Unlike the simple arctangent function, ambiguity in angle assignment is avoided, which is important for reliable angle determination throughout the cycle.

[0034] In some embodiments, the shaft is constructed to be non-ferromagnetic. This means that the shaft material has no magnetic properties or only negligible magnetic properties, and therefore does not affect or distort the magnetic field of the permanent magnet. A non-ferromagnetic shaft prevents the magnetic field of the permanent magnet from being extracted or distorted through the shaft material. This can improve the quality of the measurement signal and increase the accuracy of angle determination.

[0035] According to some embodiments, the device includes N=3k (k≥2) magnetic field sensors arranged around the axis at uniform angular distances of 360° / N. An evaluation unit is configured to divide the N magnetic field sensors into k subsets, each subset containing three magnetic field sensors, wherein the three magnetic field sensors in each subset are staggered by 120° from each other. For each subset, the evaluation unit performs a Clarke transform on the associated three sensor signals to obtain each sine and cosine signal. The evaluation unit determines a sub-angle from each sine-cosine pair using an arctangent function. The evaluation unit calculates the final rotation angle of the shaft as the average of the k sub-angles. In other words, in arrangements such as six, nine, or twelve sensors, these sensors are divided into multiple groups of three sensors each. Each group provides its own angle value. The final angle is generated by averaging all the sub-angles. This represents a scalable extension of the basic three-sensor arrangement. The scalable architecture can systematically improve angular accuracy by increasing the number of sensors. The average value, formed by multiple independent angle measurements, can reduce random measurement errors and sensor-specific biases. This concept also enables simple redundancy for security-related applications.

[0036] According to another aspect, the present invention provides a method for determining the angle of a rotation axis. The method includes detecting radial, axial, or tangential magnetic field components using at least three magnetic field sensors arranged at equidistant angular distances around a diameter-magnetized permanent magnet fixed to the axis. Each magnetic field sensor outputs a corresponding sensor signal. The method further includes deriving sine and cosine signals from the sensor signals of the at least three magnetic field sensors by means of transformation. Finally, the angle information of the axis is calculated based on the sine and cosine signals.

[0037] According to another aspect, the present invention provides an angle measurement system for 360° absolute angle identification. The system includes a rotatable shaft and a permanent magnet magnetized along its diameter, the permanent magnet being torsionally connected to the shaft. A circuit board is fixedly arranged relative to the shaft. At least three magnetic field sensors are mounted on the circuit board at equidistant angular distances around the permanent magnet, wherein each magnetic field sensor is configured to detect a radial magnetic field component. A processor receives sensor signals from the at least three magnetic field sensors, derives sine and cosine signals by means of transformation, and calculates the absolute angle value of the shaft. The angle measurement system can be implemented as a completely self-contained unit for industrial applications. The integration of all components on the circuit board enables a compact and inexpensive system solution.

[0038] According to another aspect, the present invention provides a computer program product comprising instructions that, when executed by a processor, cause the processor to receive sensor signals from at least three magnetic field sensors arranged at equidistant angular distances around a permanent magnet magnetized along its diameter. Furthermore, the processor is prompted to derive sine and cosine signals from the sensor signals by means of transformation, and to calculate angle information based on the sine and cosine signals.

[0039] Those skilled in the art will recognize that the above embodiments and features are not limited to the combinations described herein, but can be combined with each other in various ways. Features of embodiments relating to the number and arrangement of magnetic field sensors can, for example, be combined with features relating to the design, transformation method, or calibration method of the magnetic field sensing element. Similarly, embodiments describing a three-sensor arrangement with Clarke transform can be combined with embodiments involving differential signal detection, elliptic fitting, or specific magnet geometry. Features of the first aspect relating to a device having at least two magnetic sensor devices and angular offsets associated with magnetic pole pairs can here be combined with features of the second aspect relating to a device having at least three equidistantly arranged magnetic field sensors and transformation, if this is technically meaningful and not contradictory. Therefore, the invention is not limited to the explicitly described combinations, but includes all technically feasible combinations of the disclosed features.

[0040] Further features and advantages of the invention will be recognized by those skilled in the art upon reading the following detailed description and upon viewing the accompanying drawings. Attached Figure Description

[0041] The invention is illustrative and is shown in the accompanying drawings without limitation, in which the same reference numerals refer to similar or identical elements. Elements in the drawings are not necessarily drawn to scale. Features of the different examples shown can be combined unless they are mutually exclusive.

[0042] Figure 1 An axial arrangement of two sensor devices with axially spaced magnetic field sensing elements is shown, the magnetic field sensing elements being located at the same radial distance from the axis of rotation and thus enabling high stray field robustness;

[0043] Figure 2A One embodiment is shown in which the magnetic field sensing element is radially displaced from the center of the shaft and arranged in a plane perpendicular to the axis of rotation.

[0044] Figure 2B The diagram shows a tangential arrangement of magnetic field sensing elements, which are located at the same radial height but tangentially staggered in a plane perpendicular to the axis of rotation.

[0045] Figure 3 The different spatial orientations of all three arrangements (axial, radial, and tangential) and their magnetic sensor elements are shown in a comparative manner.

[0046] Figure 4 Detailed measurement results of an axial sensor arrangement with high robustness to disturbance fields and small measurement errors throughout the entire rotation of the shaft are shown.

[0047] Figure 5 Detailed measurement results for a radial sensor arrangement are shown, which exhibits reduced robustness relative to stray fields due to the varying radial distances of the sensor elements.

[0048] Figure 6 Detailed measurement results are shown for a tangential sensor arrangement, in which robustness is slightly reduced relative to magnetic interference fields due to the tangentially staggered sensor elements.

[0049] Figure 7 An embodiment of a device having three equidistantly arranged magnetic field sensors is shown; and

[0050] Figure 8 An embodiment of a device having six equidistantly arranged magnetic field sensors is shown. Detailed Implementation

[0051] Known solutions for off-axis (OoS) angle measurement include magnetic and inductive solutions. Magnetic solutions are based on an arrangement of two linear sensors using Hall or xMR techniques, oriented at a 90° angle to each other. Here, the first sensor generates a sinusoidal signal, and the second sensor generates a cosine signal, thereby allowing the angular orientation of the axis to be calculated, for example, using the ATAN2 function. However, due to the single-cell concept used, this solution exhibits reduced robustness relative to stray fields.

[0052] The inductor solution uses a static circuit board design with a transmitting coil, two receiving coils, and a conductive rotor. However, this system requires a complex mechanical structure because the coils and rotor must be arranged around a shaft. Furthermore, miniaturization is limited due to low signal strength (SNR), necessitating the use of large-diameter or multi-layer circuit boards to ensure sufficient inductance.

