Device and method for determining the orientation of a magnet, and a joystick

Abstract

To provide a method of determining an orientation (α, β) of a magnet which is pivotable about a reference position (Pref) having a predefined position relative to a semiconductor substrate.SOLUTION: The method comprises a) determining at least two of the following magnetic field gradients: i) a first magnetic field gradient (dBx / dx); ii) a second magnetic field gradient (dBy / dy); iii) a third magnetic field gradient (dBz / dx); and iv) a fourth magnetic field gradient (dBz / dy). The method also comprises b) determining a first angle (α) based on at least one of the magnetic field gradients, and c) determining a second angle (β) based on at least one of the magnetic field gradients. A sensor device is configured for implementing this method. A sensor system includes such a sensor device and a magnet, and is optionally connected to a joystick.SELECTED DRAWING: Figure 5

Description

Technical Field

[0001] The present invention generally relates to the field of magnetic position sensor systems, devices, and methods, and more specifically, to a magnetic position sensor system for measuring the orientation of a magnet pivotable about a fixed reference point. The present invention also relates to a position sensor system in which the magnet is connected to a joystick.

Background Art

[0002] Magnetic position sensor systems, particularly linear or angular position sensor systems, are known in the art. There are many variations of position sensor systems that address one or more of the following requirements: using a simple or inexpensive magnetic structure, using a simple or inexpensive sensor device, being able to measure over a relatively large range, being able to measure with high accuracy, requiring only simple arithmetic, being able to measure quickly, being very robust to positioning errors, being very robust to external fields, providing redundancy, being able to detect errors, being able to detect and correct errors, having a good signal-to-noise ratio (SNR), having only one degree of freedom (translation or rotation), having two degrees of freedom (e.g., one translation and one rotation, or two rotations), etc.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] In many known systems, the system has only one degree of freedom, for example, rotating about one axis or translating along one axis.

[0005] Magnetic position sensor systems in which the magnet has at least two degrees of freedom are also known in the art from Patent Document 1 filed on February 28, 2021, which discloses, for example, a magnet that is movable along an axis and rotatable about the axis, or from Patent Document 2 that discloses a circuit including at least one trained neural network for determining information regarding the position, orientation, or alignment of the magnet. These examples show that position sensor systems in which the magnet has at least two degrees of freedom are much more complex than systems having only one degree of freedom.

[0006] There is always room for improvement or alternatives.

[0007] An object of embodiments of the present invention is to provide a sensor device, a position sensor system, and a method for determining the orientation (α, β) of a magnet.

[0008] An object of embodiments of the present invention is to provide a sensor device, a position sensor system, and a method for determining the orientation (α, β) of a cylindrical magnet pivotable about a fixed reference point. The fixed reference point may be located at a predetermined height above or below the semiconductor substrate (where "above" means on the same side of the substrate as the magnet and "below" means on the opposite side of the substrate from the magnet).

[0009] A specific object of embodiments of the present invention is to provide a sensor device, a position sensor system, and a method for determining the orientation (α, β) of the axis of an axially magnetized cylindrical magnet pivotable about a reference position located on a semiconductor substrate.

Means for Solving the Problems

[0010] In a preferred embodiment, the orientation is determined in a manner that is highly robust to an external magnetic field (also known as a "stray magnetic field").

[0011] A particular object of embodiments of the present invention is to provide a joystick with such a magnet, and the orientation of the joystick is determined with improved accuracy in a way that is substantially insensitive to, for example, a disturbance field.

[0012] These objects are achieved by embodiments of the present invention.

[0013] According to a first aspect, the present invention provides a sensor device for determining the orientation of a magnet (e.g., a two-pole magnet) having an axis, the sensor device comprising a semiconductor substrate including a plurality of magnetic sensors configured to determine at least two of the magnetic field gradients: i) a first magnetic field gradient (e.g., dBx / dx) of a first magnetic field component oriented in a first direction parallel to the semiconductor substrate along a first direction; ii) a second magnetic field gradient (e.g., dBy / dy) of a second magnetic field component oriented in a second direction parallel to the semiconductor substrate and perpendicular to the first direction along a second direction; iii) a third magnetic field gradient (e.g., dBz / dx) of a third magnetic field component oriented in a third direction perpendicular to the semiconductor substrate along the first direction; and iv) a fourth magnetic field gradient (e.g., dBz / dy) of the third magnetic field component oriented in the third direction along the second direction, the sensor device further comprising a processing circuit configured to determine a first angle (e.g., α) and a second angle (e.g., β) based on at least some of the magnetic field gradients.

