Patent Description:
Various magnetic position sensor systems have been previously described, some of which included provisions to reduce the influence of magnetic noise on the output signal. <CIT> for instance disclosed a rotation angle detector comprising a magnet arranged to rotate around a rotation axis and a magnetic detection circuit comprising a first and second pair of magnetic detection elements arranged away from the rotation axis and having a predetermined interval between them. Therein, each of the first and second pair of magnetic detection elements is sensitive to both a first magnetic field in a circumferential direction and a second magnetic field in a normal direction. An output signal representative of the rotation angle of the magnet is then based on the outputs of said first and said second pair of magnetic detection elements.

In <CIT>, the target to be detected is thus as such a magnet. By contrast, <CIT> disclosed a displacement detection device comprising a rotating measurement target with a concave or convex portion on its circumferential surface, a sensor having detection elements arranged in pairs with a predetermined interval and a magnet behind (with respect to the target) the sensor. The detection elements detect the displacement of the concave or convex portion as changes in the magnetic flux densities in the rotational axis direction and radial direction of the measurement target.

<CIT> shows a rotary position sensor system. An axially-magnetized ring magnet can be used.

However, there is still a need in the art for magnetic position sensor systems which can detect targets without particular surface features (e.g. a concave or convex portion); and this preferably within a fairly broad range in space.

It is an object of the present invention to provide good magnetic position sensor systems for ferromagnetic targets. It is a further object of the present invention to provide good methods associated therewith. This objective is accomplished by systems and methods according to the present invention.

It is an advantage of embodiments of the present invention that they have a relatively large target sensing range.

It is an advantage of embodiments of the present invention that the sensing topology used-e.g. using gradient sensing-reduces the influence of magnetic noise. It is a further advantage of embodiments of the present invention that the influence of magnetic noise is reduced or even eliminated (e.g. making the magnetic position sensor system stray field immune).

It is an advantage of embodiments of the present invention that the sensors can be implemented using various sensor elements and arrangements thereof.

It is an advantage of embodiments of the present invention that the output of the sensors can be conveniently transformed into a position signal.

It is an advantage of embodiments of the present invention that they can be implemented in a relatively straightforward and economical fashion,.

The invention is merely defined by the claims. In independent device claim <NUM>, the present invention relates to a magnetic position sensor system for a magnetic target, comprising: (i) a first sensor for measuring in a first sensing region a first magnetic field component Bx,<NUM> along a direction x and a second magnetic field component Bz,<NUM> along a direction z, orthogonal to x; (ii) a second sensor for measuring in a second sensing region-aligned to the first sensing region along the x-direction—a first magnetic field component Bx,<NUM> along the x-direction and a second magnetic field component Bz,<NUM> along the z-direction; and (iii) an axially-magnetized ring magnet arranged under the first and second sensing region such that an axial direction of the ring magnet is substantially parallel to the z-direction and-in operation-a position of the ring magnet with respect to the first and second sensing regions is fixed.

In independent method claim <NUM>, the present invention relates to a method for determining a position of a magnetic target using a magnetic position sensor system as defined in any of the previous claims, comprising: (a) measuring in a first sensing region a first magnetic field component Bx,<NUM> along a direction x and a second magnetic field component Bz,<NUM> along a direction z, orthogonal to x; (b) measuring in a second sensing region-aligned to the first sensing region along the x-direction—a first magnetic field component Bx,<NUM> along the x-direction and a second magnetic field component Bz,<NUM> along the z-direction; (c) calculating a difference dBx between Bx,<NUM> and Bx,<NUM> and a difference dBz between Bz,<NUM> and Bz,<NUM>; and (d) determining the position of the magnetic target from dBx and dBz.

Embodiments of the invention are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims, as long as they fall within the scope of the claims.

This description is given for the sake of example only, without limiting the scope of the invention which is only defined by the claims.

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.

Moreover, the terms top, bottom, above, below 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 with their antonyms under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other orientations than described or illustrated herein.

Similarly, it is to be noticed that the term "coupled", also used in the claims, should not be interpreted as being restricted to direct connections only. The terms "coupled" and "connected", along with their derivatives, may be used. Thus, the scope of the expression "a device A coupled to a device B" should not be limited to devices or systems wherein an output of device A is directly connected to an input of device B. It means that there exists a path between an output of A and an input of B which may be a path including other devices or means. "Coupled" may mean that two or more elements are either in direct physical or electrical contact, or that two or more elements are not in direct contact with each other but yet still co-operate or interact with each other.