[0053] The embodiments described below extend existing magnetic solutions for (OoS) angle measurement through a differential sensor concept. Here, a permanent magnet is combined with two differential magnetic sensor devices arranged relative to each other at an angle (e.g., 45° or 90°) associated with the magnetic pole pairs. This concept selectively uses xMR or Hall sensors and enables improved signal processing by detecting differential signals. An axial measurement arrangement is advantageous because it provides high sensitivity and improved suppression of interference fields. The described embodiments can outperform conventional systems in terms of power and robustness to interference fields, particularly by suppressing uniform interference fields. Another advantage is reduced signal distortion due to nonlinear effects in the sensor. The proposed concept is also applicable to efficient implementation using existing sensor technologies, thereby enabling simple integration into industrial applications.

[0054] Figure 1 A device 100 for determining the angle of a rotation axis 102 according to an embodiment is shown.

[0055] The device 100 includes a permanent magnet 104 having at least one pair of magnetic poles, which is fixed to a rotation shaft 102. The permanent magnet 104 can be implemented in different geometric embodiments, particularly in the form of a toroidal or disc magnet. Figure 1A ring-shaped permanent magnet 104 is shown that completely surrounds the shaft 102 radially. This ring-shaped magnet is advantageous when components are arranged space-savingly and compactly around the shaft 102, as it allows the shaft 102 to extend through its center, thus requiring very little additional axial structural space. In contrast, a disc-shaped permanent magnet is typically mounted on the end face of the shaft 102. In this case, the disc does not rest against the shaft 102, but rather axially against the ends of the shaft, thus the magnetic field is primarily axially oriented. This requires almost no additional radial space, but more structural space along the axial direction of the shaft 102. Regarding the number of pole pairs, the permanent magnet 104 can have two poles (one pole pair) or more pole pairs, such as four poles (two pole pairs). Furthermore, the shaft 102 to which the permanent magnet 104 is fixed can be composed of different materials. The shaft 102 can be made of, for example, a ferromagnetic material, such as steel, thereby strengthening the shaft and focusing the magnetic stray field. However, this can pose a challenge to measurement accuracy, as these enhanced stray fields may cause undesirable signal effects on magnetic field-sensitive elements. Alternatively, shaft 102 can also be made of non-ferromagnetic materials, such as aluminum or non-magnetic stainless steel. These materials do not attract or enhance magnetic fields, thus allowing for better control over external magnetic influences and more accurate and simpler reproduction of measurement results. Furthermore, the use of non-ferromagnetic materials allows for weight savings and better corrosion resistance when necessary.

[0056] The device 100 also includes at least two spaced-apart magnetic sensor devices 110A and 110B, arranged around axis 102 with angular offsets relative to the magnetic pole pairs, and each having at least two magnetic field sensing elements 112A and 112B that generate differential output signals. The magnetic sensor devices 110A and 110B can be implemented in various ways, wherein each sensor device 110A and 110B preferably has two magnetic field sensing elements 112A and 112B. These magnetic field sensing elements 112A and 112B can be implemented, for example, as magnetoresistive (xMR, especially TMR, AMR, or GMR) elements or Hall elements (especially vertical Hall elements, i.e., VHALL). The magnetic field sensing elements 112A and 112B can be configured as individual resistors, or alternatively, as components in a Wheatstone bridge circuit to generate differential output signals with high accuracy and better interference field protection. The angular offset between magnetic sensor devices 110A and 110B depends on the number of pole pairs of the permanent magnet 104 used. Therefore, in a bipolar magnet (i.e., one pole pair), the angular offset is typically 90°, as this corresponds to a 90° electrical angle, where sensor device 110A is positioned at the center of one pole, and the other sensor device 110B is positioned at the pole transition. Conversely, if the permanent magnet 104 has multiple pole pairs, such as four poles (two pole pairs), the angular offset is proportionally reduced to 45°. The advantage of a smaller angular offset is a more compact arrangement of the sensors and higher angular resolution, as multiple signal cycles can be detected in each mechanical rotation.

[0057] The magnetic field sensing elements 112A and 112B within the sensor devices 110A and 110B can be arranged in different ways. Figure 1 In the preferred embodiment shown, two magnetic field sensing elements 112A and 112B are arranged axially spaced apart in a plane parallel to the axis 103. This ensures that the magnetic field sensing elements experience the same magnetic conditions, thus providing optimal conditions for differential signal evaluation. Alternatively, the magnetic field sensing elements 112A and 112B may be arranged radially spaced apart in a plane extending perpendicular to the axis 103, or tangentially spaced apart along the periphery of the permanent magnet 103 in a plane extending perpendicular to the axis 103. These alternative arrangements offer advantages in terms of mechanical flexibility, enabling more compact configurations and allowing adaptation to the specific requirements of the respective applications.

[0058] Device 100 includes an evaluation unit 120 configured to receive differential output signals from at least two sensor devices 110A, 110B, and thereby determine angular information of axis 102. The evaluation unit 120 of device 100 processes and evaluates the differential signals provided by magnetic sensor devices 110A and 110B to determine the angular position of rotation axis 102. This evaluation unit can be implemented in several technical variations, such as as an application-specific integrated circuit (ASIC), a programmable microcontroller, or alternatively as a field-programmable gate array (FPGA).

[0059] When implemented as an ASIC, the differential signals generated by the magnetic field sensing elements 112A and 112B can be contained and processed directly internally. Here, the ASIC can perform signal preparation by, for example, correcting (orthogonalizing) offset, phase, and amplitude errors, and subsequently calculating the precise angular position of the axis using mathematical operations, such as the ATAN2 function. ASICs offer the advantages of being particularly compact, energy-efficient, and fast, making them suitable for industrial applications with high demands for robustness and real-time performance.

[0060] Alternatively, the evaluation unit 120 can be implemented as a microcontroller that digitizes the differential output signal of the sensor and subsequently processes it in software. The microcontroller can first perform calibration of the sensor signal, namely, correcting (orthogonalizing) offsets and phase and amplitude deviations. Subsequently, the microcontroller can calculate the precise angular position of axis 102 using a mathematical algorithm (typically the ATAN2 function). This solution allows for high flexibility in adapting to different sensors and applications, and the possibility of subsequently adding additional functionality through software updates.

[0061] When implemented as an FPGA, sensor signals can be processed through individually programmable logic structures. FPGAs enable fast and flexible simultaneous signal processing due to their parallel and high-performance signal processing capabilities. This parallel processing capability makes FPGA-based evaluation units particularly suitable for complex real-time applications that must process multiple sensor signals simultaneously, or where very high speed and adaptability requirements are necessary.

[0062] Regardless of the specific implementation, the evaluation unit 120 can perform orthogonalization of the sensor signals, correcting for offsets, phase shifts, and different signal amplitudes. Thus, the system can achieve high accuracy and reliable angle measurements even under harsh conditions with external magnetic interference fields or mechanical tolerances.

[0063] according to Figure 1The OoS system includes a ring magnet 104 fixed to a rotatable shaft 102 and magnetized along its diameter, and two differential sensor devices 110A and 110B, which are arranged with an angular offset of 90° from each other. Each sensor device 110A and 110B consists of two sensor elements 112A and 112B (e.g., xMR or VHALL). These sensor elements can be implemented as individual resistors or in a Wheatstone bridge configuration. Sensor elements 112A and 112B are sensitive to a magnetic field along the z-direction.

