阅读说明：本技术 磁传感器设备、系统和方法 (Magnetic sensor device, system and method ) 是由 N·迪普雷 L·通贝兹 G·克洛斯 Y·比多 D·戈伊瓦尔茨 于 2020-08-20 设计创作，主要内容包括：本发明涉及磁传感器设备、系统和方法。角位置传感器系统,该系统包括：围绕旋转轴可旋转的圆柱形磁体；以及角位置传感器设备,该角位置传感器设备包括：衬底,该衬底包括被配置成用于测量第一方向(X)上的第一磁场分量(Bx1)和垂直于第一方向(X)的第二方向(Y；Z)上的第二磁场分量(By1；Bz1)的多个磁敏元件；以及处理电路,该处理电路被配置成用于计算角位置(α)；该传感器设备被取向成使得第一方向(X)按周向方向取向并且第二方向(Y,Z)与旋转轴平行或正交；传感器设备位于预定义位置处,在该预定义位置处,在360°角范围上,与第一磁场分量和第二磁场分量(By1；Bz1)正交的第三磁场分量(Bz1；Bz1)的幅度可以忽略不计。(The invention relates to a magnetic sensor device, a system and a method. An angular position sensor system, the system comprising: a cylindrical magnet rotatable about a rotation axis; and an angular position sensor apparatus comprising: a substrate comprising a plurality of magneto-sensitive elements configured for measuring a first magnetic field component (Bx1) in a first direction (X) and a second magnetic field component (By 1; Bz1) in a second direction (Y; Z) perpendicular to the first direction (X); and a processing circuit configured for calculating an angular position (α); the sensor device is oriented such that the first direction (X) is oriented in a circumferential direction and the second direction (Y, Z) is parallel or orthogonal to the rotation axis; the sensor device is located at a predefined position at which the amplitude of a third magnetic field component (Bz 1; Bz1) orthogonal to the first and second magnetic field components (By 1; Bz1) is negligible over an angular range of 360 deg..)

1. An angular position sensor system (500; 900; 1000; 1100; 1200; 1300; 1400; 1500; 1600; 2500) comprising:

a permanent magnet (501; 901; 1001; 1101; 1201; 1301; 1401; 1501; 1601; 2501) for generating a magnetic field, the magnet being a ring magnet or a disc magnet, the magnet being rotatable around a rotational axis by an angular position (a) to be determined; and

an angular position sensor device (502; 902; 1002; 1102; 1202; 1302; 1402; 1502; 1602; 2502) having a substrate comprising a plurality of magneto-sensitive elements;

it is characterized in that the preparation method is characterized in that,

the magneto-sensitive element is configured for measuring at least a first magnetic field component (Bx1) in a first direction (X) and a second magnetic field component (By 1; Bz1) in a second direction (Y; Z) perpendicular to the first direction (X); and is

The sensor device further comprises a processing circuit configured for calculating the angular position (a) of the magnet based on at least the measured first (Bx1) and second (By 1; Bz1) magnetic field components; and is

The sensor device is oriented such that the first direction (X) is oriented in a circumferential direction with respect to the rotation axis and such that the second direction (Y, Z) is parallel to or orthogonal to the rotation axis; and is

The sensor device is located at a predefined position relative to the magnet, at which predefined position a third magnetic field component (Bz 1; Bz1) orthogonal to the first and second magnetic field components (By 1; Bz1) has an amplitude of less than 20% of the amplitude of the first and/or second magnetic field component over a predefined angular range.

2. The angular position sensor system of claim 1,

wherein the sensor device is located at a predefined position relative to the magnet where the third magnetic field component (Bz 1; By1) not used in the calculation of the angular position over an angular range of 360 ° has an amplitude of less than 15% of the first and/or second magnetic field component, or less than 10% of the first and/or second magnetic field component, or less than 5% of the first and/or second magnetic field component;

or wherein the sensor device is located at a predefined position relative to the magnet at which the third magnetic field component (Bz 1; By1) that was not used in the calculation of the angular position has an amplitude of less than 5 millitesla, or less than 4 millitesla, or less than 3 millitesla, or less than 2 millitesla, or less than 1 millitesla.

3. Angular position sensor system (900; 1000; 1100) according to claim 1,

wherein the magnet has an outer radius (Ro); and is

Wherein the predefined position is defined by a distance (g) below or above a bottom surface or a top surface of the magnet in a range from 1.0 to 5.0mm and by a radial distance (Rs) in a range from Ro-7mm to Ro +7mm, in a range from Ro-7mm to Ro-1mm, or in a range from Ro +1mm to Ro +7 mm.

4. Angular position sensor system (500; 1200; 1300) according to claim 1,

wherein the magnet is a ring magnet having an inner radius (Ri) and an outer radius (Ro); and is

Wherein the predefined position is defined by a distance (g) below or above a bottom surface or a top surface of the magnet in the range from 1.0 to 5.0mm and by a radial distance (Rs) in the range from Ri + (Ro-Ri) × 35% to Ri + (Ro-Ri) × 65%.

5. Angular position sensor system (1400; 1500; 1600) according to claim 1,

wherein the magnet has an outer radius (Ro) and an axial height (H); and is

Wherein the predefined position is located in a plane substantially midway between the bottom and top surfaces of the magnet and the radial distance (Rs) is in the range from Ro +1.0mm to Ro +10 mm.

6. An angular position sensor system (500; 900; 1100; 1200; 1300; 1400; 1600) according to claim 1, wherein the sensor device is oriented such that the second axis (Y) is orthogonal to the rotation axis.

7. The angular position sensor system (1000; 1500) according to claim 1, wherein the sensor device is oriented such that the second axis (Y) is parallel to the rotation axis of the magnet.

8. The angular position sensor system according to claim 1, characterized in that the sensor device comprises at least one sensor (S1), the sensor (S1) comprising an integrated magnetic concentrator structure IMC and only four horizontal hall elements (HP1, HP2, HP3, HP4) arranged at the circumference of the IMC and angularly spaced by 90 °.

9. The angular position sensor system of claim 8,

wherein the sensor device is configured for determining a first magnetic field component (Bx1) at a first sensor position (X1) oriented parallel to the substrate based on a first difference of signals obtained from a first pair of two horizontal hall elements (HP1, HP2) of the only four horizontal hall elements;

and wherein the sensor device is configured for determining a second magnetic field component (By1) oriented parallel to the substrate at the first sensor position (X1) based on a second difference of signals obtained from a second pair of two further horizontal hall elements (HP3, HP4) of the only four horizontal hall elements.

10. The angular position sensor system of claim 9,

wherein the horizontal Hall elements of the first pair are individually trimmed for determining the first magnetic field component (Bx 1);

and wherein the horizontal hall elements of the second pair are individually trimmed for determining the second magnetic field component (By 1).

11. The angular position sensor system of claim 8,

wherein the sensor device is configured for determining a first magnetic field component (Bx1) at a first sensor position (X1) oriented parallel to the substrate based on a first difference of signals obtained from a first pair of two horizontal hall elements (HP1, HP2) of the only four horizontal hall elements;

and wherein the sensor device is configured for determining a second magnetic field component (Bz1) at the first sensor position (X1) oriented orthogonal to the substrate based on a sum of signals obtained from a second pair of two further horizontal hall elements (HP3, HP4) of the only four horizontal hall elements.

12. The angular position sensor system of claim 11,

wherein the horizontal Hall elements of the first pair are individually trimmed for determining the first magnetic field component (Bx 1);

and wherein the horizontal hall elements of the second pair are individually trimmed for determining the second magnetic field component (Bz 1).

13. The angular position sensor system of claim 1,

wherein the sensor device comprises at least one sensor comprising an integrated magnetic concentrator structure IMC, first and second horizontal Hall elements located on opposite sides of the IMC, and a third horizontal Hall element located between the first and second horizontal Hall elements below the IMC; or

Wherein the sensor device comprises at least one sensor comprising a first vertical hall element oriented for measuring a first magnetic field component (Bx1) in the first direction (X) and a second vertical hall element oriented for measuring a second magnetic field component (By1) in the second direction.

14. The angular position sensor system of claim 1,

wherein the magnetic sensor device comprises a first sensor (S1), the first sensor (S1) comprising the plurality of magneto-sensitive elements configured for measuring the first magnetic field component (Bx1) oriented in the first direction (X) at the first sensor position (X1) and the second magnetic field component (By 1; Bz1) oriented in the second direction (Y; Z) perpendicular to the first direction (X); and is

Wherein the magnetic sensor device further comprises a second sensor (S2), the second sensor (S2) comprising a plurality of magneto-sensitive elements configured for measuring a third magnetic field component (Bx2) oriented in the first direction (X) and a fourth magnetic field component (By 2; Bz2) oriented in the second direction (Y; Z) at a second sensor position (X2) spaced apart from the first sensor position;

and wherein the processing circuitry is further configured for determining a first magnetic field gradient (dBx/dx) based on the first magnetic field component (Bx1) and the third magnetic field component (Bx2), and for determining a second magnetic field gradient (dBy/dx; dBz/dx) based on the second magnetic field component and the fourth magnetic field component;

wherein the processing circuitry is configured for calculating the angular position (a) of the magnet based on the first magnetic field gradient (dBx/dx) and the second magnetic field gradient (dBy/dx; dBz/dx).

15. The angular position sensor system of claim 1,

wherein the magnet has an outer diameter (Do) in the range from 10 to 50mm, and wherein the magnet has a height (H) in the range from 2 to 10 mm; or

Wherein the magnet has an outer diameter (Do) in the range from 15 to 30mm, and wherein the magnet has a height (H) in the range from 2 to 5 mm; or

Wherein the magnet has an outer diameter (Do) in the range from 15 to 30mm, and wherein the magnet has a height (H) in the range from 5 to 10 mm.

16. The angular position sensor system of claim 1,

wherein the sensor device is located at a radial distance (Rs) of at least 5mm from the axis of rotation.

17. The angular position sensor system of claim 1,

wherein the magnet is a two-pole magnet; or

Wherein the magnet is a quadrupole magnet; or

Wherein the magnet is a multi-pole magnet having at least six poles.

Technical Field

The present invention relates generally to the field of magnetic sensor systems and devices and methods, and more particularly to angular position sensor systems, angular position sensor devices and methods of determining angular position.

Background

Magnetic sensor systems, in particular angular position sensor systems, are known in the art. They offer the advantage that the angular position can be measured without physical contact, avoiding problems of mechanical wear, scratching, rubbing, etc.

There are many variations of position sensor systems that address one or more of the following needs: the use of simple or inexpensive magnetic structures, the use of simple or inexpensive sensor devices, the ability to measure over a relatively large range, the ability to make high precision measurements, the need for simple calculations, the ability to make high speed measurements, the ability to be highly robust to positioning errors, the ability to be highly robust to external interference fields, the provision of redundancy, the ability to detect errors, the ability to detect and correct errors, the ability to have a good signal-to-noise ratio (SNR), and the like.

Often, two or more of these requirements conflict with each other, and therefore a tradeoff is required.

US2018/0372475a1, the entire content of which is incorporated herein by reference, discloses a device for rotation angle detection.

There is always room for improvement or replacement.

Disclosure of Invention

It is an object of embodiments of the present invention to provide a magnetic position sensor system capable of determining the angular position of a sensor device relative to a magnet.

It is an object of embodiments of the present invention to provide a magnetic position sensor system in which the position can be determined with improved accuracy.

It is an object of embodiments of the present invention to provide a magnetic position sensor system having (1) improved robustness to cross-talk (e.g. between different magnetic field components Bx, By, Bz), and/or (2) improved robustness to external disturbing fields, and/or (3) improved robustness to long-term drift (e.g. caused By mechanical stress variations on the sensor device), and preferably all three improved robustness.

It is an object of embodiments of the present invention to provide a magnetic position sensor system with improved robustness to (1) cross-talk and (2) external disturbing fields.

It is an object of embodiments of the present invention to provide a magnetic position sensor system with improved robustness to (1) cross-talk and (2) long-term drift.

It is an object of embodiments of the present invention to provide a magnetic position sensor system with improved robustness to (1) external interference fields and (2) long term drift.

These objects are accomplished by embodiments of the present invention.

According to a first aspect, the present invention provides an angular position sensor system comprising: a permanent magnet for generating a magnetic field, the magnet being a cylindrical magnet (e.g. a ring magnet or a disc magnet) rotatable about an axis of rotation by an angular position to be determined; and an angular position sensor apparatus having a substrate including a plurality of magnetic sensing elements; wherein the magnetic sensitive elements are configured to measure at least a first magnetic field component (e.g., Bx1) oriented in a first direction (e.g., X) and a second magnetic field component (e.g., By1 or Bz1) oriented in a second direction (e.g., Y or Z) perpendicular to the first direction; and the sensor device further comprises a processing circuit configured for calculating an angular position of the magnet based on at least the measured first and second magnetic field components; and the sensor device is oriented such that the first direction (e.g., X) is oriented in a circumferential direction with respect to said axis of rotation and such that the second direction (e.g., Y, Z) is parallel to or orthogonal to the axis of rotation; and the sensor device is located at a predefined position relative to the magnet at which, over a predefined angular range, the amplitude of a third magnetic field component (e.g. Bz1) orthogonal to the first and second magnetic field components (e.g. By1) has an amplitude that is less than 20% of the amplitude of the first magnetic field component (e.g. Bx1) and/or has an amplitude that is less than 20% of the amplitude of the second magnetic field component (e.g. By 1).

Those having the benefit of this disclosure and the insight that, especially after being informed that there is a "ring-shaped region" in which two orthogonal magnetic field components essentially behave like sine and cosine signals and the third orthogonal magnetic field component has a much smaller amplitude, the position of this ring-shaped region can be easily determined, for example by performing a computer simulation on a ring-shaped magnet of a given size and for a "given configuration", for example at a given distance from the magnet "near the corners", "near the equator" or "below/above the magnet". To the inventors' knowledge, the presence of such regions is not known in the art.

Although it is believed that the invention works with magnets of any size, in a preferred embodiment the angular position sensor system comprises a small magnet, for example having an outer diameter in the range from 10 to 50mm and a height in the range from 2 to 10mm, and the sensor device will be located at an axial distance from the magnet in the range from 0.5 to about 5.0mm, and/or at a radial distance up to 10mm from the magnet.

Preferably, the sensor device is located in a position where the ratio of the amplitude of the third component (e.g., | Bz |) to the amplitude of the first and/or second magnetic field component (e.g., | Bx | and/or | By |) is < 15%, or < 10%, or < 5%, or ideally substantially equal to zero.

In an embodiment, the predefined angular range (in which the amplitude of the third magnetic field component is less than 20% or 15% or 10% or 5% of the amplitude of the first magnetic field component and/or the second magnetic field component) is a range of at least 180 °, or at least 210 °, or at least 240 °, or at least 270 °, or at least 300 ° or at least 330 °, or the entire 360 ° range.

The position sensor device is preferably arranged near the magnet, for example at a distance of less than 10mm, for example at a distance of less than 5mm, or less than 2.5mm, but preferably at least 0.5 mm.

The position sensor device is preferably arranged at a radial distance Rs greater than 0 (e.g. at least 2mm, or at least 3mm, or at least 5mm, or at least 10mm) from the axis of rotation, thus defining an "off-axis" position. Or in other words, the sensor device is preferably offset from the axis of rotation by at least 2 mm.

In an embodiment, the magnet is a ring magnet. The ring magnet may be axially magnetized or diametrically magnetized.

In an embodiment, the magnet is a disc magnet. The disc magnet may be axially magnetized or diametrically magnetized.