The following terms are provided solely to aid in the understanding of the invention.

As used herein, and unless otherwise specified, a magnetic material is material which has a strong magnetization in an applied magnetic field; e.g. having a magnetic susceptibility χ of (in SI units) <NUM> or more, preferably <NUM> or more, yet more preferably <NUM> or more, such as <NUM>, <NUM> or <NUM> or more. The magnetic material may be a hard magnetic material (e.g. having an intrinsic coercivity Hci of <NUM> A/m or more) or a soft magnetic (e.g. having an intrinsic coercivity Hci of less than <NUM> A/m). In general, the magnetic material may have a bulk magnetization in the absence of a magnetic field (i.e. it may be a permanent magnet), but often will not. Thus, the magnetic material will often-in the absence of a magnetic field-either not be magnetized or have magnetic domains oriented such (e.g. randomly) that they cancel each outer out, so that is does not display any appreciable bulk magnetization. In preferred embodiments, the magnetic material may be a ferromagnetic material (e.g. a soft ferromagnetic material).

As used herein, and unless otherwise specified, a ring magnet is magnet having a hole (i.e. a through-hole) therein along its axial direction. Most typically, a cross-section through the ring magnet perpendicular to its axial direction may have a circular inner boundary and a circular outer boundary; in other words, the cross-section may be an annulus. Notwithstanding, the inner and outer boundary of the cross-section may more generally have any shape, such as a polygonal or even an irregular shape. The inner and outer boundary need also not have the same shape, but may be selected independently; for example the outer boundary could be circular and the inner boundary could be polygonal. Likewise, the height (H) of ring magnet need in general not be constant across its diameter (e.g. the ring magnet may have the shape of a torus), but will nevertheless in embodiment often be constant. Note that in the case of a non-circular inner and/or outer boundary, it may be more natural to speak more generally about the (inner/mean/outer) width along the x-direction instead of the (inner/mean/outer) diameter. In such cases, these terms may thus be exchanged as useful.

As used herein, and unless otherwise specified, a first direction may be considered substantially parallel to a second direction if it makes an angle with the second direction of between -<NUM>° and <NUM>°, preferably between -<NUM>° and <NUM>°, more preferably between -<NUM>° and <NUM>°, yet more preferably between -<NUM>° and <NUM>°, most preferably (perfectly) parallel (i.e. <NUM>°).

In a first aspect, the present invention relates to a magnetic position sensor system for a magnetic target, comprising: (i) a first sensor for measuring in a first sensing region a first magnetic field component Bx,<NUM> along a direction x and a second magnetic field component Bz,<NUM> along a direction z, orthogonal to x; (ii) a second sensor for measuring in a second sensing region-aligned to the first sensing region along the x-direction—a first magnetic field component Bx,<NUM> along the x-direction and a second magnetic field component Bz,<NUM> along the z-direction; and (iii) an axially-magnetized ring magnet arranged under the first and second sensing region such that an axial direction of the ring magnet is substantially parallel to the z-direction and-in operation-a position of the ring magnet with respect to the first and second sensing regions is fixed.

An example of such a magnetic position sensor system <NUM> is schematically depicted in <FIG>, showing a magnetic target <NUM>, first sensor <NUM> and second sensor <NUM> (in a sensor chip <NUM> with chip substrate <NUM> and packaging <NUM>) and ring magnet <NUM> with axial direction <NUM>. Also depicted are sensing region <NUM> and <NUM> of the first and second sensors <NUM> and <NUM>, respectively.