[0064] In a preferred embodiment, the chip plane is oriented parallel to the surface or peripheral side (YZ plane) of axis 102. Therefore, sensor devices 110A and 110B detect the axial magnetic field generated by permanent magnet 104. The sensor output is a differential signal generated by the difference between the first and second magnetic field sensing elements 112A and 112B. In this way, uniform stray fields are suppressed. The sensor signal is forwarded to a microcontroller or ASIC 120, which performs optional orthogonalization (correcting the offset, phase, and amplitude of the sine and cosine sensor signals) and thereby calculates the axis angle.

[0065] The preferred embodiment offers several advantages. One of the most important aspects is increased robustness against stray fields. The two sensor elements 112A and 112B of sensor devices 110A and 110B are positioned in a symmetrical magnetic field, such that the sensor elements are exposed to the same absolute magnetic field strength. This improves stray field suppression because potential sensitivity differences caused by the nonlinearity of the TMR sensor are reduced. Furthermore, the ferromagnetic shaft 102 acts as a flux concentrator due to its high permeability and enhances magnetic stray fields. However, due to the symmetrical arrangement of sensor elements 112A and 112B and their equal distance from the shaft 102, the two sensor devices 110A and 110B are exposed to the same stray field, thereby substantially compensating for interference effects.

[0066] Another advantage comes from its compact design. The system can also be used for smaller diameter shafts 102, and the overall external diameter can be reduced compared to induction systems. A feasibility study based on FEM simulations confirms that a maximum module with a diameter of only 16 mm can be achieved for a 5 mm diameter shaft 102. Conversely, a similar induction system with the same mechanical dimensions achieves lower measurement accuracy.

[0067] Furthermore, compared to sensing systems, the preferred implementation provides higher measurement accuracy, which is particularly advantageous in applications where high precision is required.

[0068] In addition to functional advantages, cost advantages are also achieved. Due to the high sensitivity of the TMR sensor, the system can also operate using rare-earth-free magnets (such as ceramic magnets). This reduces material costs and enables more economical manufacturing of the system without compromising effective power.

[0069] Figure 2A The device 100 shown illustrates another embodiment of an angle measuring device for a rotating shaft 102.

[0070] The device 100 also includes a permanent magnet 104 magnetized along its diameter, which is fixedly connected to the shaft 102 and thus rotates with the shaft. The permanent magnet 104 is configured to have two opposing magnetic poles (north and south poles). Two magnetic sensor devices 110A and 110B are positioned around the permanent magnet 104, each containing two magnetic field sensing elements 112A and 112B. These magnetic field sensing elements 112A and 112B of the sensor devices 110A and 110B are positioned radially at a distance from the center of the shaft 102 and lie in a plane (XY plane) extending perpendicular to the axis 103 of rotation of the shaft 102. In the view shown, sensor device 110A and its two magnetic field sensing elements are positioned to the right of the magnet 104, while sensor device 110B is arranged above the magnet 104. The two sensor devices 110A and 110B have an angular offset (electrical angle) of 90° from each other.

[0071] Two magnetic sensor devices 110A and 110B detect changes in the magnetic field generated by the rotation of a permanent magnet 104 magnetized along its diameter. Corresponding sensor elements 112A and 112B detect magnetic fields of varying intensities based on their radially different orientations. Sensor device 110A primarily detects the magnetic field along the x-direction, while sensor device 110B primarily measures the magnetic field along the y-direction. This spatial arrangement generates differential output signals (sine and cosine), from which the angular orientation of axis 102 can be accurately determined in a subsequent evaluation unit (e.g., an ASIC or microcontroller). This differential measurement allows for effective compensation against external uniform magnetic interference fields. However, the radially staggered arrangement of the magnetic field sensing elements can lead to differences in signal strength and potentially a greater influence from non-uniform magnetic fields. These differences can be compensated for by subsequent signal normalization or calibration in the evaluation unit to ensure reliable angle determination.

[0072] In contrast, Figure 1In this arrangement, magnetic field sensing elements 112A and 112B are radially equidistant from the permanent magnet 104, resulting in symmetrical detection of the magnetic field. Consequently, the two magnetic field sensing elements 112A and 112B are exposed to the same magnetic field gradient, ensuring uniform signal strength and better suppression of uniform interference fields. This symmetrical arrangement ensures that external magnetic interference fields are essentially eliminated, as they have the same effect on both sensors. This improves robustness against interference fields and reduces the need for complex correction measures in signal processing.

[0073] In summary, it can be said that the different radial orientations of magnetic field sensing elements 112A and 112B ( Figure 2A This may lead to greater signal distortion and less interference field suppression, while Figure 1 The axial arrangement within the sensor allows for better robustness to interference fields and more accurate measurements. This is especially important when sensors cannot be placed at the same distance. Figure 2A However, radial differences can also be used to detect specific field distributions or circumvent mechanical limitations, depending on the application.

[0074] Figure 2B The illustrated device 100 illustrates an additional embodiment for determining the angle of the rotation axis 102 by means of two magnetic sensor devices 110A and 110B, which are positioned in a plane extending perpendicular to the rotation axis 103 of the axis.

[0075] Device 100 includes a permanent magnet 104, which is magnetized along its diameter and fixedly connected to a rotation shaft 102. Two sensor devices 110A and 110B each have two magnetic field sensing elements 112A and 112B, arranged tangent to a circle around shaft 102, with the two sensor devices 110A and 110B having a defined angular offset of 90° from each other. Sensor device 110A is located to the right of permanent magnet 104, while sensor device 110B is located above magnet 104. The indicated direction (Bsense) shows which magnetic field components are primarily detected by the respective sensor devices 110A (y-direction) and 110B (x-direction).

[0076] The magnetic field sensing elements 112A and 112B of sensor devices 110A and 110B detect changes in the magnetic field of the permanent magnet 104 caused by rotation through shaft 102. The tangential arrangement of sensor elements 112A and 112B detects changes in the magnetic field appearing along the periphery of the rotating magnet 104. Because the two sensor elements 112A and 112B within each sensor device 110A and 110B are tangentially offset, they utilize phase shift to detect the magnetic field. Sensor device 110A primarily measures the vertical field component (in the y-axis direction), while sensor device 110B primarily measures the horizontal field component (in the x-axis direction).

[0077] The staggered tangential arrangement enables the generation of differential output signals (composed of sine and cosine signals), from which the connected evaluation unit 120 can accurately calculate the angular attitude of the axis. However, by positioning the magnetic field sensing elements 112A and 112B along the tangent, the sensitivity to interference fields may increase slightly, as external magnetic interference can act with varying intensities along this tangent. This effect can be reduced through appropriate signal processing, such as calibration or orthogonalization within the evaluation unit. The advantage of this tangential arrangement is that it allows for a particularly compact design and can be flexibly integrated into applications with limited radial or axial structural space.