In an embodiment, the magnet is a two-pole magnet, for example, a diametrically magnetized two-pole ring magnet, or a diametrically magnetized two-pole disc magnet, or an axially magnetized two-pole ring magnet, or an axially magnetized two-pole disc magnet.

In an embodiment, the magnet is a quadrupole magnet, such as an axially magnetized quadrupole ring magnet or an axially magnetized quadrupole disk magnet.

In embodiments, the magnet is a multi-pole magnet having at least four poles, for example, an axially magnetized multi-pole ring magnet, or an axially magnetized multi-pole disk magnet having four poles, or having six poles, or having eight poles, or having ten poles, or having twelve poles. In an embodiment, the magnet has an outer radius Ro and the predefined position of the sensor device is defined by a distance "g" below the bottom surface or above the top surface of the magnet in the range from 1.0 to 5.0mm or in the range from 1 to 4mm or in the range from 1 to 3 mm; and is defined by a radial distance "Rs" in the range from Ro-7mm to Ro +7mm, or in the range from Ro-5mm to Ro +5mm, or in the range from Ro-3mm to Ro +3mm, or in the range from Ro-7mm to Ro-1mm, or in the range from Ro-5mm to Ro-1mm, or in the range from Ro-3mm to Ro-1mm, or in the range from Ro +1mm to Ro +7mm, or in the range from Ro +1mm to Ro +5mm, or in the range from Ro +1mm to Ro +3 mm.

For example, the distance (gap) between the plane and the bottom or top surface of the magnet may be equal to about 1.0mm, or about 1.2mm, or about 1.4mm, or about 1.6mm, or about 1.8mm, or about 2.0mm, or about 2.2mm, or about 2.4mm, or about 2.6mm, or about 2.8mm, or about 3.0mm, or about 3.2mm, or about 3.4mm, or about 3.6mm, or about 3.8mm, or about 4.0 mm.

In an embodiment, the distance "g" is a predefined gap distance, and the value of Rs is determined by simulating the gap distance.

In an embodiment, the magnet is a ring magnet having an inner radius "Ri" and an outer radius "Ro"; and the predefined position is defined by a distance "g" below or above the bottom surface of the magnet in the range from 1.0 to 5.0mm, or from 1.0 to 4.0mm, or from 1.0 to 3.0mm, and by a radial distance "Rs" in the range from Ri + Δ R35% to Ri + Δ R65%, where Δ R ═ is (Ro-Ri).

In an embodiment, the radial distance is a value ranging from Ri + Δ R40% to Ri + Δ R90%.

In an embodiment, the radial distance is a value ranging from Ri + Δ R35% to Ri + Δ R48%.

In an embodiment, the radial distance is a value ranging from Ri + Δ R52% to Ri + Δ R65%.

In an embodiment, the distance "g" is a predefined gap distance, and the value of Rs is determined by simulating the gap distance.

In an embodiment, the magnet has an outer radius "Ro" and an axial height "H", and the predefined position is located in a plane substantially midway between the bottom and top surfaces of the magnet, and the radial distance "Rs" is in the range from Ro +1.0mm to Ro +10 mm.

In an embodiment, the sensor device is oriented such that the second axis (e.g. Y) is orthogonal to the rotation axis. Preferably, the Y axis intersects the rotation axis orthogonally.

In an embodiment, the sensor device is oriented such that the second axis (e.g. Y) is parallel to the rotational axis of the magnet.

In an embodiment, the sensor device comprises at least one sensor comprising an integrated magnetic concentrator structure (IMC) and only four horizontal hall elements arranged on a circumference of said IMC and angularly spaced apart by 90 °. Preferably, two of the hall elements are located on the X-axis, and two of the hall elements are located on the Y-axis perpendicular to the X-axis.

Or more specifically, in an embodiment, the substrate comprises a first sensor (S1) located at a first position (X1) on the predefined axis (X) and a second sensor (S2) located at a second position (X2) on said predefined axis (X) spaced apart (Δ X) from the first position (X1); the first sensor (S1) comprises a first IMC structure (IMC1) and four horizontal hall elements, including first and second and third horizontal hall elements and a fourth horizontal hall element (HP1, HP2, HP3, HP4), the first and second horizontal hall elements (HP1, HP2) being located at an edge of the first IMC structure (IMC1), on the predefined axis (X) and defining a first line segment on the axis (X), the third horizontal hall element (HP3) and optionally the fourth horizontal hall element (HP4) being located on a first vertical bisector (Y1) of the first line segment at the edge of the first IMC structure (IMC 1); the second sensor (S2) comprises a second IMC structure (IMC2) and four horizontal hall elements, including fifth and sixth and seventh horizontal hall elements and an eighth horizontal hall element (HP5, HP6, HP7, HP8), the fifth and sixth horizontal hall elements (HP5, HP6) being located at an edge of the second IMC structure (IMC2), on the axis (X) and defining a second line segment on the axis (X), the seventh and eighth horizontal hall elements (HP7, HP8) being located at an edge of the second IMC structure (IMC2), on a second vertical bisector (Y2) of the second line segment (Y2); and wherein the position sensor device further comprises a processing circuit (620), the processing circuit (620) being configured for: determining an in-plane magnetic field component (Bx1) at the first position (X1) based only on signals obtained from the first and second horizontal hall elements (HP1, HP 2); determining an in-plane magnetic field component (By1) and/or an out-of-plane magnetic field component (Bz1) at the first position (X1) based only on signals obtained from the third and fourth horizontal hall elements (HP3, HP 4); determining an in-plane magnetic field component (Bx2) at the second position (X2) based only on signals obtained from the fifth and sixth horizontal hall elements (HP5, HP 6); determining an in-plane magnetic field component (By2) and/or an out-of-plane magnetic field component (Bz2) at the second position (X2) based only on signals obtained from the seventh and eighth horizontal hall elements (HP7, HP 8); and wherein the processing circuitry is further configured for determining an angular position (α) of the sensor device relative to the magnetic field source based on the first and second in-plane magnetic field components (Bx1, Bx2) and based on the in-plane magnetic field components (By1, By2) or based on the first and second out-of-plane magnetic field components (Bz1, Bz 2).

Thus, in brief, this arrangement uses two sensors each having four hall elements, rather than, for example, two sensors as shown in fig. 1 each having only two hall elements.

The advantage of this arrangement is that it allows individual trimming of the hall elements of each sensor, in order to obtain more accurate results for both Bx and Bz (or Bx and By), which is not possible in the configuration of fig. 1, in each sensor two hall elements are used to measure both Bx and Bz, so trimming to optimize for Bx negatively affects the measurement of Bz and vice versa.

The main advantage is that the measurements of the in-plane magnetic field components (Bx1, Bx2) and the out-of-plane magnetic field components (Bz1, Bz2) or the in-plane magnetic field components (By1, By2) are derived from the signals obtained from the different hall elements. In this way, electrical decoupling is achieved, in particular with lower crosstalk and thus higher accuracy than in the prior art (e.g. fig. 1).

A further advantage of this structure is that the in-plane magnetic field component (Bx) can be measured with a passive amplification factor (typically on the order of about 5), since the IMC structure improves the signal-to-noise ratio (SNR) and thus further improves accuracy.

The main advantage is that the first hall element and the second hall element on the one hand, and the third hall element and the optional fourth hall element on the other hand are located at the edge or below the IMC structure or IMC assembly. And the same applies to the hall element of the second sensor. In this way, the hall elements of each sensor are mechanically coupled and therefore subjected to substantially the same temperature and mechanical stress. Thus, due to temperature variations and/or mechanical stresses and/or other environmental or aging effects, the signals obtained from these hall elements drift in the same manner, resulting in a position sensor with reduced long term drift.

The sensor device is ideally adapted to measure the magnetic field in the following way: the Bx and Bz (or By) components measured By the sensor device vary depending on the position, e.g. according to sine and cosine functions, and the third component (By or Bz) seen By the sensor device is substantially zero (e.g. less than 20% of the amplitude of the Bx component or less than 10% of the amplitude of the Bx component or less than 5% of the amplitude of the Bx component). Indeed, By using a specific structure with three or four horizontal hall elements at the edges of the IMC or below the IMC, any potential cross-talk from the Bx component of the magnetic field to the Bz component measured By the device is substantially eliminated, and there is no potential cross-talk of the By component to the Bz component, since there is no (significant) By component. Thus, the cross-talk from the in-plane field component (Bx or By or a combination thereof) to the Bz value is negligible.

Finally, it is advantageous to use two sensors instead of only one, since it allows to determine the spatial gradient signals of Bx and Bz (or By), denoted dBx/dx and dBz/dx (or dBy/dx). The advantage is that the position is calculated based on the gradient signals and not on the original magnetic field values, since the gradient signals are substantially insensitive to external disturbing fields, which further contributes to a higher accuracy.

The third and fourth hall elements may be located on a perpendicular bisector (Y1) of a first line segment defined by the first and second hall elements. Likewise, the seventh hall element and the eighth hall element may be located on a perpendicular bisector (Y2) of a second line segment defined by the fifth hall element and the sixth hall element.

The processing unit may be configured for determining the first in-plane magnetic field component (Bx1) based on a difference between signals obtained from the first and second horizontal hall elements (HP1, HP2), and/or for determining the in-plane magnetic field component By1 based on a difference between signals obtained from the third and fourth horizontal hall elements (HP3, HP4), and/or for determining the out-of-plane magnetic field component (Bz1) based on a sum of signals obtained from the third and fourth horizontal hall elements (HP3, HP4), and similarly for the second sensor. Or in other words, the sensor device may determine Bx1 based on signals obtained from HP1 and HP2, and Bx2 based on HP3 and HP4, and Bz1 based on HP5 and HP6, and Bz2 based on HP7 and HP 8. Therefore, the signals HP1 and HP2 are not used to determine Bz 1. Therefore, the common mode signals from HP1 and HP2 have no effect on the value of Bz1 compared to prior art solutions. Likewise, the signals from HP5 and HP6 are not used to determine Bz 2. The subtraction and summation of the signals may be performed in the analog domain or the digital domain.

In an embodiment, the sensor device is configured for determining a first magnetic field component (Bx1) at the first sensor position oriented parallel to the substrate based on a first difference of signals obtained from a first pair of two horizontal hall elements (HP1, HP2) of the only four horizontal hall elements; and wherein the sensor device is configured for determining a second magnetic field component (By1) at the first sensor position oriented parallel to the substrate based on a second difference of signals obtained from a second pair of two further horizontal hall elements (HP3, HP4) of the only four horizontal hall elements.

Optionally, the horizontal hall elements in the first pair are individually trimmed to determine the first magnetic field component (Bx 1); and the horizontal hall elements in the second pair are individually trimmed to determine the second magnetic field component (By 1).

In an embodiment, the sensor device is configured for determining a first magnetic field component (Bx1) at the first sensor position oriented parallel to the substrate based on a first difference of signals obtained from a first pair of two horizontal hall elements (HP1, HP2) of the only four horizontal hall elements; and the sensor device is configured for determining a second magnetic field component (Bz1) at the first sensor position (e.g. X1) oriented orthogonal to the substrate based on a sum of signals obtained from a second pair of two further horizontal hall elements (HP3, HP4) of the only four horizontal hall elements.

Optionally, the horizontal hall elements in the first pair are individually trimmed to determine the first magnetic field component (Bx 1); and the horizontal Hall elements in the second pair are individually tailored to determine said second magnetic field component (Bz1)

Wherein the sensor device comprises at least one sensor comprising an integrated magnetic concentrator structure (IMC), a first and a second horizontal Hall element located on opposite sides of the IMC, and a third horizontal Hall element located between the first and second horizontal Hall elements under the IMC.

Or more specifically, in an embodiment, the sensor device may include a first sensor (S1) and a second sensor (S2), wherein the first sensor (S1) includes only three horizontal hall elements (HP1, HP2, HP3), the first and second horizontal hall elements being located on opposite sides of the first IMC structure (IMC1), the third horizontal hall element (HP3) being located underneath the first IMC structure (e.g., midway between the first and second hall elements); and wherein the second sensor (S2) comprises only three horizontal hall elements (HP5, HP6, HP7), the fifth and sixth horizontal hall elements being located on opposite sides of the second IMC structure (IMC2), the seventh horizontal hall element (HP7) being located below the second IMC structure (e.g., midway between the fifth and sixth horizontal hall elements); and wherein the processing circuit (620) is further configured for: determining a first difference (diff1) between signals obtained from a first and a second horizontal hall element (HP1, HP2) indicative of a first in-plane magnetic field component (Bx 1); and for determining a second difference (diff2) between signals obtained from the fifth and sixth horizontal hall elements (HP5, HP6) indicative of the second in-plane magnetic field component (Bx 2); and for obtaining a third signal from a third hall element (HP3) indicative of the first out-of-plane magnetic field component (Bz 1); and for obtaining a seventh signal from a seventh hall element (HP7) indicative of a second out-of-plane magnetic field component (Bz 2); and wherein the processing circuitry is configured to determine the position based on the first and second differences (diff1, diff2) and based on the third and seventh signals. Or simply, in this embodiment (e.g., illustrated in fig. 8), the sensor device determines Bx1 based on signals obtained from HP1 and HP2, Bx2 based on HP5 and HP6, Bz1 based on HP3, and Bz2 based on HP 7. Therefore, the signals HP1 and HP2 are not used to determine Bz 1. Likewise, the signals from HP5 and HP6 are not used to determine Bz 2. The subtraction and summation of the signals may be performed in the analog domain or the digital domain.

In an embodiment (with only a single sensor), the IMC structure is a single disk-like IMC.

In an embodiment (with two sensors spaced apart by Δ X), the first IMC structure (IMC1) includes a single IMC component, while the second IMC structure (IMC2) includes a single IMC component.

The advantage is that a single IMC assembly or object (per sensor) is used, since it more evenly spreads the effects of local defects and/or local mechanical stress concentrations and/or temperature variations to three or four horizontal hall elements. This is beneficial for robustness to long term drift and environmental variations, since all hall elements (each sensor) are exposed to substantially the same effect.

In an embodiment (with two sensors spaced apart by ax), each of the first and second integrated magnetic concentrators has a substantially circular or substantially elliptical shape.

A circular integrated magnetic concentrator is also known as an "IMC disc".

Such IMCs have the advantage of being easy to manufacture and reduce the risk of mechanical stress concentrations (as opposed to shapes with sharp edges). The substantially circular or substantially elliptical shape also has a positive effect on the smooth bending of the magnetic field lines from any direction, which may facilitate a proper placement of the sensor device with respect to the magnetic structure.

In an embodiment (with a single sensor), the IMC structure is composed of four separate IMC elements (see, e.g., the sensor on the left side of fig. 4).

In the present embodiment (with two sensors spaced Δ X apart), each of the IMC structures consists of four separate IMC elements (see fig. 4). In the present embodiment, each hall element is associated with its own IMC assembly. Each of these individual integrated magnetic concentrator components may have a substantially circular or oval shape or a raindrop or teardrop shape. The same advantages as mentioned above are also applicable here.

In an embodiment, each of the hall elements is individually trimmed. In this way, the effects of process variations may also be reduced or eliminated.

In an embodiment, the sensor device comprises at least one sensor comprising a first vertical hall element oriented for measuring a first magnetic field component (e.g. Bx1) in said first direction (e.g. X) and a second vertical hall element oriented for measuring a second magnetic field component (e.g. By1) in said second direction (e.g. Y).

In an embodiment, a position sensor apparatus includes two sensors (e.g., S1, S2) spaced apart in the first direction (e.g., X) for measuring a first magnetic field gradient (e.g., dBx/dx) and a second magnetic field gradient (e.g., dBy/dx; dBz/dx); and the processing circuitry is configured to calculate an angular position of the magnet based on the first gradient and the second gradient.