The sensing regions of the first and second sensors are the regions in which they sense their respective magnetic field components Bx,<NUM>|Bz,<NUM> and Bx,<NUM>|Bz,<NUM>. If the magnetic field components in the x- and z-direction within one sensor are measured at (substantially) the same point or spot in space, the sensing region is thus simply that point/spot. However, each of the sensors may also comprise distinct sensing elements for determining the magnetic field components in the x- and z-direction. This is for example schematically depicted in <FIG> and <FIG>, in which first sensor <NUM> has first sensing element <NUM> for measuring Bx,<NUM> and second sensing element <NUM> for measuring Bz,<NUM>. Likewise, second sensor <NUM> has first sensing element <NUM> for measuring Bx,<NUM> and second sensing element <NUM> for measuring the Bz,<NUM>. The first sensing elements <NUM> and <NUM> may for instance have a maximum axis of sensitivity perpendicular to the z-direction; they could for example be vertical Hall elements or magnetoresistance elements. The second sensing elements <NUM> and <NUM> may for instance have a maximum axis of sensitivity parallel to the z-direction; they could for example be horizontal Hall elements. When the sensors comprise distinct sensing elements, these sensing elements may not measure at the same point/spot in space but at two points/spots separated by a short distance (typically in the same order of magnitude as the size of the sensing elements, i.e. tens to hundreds of micron; for example between <NUM> and <NUM>, e.g. between <NUM> and <NUM>). In such cases, the sensing region is a region (e.g. a 1D or 2D area) defined by and comprising these sensing points or spots.

<FIG> schematically depicts still a further illustrative setup with distinct sensing elements but which do not measure Bx,<NUM>, Bz,<NUM>, Bx,<NUM> and Bz,<NUM> directly. Instead, each of sensor <NUM> and <NUM> is made up of two distinct sensing elements but having both a maximum axis of sensitivity parallel to the z-direction (e.g. horizontal hall elements), together with a magnetic concentrator <NUM> (e.g. a soft magnetic disk). The magnetic concentrator <NUM> bends the magnetic field lines and allows measurement of both in-plane and out-of-plane magnetic field components by the sensing elements. The sensing elements then output measured field components Bl,<NUM>, Br,<NUM>, Bl,<NUM> and Br,<NUM>, which can be linearly combined into the x-and z-field components: Bx,<NUM> = (Bl,<NUM> - Br,<NUM>)/<NUM>, Bz,<NUM> = (Bl,<NUM> + Br,<NUM>)/<NUM>, Bx,<NUM> = (Bl,<NUM> - Br,<NUM>)/<NUM> and Bz,<NUM> = (Bl,<NUM> + Br,<NUM>)/<NUM>.

The first and second sensors-and thus the first and second sensing region-are typically separated from each other by a predetermined distance (typically in the order of mm, such as about <NUM> to <NUM>). In general, the distance between the points/spots at which Bx,<NUM> and Bx,<NUM> are measured can be referred to as dx<NUM>, while the distance between the points/spots at which Bz,<NUM> and Bz,<NUM> are measured can be referred to as dx<NUM>. In specific cases, it may be that dx<NUM> = dx<NUM> = dx; this is for instance so when the first and second sensing regions are sensing points/spots (cf. supra), or simply when the sensing elements are specifically arranged to the effect (e.g. they are aligned along the y-direction). The latter is schematically depicted in <FIG>, whereas a situation in which dx<NUM> ≠ dx<NUM> is schematically depicted in <FIG>.

In embodiments, the magnetic position sensor system may further comprise a substrate arranged such that the first and second sensor are above the substrate and the ring magnet is below the substrate. For example-as schematically depicted in <FIG>-the first and second sensor <NUM> and <NUM> (e.g. the sensor chip <NUM> in which they are integrated; cf. infra) may be mounted above the substrate <NUM> and the ring magnet <NUM> may be mounted below the substrate <NUM>. In embodiments, the substrate may be a printed circuit board (PCB).

In embodiments, the axial direction of the ring magnet may (substantially) bisect a line segment connecting the first and second sensing region (e.g. connecting the centre of both region). In other words, the axial direction of the ring magnet may be the perpendicular bisector of said line segment. In embodiments, the axial direction may be considered to substantially bisect the line segment if its point of intersection is within a distance from the centre of the line segment of <NUM>% or less of the total length of the line segment, preferably <NUM>% or less, more preferably <NUM>% or less, yet more preferably <NUM>% or less.

Notwithstanding, an offset in the x-direction between the ring magnet and the first and second sensing regions, may be considered if an offset in the target sensing range is desired. Indeed, such an offset of the ring magnet could offset the target sensing range in the same direction, but typically in a nonlinear (and difficult to predict) manner. As such, some trial-and-error could be required to find a suitable ring magnet offset to achieve the desired target sensing range.