[0014] In one embodiment, the sensor element is configured to determine only two magnetic field gradients, namely dBz / dx and dBz / dy, and the processing unit is configured to determine a first angle (e.g., α) as a function of only one magnetic field gradient, namely dBz / dx, and to determine a second angle (e.g., β) as a function of only one magnetic field gradient, namely dBz / dy.

[0015] The first angle may be formed between the positive projection of the axis A of the magnet on the first virtual plane XZ parallel to the first direction X and the third direction Z, and the second angle may be formed between the positive projection of the axis A of the magnet on the second plane YZ parallel to the second direction Y and the third direction Z.

[0016] The magnet may be a cylindrical magnet.

[0017] The magnet may be a two-pole magnet, for example, a cylindrical two-pole magnet, or a two-pole bar magnet, or a two-pole spherical magnet.

[0018] The magnet may be an axially magnetized ring magnet or an axially magnetized disk magnet.

[0019] The cylindrical magnet may have an outer diameter in the range of 3.0 mm to 15.0 mm, or in the range of 4.0 mm to 12.0 mm, or in the range of 4.0 mm to 10.0 mm.

[0020] The cylindrical magnet may have a height H (axial direction) and an outer diameter D such that the ratio of this height to the outer diameter (H / D) is within the range of 20% to 100%, within the range of 20% to 80%, or within the range of 25% to 75%, for example, a value of about 50%.

[0021] In one embodiment, the processing circuit is configured to determine the first angle based on at least a first magnetic field gradient (e.g., dBx / dx) and a third magnetic field gradient (e.g., dBz / dx), and to determine the second angle based on only at least a second magnetic field gradient (e.g., dBy / dy) and a fourth magnetic field gradient (e.g., dBz / dy).

[0022] In one embodiment, the processing circuit is configured to determine the first angle based on only the first magnetic field gradient (e.g., dBx / dx) and the third magnetic field gradient (e.g., dBz / dx), and to determine the second angle based on only the second magnetic field gradient (e.g., dBy / dy) and the fourth magnetic field gradient (e.g., dBz / dy).

[0023] In one embodiment, the plurality of magnetic sensors includes a first sensor, a second sensor, a third sensor, and a fourth sensor. The first sensor located at the first sensor location and the second sensor located at the second sensor location are located on a first virtual line oriented in a first direction and are separated from each other by a first distance. The first sensor is configured to measure a first magnetic field component oriented in the first direction and a second magnetic field component oriented in a third direction. The second sensor is configured to measure a third magnetic field component oriented in the first direction and a fourth magnetic field component oriented in the third direction. The third sensor located at the third sensor location and the fourth sensor located at the fourth sensor location are located on a second virtual line oriented in a second direction and are separated from each other by a second distance. The third sensor is configured to measure a fifth magnetic field component oriented in the second direction and a sixth magnetic field component oriented in the third direction. The fourth sensor is configured to measure a seventh magnetic field component oriented in the first direction and an eighth magnetic field component oriented in the third direction.

[0024] Using such a configuration, the first magnetic field gradient (e.g., dBx / dx) may be based on the difference between the first magnetic field component and the third magnetic field component. The second magnetic field gradient (e.g., dBz / dx) may be based on the difference between the second magnetic field component and the fourth magnetic field component. The third magnetic field gradient (e.g., dBy / dy) may be based on the difference between the fifth magnetic field component and the seventh magnetic field component. The fourth magnetic field gradient (e.g., dBz / dy) may be based on the difference between the sixth magnetic field component and the eighth magnetic field component.

[0025] In an embodiment, the first angle (α) is determined according to the formula α = K1 * atan2(dBz / dx, dBx / dx) where α is the first angle, atan2() is the arctangent function of two arguments, dBx / dx is the first magnetic field gradient, dBz / dx is the third magnetic field gradient, and K1 is a first predetermined constant. The second angle (β) is determined according to the formula β = K2 * atan2(dBz / dy, dBy / dy) Determined according to the formula, where β is the second angle, atan2() is the arctangent function of two arguments, dBy / dy is the second magnetic field gradient, dBz / dy is the fourth magnetic field gradient, and K2 is the second predetermined constant.