In an embodiment, the magnetic sensor device comprises a first sensor (S1), the first sensor (S1) comprising a plurality of magneto-sensitive elements configured for measuring said first magnetic field component (Bx1) oriented in said first direction (X) and said second magnetic field component (By 1; Bz1) oriented in said second direction (Y; Z) perpendicular to the first direction (X) at a first sensor position (X1); and the magnetic sensor device further comprises a second sensor (S2), the second sensor (S2) comprising a plurality of magneto-sensitive elements configured for measuring a third magnetic field component (Bx2) oriented in said first direction (X) and a fourth magnetic field component (By 2; Bz2) oriented in said second direction (Y; Z) at a second sensor position (X2) spaced apart from the first sensor position; and the processing circuitry is further configured for determining a first magnetic field gradient (dBx/dx) based on the first and third magnetic field components (Bx1, Bx2), and for determining a second magnetic field gradient (dBy/dx; dBz/dx) based on the second and fourth magnetic field components; and the processing circuitry is configured to calculate an angular position (a) of the magnet based on the first magnetic field gradient (dBx/dx) and the second magnetic field gradient (dBy/dx; dBz/dx).

In an embodiment, the processing unit is configured for calculating two in-plane field gradients dBx/dx and dBy/dx and for determining the angular position based on these gradients (e.g. as a function of the ratio of these gradients, e.g. an goniometric function). A further advantage is that this ratio is also highly robust against demagnetization effects or certain positioning errors, since the numerator and denominator vary in substantially the same way.

In an embodiment, the processing unit is configured for calculating the in-plane field gradient dBx/dx and the out-of-plane field gradient dBz/dx and for determining the angular position based on these gradients (e.g. as a function of the ratio of these gradients, e.g. an goniometric function). A further advantage is that this ratio is also highly robust against demagnetization effects or certain positioning errors, since the numerator and denominator vary in substantially the same way.

In-plane magnetic field gradients are typically calculated as the difference between in-plane magnetic field components, while out-of-plane magnetic field gradients are typically calculated as the difference between out-of-plane magnetic field components.

In addition to the above advantages, a further advantage is that the gradient signal has a reduced sensitivity to external disturbing fields. By determining the relative position based on these gradients, the determined position is more robust to external disturbing fields.

In an embodiment, the angular position is determined according to the formula of case (a) or case (b) or case (c) or case (d) of fig. 3.

In an embodiment, the processing unit is configured to determine the position using the lookup table using the ratio as an index.

In an embodiment, the processing unit is configured for determining the position using a mathematical formula (e.g. an angle measuring formula, e.g. an arctan function).

In an embodiment, the magnet has an outer diameter "Do" in the range from 10 to 50 mm; and has a height "H" in the range from 2 to 10 mm.

In embodiments, the ratio of the outer diameter Do to the height H is a value in the range from 0.1 to 2.0, or from 0.2 to 1.5, or from 0.2 to 1.0, or from 0.5 to 2.0, or from 0.5 to 1.5.

In an embodiment, the sensor device is located at a distance of at least 5mm from the axis of rotation.

In an embodiment, the magnet is a two-pole magnet.

In an embodiment, the magnet is a quadrupole magnet.

In embodiments, the magnet is a multi-pole magnet having 6 poles, or having 8 poles, or having 10 poles, or having 12 poles.

Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features from dependent claims may be combined with features of the independent claims and features of other dependent claims as appropriate and not merely as explicitly set out in such claims.

These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.

Drawings

FIG. 1 is a schematic block diagram of a sensor architecture that may be used in a position sensor device. The structure includes a first sensor at a first position X1 and a second sensor at a second position X2 along the X-axis, each sensor including an Integrated Magnetic Concentrator (IMC) and a pair of two horizontal hall elements disposed on opposite sides of the IMC. The in-plane magnetic field gradient (dBx/dx) and the out-of-plane magnetic field gradient (dBz/dx) can be measured by the device and from this the linear or angular position of the sensor device relative to the magnet is derived.

Fig. 2 is a schematic block diagram of a sensor structure as a variation of fig. 1.

FIG. 3 is a schematic block diagram of a sensor structure as may be used in embodiments of the present invention, including two sensors spaced along the X-axis, each sensor having an IMC structure and four horizontal Hall elements.

FIG. 4 is a schematic block diagram of another sensor configuration as may be used in embodiments of the present invention, including two sensors spaced along the X-axis, each sensor having an IMC structure and four horizontal Hall elements.

Fig. 5 shows an angular position sensor system according to an embodiment of the invention, which system comprises a ring-shaped magnet and a sensor device movable relative to the magnet (or vice versa), the sensor device having a sensor structure as shown in fig. 3.

FIG. 6 is a schematic block diagram of an exemplary position sensor apparatus, showing further details regarding processing circuitry thereof, in accordance with an embodiment of the present invention.

Fig. 7 is a flow chart of a method for determining the position of a sensor device (e.g., having a structure as shown in fig. 3, 4, or 8) relative to a magnet as may be used in the system of fig. 5.

FIG. 8 is a schematic block diagram of another exemplary sensor structure as may be used in embodiments of the present invention, including two sensors spaced apart along the X-axis, each sensor having an IMC structure and only three horizontal Hall elements.

Fig. 9-16 illustrate examples of angular position sensor systems according to embodiments of the present invention. Three configurations are shown, referred to herein as: (i) "near the edge"; (ii) (ii) "above or below the magnet", and (iii) "near the equator".

In fig. 9, the sensor device is located near the outer edge of the magnet and is oriented and configured to measure dBx/dx and dBz/dx and is located at a position where | By |/| Bx | < 20% as seen By the sensor.

In fig. 10, the sensor device is located near the outer edge of the magnet and is oriented and configured to measure dBx/dx and dBy/dx and is located at a position where | Bz |/| Bx | < 20% as seen by the sensor.

In fig. 11, the sensor device is located near the outer edge of the magnet and is oriented and configured to measure Bx and Bz, and is located at a position where | By |/| Bx | < 20% as seen By the sensor.

In fig. 12, the sensor device is located near the top or bottom surface of the ring magnet, substantially midway between the inner and outer diameters, and is oriented and configured to measure dBx/dx and dBy/dx, and is located at a position where | Bz |/| Bx | < 20% as seen by the sensor.

In fig. 13, the sensor device is located near the top or bottom surface of the ring magnet, substantially midway between the inner and outer diameters, and is oriented and configured to measure Bx and By, and is located at a position where | Bz |/| Bx | < 20% as seen By the sensor.

In fig. 14, the sensor device is located outside the outer diameter of the magnet, in a plane substantially midway between the upper and lower surfaces of the magnet, and is oriented and configured to measure dBx/dx and dBy/dx, and is located at a position where | Bz |/| Bx | < 20% as seen by the sensor.

In fig. 15, the sensor device is located outside the outer diameter of the magnet, in a plane substantially midway between the upper and lower surfaces of the magnet, and is oriented and configured to measure dBx/dx and dBz/dx, and is located at a position where | By |/| Bx | < 20% as seen By the sensor.

In fig. 16, the sensor device is located outside the outer diameter of the magnet, in a plane substantially midway between the upper and lower surfaces of the magnet, and is oriented and configured to measure Bx and By, and is located at a position where | Bz |/| Bx | < 20% as seen By the sensor.

Fig. 17-24 show simulations of the magnetic field components of various exemplary magnets oriented radially inward or radially outward at different positions relative to the magnets.

Part (a) of fig. 17 to part (e) of fig. 17 show simulations of the magnitude of a radially inwardly or radially outwardly directed magnetic field component of a first exemplary ring magnet (having an OD of 15mm, an ID of 5mm, and an H of 2.5mm) in a plane at a distance of 2mm below the bottom surface of the magnet, which magnetic field component corresponds to a By component that is sensible By the sensor device of fig. 9 or 11 or a Bz component that is sensible By the sensor device of fig. 10.

As a variation of fig. 17, part (a) to part (e) of fig. 18 show simulations of the magnitude of a radially inwardly or radially outwardly directed magnetic field component of a second exemplary ring magnet (having an OD of 30mm, ID of 20mm, H of 10mm) in a plane at a distance of 2mm below the bottom surface of the magnet.

Part (a) to part (d) of fig. 19 show another representation of a simulation of the magnitude of the radially inwardly or radially outwardly directed magnetic field component of the exemplary ring magnet of fig. 17 (having an OD of 15mm, an ID of 5mm, and an H of 2.5mm) in a plane at a distance of 2mm below the bottom surface of the magnet.

Part (a) of fig. 20 shows a graph of the magnitude of the magnetic field components Bx, By, Bz of the magnetic field of fig. 19 in a plane 2mm below the bottom surface of the magnet, on a circle having a radius Rs, as a function of the radius Rs.

Part (b) of fig. 20 illustrates a graph of a ratio of the By amplitude to the Bx amplitude of a part of part (a) of fig. 20 in an enlarged scale.

Part (a) of fig. 21 to part (e) of fig. 21 show simulations of the magnitude of an axially oriented magnetic field component of an exemplary magnet (having an OD of 30mm, ID of 20mm, H of 10mm) in a plane at a distance of 2mm below the bottom surface of the magnet, which magnetic field component corresponds to a Bz component that can be sensed by the sensor device of fig. 12 or 13.

As a variation of fig. 21, part (a) of fig. 22 to part (d) of fig. 22 show simulations of the magnitude of an axially oriented magnetic field component of an exemplary magnet (having an OD of 15mm, an ID of 5mm, and an H of 2.5mm) in a plane at a distance of 2mm below the bottom surface of the magnet.

Part (a) of fig. 23 and part (b) of fig. 23 show the magnetization of an exemplary diametrically magnetized ring magnet (with OD of 10mm, ID of 5mm and H of 5mm) as may be used in the angle sensor system of fig. 14, 15 or 16.

Part (a) of fig. 24 shows a graph of the magnitude of the magnetic field components Bx, By, Bz of the magnetic field of fig. 23 in a plane perpendicular to the axis of rotation at half the height of the magnet, on a circle with a radius Rs, as a function of the radius Rs.

Part (b) of fig. 24 illustrates a graph of a ratio of the By amplitude to the Bx amplitude of a part of part (a) of fig. 24 in an enlarged scale.

Part (a) of fig. 25 to part (g) of fig. 25 show a variant of the angular position sensor system of fig. 12 or 13 using axially magnetized quadrupole magnets.

Fig. 26(a) to 26(c) show in grayscale simulations of the magnitude of the radially, circumferentially and axially oriented magnetic field components of an exemplary quadrupole magnet (having an OD of 12mm, an ID of 8mm, and an H of 4mm) in a plane at a distance of 3mm below the bottom surface of the magnet, as may be used in the angular position sensor system of fig. 25.

Parts (a) to (c) of fig. 27 show the same plots as parts (a) to (c) of fig. 26 at 10 dither levels.

Fig. 28 shows the same data as part (a) of fig. 26, but presented in a clear image, showing an annular region in which the magnitude of the radial component is less than 30% of the maximum magnetic field component measurable at different locations in the same plane.

Fig. 29 shows the same data as fig. 26(a) and fig. 28, but presented in a different grayscale, showing an annular region in which the magnitude of the radial component is less than about 11% of the maximum magnetic field component measurable at different locations in the same plane.

The drawings are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. Any reference signs in the claims shall not be construed as limiting the scope. The same reference numbers in different drawings identify the same or similar elements.

Detailed Description

The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims. The drawings described are only schematic and are non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn on scale for illustrative purposes. The dimensions and relative dimensions do not correspond to a true reduction in the practice of the invention.

Moreover, the terms first, second, and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequential order temporally, spatially, in ranking, or in any other manner. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

Furthermore, the terms top, bottom, and the like in the description and the claims are used for descriptive purposes and not necessarily for describing relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other orientations than described or illustrated herein.

It is to be noticed that the term 'comprising', used in the claims, should not be interpreted as being limitative to the means listed thereafter; it does not exclude other elements or steps. Accordingly, the terms are to be interpreted as specifying the presence of the stated features, integers, steps or components as referred to, but do not preclude the presence or addition of one or more other features, integers, steps or components, or groups thereof. Thus, the scope of the expression "an apparatus comprising means a and B" should not be limited to an apparatus consisting of only components a and B. This means that for the present invention, the only relevant components of the device are a and B.

Reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments as will be apparent to one of ordinary skill in the art in view of the present disclosure.

Similarly, it should be appreciated that in the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.

Furthermore, although some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are intended to be within the scope of the invention and form different embodiments, as will be understood by those skilled in the art. For example, in the appended claims, any of the claimed embodiments can be used in any combination.

In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

In this document, unless explicitly mentioned otherwise, the term "magnetic sensor device" or "sensor device" refers to a device comprising at least one "magnetic sensor" or at least one magnetic "sensor element", preferably integrated in a semiconductor substrate. The sensor device may be comprised in a package (also referred to as "chip"), but this is not absolutely necessary. The sensor device may be configured for measuring at least two in-plane magnetic field components (referred to herein as Bx and By), or for measuring at least one in-plane magnetic field component (e.g., Bx) and at least one out-of-plane magnetic field component (e.g., Bz).

In this document, the term "sensor element" or "magnetic sensor" may refer to a component or a group of components or sub-circuits or structures capable of measuring a magnetic quantity, such as, for example, a magnetoresistive element, a GMR element, an XMR element, a horizontal hall plate, a vertical hall plate, a wheatstone bridge comprising at least one (but preferably four) magnetoresistive elements, or the like, or a combination thereof.

In certain embodiments of the present invention, the term "magnetic sensor" may refer to an arrangement comprising one or more Integrated Magnetic Concentrators (IMCs) and one or more horizontal hall elements, such as a disk-shaped IMC and two or four horizontal hall elements arranged near the periphery of the IMC.

In this document, the expressions "in-plane component of the magnetic field vector" and "projection of the magnetic field vector in the plane of the sensor" mean the same. If the sensor device is implemented in a semiconductor substrate, this also means that the "magnetic field component is parallel to the semiconductor plane".

In this document, the expressions "out-of-plane component of the vector" and "Z component of the vector" and "projection of the vector on an axis perpendicular to the sensor plane" mean the same.

Embodiments of the invention are generally described using an orthogonal coordinate system that is fixed to the sensor device and has three axes X, Y, Z, with the X and Y axes located in the substrate and the Z axis perpendicular to the substrate. Furthermore, the X-axis is preferably oriented "parallel to the direction of relative movement" in the case of a linear position sensor, or "tangential to the motion trajectory" in the case of a curved motion trajectory, or "circumferential direction" (i.e. tangential to an imaginary circle having a center on the axis of rotation) in the case of an angular position sensor system comprising a rotatable magnet. In the case of an angular position sensor system, one of the other axes (Y or Z) is preferably oriented parallel to the axis of rotation of the magnet. For example, in fig. 11 to 15 and 25, the Z axis is parallel to the rotational axis of the magnet, while in fig. 16 and 17, the Y axis is parallel to the rotational axis.

In this document, the expressions "spatial derivative" or "spatial gradient" or "gradient" are used as synonyms. In the context of the present invention, the gradient is typically determined as the difference between two values measured at two locations spaced apart in the X-direction. In theory, the gradient is usually calculated as the difference between two values divided by the distance "dx" between the sensor positions, but in practice the division by "dx" is usually neglected, since the measured signal needs to be scaled anyway.

In this document, the term "amplitude of the magnetic field component By" means "the maximum of the absolute value of the By signal over a 360 ° rotation", and so do Bx and Bz.

In this document, for example, the "part e of fig. 19" without parentheses has the same meaning as the part (e) of fig. 19 with parentheses, and the same holds for other pictures.