In embodiments, a top of the ring magnet may be at a height (hm) below the first and second sensing region of between <NUM>% and <NUM>% of a mean diameter (Dm; i.e. the average of the inner diameter Di and outer diameter Do) of the ring magnet, preferably between <NUM>% and <NUM>%, more preferably between <NUM>% and <NUM>%, yet more preferably between <NUM>% and <NUM>%.

In embodiments, an inner diameter (Di) of the ring magnet may be between <NUM>% and <NUM>% of an outer diameter (Do) of the ring magnet, preferably between <NUM>% and <NUM>%, more preferably between <NUM>% and <NUM>%, yet more preferably between <NUM>% and <NUM>%, most preferably between <NUM>% and <NUM>%.

In embodiments, the magnetic position sensor system may further comprise a signal processing circuit. In embodiments, the signal processing circuit may comprise a first difference module for outputting a difference dBx between Bx,<NUM> and Bx,<NUM>, and a second difference module for outputting a difference dBz between Bz,<NUM> and Bz,<NUM>. In embodiments, the signal processing circuit may further comprise a module for generating an output signal from dBx and dBz. Such a signal processing circuit <NUM> is schematically depicted in <FIG>, showing difference modules <NUM> and <NUM> for calculating an outputting dBx and dBz from Bx,<NUM>, Bx,<NUM>, Bz,<NUM> and Bz,<NUM> output by sensors elements <NUM>, <NUM>, <NUM> and <NUM>. Further illustrated is an output generating module <NUM> for e.g. calculating an atan2 using dBx and dBz or comprising a lookup table (LUT), and then sending the results off-chip through output/interface <NUM>.

In embodiments, the first and second sensors-and, if present, the signal processing circuit-may be integrated in a single integrated circuit (IC); for example on a single IC substrate.

Although the magnetic position sensor system of the present invention is typically used with the ring magnet position fixed with regard to the first and second sensing regions, it will be clear that one can always make the ring magnet movable (e.g. possibly to allow making some adjustments in between measurements) but simply not use it while in operation (e.g. while performing the method in accordance with the second aspect). In other embodiments, the position of the ring magnet may be permanently fixed with respect to the first and second sensing regions.

In embodiments, any feature of any embodiment of the first aspect may independently be as correspondingly described for any embodiment of any of the other aspects.

In a second aspect, the present invention relates to a method for determining a position of a magnetic target using a magnetic position sensor system as defined in any of the previous claims, comprising: (a) measuring in a first sensing region a first magnetic field component Bx,<NUM> along a direction x and a second magnetic field component Bz,<NUM> along a direction z, orthogonal to x; (b) measuring in a second sensing region-aligned to the first sensing region along the x-direction—a first magnetic field component Bx,<NUM> along the x-direction and a second magnetic field component Bz,<NUM> along the z-direction; (c) calculating a difference dBx between Bx,<NUM> and Bx,<NUM> and a difference dBz between Bz,<NUM> and Bz,<NUM>; and (d) determining the position of the magnetic target from dBx and dBz.

In embodiments, a width (W) of the magnetic target along the x-direction may be between <NUM>% and <NUM>% of a mean diameter (Dm) of the ring magnet, preferably between <NUM>% and <NUM>%, more preferably between <NUM>% and <NUM>%. The target to be detected is typically not particularly limited by its shape. Nevertheless, the method of the present invention is particularly suited for detecting magnetic targets having a size not exceeding that of the ring magnet by too much. Indeed, once the target becomes exceedingly large, a displacement in the x-direction could well be such that it does not change the magnetic field components measurable by the magnetic position sensor system, thereby hindering the detection of the target and/or the movement. In such a case, an approach such as in <CIT> may prove more fruitful.

Moreover, although not necessarily strictly limited thereto, the method of the present invention is particularly suited to detect a linear motion (parallel to the x-direction) of the target. In the regard, the magnetic position sensor system could also be referred to as a magnetic linear position sensor system.

In embodiments, the magnetic target may be at a fixed height (ht) above the first and second sensing region. In embodiments, the fixed height (ht) may be between <NUM>% and <NUM>% of a mean diameter (Dm) of the ring magnet, preferably between <NUM>% and <NUM>%, more preferably between <NUM>% and <NUM>%.