[0078] Radial measurement ( Figure 2A ) and tangential measurement ( Figure 2B The implementation method of ) is also applicable to OoS angle measurement. However, here, the ability to suppress stray fields is relatively less effective compared to axial measurement ( Figure 1 The radial measurement decreased slightly. Figure 2A This is based on two sensor elements 112A and 112B with different radial air gaps. Therefore, sensor elements 112A and 112B are exposed to different magnetic offsets, which limits stray field suppression in the case of nonlinear TMR characteristics. Secondly, the stray field is attracted by the ferromagnetic shaft 102. Therefore, the magnetic field sensing element 112A, located near the shaft 102, is exposed to a stronger stray field compared to the much farther-located magnetic field sensing element 112B. Tangential sensor arrangement ( Figure 2B It is also related to the enhancement of stray field through ferromagnetic axis 102.

[0079] In this embodiment, shaft 102 may also be made of a non-ferromagnetic material, such as aluminum, copper, or non-magnetic stainless steel. This material choice offers several advantages in terms of stray field suppression and system measurement accuracy.

[0080] The advantage of a non-ferromagnetic shaft is that it does not enhance or distort magnetic stray fields. In a ferromagnetic shaft, magnetic flux lines can be concentrated and redirected, which can lead to non-uniform magnetic field distributions near magnetic sensors 110A and 110B. This can be particularly problematic in radial or tangential sensor configurations, as the sensors are positioned at different distances from the shaft and thus experience varying degrees of interference field influence. Non-ferromagnetic shafts prevent this effect and ensure a more uniform magnetic field distribution around the shaft.

[0081] Furthermore, the non-ferromagnetic shaft improves the reproducibility of measurements because the magnetic field of the permanent magnet 104 is formed independently of the shaft material. This simplifies sensor calibration, as no additional correction is needed for signal deviations caused by stray fields.

[0082] Another advantage lies in material selection and manufacturing costs. Non-ferromagnetic materials, such as aluminum or certain plastics, are generally lighter than steel or other ferromagnetic metals, which can be advantageous in applications with high rotational speeds or strict weight limitations. Furthermore, in many cases, they offer better corrosion resistance, which improves the long-term stability of the system.

[0083] Therefore, by using the non-ferromagnetic shaft 102, it is possible to achieve angle measurements that are generally more robust, more accurate, and more resistant to interference fields, which is particularly advantageous in environments with strong external magnetic fields or high requirements for signal stability.

[0084] Figure 3 Three different implementations of an off-axis (OoS) angle measuring device (axial, radial, and tangential measurement) are shown. The angle measuring device consists of a rotating shaft 102, a permanent magnet 104 magnetized along the diameter and fixed thereon, and two magnetic sensor devices 110A and 110B.

[0085] The left figure shows the relationship with Figure 1 In the corresponding arrangement, two sensor devices 110A and 110B are radially equidistant from the center of shaft 102. Within each sensor device, magnetic field sensing elements 112A and 112B are axially spaced and primarily detect the axial magnetic field along the rotation axis 103 of shaft 102. In particular, this arrangement is characterized by its high robustness to disturbance fields because the two magnetic field sensing elements detect the magnetic field almost identically and can effectively compensate for uniform external disturbance fields.

[0086] According to Figure 2AIn the intermediate diagram, the two sensor devices 110A and 110B are also radially located at the same distance from the shaft 102 and positioned in a plane extending perpendicular to the axis of rotation. However, within each sensor device, the magnetic field sensing elements 112A and 112B are arranged radially at different distances from the center of the shaft 102. This radial difference results in the sensor elements detecting different magnetic field strengths. The advantage of this radial arrangement is that it provides greater flexibility in mechanical integration. However, additional signal normalization or calibration is required to balance the differences in magnetic field strength.

[0087] according to Figure 2B The right figure illustrates an arrangement in which two sensor devices 110A and 110B are radially equidistant from the shaft 102 and positioned in a plane perpendicular to the axis of rotation. However, within each sensor device, the magnetic field sensing elements 112A and 112B are tangentially offset, meaning these elements are located on the tangent of a circle surrounding the shaft 102. Thus, they detect changes in the magnetic field along the periphery of the axis of rotation in a phase-shifted manner. This tangential arrangement is particularly suitable for achieving compact and space-saving structures, but may be more susceptible to external non-uniform magnetic fields, and therefore requires appropriate signal processing to compensate for these effects if necessary.

[0088] therefore, Figure 3 Three specific implementations of the described system are shown in general, which can be selected according to the requirements for measurement accuracy, structural space, robustness to disturbance fields, and integration possibilities.

[0089] Figure 4 The functional mode and advantages of the axial arrangement of magnetic sensor elements 112A and 112B in the angle measurement of the rotating axis are shown in detail.

[0090] exist Figure 4 The left-hand area shows the output signals of two axially arranged magnetic sensor devices 110A and 110B (sensor 1 above, sensor 2 below). The curves represent the magnetic field (Bx component) generated by the permanent magnet 104, which varies sinusoidally and cosinely throughout the rotation of the shaft 102. It is clear that each of the two sensor devices 110A and 110B has two measurement points (two magnetic field sensing elements 112A and 112B), which easily detect different signals due to their axial distance.

[0091] Figure 4 The central region illustrates how multiple single signals from two measurement points within each sensor device 110A, 110B are differentially generated. These differential signals (solid and dashed lines) are substantially free of uniform magnetic interference fields, thereby enabling more robust angle determination.

[0092] Finally, Figure 4 The right side shows the measurement accuracy. Curve 410 represents the measured angle over the entire 360° rotation, while curve 420 shows the measurement error occurring here in degrees. A very small measurement error can be seen here, located in a narrow range near zero. This, in particular, demonstrates the high accuracy and robustness of the axial measurement method in terms of suppressing interference fields and minimizing errors that might arise through nonlinear characteristics such as TMR nonlinearity.

[0093] Figure 5 An embodiment of a magnetic axis external angle measurement system is shown, wherein magnetic field sensitive sensor elements 112A and 112B are positioned radially at different distances from the center of the rotation axis.

[0094] Figure 5 The left side first shows the signals detected by two radially positioned magnetic field sensing elements 110A and 110B (sensor 1 above, sensor 2 below) within the sensor device 110A. The two different radial positions result in each element being positioned at a different distance from the permanent magnet 104, and correspondingly, having different signal strengths (signal amplitudes). It is clearly seen in the figure that different magnetic field signals of varying strengths are generated in different air gaps (e.g., 0.7 mm and larger or smaller distances).

[0095] exist Figure 5 The middle section illustrates how a differential output signal is formed by differentially forming the signals within each sensor device 110A, 110B (“BxDown” minus “BxUp”). This differential forming results in a sinusoidal or cosine signal used to determine the rotation angle of shaft 102.

[0096] Figure 5 The right side illustrates the angle measurement during the entire rotation of the shaft from 0° to 360° and the angle measurement error that occurs therein. Curve 510 shows the measured angle, while curve 520 illustrates the associated measurement error in degrees. The measurement error here is very small, which confirms the basic suitability of the radial arrangement; however, slight signal deviations may occur due to different radial positioning of the sensor elements.