[0026] In an embodiment, the first angle (α) is given by the formula α = K1 * atan2(K3 * dBz / dx, dBx / dx) Determined according to the formula, where α is the first angle, atan2() is the arctangent function of two arguments, dBx / dx is the first magnetic field gradient, dBz / dx is the third magnetic field gradient, K1 and K3 are predetermined constants, and the second angle (β) is given by the formula: β = K2 * atan2(K4 * dBz / dy, dBy / dy) Determined according to the formula, where β is the second angle, atan2() is the arctangent function of two arguments, dBy / dy is the second magnetic field gradient, dBz / dy is the fourth magnetic field gradient, and K2 and K4 are predetermined constants.

[0027] In one embodiment, the magnet is movable such that the virtual axis of the magnet is pivotable about a reference point (e.g., Pref) having a predetermined position with respect to the semiconductor substrate.

[0028] In one embodiment, the reference point (e.g., Pref) is located on the semiconductor substrate and thus in the same plane as the sensor.

[0029] In one embodiment, the reference point (e.g., Pref) is located on an imaginary axis perpendicular to the semiconductor substrate at a predetermined non-zero distance (e.g., dref) from the semiconductor substrate, either above or below the semiconductor substrate. The reference point and the magnet may be located on the same side or opposite sides of the semiconductor substrate. The reference point may be located between the substrate and the magnet when the magnet is in its neutral position (i.e., when its axis is oriented perpendicular to the semiconductor substrate) or within the space defined by the magnet (when in its neutral position), or the magnet (when in its neutral position) may be located between the reference position and the semiconductor substrate.

[0030] In certain embodiments, the ratio (dref / H) of the distance “dref” to the (axial) height H of the magnet can be a value within the range of 50% to 200%, or within the range of 50% to 150%, or within the range of 75% to 125%.

[0031] In one embodiment, a first distance (e.g., ΔX) between a first sensor location and a second sensor location is substantially equal to a second distance (e.g., ΔY) between a third sensor location and a fourth sensor location. In this embodiment, the sensors may be located on a virtual circle. The reference point may be located at the center of this circle, or may be perpendicular to the substrate and located at a predetermined non-zero distance from the substrate on a virtual line passing through the center of the circle.

[0032] In one embodiment, a first distance (e.g., ΔX) between a first sensor location and a second sensor location is at least 5% greater than or at least 5% less than a second distance (e.g., ΔY) between a third sensor location and a fourth sensor location. In this embodiment, the sensors may be located on a virtual ellipsoid. The reference point may be located at the center of this ellipse, or may be perpendicular to the substrate and located at a predetermined non-zero distance from the substrate on a virtual line passing through the center of the ellipse.

[0033] In one embodiment, each of the four sensors comprises an integrated magnetic concentrator and two horizontal Hall elements.

[0034] The integrated magnetic concentrator (also known as an “integrated flux concentrator”) may have a disk shape with a diameter in the range of 150 μm to 250 μm, for example, in the range of 170 μm to 230 μm, for example, equal to about 200 μm.

[0035] In one embodiment, the first sensor includes a first integrated magnetic concentrator and first and second horizontal Hall elements located on opposite sides of a first IMC on a first virtual line oriented in a first direction, the second sensor includes a second integrated magnetic concentrator and third and fourth horizontal Hall elements located on a first virtual line on opposite sides of a second IMC, the third sensor includes a third integrated magnetic concentrator and fifth and sixth horizontal Hall elements located on opposite sides of a third IMC on a second virtual line oriented in a second direction, and the fourth sensor includes a fourth integrated magnetic concentrator and seventh and eighth horizontal Hall elements located on a second virtual line on opposite sides of a fourth IMC.

[0036] An example of such an arrangement is shown in FIG. 5.

[0037] In one embodiment, each of the four sensors includes a horizontal Hall element and a vertical Hall element. In this embodiment, the sensor device preferably does not include a magnetic flux concentrator (IMC).

[0038] In one embodiment, each of the four sensors includes a horizontal Hall element and at least one magnetoresistive sensor element. Also, in this embodiment, the sensor device preferably does not include a magnetic flux concentrator (IMC).

[0039] In one embodiment, the first sensor includes a first horizontal Hall element and a first vertical Hall element, the second sensor includes a second horizontal Hall element and a second vertical Hall element, each of the first vertical Hall element and the second vertical Hall element has an axis of maximum sensitivity oriented in a first direction, the third sensor includes a third horizontal Hall element and a third vertical Hall element, the fourth sensor includes a fourth horizontal Hall element and a fourth vertical Hall element, and each of the third vertical Hall element and the fourth vertical Hall element has an axis of maximum sensitivity oriented in a second direction.