In embodiments, the position determined in step d may be related to <MAT> In embodiments, the position may be linearly related to (e.g. proportional to) one of the above expressions. Herein dBx is Bx,<NUM> - Bx,<NUM>, dBz is equal to Bz,<NUM> - Bz,<NUM>, dx<NUM> is the distance between the two sensing spots at which the magnetic field component Bx,<NUM> and the magnetic field component Bx,<NUM> are measured, and dx<NUM> is the distance between the two sensing spots at which the magnetic field component Bz,<NUM> and the magnetic field component Bz,<NUM> are measured. If dx<NUM> = dx<NUM>, the above expressions thus simplify to dBx/dBz and k. Moreover, k is an optional factor to allow amplitude correction between the field gradients. Note though that since k is a simple multiplication factor in the above expressions, a position related to k. <MAT> is also related to <MAT>.

In embodiments, the position determined in step d may more specifically be related to <MAT>, wherein atan2(y, x) is a function which modifies the arctangent atan(y/x) based on the signs of x and y (i.e. based on a form of quadrant detection) so that the range of the function becomes [<NUM>°, <NUM>°]. Again, if dx<NUM> = dx<NUM>, this expression simplifies to atan2(dBz/k. Note that the choice of which term to use as x and which as y (i.e. the choice of numerator and denominator in the atan function) only changes the location of <NUM>°, while the sign of these terms only changes the slope (ascending or descending) of the atan2 output, so that both can be arbitrarily selected. As such, the position determined in step d may likewise be related to <MAT> <MAT> or <MAT>.

In embodiments, determining the position in step d may further comprise linearizing an intermediate result (e.g. dBx/dx<NUM> and dBz/dx<NUM> as such, the ratio of both or the an atan2 of both) to obtain the position. In some embodiments, linearizing the intermediate result may be performed using a linearization function. Such a linearization function could for example be derived from a measured response of the intermediate results in function of the position (see e.g. Example <NUM> and Example <NUM>). In other embodiments, linearizing the intermediate result may be performed using on a lookup table, optionally using interpolation between the lookup table data points. In embodiments, the lookup table could be based on any of dBx/dx<NUM> and dBz/dx<NUM> as such, the ratio of both or the atan2 of both. Using the ratio (or the atan2, which uses said ratio indirectly) is advantageous in that it reduces or cancels out the influence of temperature; indeed, temperature effects which impact dBx/dx<NUM> and dBz/dx<NUM> are typically proportional, so that the ratio of dBx/dx<NUM> and dBz/dx<NUM> tends to remain substantially unaffected.

In embodiments, any feature of any embodiment of the second aspect may independently be as correspondingly described for any embodiment of any of the other aspects.

In a third aspect, the present invention relates to a use of an axially magnetized ring magnet in a magnetic position sensor system for a magnetic target, for extending a range within which the magnetic position sensor system can sense the magnetic target.

The effect of the ring magnet on the range within which the magnetic position sensor system can sense (e.g. detect and/or determine the position of) the magnetic target is for instance illustrated in Example <NUM>, Example <NUM> and the Comparative Example below, wherein it is clear that the use of a ring magnet (i.e. with a hole along the axial direction) yields a much more performant magnetic position sensor system than when using a similar disk magnet (i.e. without hole). Without being bound by theory, it is believed that the hole in the ring magnet spreads the spatial gradients over a longer distance and thereby results in a considerably longer sensing range.

In embodiments, the range may be extended to between <NUM>% and <NUM>% of a mean diameter (Dm) of the ring magnet, preferably between <NUM>% and <NUM>%, more preferably between <NUM>% and <NUM>%, yet more preferably between <NUM>% and <NUM>%.

The extension of the sensing range is typically governed by an interplay of the inner diameter (Di) and outer diameter (Do) of the ring magnet. On the one hand, the effect of the hole spreading the spatial gradients over longer distances leads to the range being related to the inner diameter (Di). On the other hand, the outer diameter (Do) indirectly determines the amount of magnetic material and thus also the magnet's strength, in turn also influencing the sensing range.

In embodiments, any feature of any embodiment of the third aspect may independently be as correspondingly described for any embodiment of any of the other aspects.

It is clear that other embodiments of the invention can be configured according to the knowledge of the person skilled in the art without departing from the true technical teaching of the invention, the invention being limited only by the terms of the appended claims.