Note that in the present application, the reference numerals "HP 1", "HP 2", … … "HPn" may refer to the first, second, … …, nth hall element itself, or to a signal provided by the element. The intended meaning shall be clear from the context.

The present invention generally relates to an angular magnetic position sensor system comprising a sensor device and a magnetic source, such as a permanent magnet.

More particularly, the invention relates to a magnetic sensor system comprising a magnetic sensor device movable with respect to a permanent magnet, the system having improved accuracy in one or both or all of the following areas:

improved robustness to "cross-talk",

improved robustness to external interference fields,

improved robustness to long-term drift (in particular related to mechanical stress).

The technical problem(s) underlying the present invention, the technical solution(s) provided herein and the differences with existing solutions can best be explained with the aid of fig. 1 and 2.

FIG. 1 shows a sensor structure including a first sensor S1 located at a first position X1 on the X-axis and a second sensor S2 located at a second position X2 on the X-axis spaced from X1. Each of the first sensor S1 and the second sensor S2 includes a disk-shaped Integrated Magnetic Concentrator (IMC) and two horizontal hall elements disposed on the X-axis on opposite sides of the IMC.

The sensor structure shown in fig. 1 is also described in patent application EP19207358.3 filed by the same applicant on 6.11.2019, which claims priority from EP18205705.9 filed on 12.11.2018, both of which are incorporated herein by reference in their entirety. However, in the case where there is a conflict, the information in this document controls. In this document, sensors S1, S2 are used to determine in-plane magnetic field gradients (dBx/dx) and out-of-plane magnetic field gradients (dBz/dx) in order to determine the angular position of a sensor device including these sensors relative to a magnetic structure.

For the understanding of the invention it is sufficient to know that the signals from the two hall elements (also called "hall plates") of each sensor can be used to determine both the in-plane magnetic field component Bx (parallel to the sensor substrate) and the out-of-plane magnetic field component Bz (perpendicular to the sensor substrate). More specifically, the in-plane magnetic field component Bx can be calculated by subtracting the two signals, and the out-of-plane magnetic field component Bz can be calculated by summing the two signals. This can be expressed mathematically as follows:

Bx1＝(HP2-HP1)[1]

Bz1＝(HP1+HP2)[2]

although a simple and elegant solution, this structure may suffer from "crosstalk" or "common mode" problems. Indeed, it can be appreciated from equations [1] and [2] that one or both of Bx1 and Bz1 may be inaccurate if there is any mismatch, for example, due to geometric layout mismatches, and/or due to mismatches in the bias circuits and/or readout circuits of these hall plates, and/or due to offset errors of operational amplifiers typically used in readout circuits, or mismatches in magnetic gain or sensitivity. For example, if the sensitivity of HP1 and the sensitivity of HP2 do not match, a magnetic field oriented in the Z-direction (perpendicular to the substrate) may erroneously result in a non-zero value for Bx 1. This phenomenon is referred to as "leakage from the Bz field to the Bx component being measured", or "cross-talk from the Z component to the X component". Also, in the case of a mismatch, a magnetic field oriented parallel to the sensor plane may erroneously result in a non-zero value for Bz.

Of course, such mismatches are limited as much as possible using known techniques (e.g., by using the same layout notation and/or by laser trimming, and/or by using so-called "spin current" readout techniques), but there are limitations to techniques that are practically and economically feasible in a production environment. Therefore, a certain degree of mismatch will always exist. Even more difficult to control is a mismatch that drifts over time, such as a mismatch related to changes in mechanical stress (e.g., stress applied by a molding compound of a plastic package).

In anticipation of further improving the accuracy of the sensor system, the inventors thought to reduce crosstalk by "decoupling" the measurement of the Bx component and the measurement of the Bz component, and they thought to the structure proposed in fig. 2, in which a dedicated horizontal hall element HP5 is added to the first sensor S1 to measure the Bz component at the first position X1, and a dedicated horizontal hall element HP6 is added to measure the Bz component at the second position X2. Hall element HP5 is spaced from HP1 and HP2 by at least 1.5 times the distance between HP1 and HP2, so as to decouple HP5 from HP1 and HP 2; and also, hall element HP6 is spaced from HP4 and HP5 by at least 1.5 times the distance between HP4 and HP5, so as to decouple HP6 from HP4 and HP 5. It is expected that by using dedicated sensor elements and by positioning these sensors relatively far from the respective IMC structure, accuracy will be improved due to the decoupling.

This structure was constructed and evaluated, but surprisingly showed that the accuracy of the signals Bx and Bz was not improved. Analysis has shown that the structure of fig. 2 suffers from "drift problems" that may be related to temperature mismatch and/or mechanical stress mismatch between the hall elements.

Based on these insights, and contrary to their original idea (of fig. 2) of "decoupling maximally" the measurements of Bx and Bz, the inventors realized that: it is preferable to electrically and magnetically decouple the measurements of Bx and Bz, but mechanically couple the measurements of Bx and Bz in order to improve (short and long term) accuracy. To the best of the inventors' knowledge, this particular combination of coupling and decoupling, as clearly elucidated herein, is not known in the art.

Further, the inventors thought that: the cross-talk is reduced by positioning the sensor device in a specific position relative to the magnet, i.e. a position where one of the magnetic field components is much smaller than the other magnetic field components, e.g. at least 5 times smaller in amplitude (i.e. maximum 20%), or at least 10 times smaller (i.e. maximum 10%), or has an amplitude of less than 5% of the other amplitude, or ideally substantially equal to zero. And in the preferred embodiment, this insight is also used. The remainder of this document describes various proposed solutions and contains four main parts:

in fig. 3 to 8, several sensor structures are proposed (as will be further clarified, these sensor structures have IMCs and horizontal hall elements, but these sensor structures are not the only sensor structures that can be used in embodiments of the invention),

in fig. 10 to 16, several sensor arrangements are proposed, showing several preferred positions (herein also referred to as "sweet spots") of the sensor device relative to the magnetic structure,

simulation results and graphs are shown in fig. 17 to 24 to visualize the "sweet spot" of several exemplary bipolar magnets.

The sensor system with quadrupole magnets is depicted in fig. 25, and the simulation results are shown in fig. 26 to 29 to visualize the "sweet spot" of an exemplary quadrupole magnet.

In the embodiment illustrated in fig. 14 to 16, the sensor device is located substantially in the plane of symmetry of the magnet. In other embodiments, the sensor device is not located in the plane of symmetry of the magnet, but rather is located outside the plane of symmetry of the magnet.

The invention provides an angular position sensor system comprising a permanent magnet for generating a magnetic field and a magnetic sensor device for measuring said magnetic field. The magnet is movable relative to the sensor device, or vice versa. The permanent magnet is a cylindrical magnet (e.g. a ring magnet or a disc magnet) and can be rotated around the rotation axis by an angle alpha, which needs to be determined by the sensor device. The angular position sensor device has a substrate comprising a plurality of magneto-sensitive elements configured for measuring at least a first magnetic field component (Bx1) oriented in a first direction (X) and a second magnetic field component (By1 or Bz1) oriented in a second direction (Y or Z) perpendicular to the first direction (X). The sensor device further comprises a processing circuit configured for calculating an angular position (α) of the magnet based on at least the measured first and second magnetic field components (Bx1 and By 1; or Bx1 and Bz 1; or Bx1, Bx2, By1 and Bz 2; or Bx1, Bx2, Bz1 and Bz 2). The sensor device is oriented such that the first direction (X) is oriented in a circumferential direction with respect to said axis of rotation and such that the second direction (Y or Z) is parallel to the axis of rotation or orthogonal to (e.g. orthogonally intersecting) the axis of rotation. The sensor device is located at a predefined position relative to the magnet, wherein the amplitude of a third magnetic field component (Bz1 or By1) orthogonal to the first and second magnetic field components has an amplitude of less than 20% of the amplitude of the first magnetic field component (Bx1), preferably less than 15%, or less than 10%, or less than 5%, or ideally substantially equal to zero, within a predefined angular range.

The expression "circumferential direction with respect to the rotation axis" means "tangent to an imaginary circle that lies in an imaginary plane perpendicular to the rotation axis and has a center on the rotation axis".

In some embodiments, the ring magnet or the disc magnet is diametrically magnetized.

In some embodiments, the ring magnet or the disc magnet is axially magnetized.

In a preferred embodiment, the predefined angular range is at least 180 °, or at least 270 °, or 360 °.

An advantage of such a position sensor system is that it can measure the magnetic field components more accurately, more particularly in a manner that is less sensitive to cross-talk between the magnetic field components.

In a preferred embodiment, the sensor device assumes a position in one of the following three "sweet spots" with respect to the magnet:

(1) in a plane β perpendicular to the axis of rotation, the predefined distance from the flat bottom or top surface of the magnet is from 0.5 to 5.0mm, or from 1.0mm to 4.0mm, or from 1.0 to 3.0mm, or from 1.5 to 2.5mm (e.g., where the distance is equal to about 2 mm), and the radial distance Rs is from 40% to 60% or from 40% to 48% of the outer radius (in the case of a disc magnet) or the radial distance Rs is a position between (e.g., substantially midway between) the inner radius Ri and the outer radius Ro of the ring magnet (referred to herein as "above or below the magnet"), e.g., as shown in fig. 12, 13, or 29. The sensor device may be oriented such that its substrate is perpendicular or parallel to the rotation axis;

(2) in a plane perpendicular to the axis of rotation passing through the center of the magnets, the radial distance Rs is from about 102% to 150%, or from about 103% to 140%, or from about 105% to 125% of the outer radius of the toric or discoidal magnet (referred to herein as "near the equator"), for example, as shown in fig. 14, 15, 16. The sensor device can be oriented such that the substrate is perpendicular to the axis of rotation (e.g., fig. 14, 16) or parallel to the axis of rotation (e.g., fig. 15);

(3) the predefined distance from the flat bottom or top surface of the magnet in a plane perpendicular to the axis of rotation is from 0.5 to 5.0mm, or from 1.0mm to 4.0mm, or from 1.0 to 3.0mm, or from 1.5 to 2.5mm (e.g., where the distance is equal to about 2 mm), and the radial distance is from 90% to 110% of the outer radius of the ring-shaped or disc-shaped magnet or from 90% to 98%, or from 102% to 110% of the outer radius of the ring-shaped or disc-shaped magnet (referred to herein as "near corner"), e.g., as shown in fig. 5, 9, 10, 11. The sensor device can be oriented such that the substrate is perpendicular to the axis of rotation (e.g., fig. 5, 9, 11) or parallel to the axis of rotation (e.g., fig. 10).

In a preferred embodiment, the sensor device may also be configured for measuring a first magnetic field component (e.g. Bx) and a second magnetic field component (e.g. By or Bz) also at a second position X2 spaced apart from the first position X1 along the X-axis, and the processing circuitry may be further adapted for determining a first magnetic field gradient (e.g. dBx/dx) and a second magnetic field gradient (e.g. dBy/dx or dBz/dx) and for determining the angular position of the magnet based on these gradients. Examples are shown in particular in fig. 5, 9, 10, 12, 14, 15, 25. Such embodiments provide the additional advantage of being highly robust to external disturbing fields.

In a preferred embodiment, the sensor device may also use a sensor structure comprising one or more sensors, each sensor comprising an IMC structure comprising one or more IMC elements, and each sensor comprising a plurality of horizontal hall elements, for example four horizontal hall elements per sensor position (e.g. as shown in fig. 3 or 4), or only three horizontal hall elements per sensor position (e.g. as shown in fig. 8). Such embodiments provide the additional advantage of being highly robust to mechanical stress and/or long term drift, since the temperature of the hall elements and the mechanical stress sensed by the hall elements are substantially the same.

These are the main fundamental principles of the invention.

Reference is now made to the drawings.

Fig. 1 and 2 have been described above. In short, fig. 1 shows a structure for measuring magnetic field components Bx oriented in the X-direction (parallel to the plane of the substrate comprised in the sensor device) and Bz oriented in the Z-direction (perpendicular to the plane of the substrate) at two positions X1, X2 spaced apart along the X-axis. This structure functions functionally but may suffer from crosstalk in case of mismatch.

FIG. 2 shows a sensor configuration having a first sensor S1 and a second sensor S2 spaced along the X axis. The first sensor S1 includes an IMC and three horizontal hall elements HP1, HP2, HP5, a first element HP1 and a second element HP2 arranged at the periphery of the IMC, a third element HP5 positioned relatively far from the IMC so as to decouple Bz measurements (using only HP5) from Bx measurements (using only HP1 and HP 2). Likewise, the second sensor S2 includes a second IMC with two horizontal hall elements HP4, HP5 and includes a horizontal hall element HP6, the horizontal hall element HP6 being positioned relatively far from the IMC so as to decouple Bz measurements (using HP6 only) from Bx measurements (using HP4 and HP5 only). Such structures function functionally but are sensitive to mechanical stress variations and long term drift problems.

Fig. 3 is a schematic block diagram of a first exemplary sensor structure proposed by the present invention.

This structure can be used to measure both the in-plane magnetic field component Bx (parallel to the sensor plane) and the out-of-plane magnetic field component Bz (perpendicular to the sensor plane) at two different positions X1, X2, allowing determination of both the in-plane gradient (dBx/dx) and the out-of-plane gradient (dBz/dx), in addition to having reduced cross-talk and reduced drift problems.

The sensor structure (or "sensor arrangement") of fig. 3 comprises two sensors S1, S2, each having an IMC structure and four horizontal hall elements angularly spaced by 90 ° arranged at the periphery of the IMC structure. The sensor structure may be used for measuring a first in-plane magnetic field component Bx1 at a first position X1, a second in-plane magnetic field component Bx2 at a second position X2, and for measuring an out-of-plane magnetic field component Bz1, Bz2 at said first position X1, second position X2. The in-plane magnetic field gradient dBx/dx may be calculated from the values Bx1, Bx2, and the out-of-plane magnetic field gradient dBz/dx may be calculated from the values Bz1, Bz 2.

Fig. 3 case (b) shows a set of equations that can be used to determine the angular position of the sensor device relative to the magnet (or vice versa) based on an arctan function of the ratio of the first and second magnetic field gradients, but this is not absolutely necessary, and for example, a processor with a look-up table (and optionally also linear interpolation) for converting the ratio into angular positions can also be used.

To reduce potential cross talk between the magnetic field components, the measurement of Bx1 is based only on the signals obtained from HP1 and HP2, and the measurement of Bz1 is based only on the signals obtained from HP3 and HP4, and the measurement of Bx2 is based only on the signals obtained from HP5 and HP6, and the measurement of Bz2 is based only on the signals obtained from HP7 and HP8, and the structure is preferably located where the amplitude of the By component (denoted as | By |) is less than 20% of the amplitude | Bx | and/or less than 20% of the amplitude | Bz |. In this way, the potential leakage from Bz to Bx is reduced by at least a factor of 5. If the sensor device is located at a position where | By | is less than 10% of | Bx | and/or | Bz |, then the crosstalk is reduced By at least a factor of 10, etc. It will be further described where such locations actually exist, and where they are approximately located.

However, the sensor structure of FIG. 3 may also be used to measure the two in-plane magnetic field gradients dBx/dx and dBy/dx using the set of equations set forth in case (d) of FIG. 3 (e.g., as may be used in the angle sensor systems of FIGS. 12 and 14). In this case, the sensor device is preferably located where the amplitude of the Bz component (as seen By the sensor device) is small compared to the amplitude of Bx and/or By (as seen By the sensor device).