[0040] In one embodiment, the processing circuit is integrated into a semiconductor substrate. Therefore, in this embodiment, the sensor element and the processing circuit are integrated on a single substrate.

[0041] According to a second aspect, the present invention also provides a position sensor system including a sensor device according to the first aspect and a magnet pivotable about a reference point (e.g., Pref) having a predetermined position with respect to a semiconductor substrate. This means that, for example, as shown in FIG. 1, the magnet is movable such that it rotates about a predetermined reference position. The magnet has a cylindrical or spherical shape, and the magnet may be rotatable about its own axis, although such rotation does not change the magnetic field lines.

[0042] The magnet may be, for example, a two-pole magnet having a cylindrical, rod-like, or spherical shape.

[0043] In one embodiment, the system further comprises a joystick connected to the magnet.

[0044] According to a third aspect, the present invention also provides a method for determining the orientation (e.g., using two angles α, β) of a magnet pivotable about a reference point (e.g., Pref) having a predetermined position with respect to a semiconductor substrate, the method comprising: a) magnetic field gradients: i) a first magnetic field gradient (e.g., dBx / dx) of a first magnetic field component oriented in a first direction parallel to the semiconductor substrate along a first direction; ii) a second magnetic field gradient (e.g., dBy / dy) of a second magnetic field component oriented in a second direction parallel to the semiconductor substrate and perpendicular to the first direction along a second direction; iii) a third magnetic field gradient (e.g., dBz / dx) of a third magnetic field component oriented in a third direction perpendicular to the semiconductor substrate along the first direction; and iv) a fourth magnetic field gradient (e.g., dBz / dy) of the third magnetic field component oriented in the third direction along the second direction, determining at least two of them; b) determining a first angle formed between a positive projection of the axis of the magnet on a first virtual plane (e.g., XZ) parallel to the first direction (e.g., X) and the third direction (e.g., Z) based on at least some of the magnetic field gradients; c) determining a second angle formed between a positive projection of the axis of the magnet on a second virtual plane (e.g., YZ) parallel to the second direction and the third direction based on at least some of the magnetic field gradients.

[0045] In one embodiment, step a) includes determining only two magnetic field gradients, namely dBz / dx and dBz / dy, step b) includes determining a first angle (e.g., α) as a function of only one magnetic field gradient, namely dBz / dx, and step c) includes determining a second angle (e.g., β) as a function of only one magnetic field gradient, namely dBz / dy.

[0046] In one embodiment, the first angle is determined based on at least a first magnetic field gradient (e.g., dBx / dx) and a third magnetic field gradient (e.g., dBz / dx), and the second angle is determined based on at least a second magnetic field gradient (e.g., dBy / dy) and a fourth magnetic field gradient (e.g., dBz / dy).

[0047] In one embodiment, the first angle is determined based on only the first magnetic field gradient (e.g., dBx / dx) and the third magnetic field gradient (e.g., dBz / dx), and the second angle is determined based on only the second magnetic field gradient (e.g., dBy / dy) and the fourth magnetic field gradient (e.g., dBz / dy).

[0048] In an embodiment, the first angle is given by the formula α = K1 * atan2(dBz / dx, dBx / dx) where α is the first angle, atan2() is the arc tangent function of two arguments, dBx / dx is the first magnetic field gradient, dBz / dx is the third magnetic field gradient, K1 is a first predetermined constant, and the second angle is given by the formula β = K2 * atan2(dBz / dy, dBy / dy) where β is the second angle, atan2() is the arc tangent function of two arguments, dBy / dy is the second magnetic field gradient, dBz / dy is the fourth magnetic field gradient, and K2 is a second predetermined constant.

[0049] In an embodiment, the first angle is given by the formula α = K1 * atan2(K3 * dBz / dx, dBx / dx) is determined according to, where α is the first angle, atan2() is the arctangent function of two arguments, dBx / dx is the first magnetic field gradient, dBz / dx is the third magnetic field gradient, K1 and K3 are predetermined constants, and the second angle is given by the formula β = K2 * atan2(K4 * dBz / dy, dBy / dy) is determined according to, where β is the second angle, atan2() is the arctangent function of two arguments, dBy / dy is the second magnetic field gradient, dBz / dy is the fourth magnetic field gradient, and K2 and K4 are predetermined constants.

[0050] Specific and preferred embodiments of the present invention are described in the appended independent and dependent claims. Features from the dependent claims are not merely those explicitly recited in the claims, but may be combined as appropriate with the features of the independent claims and the features of other dependent claims.