[0097] Radial arrangement offers the advantage of greater flexibility in mechanical integration; however, stray field suppression is slightly reduced due to the varying radial distances between sensor elements. This is because the sensor elements are exposed to different magnetic field strengths, which can lead to a decrease in interference field suppression due to the nonlinear characteristics of the sensor used (e.g., a TMR sensor). However, in practice, this can be compensated for by calibration or signal correction in the evaluation unit.

[0098] Figure 6 An embodiment of a magnetic axis external angle measurement system with a tangential sensor arrangement is shown.

[0099] Figure 6 The left side first shows the raw output signals (“BySignals”) of the two sensor devices 110A and 110B. Due to their tangential arrangement, magnetic field sensing elements 112A and 112B detect tangentially oriented magnetic fields along the periphery of the rotation axis 102. Here, the two magnetic field sensing elements 112A and 112B within each sensor device 110A and 110B are arranged tangentially offset from each other, but are positioned at the same radial distance from the axis 103. Therefore, the signals of the two elements 112A and 112B within each sensor device 110A and 110B have similar amplitudes, but with a slight phase shift due to their peripheral positions.

[0100] exist Figure 6 The middle section shows how differential sine and cosine output signals are generated through differential formation between two tangentially offset sensor elements 112A and 112B within each sensor device 110A and 110B. These differential signals enable precise calculation of the angular attitude of the axis.

[0101] Finally, Figure 6 The right-hand side shows the angle measurements over a full 360° rotation. Curve 610 illustrates the angle measurements, while curve 620 shows the measurement error that occurs during the rotation of the shaft. The measurement error shown remains small but has occasional peaks, which can be attributed to increased sensitivity to stray fields due to the tangential arrangement. In the tangential arrangement, magnetic stray fields are partially enhanced, particularly in ferromagnetic shafts, which may result in slightly reduced robustness relative to disturbance effects. The characteristic of the tangential arrangement remains the possibility of a very compact structural configuration, which is particularly useful in applications with limited structural space. High angle measurement accuracy can also be achieved in this arrangement through appropriate signal processing, for example, by means of a microcontroller or an ASIC with subsequent signal correction.

[0102] In summary, a magnetic OoS angle measurement system is proposed, comprising a permanent magnet (ring-shaped or disk-shaped) magnetized along its diameter and two differential sensors 110A and 110B arranged with an angular offset (electrical angle) of 90° from each other. One sensor is located at the center of the magnetic poles, while the other sensor is positioned at the magnetic pole transition region. During shaft rotation, the two sensors provide differential output signals (sine and cosine signals) with high stray field robustness. The angular position of the shaft can be calculated from these signals using an ASIC or microcontroller.

[0103] In a preferred embodiment, the chip is oriented parallel to the axis (YZ plane), wherein sensor elements 112A, 112B (xMR or VHALL sensors) respond to an axial magnetic field generated by a permanent magnet.

[0104] In the second embodiment, the chip is oriented in the XY plane, so that the sensor element is sensitive to the radial magnetic field component. Here, the first and second sensor elements 112A and 112B are positioned at different radial distances from the magnet, thus creating an air gap difference between them.

[0105] In the third embodiment, the chip is also oriented in the XY plane; however, the sensor element here responds to a tangential magnetic field. In this configuration, the sensor element is located at the same radial distance from the center of the axis or magnet.

[0106] Figure 7 A schematic diagram of a device 200 for determining the angle of a rotation axis 102 according to another embodiment is shown. The device 200 includes at least three magnetic field sensors 210 (210A, 210B, 210C) and an evaluation unit 220, which are arranged around a permanent magnet 104 fixed to the axis 102.

[0107] The permanent magnet 104 can be constructed as a ring-shaped or disk-shaped magnet magnetized along its diameter, as described, for example, in conjunction with the foregoing embodiments. In some embodiments, the permanent magnet 104 can be implemented as a low-cost ferrite magnet without rare-earth elements.

[0108] Relative to combination Figures 1 to 6 The described embodiment with two magnetic field sensors, according to Figure 7 The device 200 has three magnetic field sensors 210A, 210B, and 210C. These three magnetic field sensors 210A, 210B, and 210C can be arranged around the permanent magnet 104 at equidistant angular distances of 120° each, as shown below. Figure 7 As shown. Here, the magnetic field sensor 210 can be arranged radially outside the permanent magnet 104, so that the magnetic field generated by the permanent magnet 104 is detected by the magnetic field sensor 210 substantially in the radial direction. This symmetrical arrangement can help to at least partially compensate for errors caused by magnetization and geometric defects of the permanent magnet 104, such as inhomogeneities of the magnet material, variations in remanent flux density, or irregularities caused by manufacturing.

[0109] In some embodiments, the air gap between the permanent magnet 104 and the magnetic field sensor 210 may be greater than 3 mm. An increased air gap can help reduce the impact on higher harmonics of the magnetic field, as these harmonics weaken more than the fundamental frequency with increasing distance from the permanent magnet 104. This can improve signal quality and reduce angle calculation errors. Furthermore, a larger air gap reduces the mechanical requirements for the mounting accuracy of the magnetic field sensor 210 and allows for simpler integration into surrounding systems.

[0110] Each of the three magnetic field sensors 210A, 210B, and 210C is configured to detect a component of the magnetic field generated by the permanent magnet 104 and output a corresponding sensor signal. In some embodiments, each magnetic field sensor 210 may be configured to detect the radial component of the magnetic field. In alternative embodiments, axial or tangential field components may also be detected, as described in conjunction with the preceding figures.

[0111] In some embodiments, the magnetic field sensor 210 may be configured as a TMR sensor, which is particularly suitable for high-resolution angle measurement applications due to its high sensitivity and low noise. Alternatively, the magnetic field sensor 210 may be configured as other types of xMR sensors or vertical Hall sensors.

[0112] In some embodiments, each magnetic field sensor 210 can be configured as a differential sensor with two magnetic field-sensitive measurement elements, wherein the respective magnetic field sensor 210 can be configured to form a differential signal from the measurement signals of its two measurement elements. A differential measurement arrangement can achieve greater robustness relative to uniform interference fields, such as external stray fields. The spatial arrangement of the two magnetic field-sensitive measurement elements of each magnetic field sensor 210 can here be selected, as described in conjunction with the preceding figures, such that the axial field component or the tangential field component is detected differentially.

[0113] Evaluation unit 220 is configured to receive sensor signals from three magnetic field sensors 210A, 210B, and 210C, and thereby derive sine and cosine signals by means of transformation. In some embodiments, the transformation may be a Clarke transform, applied to the three sensor signals, which are staggered by 120° respectively, to produce two orthogonal signal components. Based on the thus obtained sine and cosine signals, evaluation unit 220 can calculate the angular information of axis 102, for example, using the atan2 function.