The sensor S1 of fig. 3 includes a single Integrated Magnetic Concentrator (IMC) and four horizontal hall elements HP1, HP2, HP3, HP4 (also referred to as "horizontal hall plates"). The IMC has a disc shape, but other shapes, such as an elliptical shape, may be used. The hall elements are arranged in the vicinity of the IMC and are angularly spaced 90 ° at or near the periphery of the IMC. The second sensor S2 has a similar structure, with four horizontal hall elements HP5, HP6, HP7, HP8 arranged in the vicinity of the second IMC concentrator pan IMC 2.

The first sensor S1 is located at a first position X1 on the substrate and the second sensor S2 is located at a second position X2 on the substrate spaced apart from X1 by a predefined distance Δ X, thus X2 ═ X1+ Δ X in the X direction. As mentioned above, the sensor device is preferably oriented such that the X-axis of the sensor device is oriented in a circumferential direction with respect to the rotational axis of the magnet (not shown in fig. 3).

The two hall elements HP1, HP2 of the first sensor S1 are located on the X-axis, and the two hall elements HP5, HP6 of the second sensor S2 are located on the X-axis. The other two elements HP3, HP4 of the first sensor S1 are located on an axis Y1 perpendicular to the X axis, and the other two elements HP7, HP8 of the second sensor S2 are located on an axis Y2 also perpendicular to the X axis. More specifically, the sensor elements HP1, HP2 define a first line segment on the X-axis, and the sensor elements HP3, HP4 lie on a perpendicular bisector Y1 of the first line segment. Likewise, the sensor elements HP5, HP6 define a second line segment on the X-axis, and the sensor elements HP7, HP8 lie on the perpendicular bisector Y2 of this second line segment.

The values of the in-plane magnetic field component Bx1 are determined as a function of the signals HP1 and HP2 only (independent of HP3, HP4), while the values of the out-of-plane magnetic field component Bz1 are determined as a function of the signals HP3, HP4 only (independent of HP1, HP 2). Thus, signals Bx1 and Bz1 are "electrically decoupled".

Furthermore, due to the perpendicular arrangement of the first pair of hall elements comprising HP1, HP2 on the one hand and the second pair of hall elements comprising HP3, HP4 on the other hand, the measurements of Bx1 and Bz1 are also "magnetically decoupled".

Furthermore, since the hall elements HP 1-HP 4 are arranged near the outer periphery of the first IMC structure, these four hall elements will have substantially the same temperature and they will be subjected to substantially the same mechanical stress, so they are "thermally and mechanically coupled". The combination of the "electrical and magnetic decoupling" and the simultaneous "thermal and mechanical coupling" of the two pairs of horizontal hall elements improves accuracy by reducing cross talk and by reducing mechanical stress variations, especially when the position is determined as a function of the ratio of the signals, since the effects from temperature and mechanical stress can occur in both the numerator and denominator of such ratio and thus substantially cancel out.

As shown in the formula of case (b) of fig. 3, the gradient of the in-plane magnetic field component can be calculated as: dBx/dx-Bx 2-Bx1, and the gradient of the out-of-plane magnetic field components can be calculated as: dBz/dx ═ Bz2-Bz 1. This is an advantage of using a gradient, since it automatically reduces or cancels out the influence of the (constant) external disturbing field.

The angular position of the sensor device can then be calculated based on the ratio of these gradients (e.g. using a look-up table, or using a goniometric function), e.g. using the arctangent function of the ratio, optionally after multiplication with a predefined constant K, in case the magnitude of | dBx/dx | is not the same as the magnitude of | dBz/dx |. An advantage of using a look-up table is that any angular non-linear transformation can be automatically included in the look-up table.

Fig. 3 case (a) provides a set of equations that can be used to determine angular position when measuring Bx and Bz using a sensor structure similar to that of fig. 3 (but with only a single sensor), as can be used, for example, in the sensor system of fig. 11 part (e) or fig. 25 part (c).

Case (d) of FIG. 3 provides a set of equations that may be used to determine angular position when measuring dBx/dx and dBy/dx using the sensor structure of FIG. 3, as may be used, for example, in the sensor systems of FIGS. 12 and 14.

Case (c) of fig. 3 provides a set of formulas that can be used to determine angular position when measuring Bx and By using a sensor structure similar to that of fig. 3 (but with only a single sensor), as can be used, for example, in the sensor systems of fig. 13 or 16.

Fig. 4 is a schematic block diagram of a second exemplary sensor structure as may be used in embodiments of the present invention, including two sensors S1, S2, each having an IMC structure and four horizontal hall elements.

The sensor structure is a variant of the sensor structure of fig. 3, the main difference being that the IMC structure of the first sensor and the IMC structure of the second sensor each comprise four separate integrated magnetic concentrator assemblies IMC1a-d and IMC2a-d, one integrated magnetic concentrator assembly for one horizontal hall element, instead of having a single disk-shaped IMC. These individual IMC components preferably have a smooth shape, such as a circle, or an ellipse, or a tear drop, a rain drop, etc.

The same benefits as described above with respect to reduced cross talk and reduced long term drift (e.g., related to temperature differences and/or mechanical stress differences) are also applicable here, as each of these hall elements will also be subjected to substantially the same temperature and the same mechanical stress, as they are covered by similar IMC components. The sensor structure of fig. 3 and 4 is highly symmetrical: they all have four axes of symmetry (X, Y and 45 ° diagonal) and they appear identical after a 90 ° rotation. The same formulas as in the case (a) to the case (d) in fig. 3 are applicable.

Although not explicitly shown further, the sensor structure of fig. 4 (or its individual sensor) may be used in all embodiments in which the sensor structure of fig. 3 (or its individual sensor) may be used.

Fig. 5 shows a position sensor system 500, which position sensor system 500 comprises a two-pole magnet 501 (more specifically a diametrically magnetized ring magnet) and comprises a sensor device 502 in the form of an integrated semiconductor component. The ring magnet 501 is movable relative to the sensor device 502 or vice versa. More specifically, the ring magnet 501 is rotatable about an axis of rotation 515 (e.g., when mounted to a rotor or to a shaft), while the sensor device typically has a fixed position (e.g., mounted to a stator or to a frame that supports the shaft). Sensor device 502 includes a sensor structure having one or two sensors (e.g., as shown in fig. 3 or fig. 4) and includes electronics as will be further described in fig. 6.

In the embodiment of fig. 5, the sensor device 502 is located in a plane β parallel to the upper surface of the magnet 501, e.g. at a distance of from about 1.0mm to about 3.0mm (e.g. equal to about 2.0mm) from said top surface 503, but the invention will also work if the sensor device is located at said distance from the bottom surface 504 of the ring magnet. The sensor device 502 is oriented with its internal X-axis tangent to the direction of relative movement (i.e. tangent to an imaginary circle shown in dashed lines) and with its internal Y-axis perpendicular to the tangent. Preferably, the Y-axis is located midway between the axis Y1 of the first sensor S1 and the axis Y2 of the second sensor S2, and perpendicularly intersects the rotational axis 515. Thus, sensor device 502 is oriented such that its substrate containing the horizontal hall elements and the X-axis and Y-axis is perpendicular to rotational axis 515, and the Z-axis (perpendicular to the substrate) is parallel to rotational axis 515.

At the sensor position shown, near the circular outer edge of the top or bottom surface of the magnet, the Bx and Bz components vary substantially like sine and cosine functions of the angular position α, which may have different amplitudes. Thus, the formula of case (a) of FIG. 3 based on Bx and Bz, or the formula of case (b) of FIG. 3 based on dBx/dx and dBz/dx, can be used to determine the angular position α.

To reduce or further reduce potential cross talk, the sensor device 502 is preferably located at a position relative to the magnet, for example, a radial distance Rs, wherein the magnitude of the By component is less than 20% of the magnitude of the Bx component or less than 15% of the magnitude of the Bx component or less than 10% of the magnitude of the Bx component or less than 5% of the magnitude of the Bx component, and/or wherein the magnitude of the By component is less than 20% of the magnitude of the Bz component or less than 15% of the magnitude of the Bz component or less than 10% of the magnitude of the Bz component or less than 5% of the magnitude of the Bz component. More preferably, for any angular position α of the magnet of the measurement range, sensor device 502 is located at a position where one or both of | By |/| Bx | and | By |/| Bz | is less than 15%, or even less than 10%, or even less than 5%, or where the value of | By | is substantially equal to zero.

It was surprisingly found that such positions actually exist (see for example fig. 17 and 18 for two-pole magnets, and 25 to 29 for multi-pole magnets), and it is almost incredible that the positions where this condition is fulfilled comprise a small annular area over the whole 360 ° around the axis of rotation of the magnet, which means that the amplitude of the By component is at least 5 times (even 10 times or more) smaller than the amplitude of Bx and/or Bz for any angular position of the magnet when the sensor device is located at this position.

Reference is made back to fig. 5.

In an embodiment, or in an operation mode, the values of Bx1 and Bz1 obtained from the first sensor S1 are used to calculate a first angle α 1, for example according to the formula α 1-arctan (K × Bx1/Bz1), and the values of Bx2 and Bz2 obtained from the second sensor S2 are used to calculate a second angle α 2, for example according to the formula α 2-arctan (K × Bx2/Bz2), where K is a predefined constant, which is typically different from 1.0 in case the magnitudes of Bx and Bz are not the same. The value of α 2 is slightly offset from the value α 1 because the position of the sensor S2 is slightly different from the position of S1, but the offset can be compensated for because it is fixed. Such sensor devices provide redundancy, but are sensitive to external interfering fields. If the values of α 1 and α 2 deviate by more than a predefined threshold, an error will be detected (false detection) and a warning signal or error signal may be output. Otherwise, the value of α 1 or α 2, or the average of α 1 and α 2 (optionally compensated with the offset) may be provided as the angular position to be measured.

In another or further embodiment, such as in another mode of operation, the values Bx1, Bx2, Bz1, Bz2 are further processed to obtain values for the in-plane field gradient dBx/dx and the out-of-plane field gradient dBz/dx, and to calculate the ratio of these gradients, and to determine the angular position of the sensor device based on the ratio, for example using the goniometric formula in case (b) of fig. 3, or using a look-up table (optionally with interpolation). The values of such tables may be determined in a known manner (e.g., by design, by simulation, by calibration, or by a combination of these manners), and may be stored in a non-volatile memory 621 (e.g., flash or EPROM or EEPROM) or the like. The advantage of using the ratio of the magnetic field gradients to calculate the angular position is because it makes the result highly insensitive to aging effects (e.g. demagnetization effects) and highly insensitive to external magnetic interference fields.

In a variant of fig. 5 (not shown), the sensor device will be rotated 90 ° around its X-axis, such that its Y-axis is parallel to the rotational axis 515 of the magnet and the Z-axis is parallel to the magnet surface, and optionally the sensor device may be located at a slightly larger distance from the upper or lower magnet surface. In this configuration, the Bx and By components will behave essentially like sine and cosine functions. According to an aspect of the invention, the sensor device will preferably be located at a radial distance Rs at which the amplitude of the Bz component (sensible By the sensor device) will be less than 20% of the amplitude of the Bx component and/or the By component. In this case, the angular position α of the magnet can be determined using the formula of case (c) or (d) of fig. 3. This embodiment has the advantage that both the Bx and By components are passively amplified By IMC By substantially the same factor, which is not the case for Bz in the embodiment of fig. 5, but the disadvantage is that the sensor device typically needs to be positioned slightly further away from the magnet due to its size.

FIG. 6 is a schematic block diagram of an exemplary position sensor apparatus 602 as may be used in embodiments of the present invention. Position sensor devices are known in the art, but a brief description is provided for completeness.

The position sensor device 602 of fig. 6 comprises a plurality of horizontal hall elements (in the example: HP1 to HP8) arranged in a specific manner on a semiconductor substrate, which are not shown in fig. 6, but are, for example, as shown in fig. 3 or 4.

The position sensor device 602 further comprises a processing circuit, e.g. a programmable processing unit 620, the programmable processing unit 620 being adapted to determine (e.g. calculate) values Bx1, Bz1, Bx2 and Bz2, e.g. by summing or subtraction, based on the signals obtained from the horizontal hall elements, and to calculate the in-plane magnetic field gradient dBx/dx and the out-of-plane magnetic field gradient dBz/dx at two different positions, e.g. using one or more of the equations shown in case (b) of fig. 3.

The processing unit 620 is preferably further adapted to determine the angular position based on the ratio of these gradient signals, e.g. using a look-up table and interpolation, or by using a goniometric function (e.g. an arctangent function) or in any other suitable way.

The angle value may be output by the controller, optionally together with an error indication signal that may be used for functional safety. The error indication signal may indicate whether the values of Bx1, Bx2, Bz1, Bz2 sufficiently match, for example, by testing whether the difference between Bx1 and Bx2 is sufficiently small, and/or based on whether the difference between Bz1 and Bz2 is sufficiently small, or in other suitable manners.

Although not explicitly shown, the sensor apparatus 602 typically further includes biasing circuitry, readout circuitry, one or more amplifiers, analog-to-digital converters (ADCs), and the like. Such circuits are well known in the art and are not the primary focus of the present invention.

However, the invention is not limited to a sensor device having eight horizontal hall elements arranged for measuring the in-plane magnetic field gradient dBx/dx and the out-of-plane magnetic field gradient dBz/dx, and in a variant the processing unit 620 is adapted to determine (e.g. calculate) the values Bx1, By1, Bx2 and By2, e.g. By summing or subtraction or directly, e.g. using one or more of the formulae shown in case (d) of fig. 3, based on the signals obtained from the horizontal hall elements, and to calculate the in-plane magnetic field gradient dBx/dx in a first direction X and the in-plane gradient dBy/dx in a second direction Y perpendicular to X, e.g. using one or more of the formulae shown in case (d) of fig. 3.

However, the invention is not limited to sensor devices with eight horizontal hall elements, and sensor structures with different numbers and/or different types of magnetic sensor elements may also be used. For example, in a variation of the sensor apparatus of fig. 6, the position sensor apparatus may comprise a plurality of magnetic sensing elements selected from the group consisting of: horizontal hall elements, vertical hall elements, magnetoresistive elements (e.g., XMR or GMR elements), etc., such as:

part (f) of fig. 9, part (e) of fig. 15, part (d) of fig. 25, part (f) showing an example of a sensor arrangement with two sensors spaced along the X-axis, each sensor comprising one horizontal hall element and one vertical hall element without IMC;

part (e) of fig. 11, part (c) of fig. 13, part (c) of fig. 16, part (c) of fig. 25 show examples of sensor arrangements with a single sensor comprising an IMC and four horizontal hall elements;

part (f) of fig. 11, part (e) of fig. 15, part (d) of fig. 25 show examples of sensor arrangements with a single sensor comprising a horizontal hall element and a vertical hall element without IMC;

part (d) of fig. 13, part (d) of fig. 16 show an example of a sensor arrangement with a single sensor comprising two vertical hall elements without IMC;

part (e) of fig. 10, part (d) of fig. 12, part (e) of fig. 12, part (d) of fig. 14 show examples of sensor arrangements with two sensors spaced along the X-axis, each sensor comprising two vertical hall elements without IMCs;

other sensor configurations may be used.

Fig. 7 illustrates a method for determining an angular position using a sensor device comprising two sensors S1, S2 as described in fig. 3 or 4 or as will be described in fig. 8, each sensor having an IMC structure (the IMC structure comprises one or more IMC components) and having three or four horizontal hall elements.