[0051] These and other aspects of the present invention will be apparent from, and elucidated with reference to, the embodiments described hereinafter.

Brief Description of the Drawings

[0052]

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Mode for Carrying Out the Invention

[0053] The drawings are only schematic and non-limiting. In the drawings, the sizes of some elements may be exaggerated and may not be drawn to scale for illustrative purposes. Any reference signs within the scope of the claims shall not be construed as limiting the scope. In different drawings, the same reference signs refer to the same or similar elements.

[0054] The present invention is described with respect to specific embodiments and with reference to specific drawings, but the present invention is not limited thereto and is limited only by the scope of the claims.

[0055] The first, second, and similar terms in this description and the claims are used to distinguish similar elements and are not necessarily used to describe an order in any temporal, spatial, ranking, or any other way. The terms so used are interchangeable under appropriate circumstances, and it is to be understood that the embodiments of the invention described herein are operable in an order other than that described or illustrated herein.

[0056] Terms such as upper and lower in this description and the claims are used for illustrative purposes and are not necessarily used to describe relative positions. The terms so used are interchangeable under appropriate circumstances, and it is to be understood that the embodiments of the invention described herein are operable in an orientation other than that described or illustrated herein.

[0057] It should be noted that the term "comprising" used in the claims should not be construed as being limited to the means recited thereafter and does not exclude other elements or steps. Thus, it is construed as specifying the presence of the recited features, integers, steps, or components, but does not exclude the presence or addition of one or more other features, integers, steps, or components, or groups thereof. Thus, the scope of the expression "a device comprising means A and B" should not be limited to a device consisting only of components A and B. This means, with respect to the present invention, that the relevant components of the device are only A and B.

[0058] Throughout this specification, "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 invention. Thus, the 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 refer to the same embodiment. Further, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, as will be apparent to those skilled in the art from this disclosure.

[0059] Similarly, in the description of exemplary embodiments of the present invention, it should be understood that various features of the present invention may be grouped in a single embodiment, drawing, or description thereof for the purpose of streamlining the disclosure and facilitating the understanding of one or more of the various aspects of the invention. However, this method of disclosure should not be construed as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims show, aspects of the invention are not all in all of the features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are expressly incorporated into this detailed description, and each claim stands on its own as a separate embodiment of the invention.

[0060] Furthermore, some embodiments described herein include some other features included in other embodiments and do not include other features, but combinations of features of different embodiments are within the scope of the invention, as will be understood by those skilled in the art, and form different embodiments. For example, in the following claims, any combination of the embodiments recited in the claims can be used.

[0061] 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 so as not to obscure the understanding of this description.

[0062] In this document, unless otherwise explicitly stated, the terms "magnetic sensor device" or "sensor device" preferably refer to a device that includes at least one "magnetic sensor" or at least one magnetic "sensor element" integrated on a semiconductor substrate. The sensor device may be included in a package, also called a "chip", but this is not absolutely necessary.

[0063] In this document, the terms "sensor element" or "magnetic sensor element" or "magnetic sensor" can refer to a component or group of components, or a sub-circuit, or a structure that can measure 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 including at least one (preferably four) magnetoresistive elements, or a combination thereof.

[0064] In certain embodiments of the invention, the terms "magnetic sensor" or "magnetic sensor structure" may refer to an arrangement that includes one or more integrated magnetic concentrators (IMCs), also known as integrated flux concentrators, and one or more horizontal Hall elements disposed near the periphery of a disk-shaped IMC, such as an IMC in which two horizontal Hall elements are arranged at 180° intervals from each other, or an IMC in which four horizontal Hall elements are arranged at 90° intervals from each other.

[0065] In this document, the expressions "in-plane component of the magnetic field vector" and "projection of the magnetic field vector on the sensor plane" mean the same thing. When the sensor device is a semiconductor substrate or includes a semiconductor substrate, this also means the "magnetic field component parallel to the semiconductor plane". These components may be labeled Bx, By.

[0066] In this document, the expressions "out-of-plane component of a vector", "Z-component of a vector", and "projection of a vector on an axis perpendicular to the sensor plane" mean the same thing. This component may be labeled Bz.

[0067] Embodiments of the present invention are typically described using a Cartesian coordinate system fixed to a sensor device and having three axes X, Y, Z, where the X-axis and Y-axis are parallel to the substrate and the Z-axis is perpendicular to the substrate.