[0114] For illustration, assume that the three magnetic field sensors 210A, 210B, and 210C are in the angular orientation of axis 102. The following sensor signals are output:

[0115] Here, A represents the signal amplitude, and the three signals are staggered by 120° from each other. The Clarke transform can be used on these three signals to generate two orthogonal signal components S. α and S β :

[0116] It can be generated by using sensor signals:

[0117] Therefore, the obtained signal component S α and S β Corresponding to a sinusoidal signal or a sinusoidal signal, it can be directly used for angle calculation. The evaluation unit 220 can thus calculate the angle information of shaft 102 according to the following relationship:

[0118] The advantage of this approach is that the common-mode share (common-mode offset) superimposed on all three sensor signals is algebraically eliminated through the Clarke transform. This can help reduce measurement errors that may be caused by temperature shifts, aging, or external interference fields without requiring explicit offset calibration.

[0119] Alternatively, the transformation may include a linear transformation based on the Moore-Penrose pseudoinverse, least squares estimation, or discrete Fourier transform. The choice of transformation may depend on the specific arrangement of the magnetic field sensor 210 and the corresponding requirements for computational cost and robustness.

[0120] In some embodiments, the evaluation unit 220 may further include signal preparation, which may perform offset and amplitude corrections before angle calculations and optionally perform ellipse fitting of the input signal. The calibration step can help reduce residual systematic errors in the sensor signal.

[0121] For illustration, assume that evaluation unit 220 provides two signal components S after applying the Clarke transform. α and S β Ideally, it has the following form .

[0122] However, in practice, these signals can be represented by the summed offset fraction O. α O β Through their different amplitudes A α ≠Aβ And obtained through the phase misalignment error δ, the actual signal can take the following form:

[0123] If these erroneous signals are used directly for the atan2 function, this can lead to periodic angular errors. These errors can be caused, for example, by manufacturing tolerances of the magnetic field sensor 210, by mechanical mounting tolerances, by temperature drift, or by inhomogeneities of the permanent magnet 104.

[0124] In the first step, evaluation unit 220 can determine and subtract the offset share O. α and O β The offset component can be estimated, for example, as a signal. and Average time during the complete turnaround of shaft 102:

[0125] After the offsets are subtracted, the offset-corrected signal is preserved:

[0126] In the second step, the evaluation unit 220 can perform amplitude correction to establish that the amplitudes of the two signal components are equal. For example, amplitude A α and A β It can be estimated as the maximum value of the corresponding offset-corrected signal during the full turnaround:

[0127] The amplitude-corrected signal can be normalized to a common reference amplitude A. ref To calculate:

[0128] In some embodiments, the evaluation unit 220 may selectively perform elliptic fitting to correct remaining errors, particularly the phase misalignment error δ between the two signal components. The basic idea of ​​elliptic fitting is to correct the phase misalignment error δ between the two signal components by... Apply on The resulting Lissajous figure describes a circle in the absence of errors. Amplitude differences and phase misalignment errors deform this circle into an ellipse, as shown in the subsequent equations:

[0129] Evaluation unit 220 can be configured to, for example, use least squares to evaluate signal pairs detected during operation ( , Estimate the parameters of the ellipse (especially the semi-axis and orientation). Then, evaluation unit 220 can calculate a linear transformation matrix M from the estimated ellipse parameters, which maps the ellipse to the unit circle: [ ] =M[ ]

[0130] Therefore, the corrected signal and According to =atan2( The data is sent to the angle calculation.

[0131] In some embodiments, the calibration parameters may be determined once during the calibration phase, such as during the first run of device 200, and stored in the non-volatile memory of evaluation unit 220. In other embodiments, evaluation unit 220 may be configured to adaptively update the calibration parameters during continuous operation to continuously compensate for slow changes in sensor characteristics, such as due to aging or temperature fluctuations.

[0132] The evaluation unit 220 may be configured as an application-specific integrated circuit (ASIC), a microcontroller, or a field-programmable gate array (FPGA), or a combination of these components, as described in conjunction with previous embodiments.

[0133] Figure 8 A schematic diagram of another embodiment of the device 200 for determining the angle of the rotation axis 102 is shown. Figure 8 The illustrated embodiments and Figure 7 The difference in the described embodiment is that, instead of three magnetic field sensors, six magnetic field sensors 210 (210-1, 210-2, 210-3, 210-4, 210-5, 210-6) are provided. These magnetic field sensors can be arranged around the permanent magnet 104 at equidistant angular distances of 60° each, as shown below. Figure 8 As shown.

[0134] Regarding the structure and function of permanent magnet 104, shaft 102, and evaluation unit 220, Figure 7 The relevant implementation plans are applicable accordingly.

[0135] Evaluation Unit 220 (in Figure 8 (Not explicitly shown in the document) It can be configured to first calculate three intermediate signals D from six sensor signals. a D b Dc Each intermediate signal here can be formed by the difference between the sensor signals of two opposing magnetic field sensors:

[0136] in, S k The sensor signal represents the magnetic field sensor 210-k. The three opposing sensor pairs are (210-1, 210-5), (210-2, 210-6) and (210-3, 210-4), wherein each sensor and its corresponding opposing pair are arranged 180° apart.

[0137] For illustration, assume the six magnetic field sensors 210-1 to 210-6 are in angular orientation along axis 102. The following sensor signals are output, where, This indicates the corresponding angular position of sensor 210-k around the permanent magnet 104: S k ( ) = A·cos( -

[0138] Because each sensor 210-k and its opposite pair are arranged 180° apart, the appropriate signal for the corresponding signal is:

[0139] Differential forming thus provides for each sensor pair:

[0140] Among them, the angular positions of the three reference sensors 210-1, 210-2, and 210-3 , , They are spaced 120° apart from each other. Therefore, the intermediate signal D formed in this way a D b D c Having and in Figure 7 In the three-sensor example described, the sensor signals are identical but 120° out of phase with each other, yet have twice the signal amplitude of 2A. This increased signal amplitude can help improve the signal-to-noise ratio and increase the accuracy of angle determination.

[0141] Evaluation unit 220 can be configured to apply the Clarke transform to the three intermediate signals D. a D b Dc In order to derive the sinusoidal signal S β S and cosine signal S α Calculations are performed here in conjunction with... Figure 7 The embodiments described above are carried out similarly, except that the input signal to be transformed is the intermediate signal D. a D b D c :

[0142] Based on S α and S β The evaluation unit 220 can be based on =atan2( The angle information is calculated. Figure 8 The signal curve 240 shown in the lower right corner of the image shows the generated sine signal (shown as a solid line, signal 1) and the cosine signal after applying the Clarke transform (shown as a dashed line, signal 2).

[0143] Figure 8 The arrangement of the six sensors shown is relative to the... Figure 7 The advantages of the three-sensor arrangement include greater robustness relative to external interference fields and installation errors. Because the differential signal only detects the antisymmetric portion of the magnetic field, uniform external stray fields acting equally on all six sensors are effectively suppressed through differential formation.

[0144] Furthermore, installation tolerances, such as the eccentric arrangement of the circuit board (PCB eccentricity), can be at least partially compensated by the symmetrical arrangement of mutually opposing sensor pairs.

[0145] This helps reduce adjustment costs during installation and improves the robustness of device 200 relative to tolerances caused by manufacturing.