The method 700 includes the steps of:

an optional step a) is to provide 701 a first sensor S1 comprising three or four horizontal hall elements at a first position X1 and a second sensor S2 comprising three or four horizontal hall elements at a second position X2 spaced apart from the first position X1 in the first direction X.

b) Determining 702 a first in-plane magnetic field component (e.g., Bx1) using two horizontal hall elements (e.g., HP1, HP2) of the first sensor S1, and determining a first out-of-plane magnetic field component (e.g., Bz1) using one (e.g., HP3 of fig. 8) or two other hall elements (e.g., HP3, HP4 of fig. 3 or 4) of the first sensor S1;

c) determining 703 a second in-plane magnetic field component (e.g., Bx2) using two horizontal hall elements (e.g., HP5, HP6) of the second sensor S2, and determining a second out-of-plane magnetic field component (e.g., Bz2) using one (e.g., HP7 of fig. 8) or two other hall elements (e.g., HP7, HP8 of fig. 3 or 4) of the second sensor S2;

d) the angular position is determined 704 based on the first and second in-plane magnetic field components (e.g., Bx1, Bx2) and based on the first and second out-of-plane magnetic field components (e.g., Bz1, Bz 2).

The method may further comprise the steps of: the sensor device comprising the first sensor S1 and the second sensor S2 is arranged with respect to a magnetic source in the following manner: such that the inner X-axis defined by the position X1 of the first sensor S1 and the position X2 of the second sensor S2 is tangent to an imaginary circle lying in a plane perpendicular to the axis of rotation of the magnet and having its center on the axis of rotation, and such that the Y-axis of the sensor device is located midway between the first sensor position X1 and the second sensor position X2 and parallel to the substrate, intersects the axis of rotation 515, and is perpendicular to said axis of rotation 515. This means that the Z-axis perpendicular to the sensor device substrate is parallel to the rotation axis 515.

According to an important aspect of the invention, the sensor device is also preferably located (relative to the magnet) at a position at which the By component(s) of the magnetic field seen By the sensor device (which By component is oriented in the radial direction of the magnet) have an amplitude that is less than 20% of the amplitude of the Bx component(s) oriented in the circumferential direction of the magnet, or less than 15% of the amplitude of the Bx component(s), or less than 10% of the amplitude of the Bx component(s), or less than 5% of the amplitude of the Bx component(s), and/or less than 20% or 15% or 10% or 5% of the amplitude of the Bz component oriented in the axial direction of the magnet at said position, preferably for each angle of the entire 360 ° range of the magnet.

This method 700 corresponds to the formula of case (b) of fig. 3, but the invention is not limited thereto, and similar methods for the other set of formulas of fig. 3, or similar formulas for other sensor structures as described herein (see, e.g., fig. 8), or similar formulas for other sensor structures even not explicitly detailed herein, can be readily formulated with necessary modifications.

For example, a method suitable for use in fig. 14, where the sensor device is arranged "near the equator", and where the sensor device is oriented with its semiconductor substrate perpendicular to the axis of rotation, the sensor device will measure two in-plane components Bx and By, and will preferably be located at a position where | Bz | is small relative to | Bx | and/or | By | which can also be expressed as: at any angular position of the magnet, the axial field of the magnet is smaller than the circumferential and/or radial field of the magnet.

The method may also be reformulated for embodiments having only a single sensor position, e.g., as in part (c) of fig. 11 or 13 or 16 or 25, part (d) of fig. 25.

Fig. 8 shows an example of a sensor structure with a first sensor S1 and a second sensor S2, the first sensor S1 having an IMC structure IMC1 (having a disc shape in the example of fig. 8) and only three horizontal hall elements HP1, HP2, HP3, the second sensor S2 being spaced apart from the first sensor along the X-axis and having a similar IMC structure IMC2 and only three horizontal hall elements HP5, HP6, HP 7.

All horizontal hall elements are located on the X-axis. Elements HP1 and HP2 are located on opposite sides of IMC1, and element HP3 is located midway between HP1 and HP2, at the center of IMC1, and below IMC 1. Contrary to what most people believe, the hall element HP3 is fully capable of measuring the magnetic field component Bz1 oriented perpendicular to the substrate, despite its being located below the IMC. Likewise, elements HP5 and HP6 are located on opposite sides of IMC2, and element HP7 is located midway between HP5 and HP6, at the center of IMC2, and below IMC 2. Due to their orientation and their central position, elements HP3 and HP7 do not pick up the Bx field or the By field, but only measure the Bz field, and are therefore magnetically decoupled from HP1, HP2 and HP5, HP6, respectively. Since the signals of HP3 are not used to determine Bx1, and the signals of HP1 and HP2 are not used to determine Bz1, sensor elements HP1 and HP2 are also electrically decoupled from HP 3.

Importantly, hall element HP3 experiences substantially the same mechanical stresses as HP1 and HP2, since they are located underneath the same IMC disc, and since the position of hall element HP3 is midway between HP1 and HP2, the temperature of HP3 is substantially equal to the temperature of HP1 and HP 2. Also, the hall element HP7 experiences substantially the same mechanical stress and has substantially the same temperature as HP5 and HP 6.

In view of the foregoing, it will be appreciated by those skilled in the art having the benefit of this disclosure that the sensor structure of fig. 8 provides many or all of the same advantages as the sensor structure of fig. 3 or 4 in terms of accuracy, particularly in terms of insensitivity to external interfering fields, reduced sensitivity to crosstalk (particularly Bx to Bz, and vice versa), reduced sensitivity to mechanical stress, and reduced long-term drift.

Fig. 9 to 16 show an example of an angular position sensor system comprising a permanent magnet rotatable about an axis of rotation and a sensor device located in the vicinity of the magnet. Before describing the embodiments separately, a general review is first given.

In contemplated embodiments, the magnet is preferably an axially or diametrically magnetized two-pole ring magnet having an inner diameter ID of at least 5mm (e.g., about 8mm) and an outer diameter in the range of from 10mm to 50mm (e.g., from 15mm to 45mm) (e.g., equal to about 20mm, or equal to about 25mm, or equal to about 30 mm); and has a height H in the range from 2 to 10mm (e.g., equal to about 2.5mm or equal to about 5.0 mm). In an alternative embodiment, the magnet is a disc magnet having an outer diameter OD range and a height range specified for a ring magnet.

The embodiments of fig. 9-16 differ primarily in the relative position and orientation of the sensor device with respect to the magnet. The sensor devices shown in fig. 9 to 16 may comprise a sensor structure as explicitly shown, but the invention is not limited to the specific examples shown and other sensor structures may also be used, such as any of the sensor structures shown in fig. 3 or 4 or 8, but other suitable sensor structures may also be used, such as sensor structures having one or more magneto-resistive elements.

The sensor devices of these sensor systems comprise a semiconductor substrate with one or more sensors, each sensor comprising a plurality of sensor elements configured for measuring magnetic field components in at least two orthogonal directions (e.g. two of the three directions are selected from the group consisting of radial, circumferential or axial with respect to the axis of rotation of the magnet). In the figures, three orthogonal axes X, Y, Z are fixed to the sensor device. The X-axis and the Y-axis are parallel to the substrate (e.g. the semiconductor substrate of the sensor device) and the Z-axis is perpendicular to the substrate, so the Bx-component and the By-component are referred to as "in-plane magnetic field components" and the Bz-component is referred to as "out-of-plane magnetic field components".

In an embodiment of the invention, the sensor device is oriented with respect to the magnet such that:

1) the X-axis is oriented in the circumferential direction, i.e. tangent to an imaginary circle lying in a plane perpendicular to the axis of rotation and having a centre on said axis of rotation, and

2a) the Y axis intersects the axis of rotation orthogonally (in this case, the Z axis is parallel to the axis of rotation), or

2b) The Z-axis intersects the rotation axis orthogonally (in this case, the Y-axis is parallel to the rotation axis).

In the case of (1) + (2a), Bx is oriented in the circumferential direction of the magnet, By is oriented in the radial direction of the magnet, and Bz is oriented in the axial direction of the magnet. Thus, the By field component "seen" By the sensor device corresponds to the radial field component "seen" By the magnet, and the Bz field component "seen" By the sensor device corresponds to the axial field component "seen" By the magnet.

In the case of (1) + (2b), Bx is oriented in the circumferential direction of the magnet, Bz is oriented in the radial direction of the magnet, and By is oriented in the axial direction of the magnet. Thus, the "Bz field component" seen By the sensor device corresponds to the radial field component "seen" By the magnet, and the By field component "seen" By the sensor device corresponds to the axial field component "seen" By the magnet.

In a preferred embodiment of the invention, the sensor device (or its magnetic centre point) is positioned (relative to the magnet) in one of three positions:

i) the position referred to herein as "above or below the magnet":

at a radial distance Rs between the inner and outer radii Ri, Ro of the ring magnet (e.g., substantially midway between Ri and Ro) in a plane β at a small distance of about 1.0 to 5.0mm below the bottom surface of the cylindrical magnet or above the top surface of the cylindrical magnet, e.g., as shown in fig. 12, 13 and 25. The ideal Rs value depends on the dimensions of the magnet (inner diameter ID, outer diameter OD, height H) and on the predefined distance (g) between the plane β in which the substrate of the sensor device is located and the bottom or top surface of the magnet and its magnetization (e.g. dipolar, quadrupolar, hexapolar, diametrically magnetized, axially magnetized magnetic material) and (for a given magnet) can be easily determined by performing simulations, for example, as shown in fig. 17, 21, 22 and 29;

ii) locations referred to herein as "near corners":

in a plane β at a small distance of about 1.0 to 5.0mm below the bottom surface of the cylindrical magnet or above the top surface of the cylindrical magnet, at a radial distance Rs of about 90% to 110%, or 90% to 98%, or 102% to 110% of the outer radius Ro of the ring magnet or the disc magnet, for example, as shown in fig. 9, 10 and 11. The ideal Rs value depends on the dimensions of the magnet (inner diameter ID, outer diameter OD, height H) and on the predefined distance (g) between the plane β in which the substrate of the sensor device is located and the bottom or top surface of the magnet and its magnetization (e.g. dipolar, quadrupolar, hexapolar, diametrically magnetized, axially magnetized magnetic material) and (for a given magnet) can be easily determined by performing simulations, e.g. as shown in fig. 17 to 20. It was found that for some magnets and some distances (g) the ideal radial position Rs is larger than the outer radius Ro, for example at least 102% of the outer radius Ro (Rs ≧ Ro 102%). For some magnets and distances (g), the ideal radial position is substantially equal to the outer radius (Rs ≈ Ro). For other magnets and distances (g), the ideal radial position Rs is less than the outer radius Ro, e.g., at most 98% of the outer radius (Rs ≦ Ro × 98%).

iii) locations referred to herein as "near the equator":

in a plane β perpendicular to the axis of rotation of the magnet, at substantially half the height H of the magnet, at a radial distance Rs of about 102% to 120% of the outer radius Ro of the ring or disc magnet, as shown, for example, in fig. 14 to 16. The ideal axial position is at half the height of the magnet and the ideal radial position Rs is not critical but preferably is relatively close to the magnet, where the Bx signal is relatively large, thus providing good SNR, e.g. Rs is a value in the range from 1.0 to 10mm, or in the range from 2.0 to 7mm, e.g. equal to about 2.5mm, or equal to about 3.0mm, or equal to about 3.5mm, or equal to about 4 mm. Fig. 23 and 24 show how the amplitude of the field component in the axial direction of the magnet (Bz in fig. 14 and 16, By in fig. 15) varies as a function of the distance "g" between the plane β in which the substrate of the sensor device lies and the plane of symmetry at half the height of the magnet, for a value of Rs equal to 3.0 mm.

The following table contains a list of various combinations of the following: magnet type (column 2), figure (column 1), indication of the measured magnetic field component (column 3), position of the sensor device (column 4), indication of whether the angle is calculated based on the field component (single sensor) or based on the field gradient (two sensors) (column 5).

Table 1: list of some combinations of magnet and sensor positions and orientations

Wherein:

(i) it is referred to as "above or below the magnet",

(ii) means "near the corner" (or "near the outer edge")

(iii) It means "near the equator",

in this case, Bx, Bz, By for the sensor device are respectively the B-tangential, B-axial, and B-radial directions of the magnet

In this case, Bx, Bz, By for the sensor device are respectively the B-tangential, B-radial, B-axial directions of the magnet

"i By i is small" means i By i/i Bx i < 20% or < 15% or < 10% or < 5%, and/or i By i/i Bz i < 20% or < 15% or < 10% or < 5%, or ideally i By 0

"i Bz | is small" means | Bz |/| Bx | < 20% or < 15% or < 10% or < 5%, and/or | Bz |/| By | < 20% or < 15% or < 10% or < 5%, or ideally, | Bz | ═ 0.

The embodiments of fig. 9-16 will now be discussed in more detail.

Fig. 9 shows the angular position sensor system 900 in a front view (part (a) of fig. 9), in a top view (part (b) of fig. 9), and in a perspective view (part (c) of fig. 9). The magnet 901 may be a diametrically magnetized two-pole disc magnet or a ring magnet (part (d) of fig. 9). The sensor device 902 is located at a predefined position relative to the magnet, which is defined by the plane β and the radial distance Rs. The plane β is orthogonal to the axis of rotation of the magnet and is located at a distance "g" from the bottom surface of the magnet or from the top surface of the magnet 901.

Or more precisely, the sensor device 902 of part (e) of fig. 9 has a substrate with a sensor structure as described in fig. 3 and is oriented: such that the substrate lies substantially in a plane β and such that the X-axis of the sensor structure is oriented in a circumferential direction around the rotational axis of the magnet, or in other words such that the X-axis is tangent to an imaginary circle located in the plane β and having a radius Rs, and such that the Y-axis intersects the rotational axis of the magnet. Thus, the Z-axis perpendicular to the substrate of the sensor device is parallel to the rotational axis of the magnet.

Sensor apparatus 902 having the sensor structure of section (e) of fig. 9 is preferably configured for determining the angular position of the magnet based on the gradients dBx/dx and dBz/dx, e.g., using some or all of the equations of case (b) of fig. 3.

In a preferred embodiment of the invention, the radial position Rs is specifically chosen to be a value between the value R3 and the value R4 at which, over a predefined angular range, for example over a full 360 ° rotation of the magnet about its axis, the magnitude of the By component of the magnetic field seen By the sensor (i.e. the radial vector component of the magnetic field seen By the magnet) is less than 20% of the magnitude of the Bx component of the magnetic field seen By the sensor device (i.e. the tangential or circumferential component of the magnetic field seen By the magnet), preferably less than 15% of the magnitude of the Bx component, more preferably less than 10% of the magnitude of the Bx component or even less than 5% of the magnitude of the Bx component, and most preferably approximately equal to zero, and/or less than 20% of the magnitude of the Bz component of the magnetic field seen By the sensor device (i.e. the axial component of the magnetic field seen By the magnet), preferably less than 15% of the magnitude of the Bz component, more preferably less than 10% or even less than 5% of the amplitude of the Bz component, and most preferably approximately equal to 0.

Part (a) of fig. 10 shows in perspective a diametrically magnetized ring magnet, preferably a magnet made of NdFeB (but other suitable materials such as ferrite could be used) with an outer diameter OD of 15mm, an inner diameter of 5mm and a height H of 2.5 mm.

Part (b) of fig. 17 shows a simulation of the magnitude (i.e. the absolute value of the amplitude) of the radial magnetic field component seen By the magnet in a plane at a distance "g" of 2.0mm below the magnet, which corresponds to the magnitude of the By component, denoted By | seen By the sensor device. These simulations use "Comsol"but other tools may be used. The picture shows the amplitude in grey scale, where white corresponds to zero and black corresponds to a relatively high amplitude, e.g. in [ mT [ ]]To express, the exact value of the amplitude is not important. The radial dimensions of the magnets are superimposed in section (b) of fig. 17, but omitted in section (c) of fig. 17 to clearly show the "annular region" where | By | is less than 10% of | Bx |.