[0068] In this document, the expressions "spatial differentiation" or "differentiation" or "spatial gradient" or "gradient" are used as synonyms. In the context of the present invention, a gradient is typically determined as the difference between two values measured at two locations spaced along a particular direction. Theoretically, a gradient is typically calculated as the difference between two values divided by the distance between the sensor locations, but in practice, since the measured signal also needs to be scaled, the division by distance is often omitted.

[0069] In this application, horizontal hall plates are typically referred to by H1, H2, etc., signals from these horizontal hall plates are typically referred to by h1, h2, etc., vertical hall plates are typically referred to by V1, V2, etc., and signals from these vertical hall plates are typically referred to by v1, v2, etc.

[0070] In the context of the present invention, the expressions arctan(x,y), atan2(x,y), arccot(y / x) are considered equivalent.

[0071] The present invention relates to a magnetic position sensor system, method, and device for measuring the orientation of a magnet pivotable about a fixed reference point "Pref". This fixed reference point may be located on a semiconductor substrate or at a predetermined distance "dref" above or below the semiconductor substrate. The magnet may be connected to a joystick (not shown).

[0072] In a preferred embodiment, the system has improved accuracy, for example, because it is less sensitive to external disturbance fields.

[0073] Refer to the drawings.

[0074] FIG. 1 is a schematic diagram of a magnetic position sensor system 100 including a cylindrical magnet 101 and a sensor device 102.

[0075] The sensor device 102 includes a semiconductor substrate (not shown in FIG. 1). A coordinate system having three orthogonal axes X, Y, and Z is connected to the semiconductor substrate such that the axes X and Y are parallel to the semiconductor substrate and the axis Z is orthogonal to the semiconductor substrate.

[0076] The magnet 101 shown in FIG. 1 is a cylindrical magnet, and more specifically, a magnet 101 magnetized in the axial direction. The magnet has a virtual axis "A" that intersects the semiconductor substrate at a fixed reference point "Pref" and can rotate in various directions. Since the distance between the magnet 101 and the reference point "Pref" is constant, the system has two degrees of freedom. The task of the sensor device 102 is to determine the orientation of the magnet.

[0077] The orientation can be uniquely defined, for example, by two angles φ and ψ, where φ is the negative or positive angle of the positive projection of the axis A in the YZ plane with respect to the Z axis, and ψ is the negative or positive angle of the positive projection of the axis A in the XZ plane with respect to the Z axis. In the example shown, when the axis A of the magnet is oriented perpendicular to the semiconductor substrate, the magnetic field vector B at the intersection of the axis A and the semiconductor substrate is oriented in the negative Z direction, and φ = 0° and ψ = 0°. The magnet is preferably movable at φ in the range of at least -30° to +30° and ψ in the range of 30° to +30°. Of course, larger ranges, such as ±40°, or ±50°, or ±60° are also envisioned. However, specifying the orientation of the magnet 101 by the angles φ and ψ is not the only possible method.

[0078] Figure 2 shows another way of defining the orientation of a vector of a constant length [CP] starting from a reference point "C" and ending at a point "P" on an imaginary sphere. Although the vector [CP] is not shown, the first orthographic projection [CA] of the vector [CP] onto the plane XZ is shown, and the second orthographic projection [CB] of the vector [CP] onto the plane YZ is shown. The orientation of the axis A passing through points C and P can also be defined by a first angle α between the positive X-axis and the vector [CA], and a second angle β between the positive Y-axis and the vector [CB]. As an example, when the magnet axis is oriented perpendicular to the plane XY (i.e., perpendicular to the semiconductor substrate), which is also referred to as the "neutral position", α = 90° and β = 90°. This corresponds to the orientation of φ = 0° and ψ = 0° described above.

[0079] The following equations apply. Bx = B * cos(α) * sin(β) [1] By = B * cos(β) * sin(α) [2] Bz = B * sin(β) * sin(α) [3]

[0080] By dividing [3] by [1], the following is obtained. (Bz / Bx) = tan(α) [4] (Bz / By) = tan(β) [5]

[0081] In the equations, Bx is the magnetic field component oriented in the X direction, By is the magnetic field component oriented in the Y direction, Bz is the magnetic field component oriented in the Z direction, and B is the magnitude of the magnetic field vector.

[0082] In a preferred embodiment, the angles α and β are values within the range of 90° ± 30°, or within the range of 90° ± 40°, or within the range of 90° ± 50°, or within the range of 90° ± 60°.