[0146] In some embodiments, the evaluation unit 220 may also be configured to mutually check the reliability of the three intermediate signals 230a, 230b, and 230c in order to identify erroneous sensor signals and provide corresponding diagnostic information.

[0147] Figure 7 An arrangement with exactly three magnetic field sensors 210 (k=1) is described, and Figure 8 An arrangement with six magnetic field sensors 210 (k=2) is described, while the device 200 according to this embodiment may include a number of N=3k magnetic field sensors 210, where k≥2 is an integer.

[0148] Here, N magnetic field sensors 210 can be arranged around axis 102 at a uniform angular distance of 360° / N, resulting in a completely equidistant sensor arrangement. The corresponding embodiments described in conjunction with the preceding figures are applicable to the structure and characteristics of each magnetic field sensor 210 and the permanent magnet 104.

[0149] Evaluation unit 220 can be configured to divide N magnetic field sensors 210 into k subsets T1, T2, ..., T k Each subset contains three magnetic field sensors 210. Here, each subset T... i The three magnetic field sensors 210 can be selected such that they are arranged around the permanent magnet 104 at 120° offset from each other.

[0150] To illustrate, observation as Figure 8 The example shown has N=6 (k=2). The six magnetic field sensors 210-1 to 210-6, each with an angular distance of 60°, can be divided into two subsets:

[0151] Here, the three sensors in each subset are offset from each other by an angle of 120°, and thus form a system based on... Figure 7 A complete three-sensor arrangement.

[0152] In another embodiment with N=9 (k=3) and an angular distance of 40° between adjacent sensors, three subsets can be formed. Here, the three sensors in each subset also have an angular offset of 120° respectively.

[0153] Evaluation unit 220 can be configured to evaluate each subset T. i For three related sensor signals , , Perform the Clarke transform, such as combining Figure 7 As described. According to the Clarke transform, it is possible to apply this to each subset T. i Derive the cosine signal and sinusoidal signal Then, the evaluation unit 220 can evaluate each subset T. i Calculate the sub-angle

[0154] Evaluation unit 220 can be configured to calculate the final rotation angle of axis 102. As the average of k sub-angles:

[0155] In some embodiments, the average formation can be implemented as a weighted average, wherein different subsets can be assigned different weights, such as assigning lower weights to sensors with known higher noise or greater bias.

[0156] By increasing the number of subsets k and thus the total number of magnetic field sensors 210, a gradual improvement in angle determination accuracy can be achieved. Each additional subset provides an independent estimate of the rotation angle of shaft 102, thereby statistically reducing random measurement bias through averaging. Furthermore, systematic errors caused by magnetic field inhomogeneities or manufacturing tolerances of the individual magnetic field sensors 210 can be at least partially compensated for by spatial overscanning of the magnetic field.

[0157] In some embodiments, the evaluation unit 220 can also be configured to mutually check k sub-angles. … Credibility. If sub-angle If a sub-angle differs from the others by a preset threshold, the evaluation unit 220 can disregard that sub-angle in the average value formation and optionally output a corresponding diagnostic signal. In this way, the device 200 can continue to provide reliable angle values ​​even when each of the individual magnetic field sensors 210 malfunctions or operates incorrectly.

[0158] While specific embodiments and examples have been described in this invention, it will be understood by those skilled in the art that the invention is not limited thereto. Rather, the described embodiments can be modified and combined in various ways without departing from the scope of protection of this invention.

[0159] In particular, the various features of the described embodiments, such as the number and arrangement of magnetic field sensors, the type of magnetic field sensing element, the geometry and magnetization direction of the permanent magnet, and the design of the transformation and evaluation units for signal processing, can be selected independently of each other and combined with each other in any technically reasonable manner. Therefore, according to Figure 1 The differential axial sensor arrangement can, for example, be based on... Figure 8 A six-sensor configuration combination, or according to Figure 7 The Clarke transform can be combined with an elliptic adaptor used for calibration according to the corresponding embodiment, if this is technically feasible and not contradictory.

[0160] The terms used in this invention, such as “comprising,” “having,” “including,” and their grammatical variations, are not to be construed as definitive and do not exclude the presence of additional elements, features, steps, or components. Furthermore, singular expressions should not be construed as limiting to exactly one element unless explicitly stated otherwise.

[0161] Whenever numerical values, angular ranges, distances, or other quantitative descriptions are mentioned in this invention, they should be understood as non-deterministic examples. Those skilled in the art will recognize that different values ​​can also be selected according to the corresponding requirements of the application.

[0162] The embodiments described in this invention can be used to solve angle measurement tasks in a variety of technical application areas, particularly in automotive electronics, industrial automation, robotics and medical technology systems, but this invention is not limited to these areas.

[0163] It should be understood that the present invention includes all technically achievable combinations and modifications of the described features, even when they are not explicitly described. The scope of protection of the present invention is defined by the appended claims.

[0164] It should be noted that the specification and accompanying drawings only illustrate the principles of the proposed method and apparatus. Different arrangements of heat sources are possible in the art, and although these arrangements are not explicitly described or shown herein, they embody the principles of the invention and are included within its scope. Furthermore, all examples and embodiments outlined in this document are substantially and explicitly for illustrative purposes only, in order to assist the reader in understanding the principles of the proposed method and apparatus. In addition, all statements in this document describing the principles, aspects, and embodiments of the invention and their specific examples should also include their equivalents.

Claims

1. A device (100) for determining the angle of a rotating shaft (102), comprising: A permanent magnet (104) fixed on the rotating shaft (102) has at least one pair of magnetic poles; At least two magnetic sensor devices (110A; 110B) spaced apart from each other are arranged about the axis (102) with an angular offset relative to the magnetic pole pair, and each has at least two magnetic field sensing elements (112A). 112B), the magnetic field sensing element generates a differential output signal; and An evaluation unit (120) is configured to receive differential output signals provided by at least two sensor devices (110A; 110B) and thereby determine the angle information of the axis (102).

2. The device (100) according to claim 1, wherein, The permanent magnet (104) is constructed to be bipolar, and the at least two magnetic sensor devices (110A; 110B) are arranged around the axis (102) with an angular offset of 90° from each other.

3. The device (100) according to any one of the preceding claims, wherein, The permanent magnet (104) is constructed in the form of a ring or a disk.

4. The device (100) according to any one of the preceding claims, wherein, Each of the magnetic sensor devices (110A; 110B) includes two magnetic field sensors (112A; 112B), which are constructed as xMR or VHall sensor elements.

5. The device (100) according to any one of the preceding claims, wherein, The at least two magnetic sensor devices (110A; 110B) each have the same radial distance as the permanent magnet (104).

6. The device (100) according to any one of the preceding claims, wherein, The at least two magnetic field sensing elements (112A; 112B) of the magnetic sensor device (110A; 110B) are respectively arranged in a plane extending parallel to or perpendicular to the axis (103).