Since the grayscale picture is not generally reproduced at a very high quality by the patent office, the portion (b) of fig. 17 and the portion (c) of fig. 17 are also provided as dithered black-and-white pictures using 10 dither levels in the portion (d) and the portion (e) of fig. 17, thereby showing a step size of approximately 10% of the span. The careful reader will note that the pictures of part (d) of fig. 17 and part (e) of fig. 17 are not completely symmetrical, which is an artifact caused by the conversion of color pictures. However, the effect to be displayed (the presence and location of the annular white area) is still well visible.

Surprisingly, there is a region where the value of | By | is very small, or more precisely, the value of | By | is less than 20% of | Bx | or less than 15% of | Bx | or less than 10% of | Bx | or less than 5% of | Bx | and/or less than 20% of | Bz | or less than 15% of | Bz | or less than 10% of | Bz | or less than 5% of | Bz | or the value of | By | is substantially zero. But more surprisingly, this region is an annular region extending over the entire 360 deg. range, especially considering that the magnets are diametrically magnetized (rather than radially magnetized). The inventors decided to position the sensor device in this region (or more precisely, to position the sensor device such that its magneto-sensitive element is located in this region) such that the value of | By | seen By the sensor device will be close to zero for any angle of the magnet, thereby substantially reducing the potential cross-talk from the By field component to the value of Bx.

Some other simulations are described next before returning to fig. 9.

Fig. 18 shows the simulation results of another magnet having an outer diameter OD of 30mm, an inner diameter ID of 20mm, and a height H of 10 mm. Part (a) of fig. 18 shows the magnet in a perspective view. Part (b) of fig. 18 shows in grayscale the amplitude of the By component (as seen By the sensor device) corresponding to the radial magnetic field component for the magnet for each position in plane β located at a distance of 2mm below or above the magnet surface. A circle 1899 having a diameter of 50mm is provided by the simulation tool, but is not relevant for the present invention. Part (c) of fig. 18 shows the simulation result with five jitter levels, each level corresponding to approximately 20% of the full scale. Part (d) of fig. 18 shows the simulation results with ten jitter levels, each level corresponding to approximately 10% of full scale. Part (e) of fig. 18 shows the simulation results with seventeen dither levels, each level corresponding to approximately 6% of full scale. As mentioned above, the picture is asymmetric due to the artifact of the color conversion, but despite this anomaly, the picture clearly shows that there is a ring-shaped region where the amplitude of the By component is very small, or more precisely, the amplitude of the By component is less than 20% of the amplitude of the Bx component, or the amplitude of the By component is close to zero.

Fig. 19 shows another representation of the simulation results for the magnet shown in fig. 17, which has an outer diameter OD of 15mm, an inner diameter ID of 5mm and a height H of 2.5 mm. It should be noted that these pictures are highly symmetric and are not affected by the artifacts mentioned above, since the picture is not derived from a color picture.

Part (a) of fig. 19 shows in grayscale the magnitude of the By component (as seen By the sensor device) corresponding to the radial magnetic field component of the magnet for various positions in the plane located at a distance of 2mm below or above the magnet surface. Part (b) of fig. 19 shows the simulation result with five jitter levels, each level corresponding to approximately 20% of the full scale. Part (c) of fig. 19 shows the simulation results with ten jitter levels, each level corresponding to approximately 10% of full scale. Part (d) of fig. 19 shows the simulation results with seventeen dither levels, each level corresponding to approximately 6% of full scale.

The main purpose of this simulation is to show that the annular region in which the By component has said relatively low value and ideally is substantially equal to zero can be located at a radial position Rs that is smaller than the outer radius Ro of the ring or disc magnet, but as can be seen, also in this case, the annular region is located very close to the outer edge of the magnet, in the range from 90% to 99% of the outer radius Ro, or in the range of about 95% to 98% of the clever of the outer radius Ro.

Simulations with other magnets have shown that the envisaged annular region in which the By component has said relatively small value can be located:

i) inside the outer radius, between R3 ═ Ro × 90% and R4 ═ Ro × 98%; or

ii) substantially on the outer edge of the magnet, between R3 ═ Ro 95% and R4 ═ Ro 105%; or

iii) outside the outer radius, between R3-Ro 102% and R4-Ro 110%.

The exact range for a given magnet (given magnet material, given magnet size, given magnetization) and a given distance "g" can be easily found by one of ordinary skill having the benefit of this disclosure, for example, by conducting computer simulations. Indeed, it will be understood from the present disclosure that an annular region exists, and wherein the narrowest width of the annular region lies, for example, on a line passing through the axis of rotation of the magnet, and is parallel to the direction of magnetization (or stated otherwise: at the intersection of plane β with a second plane containing the axis of rotation and parallel to the direction of magnetization, for example, as indicated by the arrow in section (d) of FIG. 11). Thus, it is not necessary to simulate By values in all points of the 2D plane, but to simulate By values on only a single line, but of course the skilled person may also simulate By values in several points on more than one line (e.g. on two or three lines), if desired.

Part (a) of fig. 20 shows how the amplitude of the Bx, By and Bz components varies along such lines as a function of the radial distance Rs from the axis of rotation. The "sweet spot" where the magnitude of the By component is small is indicated By a rectangle in the form of a dashed line.

Part (b) of fig. 20 shows the optimum point in an enlarged view. In the example shown, if the sensor device is located at a distance Rs of from about 7.1 to about 8.4mm (and thus within an annular region having a width of about 1.3 mm), the ratio of | By | to | Bx | is less than 20%; and if the sensor device is located at a distance Rs of from about 7.5 to about 8.1mm (and thus within an annular region having a width of about 0.6 mm), the ratio of | By | to | Bx | is less than 10%, the distance Rs being greater than a typical diameter of an IMC disk, which is a value on the order of about 200 to 400 microns.

Returning to fig. 9, it can now be appreciated that when sensor device 902 is positioned inside the (white) annular region described above, the magnitude of the By component is much smaller than the magnitude of the Bx component and/or the Bz component, and thus any potential crosstalk from By to Bx and/or By to Bz is reduced By at least a factor of 5 or 10 or even more. This is one of the basic ideas of the present invention.

Part (f) of fig. 9 shows a sensor device having two sensors, each sensor having a horizontal hall element and a vertical hall element but no IMC. Horizontal hall elements are capable of measuring Bz1 and Bz 2. The vertical hall elements are capable of measuring Bx1 and Bx 2. When such a sensor device is used in the system of fig. 9, many or all of the same advantages as described above can be achieved with this sensor structure, including having a measurement range of 360 °, having reduced sensitivity to cross-talk, being highly robust to external interference fields, etc.

In another variant (not shown), the sensor structure of fig. 4 or 8 is used.

Fig. 10 shows another or further variation of the angular position system described in fig. 9, in which the sensor device 1002 is oriented such that its X-axis is tangent to an imaginary circle of radius Rs, but the Z-axis intersects the axis of rotation of the magnet, and the Y-axis is parallel to said axis of rotation (which can be obtained by rotating the sensor device 902 of fig. 9 by 90 ° about its X-axis). In this embodiment, the signals Bx and By (as seen By the sensor device) vary like sine and cosine functions of the angular position of the magnet (possibly with different amplitudes), while the Bz component (as seen By the sensor device) has an amplitude close to zero (or more precisely: | Bz |/| < 20% or < 15% or < 10% or < 5%;, and/or |/| By | < 20% or < 15% or < 10% or < 5%;, or ideally | Bz | ≈ 0).

The sensor device 1002 may for example comprise the sensor structure of fig. 3 (as shown in part (d) of fig. 10) or the sensor structure of fig. 4, and the angular position of the magnet may for example be determined using the formula of case (d) of fig. 3, with the same advantages as described above, in particular with reduced cross-talk and long-term drift, robustness against mechanical stress and against external disturbing fields. The present invention is not limited thereto, and other sensor structures, for example, the sensor structure of part (e) of fig. 8 or 10, or a sensor structure including a magnetoresistive element (not shown) configured to measure at least Bx and By may also be used.

In a variation of fig. 10 (not shown), the sensor device 1002 contains only a single sensor, and the formula of case (c) of fig. 3 can be used to determine the angular position. A disadvantage of such embodiments is that the measurement is not robust to external disturbing fields, but the advantages of reduced cross-talk and having an angular range of 360 ° still exist.

Fig. 11 shows an angular position sensor system 1100 that is a variation of the angular sensor system 900 of fig. 9. The main difference between the sensor system 1100 of fig. 11 and the sensor system 900 of fig. 9 is that the sensor device 1102 comprises a sensor structure configured for: a sensor structure measuring a single in-plane magnetic field component Bx and a single out-of-plane magnetic field component Bz, and calculating the angular position of the magnet based on these components Bx, Bz (preferably as a function of the ratio of these values), e.g. using an angle measurement function as described in case (a) of fig. 3 or using a look-up table for converting the ratio into angular position. Since the system 1100 does not use gradient signals, it is not robust to external disturbing fields, but all other advantages mentioned above for fig. 9, in particular, for example, with reduced crosstalk, apply here as well.

Various sensor devices capable of measuring the in-plane magnetic field component Bx and the out-of-plane magnetic field component Bz may be used, for example, a sensor device having a sensor structure with an IMC and four hall elements as shown in part (e) of fig. 11, or a sensor device having a sensor structure with one vertical hall element and one horizontal hall element oriented in a suitable direction as shown in part (f) of fig. 11.

In a variation of the system of fig. 11, a sensor device with a single sensor as described in fig. 4 (with four separate IMC elements) or fig. 8 (with IMC and only three horizontal hall elements) is used.

In another or a further variant (not shown), the sensor devices 1102 depicted in fig. 11 are oriented with their X-axis in a tangential direction but their Y-axis parallel to the rotational axis, in which case the Bx component (in the circumferential direction) and the By component (in the axial direction of the magnet) will be measured during actual use, and the formula of case (c) of fig. 3 is applicable. In this case, the Bz component (in the radial direction of the magnet) will be very small (ideally close to zero).

In still other embodiments, a magnetoresistive element is used as the magneto-sensitive element.

Fig. 12 shows an angular position sensor system 1200 in a front view (part (a) of fig. 12) and a top view (part (b) of fig. 12). The magnet 1201 may be a diametrically magnetized two-pole ring magnet. The sensor device 1202 is located at a position defined by the plane β and the radial distance Rs. Plane β is orthogonal to the axis of rotation of the magnet and is located at a distance "g" from the bottom surface of magnet 1201 or the top surface of the magnet (similar to what is shown in fig. 5).

The sensor device 1202 may have a sensor structure as described in fig. 3 (see part (c) of fig. 12) and be oriented such that the X-axis of the sensor structure is tangent to an imaginary circle in plane β and having a radius Rs, and such that the Y-axis of the sensor structure perpendicularly intersects the axis of rotation of the magnet, and such that the Z-axis of the sensor device is parallel to the axis of rotation of the magnet.

Sensor apparatus 1202 is preferably configured to determine the angular position of the magnet based on gradients dBx/dx and dBy/dx, e.g., according to some or all of the equations of case (d) of fig. 3.

In a preferred embodiment of the invention, the radial position Rs may be chosen in particular as a value between the value R3 and the value R4 at which, preferably over a full 360 ° rotation of the magnet about its axis, the amplitude of the Bz component of the magnetic field seen By the sensor (corresponding to the axial vector component of the magnetic field seen By the magnet) is less than 20% of the amplitude of the Bx component of the magnetic field seen By the sensor device (corresponding to the tangential or circumferential component of the magnetic field seen By the magnet), preferably less than 15%, more preferably less than 10%, or even less than 5% of the amplitude of the Bx component, and/or less than 20%, preferably less than 15%, more preferably less than 10% of the amplitude of the By component of the magnetic field seen By the sensor device (i.e. the radial component of the magnetic field seen By the magnet), Or even less than 5% of the amplitude of the By component, and ideally at a position where | Bz | ≈ 0 (approximately zero).

To fully appreciate the benefits of this embodiment of the present invention, reference is made to the simulations discussed next.

Part (a) of fig. 21 shows in perspective view a diametrically magnetized ring magnet made of NdFeB having an outer diameter OD of 30mm, an inner diameter ID of 20mm and a height H of 10 mm.

Part (b) of fig. 21 shows a simulation of the axial magnetic field component seen by the magnet at a distance "g" of 2.0mm below or above the magnet, which corresponds to the "Bz component seen by the sensor device of fig. 12". The picture shows the amplitude in grey (where white means low amplitude and black means high amplitude). The inner and outer diameters of the magnets are superimposed in section (b) of fig. 21 to better illustrate where the annular region is located. Circle 2199 having a diameter of 50mm is provided by simulation, but is not relevant for the present invention and may be ignored. The main purpose of fig. 21 is to show the presence area, more specifically the annular area where the Bz component seen by the sensor device is close to zero.

Since the grayscale picture is not generally reproduced with sufficient quality by the patent office, the portion (b) of fig. 21 is also provided as dithered black-and-white pictures in the portions (c) to (e) of fig. 21, which use 5, 10, and 17 dither levels corresponding to step sizes of about 20%, 10%, and 6% of the full scale, respectively. It should be noted that the picture of fig. 21 is not completely symmetrical, which is an artifact caused by a conversion of a color picture, but the position and width of the annular region are still very well visible, where W20% is the width in the case of | Bz |/| Bx | < 20%, W10% is the width in the case of | Bz |/| Bx | < 10%, and W6% indicates the width in the case of | Bz |/| Bx | < 6%. Width W6% < W10%, and W10% < W20%.

It is also surprising that there are regions in which the Bz component is very small, or more precisely where | Bz |/| Bx | and/or | By |/| Bz | is less than 20%, or less than 10%, or less than 5%, or | Bz | ≈ 0, and this condition is satisfied in an annular region extending over the entire 360 ° range, especially in view of the fact that the magnet is diametrically magnetized (not radially magnetized).

Fig. 22 shows the simulation results of another magnet having an outer diameter OD of 15mm, an inner diameter ID of 5mm, and a height H of 2.5 mm. Part (a) of fig. 22 shows the magnitude of the Bz component (as seen by the sensor device) corresponding to the axial component of the magnet for various positions in the plane located at a distance of 2mm below or above the magnet surface.

Part (a) of fig. 22 shows the simulation result in grayscale. Part (b) of fig. 22 shows the simulation result with five jitter levels, each level corresponding to approximately 20% of the full scale. Part (c) of fig. 22 shows the simulation results with ten jitter levels, each level corresponding to approximately 10% of full scale. Part (d) of fig. 22 shows the simulation results with seventeen dither levels, each level corresponding to approximately 6% of full scale. As mentioned above, the picture is not symmetrical due to the artifact of the color conversion, but despite the anomaly, the picture clearly shows that such regions exist, and the width of the annular region narrows as the amplitude of the permitted Bz component decreases.

Returning to fig. 12, it can now be appreciated that when sensor apparatus 1202 is positioned inside the annular region, the amplitude of the Bz component is much smaller than the amplitude of the Bx component and/or Bz component, and thus any potential crosstalk from Bz to Bx and/or By to Bz is reduced By at least a factor of 5 or 10 or even more, thus improving accuracy.

Part (c) of fig. 12 shows a sensor device having the sensor structure as described in fig. 3. Such sensor systems have many or all of the same advantages as described for fig. 9, including having a measurement range of 360 °, having reduced sensitivity to cross-talk, being highly robust to external interference fields, etc.

The sensor system 1200 may also be used with other sensor configurations, such as the sensor configuration shown in section (d) of fig. 12 or section (e) of fig. 12, having two sensors spaced apart along the X-axis, each sensor including two vertical hall elements, one vertical hall element configured to measure the Bx component and the other vertical hall element configured to measure the By component in a direction perpendicular to X.