Referring to the schematic depiction in <FIG>, a magnetic position sensor system <NUM> in accordance with the present invention was made by mounting a Melexis MLX90371 dual disk sensor chip <NUM> (MLX90371GDC-BCC-<NUM>-RE) onto a printed circuit board <NUM> (PCB) and gluing an axially magnetized ring magnet <NUM> below (behind) the sensor chip <NUM> on the opposite side of the PCB <NUM>. The axially magnetized ring magnet <NUM> was a <NUM> T NdFeB ring magnet with an annular cross-section, outer diameter Do of <NUM>, inner diameter Di of <NUM> (so that the average diameter Di was <NUM>) and height H of <NUM>. It was positioned such that its axial direction was substantially normal to the PCB <NUM> (i.e. substantially parallel to the z-direction) and substantially aligned with the sensing regions <NUM> and <NUM> of the sensor chip <NUM>'s first sensor <NUM> and second sensor <NUM> (i.e. the axial direction of the ring <NUM> substantially bisected a line segment connecting the first and second sensing regions <NUM> and <NUM>). The height difference hm between the top of the ring magnet <NUM> and the first and second sensing regions <NUM> and <NUM> was about <NUM>.

To test the magnetic position sensor system <NUM>, the magnetic position sensor system <NUM> was mounted on an adjustable stage and coupled to a Melexis daughter board (PTC04-DB-HALL06) to interface with the sensor chip <NUM>. A ferromagnetic screw bit was then positioned above (in front of) the magnetic position sensor system <NUM> as magnetic target <NUM>.

Next, the magnetic target <NUM> was held in place at a fixed distance ht from the first and second sensing regions <NUM> and <NUM>, while the magnetic position sensor system <NUM> was moved in the x-direction; thereby simulating a linear movement of the magnetic target <NUM> with respect to the magnetic position sensor system <NUM>. This caused changes in the magnetic field components Bx,<NUM> and Bz,<NUM> measured by the first sensor <NUM> and in the magnetic field components Bx,<NUM> and Bz,<NUM> measured by the second sensor <NUM>. Using-with dx<NUM>= dx<NUM>-the equation <MAT> the outputs of the first and second sensors <NUM> and <NUM> could be turned into an angle which depends on the stroke (i.e. the displacement in the x-direction). A typical response for the screw bit target <NUM> is presented in <FIG>, showing the angle-calculated from the measured magnetic field components (and setting k to <NUM>)-in function of the applied stroke for different fixed distances ht of <NUM>, <NUM> and <NUM>.

Based on this response, it was possible to formulate one or more look-up-tables and/or linearization functions to deduce-for a target <NUM> at a predefined distance ht-the (unknown) position from the calculated angle. Accordingly, it was possible for the present magnetic position sensor system <NUM> to detect a linear displacement of the target over a range of about <NUM> (between -<NUM> to <NUM> with respect to the centre between the first and second sensing regions <NUM> and <NUM>).

Example <NUM> was repeated but using as target <NUM> a ferromagnetic nut instead of the ferromagnetic screw bit. A typical response as obtained for this nut target <NUM>-for a single fixed distance ht-is presented in <FIG>. Accordingly, it was again possible for the present magnetic position sensor system <NUM> to detect a linear displacement of the nut target <NUM> over a range of about <NUM>.

Example <NUM> was repeated but using an axially magnetized disk magnet (with similar characteristics as the ring magnet) instead of the ring magnet. However, this change resulted in a setup which was notably less sensitive, to such an extent that the detectable range was reduced to about <NUM>.

Claim 1:
A magnetic linear position sensor system (<NUM>) for a magnetic target (<NUM>), comprising:
i. a first sensor (<NUM>) for measuring in a first sensing region (<NUM>)
- a first magnetic field component Bx,<NUM> along a direction x and
- a second magnetic field component Bz,<NUM> along a direction z, orthogonal to x;
ii. a second sensor (<NUM>) for measuring in a second sensing region (<NUM>)-aligned to the first sensing region (<NUM>) along the x-direction-
- a first magnetic field component Bx,<NUM> along the x-direction and
- a second magnetic field component Bz,<NUM> along the z-direction; and
iii. an axially-magnetized ring magnet (<NUM>) arranged under the first (<NUM>) and second (<NUM>) sensing region such that an axial direction (<NUM>) of the ring magnet (<NUM>) is parallel to the z-direction and-in operation-a position of the ring magnet (<NUM>) with respect to the first (<NUM>) and second (<NUM>) sensing regions is fixed.