7. The device (100) according to any one of the preceding claims, wherein, The at least two magnetic field sensing elements (112A; 112B) of the magnetic sensor device (110A; 110B) are arranged axially spaced apart in a plane extending parallel to the axis (103).

8. The device (100) according to any one of claims 1 to 6, wherein, The at least two magnetic field sensing elements (112A; 112B) of the magnetic sensor device (110A; 110B) are arranged radially spaced apart in a plane extending perpendicular to the axis (103).

9. The device (100) according to any one of claims 1 to 6, wherein, The at least two magnetic field sensing elements (112A; 112B) of the magnetic sensor device (110A; 110B) are arranged tangentially spaced apart in a plane extending perpendicular to the axis (103).

10. The device (100) according to any one of the preceding claims, wherein, The shaft is constructed to be non-ferromagnetic.

11. A method for determining the angle of a rotation axis (102), comprising: A permanent magnet (104) having at least one pair of magnetic poles is fixed on the rotating shaft (102); At least two magnetic sensor devices (110A; 110B) are arranged about the axis (102) with an angular offset relative to the magnetic pole pair and each has at least two magnetic field sensing elements (112A; 112B）； The differential output signal is detected by the at least two magnetic sensor devices (110A; 110B); and The differential output signal is evaluated to determine the angle.

12. A device (200) for determining the angle of a rotating shaft (102), comprising: A permanent magnet (104) having at least one pair of magnetic poles is fixed on the rotating shaft (102); At least three magnetic field sensors (210) are arranged around the permanent magnet (204) at equal angular distances, wherein each magnetic field sensor (210) is configured to detect the magnetic field generated by the permanent magnet (104) and output a corresponding sensor signal; and Evaluation unit (220), the evaluation unit is configured for Receive sensor signals from the at least three magnetic field sensors (210), By means of transformation, sine and cosine signals are derived from the sensor signal, and The angle information of the axis (102) is calculated based on the sine signal and the cosine signal.

13. The device (200) according to claim 12, wherein, Each magnetic field sensor (210) is configured to detect the radial component of the magnetic field generated by the permanent magnet (104).

14. The device (200) according to claim 12 or 13, wherein, The permanent magnet (104) is magnetized along its diameter.

15. The device (200) according to any one of claims 12 to 14, wherein, The transformation is the Clarke transform.

16. The device (200) according to any one of claims 12 to 15, wherein, The magnetic field sensor (210) is configured as a TMR sensor.

17. The device (200) according to any one of claims 12 to 16, wherein, Each magnetic field sensor (210) is constructed as a differential sensor having two magnetic field-sensitive measuring elements, wherein each magnetic field sensor (210) is configured to form a differential signal from the measurement signals of its two measuring elements.

18. The device (200) according to claim 17, wherein, The two magnetic field-sensitive measuring elements of each magnetic field sensor (210) are arranged such that... The axial component of the magnetic field generated by the permanent magnet (104) is detected differentially, wherein the chip plane of each magnetic field sensor (210) is oriented substantially parallel to the axis (102) or the surface of the permanent magnet (104); or The tangential component of the magnetic field generated by the permanent magnet (104) is detected differentially, wherein the magnetic field sensitive measuring elements are spaced apart from each other along the periphery of the shaft (102) tangentially and arranged at the same radial distance as the axis of the shaft (102).

19. The device (200) according to any one of claims 12 to 18, wherein, Three magnetic field sensors (210) are arranged around the permanent magnet (104) at an angular distance of 120° from each other.

20. The device (200) according to any one of claims 12 to 18, wherein, Six magnetic field sensors (210) are arranged around the permanent magnet (104) at an angular distance of 60° from each other.

21. The device (200) according to claim 20, wherein, The evaluation unit (220) is also configured to, Three intermediate signals are calculated, each formed by the difference between the sensor signals of two opposing magnetic field sensors (210); and The transformation is applied to the three intermediate signals.

22. The device (200) according to any one of claims 12 to 21, wherein, The permanent magnet (204) is constructed as a ferrite magnet.

23. The device (200) according to any one of claims 12 to 22, wherein, The permanent magnet (104) is constructed in the form of a ring or a disk.

24. The device (200) according to any one of claims 12 to 23, wherein, The magnetic field sensor (210) is arranged radially outside the permanent magnet (104).

25. The device (200) according to any one of claims 12 to 24, wherein, The air gap between the permanent magnet (204) and the magnetic field sensor (210) is greater than 3 mm.

26. The device (200) according to any one of claims 12 to 25, wherein, The evaluation unit (220) is also configured to perform calibration, which includes: The sensor signal is normalized by offset and amplitude correction; and / or Ellipse fitting is used to extract the correction factor.

27. The device (200) according to any one of claims 12 to 26, wherein, The evaluation unit (220) is configured to calculate the angle information from the sine signal and the cosine signal using the atan2 function.

28. The device (200) according to any one of claims 12 to 27, wherein, The shaft (102) is constructed to be non-ferromagnetic.

29. The device (200) according to any one of claims 12 to 30, wherein, The device (200) includes a number of magnetic field sensors (210) of N=3k (k≥2), which are arranged around the axis (102) at a uniform angular distance of 360° / N. The evaluation unit (220) is configured to divide the N magnetic field sensors (210) into k subsets, each subset containing three magnetic field sensors (210), wherein the three magnetic field sensors (210) in each subset are staggered by 120° from each other. For each subset, the evaluation unit (220) performs a Clarke transform on the three relevant sensor signals to obtain each sine and cosine signal; The evaluation unit (220) determines the sub-angle from each sine / cosine pair using the arctangent function; and The evaluation unit (220) calculates the final rotation angle of the shaft (102) as the average of k sub-angles.

30. A method for determining the angle of a rotation axis (202), comprising: The radial magnetic field component is detected by means of at least three magnetic field sensors (210), which are arranged at equal angular distances around a permanent magnet (104) fixed on the shaft (102) and magnetized along the diameter, wherein each magnetic field sensor (210) outputs a corresponding sensor signal; Sine and cosine signals are derived from the sensor signals of the at least three magnetic field sensors (210) by means of transformation; and The angle information of the axis (102) is calculated based on the sine signal and the cosine signal.

31. An angle measurement system (300) for 360° absolute angle recognition, comprising: Rotatable shaft (102); A permanent magnet (104) magnetized along the diameter is torsionally connected to the shaft (102); A circuit board, which is fixedly arranged relative to the axis (102); At least three magnetic field sensors (210) are mounted on the circuit board around the permanent magnet (104) at equal angular distances, wherein each magnetic field sensor (210) is configured to detect a radial magnetic field component. and Processor, the processor configured for Receive the sensor signals from the at least three magnetic field sensors (210). The sine and cosine signals are derived using transformation, and Calculate the absolute angle value of the axis (102).

32. A computer program product comprising instructions that, when executed by a processor, cause the processor to... Receive sensor signals from at least three magnetic field sensors (210), which are arranged at equal angular distances around a permanent magnet (104) magnetized along the diameter; Sine and cosine signals are derived from the sensor signal using a transformation; and Angle information is calculated based on the sine and cosine signals.

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