[0083] FIG. 3 shows a semiconductor substrate including a first sensor (or sensor structure) S1 located at a first sensor location X1 on the X-axis and a second sensor (or sensor structure) S2 located at a second sensor location X2 on the X-axis spaced apart from X1. Each of the first and second sensors S1, S2 includes a disk-shaped integrated magnetic concentrator (IMC) and two horizontal Hall elements disposed on the X-axis on the opposite side of the IMC. The first sensor S1 includes a first horizontal Hall element H1 configured to provide a first signal h1 and a second horizontal Hall element H2 configured to provide a second signal h2. The second sensor S2 includes a third horizontal Hall element H3 configured to provide a third signal h3 and a fourth horizontal Hall element H4 configured to provide a fourth signal h4.

[0084] To understand the present invention, it is sufficient to know that the signals h1 and h2 of the first sensor S1 can be combined to determine both the in-plane magnetic field component Bx1 (parallel to the semiconductor substrate) and the out-of-plane magnetic field component Bz1 (perpendicular to the semiconductor substrate). More specifically, the in-plane magnetic field component Bx1 is parallel to the X-axis and can be calculated by subtracting the signals h1 and h2, and the out-of-plane magnetic field component Bz1 is parallel to the Z-axis and can be calculated by adding the signals h1 and h2. This can be expressed mathematically as follows.

[0085] Bx1 = (h2 - h1) [6] Bz1 = (h2 + h1) [7]

[0086] Similarly, the in-plane magnetic field component Bx2 and the out-of-plane magnetic field component Bz2 at the second sensor location X2 can be determined, for example, according to the following equations.

[0087] Bx2 = (h4 - h3) [8] Bz2 = (h4 + h3) [9]

[0088] From these values, the in-plane magnetic field gradient dBx / dx and the out-of-plane magnetic field gradient dBz / dx can be determined, for example, according to the following equations.

[0089] ΔBx / Δx = Bx2 - Bx1

[10] ΔBz / Δx = Bz2 - Bz1

[11]

[0090] Note that the division by "Δx" is generally omitted because the distance is constant and the value obtained from the Hall element also needs to be scaled. However, the notation ΔBz / Δx (or dBz / dx) is useful in this application because it not only indicates that the difference between two Bz values is taken but also shows the direction along which it is taken, which is the X direction in the case of Δx. As is known in the art, the gradient signal is very insensitive to the disturbance field.

[0091] Note that there is a sensor device having two sensors S1 and S2 separated by a distance ΔX (not shown in FIG. 3, but see FIG. 6 for example). The first sensor S1 includes one horizontal Hall element H1 and one vertical Hall element V1 with the axis of maximum sensitivity oriented in the X direction, and the second sensor S2 includes one horizontal Hall element H2 and one vertical Hall element V2 with the axis of maximum sensitivity oriented in the X direction. Bx1, Bz1 and Bx2, Bz2 can be measured respectively, and two magnetic field gradients dBx / dx and dBz / dx can be determined. In the case where v1 is the signal obtained from V1, v2 is the signal obtained from V2, h1 is the signal obtained from H1, and h2 is the signal obtained from H2, dBx / dx can be calculated as (v2 - v1), and dBz / dx can be calculated as (h2 - h1).

[0092] FIGS. 4(a) to 4(d) are schematic views of a cylindrical magnet having a virtual axis "A" that intersects a semiconductor substrate (schematically shown by a dotted line) at a predetermined position "Pref". The axis "A" is pivotable about the reference point "Pref". Only the movement parallel to the XZ plane is shown so as not to overload the drawing.

[0093] In FIGS. 4(a) and 4(b), the sensor (schematically shown as a black square) is located at the reference position "Pref". As can be seen, the magnetic field lines passing through the sensor location have the same orientation as the mechanical orientation of the axis "A" of the magnet, and the distance "g" between the sensor and the magnet is independent of the axis orientation.

[0094] In FIGS. 4(c) and 4(d), the semiconductor substrate includes a plurality of sensors separated by a distance ΔX, and the reference position "Pref" is preferably at the center between the sensor locations. As can be seen, the orientation of the magnetic field lines at the plurality of sensor locations is no longer the same as the orientation of axis A, and the distance between each of the sensor locations and the magnet is no longer constant and depends on the orientation of axis "A".

[0095] As far as the inventors know, there is no known general analytical formula or relationship between the mechanical tilt angle of axis A and the magnetic field components (Bx, By, Bz) at two sensor locations, let alone the relationship between the mechanical tilt angle and the magnetic field gradient dBx / dx as obtained from the signals from two sensors located at a distance of Δx / 2 from the reference point. The inventors have started a research project to investigate this relationship. This relationship is highly non-linear and was expected to be very difficult to explain mathematically.