In another variant (not shown), the sensor structure of fig. 4 (with four horizontal hall elements and four discrete IMC elements) is used.

In still other embodiments, a magnetoresistive element is used as the magneto-sensitive element.

In another or further variant (not shown), the sensor device 1202 with the sensor structure of fig. 3 or 4 is oriented such that its X-axis is tangent to an imaginary circle with radius Rs, but the Z-axis intersects the axis of rotation of the magnet, and the Y-axis is parallel to said axis of rotation (as would be obtained after rotating the sensor device 1202 by 90 ° about its X-axis in the case of the system starting from part (a) of fig. 12). In this embodiment, the signals Bx and Bz (as seen By the sensor device) vary like a sine function and a cosine function (possibly with different amplitudes) of the angular position of the magnet, while the By component (as seen By the sensor device) corresponding to the axial magnetic field component (as seen By the magnet) has a much smaller amplitude than the amplitude of Bx. In this embodiment, the sensor device may use the formula of case (b) of fig. 3 to determine the angular position of the magnet, with the same advantages as described above, in particular with reduced cross-talk.

A sensor structure having two sensors each including a single horizontal hall element and a single vertical hall element without IMC, as shown in part (f) of fig. 9, may also be used.

Fig. 13 shows an angular position sensor system 1300 that is a variation of the angular sensor system 1200 of fig. 12. The main difference between the sensor system 1300 of fig. 13 and the sensor system 1200 of fig. 12 is that the sensor device 1302 comprises a sensor structure configured for: the single in-plane magnetic field component Bx and the single in-plane magnetic field component By are measured and the angular position of the magnet is calculated based on these components Bx, By, preferably as a function of the ratio of these values, for example using an angle-measuring function as described in case (c) of fig. 3 or using a look-up table for converting the ratio into an angular position. Since system 1300 does not use gradient signals, it is not robust to external disturbing fields, but all other advantages mentioned above with respect to fig. 12, in particular with reduced cross-talk, apply here as well.

All variants mentioned for fig. 12 but with only one sensor instead of two sensors are also contemplated, including all variants in which the substrate of the sensor device is perpendicular to the rotation axis and all variants in which the substrate of the sensor device is parallel to the rotation axis.

Fig. 14 shows the angular position sensor system 1400 in a front view (part (a) of fig. 14) and a top view (part (b) of fig. 14). The magnet 1401 may be a diametrically magnetized two-pole disc magnet or ring magnet (e.g., as depicted in part (d) of fig. 9). The sensor device 1402 is located at a position defined by the plane β and the radial distance Rs. This plane β is orthogonal to the axis of rotation of the magnet and is located at a distance "h" from the bottom surface, approximately midway between the top and bottom surfaces of the cylindrical magnet. This position is referred to herein as "near the equator".

The sensor device 1402 may have a sensor structure as described in fig. 3 (see part (c) of fig. 14), and is oriented such that the X-axis of the sensor structure is tangent to an imaginary circle in the plane β and having a radius Rs, and such that the Y-axis of the sensor structure perpendicularly intersects the axis of rotation of the magnet, and such that the Z-axis of the sensor device is parallel to the axis of rotation of the magnet.

The sensor device 1402 is preferably configured to determine the angular position of the magnet based on the gradients dBx/dx and dBy/dx, e.g., according to some or all of the equations of case (d) of fig. 3.

In a preferred embodiment of the invention, the height position h (in the axial direction of the magnet) is specifically chosen such that, preferably over a full 360 ° rotation of the magnet around its axis, the amplitude of the Bz component of the magnetic field seen by the sensor (i.e. the axial vector component of the magnetic field seen by the magnet) is less than 20% of the amplitude of the Bx component of the magnetic field seen by the sensor device (i.e. the tangential or circumferential component of the magnetic field seen by the magnet), preferably less than 15% of the amplitude of the Bx component, more preferably less than 10% of the amplitude of the Bx component or even less than 5% of the amplitude of the Bx component, and/or less than 20% of the amplitude of the By component of the magnetic field seen By the sensor device (i.e. the radial component of the magnetic field seen By the magnet), preferably less than 15% of the amplitude of the By component, more preferably less than 10% of the amplitude of the By component or even less than 5% of the amplitude of the By component. In this embodiment, the radial distance Rs is not critical and is preferably less than Ro x 200% or less than Ro x 150%, for example a value in the range from Ro x 102% to Ro x 120%. In a preferred embodiment, the value of Rs may be a value in the range from Ro +1mm to Ro +10mm, or a value in the range from Ro +2mm to Ro +7 mm.

To fully appreciate the benefits of this embodiment of the present invention, reference is made to the simulations discussed next.

Part (a) of fig. 23 shows in perspective view a diametrically magnetized ring magnet made of NdFeB having an outer diameter of 10mm, an inner diameter of 5mm and a height of 5 mm.

Part (b) of fig. 23 shows a simulation of magnetization on the surface of the magnet as a dither image.

Part (a) of fig. 24 shows how the magnitudes of the Bx, By and Bz components vary as a function of height position for an Rs value of 3 mm. The "sweet spot" (see above for a more precise statement) where the amplitude of the By component is "small" is indicated By a rectangle in the form of a dashed line.

Part (b) of fig. 24 shows the "best point" in an enlarged view. In the example shown, if the sensor device is located in a plane at a height of H/2 ± 0.9mm, the ratio of | Bz | to | Bx | is less than 20%; if the sensor device is located in a plane at a height of H/2 + -0.5 mm, the ratio of | Bz | to | Bx | is less than 10%.

Referring back to fig. 14, it can now be appreciated that when sensor device 1402 is positioned in this sweet spot (or sweet zone), the amplitude of the Bz component is much smaller than the amplitude of the Bx component and/or the By component, and thus any potential crosstalk from Bz to Bx and/or Bz to By is reduced By at least a factor of 5 or 10 or even more.

Part (c) of fig. 14 shows a sensor device having the sensor structure as described in fig. 3. Such sensor systems have many or all of the same advantages as described for fig. 9, including having a measurement range of 360 °, having reduced sensitivity to cross-talk, being highly robust to external interference fields, etc.

The sensor system 1400 can also be used with other sensor configurations, such as the sensor configuration shown in part (d) of fig. 14, which has two sensors spaced apart along the X-axis, each sensor including two vertical hall elements, one vertical hall element configured to measure the Bx component and the other vertical hall element configured to measure the By component in the direction Y perpendicular to X.

In another variant (not shown), the sensor structure of fig. 4 (with four horizontal hall elements and four discrete IMC elements) is used.

In still other embodiments, a magnetoresistive element is used as the magneto-sensitive element.

Fig. 15 shows another or further variant of the angular position system described in fig. 14, in which the sensor device 1502 is oriented such that its X-axis is tangent to an imaginary circle of radius Rs, but the Z-axis intersects the axis of rotation of the magnet, and the Y-axis is parallel to said axis of rotation (which can be obtained by rotating the sensor device 1402 of fig. 14 by 90 ° around the X-axis). Part (a) of fig. 15 shows the system in a front view, part (b) of fig. 15 shows the system in a top view, and part (c) of fig. 15 shows the system seen in the viewing direction a-a in a side view.

In this embodiment, the signals Bx and Bz (as seen By the sensor device) vary like sine and cosine functions of the angular position of the magnet (possibly with different amplitudes), while the By component (as seen By the sensor device) corresponding to the axial magnetic field component (as seen By the magnet) has a very small amplitude, or more precisely, | By |/| Bx | < 20% or < 10% or < 5%, or ideally close to zero.

The sensor device 1502 may for example comprise the sensor structure of fig. 3 (as shown in part (d) of fig. 15) or the sensor structure of fig. 4, and the angular position of the magnet may for example be determined using the formula of case (b) of fig. 3, with the same advantages as described above, in particular with reduced cross-talk and long-term drift, robustness to mechanical stress and to external disturbing fields. However, other sensor structures, such as the sensor structure of part (e) of fig. 8 or 15, or a sensor structure including a magnetoresistive element, may also be used.

In a variation of fig. 15 (not shown), the sensor device 1502 contains only a single sensor, and the formula of case (a) of fig. 3 can be used to determine the angular position. A disadvantage of such embodiments is that the measurement is not robust to external disturbing fields, but the advantages of (inter alia) reduced crosstalk still exist.

Fig. 16 shows a position sensor system as a variation of the system of fig. 14, wherein the sensor device 1602 contains only a single sensor instead of two sensors. Only two examples of sensor structures are shown in section (c) of fig. 16 and section (d) of fig. 16, but the invention is not limited to these sensor structures, and all variants mentioned for fig. 14 but having only one sensor instead of two sensors are also contemplated, in particular a sensor such as the one shown in fig. 4, or a sensor using magneto-resistive sensitive elements arranged for measuring two in-plane magnetic field components Bx, By, among others.

Fig. 17-20 have been discussed above and show simulation results demonstrating the presence of an annular region in a plane at a distance of about 2mm from the bottom or top surface of an exemplary ring or disc magnet, wherein one of the three magnetic field components Bx, By, Bz of a sensor device positioned in the region has an amplitude close to zero over the entire 360 ° range. This observation is utilized in the angle sensor system described in fig. 9, 10 and 11.

For completeness, it should be mentioned that there will also be annular regions for other distances in the range of 1 to 5mm from the bottom or top surface, but the radial positions thereof may be slightly different. The location can be readily found by performing simulations by those skilled in the art having the benefit of this disclosure.

Fig. 21 and 22 have been discussed above and show simulation results demonstrating the presence of an annular region in a plane at a distance of about 2mm from the bottom or top surface of an exemplary ring or disc magnet, wherein one of the three magnetic field components Bx, By, Bz of the sensor device positioned in this region has an amplitude close to zero over the entire 360 ° range. This observation is utilized in the angle sensor system described in fig. 12 and 13. There are also annular regions for other distances from the bottom or top surface.

Fig. 23 and 24 have been discussed above and show simulation results demonstrating that there is a small area (in the height direction of an exemplary ring magnet or disc magnet) where one of the three magnetic field components Bx, By, Bz of the sensor device positioned in this area has a magnitude close to zero over the entire 360 ° range. This observation is utilized in the angle sensor system described in fig. 14 to 16.

The embodiments described above are primarily illustrated using diametrically magnetized two-pole ring or disc magnets, but the invention is not so limited and works equally well with other magnets, such as axially magnetized two-pole ring or disc magnets, or axially magnetized multi-pole ring or disc magnets having at least four poles, as will be described in more detail below.

Part (a) of fig. 25 to part (g) of fig. 25 show variants of the angular position sensor system of fig. 12 or 13 using axially magnetized quadrupole (also referred to as "quadrupole") magnets. The inventors have surprisingly found an annular region in which one of the three orthogonal magnetic field components selected from the group consisting of the circumferential, axial and radial components is much smaller (e.g. less than 20%, or less than 15%, or less than 10% or less than 5%) than one or both of the other two components and the other two components behave like sine and cosine signals which may have different amplitudes. With a symmetric quadrupole magnet, the measurement range is only 180 °, but this may be sufficient for some applications.

Part (a) of fig. 25 shows the sensor system 2500 in a front view.

Part (b) of fig. 25 shows the sensor system in a top view.

Part (c) of fig. 25 and part (d) of fig. 25 show sensor structures configured to determine Bx and Bz at only one position, and show formulas similar to those of case (a) of fig. 3. With these sensor structures, the measurement is not robust to disturbing fields, but many of the other advantages mentioned above are still applicable, e.g. high insensitivity to cross-talk, long term drift due to aging, etc.

Part (e) of fig. 25 and part (f) of fig. 25 show sensor structures configured to determine Bx1 and Bz1 at a first position and Bx2 and Bz2 at a second position spaced apart from the first position in the X direction. Similar to that described above, these two sets of values may be used for redundancy purposes and/or may be used to determine angular position based on the magnetic field gradients dBx/dx and dBz/dx. Formulas similar to those of case (b) of fig. 3 are given. With these sensor structures, many of the above mentioned advantages are also applicable here, e.g. high insensitivity to cross-talk, long term drift due to aging, etc., including high sensitivity to external disturbing fields.

Part (g) of fig. 25 shows an example of such a magnet in a perspective view.

In a variation of the system of fig. 25, the magnets are not complete rings spanning an angular range of 360 °, but are only partial rings spanning an angular range of less than 360 °. In examples where the ring magnet is "semi-circular," the multi-pole ring magnet defines an angular opening angle of only 180 °, but of course other angular ranges may be used, such as, for example, about 120 °, or about 150 °, or about 210 °, or about 240 °. The same operating principle and the same advantages are also applicable.

In another variation (not explicitly shown) of the system of fig. 25, sensor device 2502 is rotated 90 ° with respect to the X-axis, resulting in an orientation similar to that of fig. 10. In this case, the sensor device measures Bx (circumferential) and By (axial), while Bz (radial) is very small. If Bz is replaced By, equations similar to those shown in section (c) of FIG. 25-section (f) of FIG. 25 are applicable.

Fig. 26 to 29 show in grayscale simulation results of an exemplary axially magnetized quadrupole magnet having an outer diameter OD of 12mm, an inner diameter ID of 8mm and a height H of 4mm in a plane at a distance of 3mm below the bottom surface of the magnet, as can be used in the angular position sensor system of fig. 25.

Part (a) of fig. 26 shows the magnitude of the radial component Br (relative to the magnet) corresponding to the By component seen By the sensor device.

Part (b) of fig. 26 shows the magnitude of the tangential component Bt (with respect to the magnet) corresponding to the Bx component seen by the sensor device.

Part (c) of fig. 26 shows the magnitude of the axial component Bz (relative to the magnet) corresponding to the Bz component seen by the sensor device.

The inner and outer radii of the ring magnet are also indicated. As can be appreciated from part (a) of fig. 26, in this case, there is also an annular region where | By |/| Bx | and/or | By |/| Bz | < 20%, or < 15%, or < 10%. It should be noted that the pictures of fig. 26 to 29 are derived from colour analogue pictures and may introduce some artefacts due to the conversion of colour pictures to greyscale pictures, but the main purpose of these pictures, i.e. to show the presence and location of the annular regions, is very well visible.

Parts (a) to (c) of fig. 27 show the same plots as parts (a) to (c) of fig. 26 at 10 dither levels. Two arc segments (corresponding to radii R3 and R4 of portion (b) of fig. 25) are added to give an impression of the size and location of the annular region.

Fig. 28 shows the same data as part (a) of fig. 26, but presented in a clear image, showing an annular region in which the magnitude of the radial component is less than 30% of the maximum magnetic field component measurable at different locations in the same plane.

Fig. 29 shows the same data as fig. 26(a) and fig. 28, but presented in a different grayscale, showing an annular region in which the magnitude of the radial component is less than about 11% of the maximum magnetic field component measurable at different locations in the same plane.

It was found that (approximately):

for | By |/| Bx | < 30%, R3 ═ 9.8mm and R4 ═ 11.6mm (thus W30 ═ 1.8mm)

For | By |/| Bx | < 22%, R3 ═ 9.9mm and R4 ═ 11.3mm (thus W22 ═ 1.4mm)

For | By |/| Bx | < 11%, R3 ═ 10.0mm and R4 ═ 11.0mm (thus W11 ═ 1.0mm)

This (as described above) is sufficient to mount sensor devices having, for example, horizontal hall elements and IMC disks, since the diameter of a typical IMC disk is typically on the order of about 200 to 400 microns.

Similar results can be obtained for quadrupole magnets having other dimensions.

Although the magnets used in the simulations are typically made of FeNdB, the invention is not so limited and other materials, such as ferrite or SmCo, may also be used.