[0096] FIG. 5 is a schematic diagram of a first sensor device 500 proposed according to the present invention.

[0097] The sensor device 500 includes i) the first magnetic field gradient dBx / dx of the first magnetic field component Bx oriented along the first direction X and parallel to the semiconductor substrate; ii) the second magnetic field gradient dBy / dy of the second magnetic field component oriented along the second direction Y, parallel to the semiconductor substrate and perpendicular to the first direction X; iii) the third magnetic field gradient dBz / dx of the third magnetic field component Bz oriented along the third direction Z perpendicular to the semiconductor substrate along the first direction X; iv) a semiconductor substrate including a plurality of magnetic sensors S1, S2, S3, S4 configured to determine a fourth magnetic field gradient dBz / dy of a third magnetic field component Bz oriented in a third direction Z along a second direction Y.

[0098] The sensor device 500 further includes a processing circuit (not shown in FIG. 5, but see, for example, FIG. 9) configured to define, based on these magnetic field gradients dBx / dx, dBy / dy, dBz / dx, dBz / dy, two angles, such as φ, ψ as shown in FIG. 1, or two angles, such as α, β as shown in FIG. 2, that define the orientation of the axis A of a magnet, for example, a magnet pivotable about a fixed reference point.

[0099] Furthermore, the inventors have surprisingly found that such angles can be defined and calculated based on such four magnetic field gradients in an analytical manner and with a relatively good approximation, for example, with an absolute error less than ±10°, even in the presence of a disturbance field. This was not expected.

[0100] The inventors have also found that this accuracy can be further improved (i.e., the absolute error is reduced to a value less than ±5° or ±3°) by post-processing, for example, remapping the angles calculated using two piecewise linear approximation functions, one for each angle.

[0101] The processing circuit may be configured to determine a first angle α formed between a positive projection of the axis A of the magnet on a first virtual plane XZ based on the first magnetic field gradient dBx / dx and the third magnetic field gradient dBz / dx, the virtual plane XZ being parallel to the first direction X and the third direction Z, and may be configured to determine a second angle β formed between a positive projection of the axis A of the magnet on a second virtual plane YZ based on the second magnetic field gradient dBy / dy and the fourth magnetic field gradient dBz / dy, the virtual plane YZ being parallel to the second direction Y and the third direction Z.

[0102] By specifying the orientation of the axis A of the magnet using these angles α, β (shown in Fig. 2), it has been found that the angles can be calculated using relatively simple mathematical formulas.

[0103] The plurality of magnetic sensors may include a first sensor S1, a second sensor S2, a third sensor S3, and a fourth sensor S4.

[0104] The first sensor S1 may be located at a first sensor location, the second sensor S2 may be located at a second sensor location, and both may be located on a first virtual line oriented in a first direction X and separated from each other by a first non-zero distance ΔX. The first sensor S1 may be configured to measure a first magnetic field component Bx1 oriented in the first direction X and a second magnetic field component Bz1 oriented in a third direction Z. The second sensor S2 may be configured to measure a third magnetic field component Bx2 oriented in the first direction X and a fourth magnetic field component Bz2 oriented in the third direction Z.

[0105] The third sensor S3 may be located at a third sensor location, the fourth sensor S4 may be located at a fourth sensor location, and both may be located on a second virtual line oriented in a second direction Y and separated from each other by a second non-zero distance ΔY. The third sensor S3 may be configured to measure a fifth magnetic field component By1 oriented in the second direction Y and a sixth magnetic field component Bz3 oriented in the third direction Z. The fourth sensor S4 may be configured to measure a seventh magnetic field component By2 oriented in the first direction X and an eighth magnetic field component Bz4 oriented in the third direction Z.

[0106] The sensor device may be further configured to determine a first magnetic field gradient dBx / dx based on a difference between a first magnetic field component Bx1 and a third magnetic field component Bx2, to determine a second magnetic field gradient dBz / dx based on a difference between a second magnetic field component Bz1 and a fourth magnetic field component Bz2, to determine a third magnetic field gradient dBy / dy based on a difference between a fifth magnetic field component By1 and a seventh magnetic field component By2, and to determine a fourth magnetic field gradient dBz / dy based on a difference between a sixth magnetic field component Bz3 and an eighth magnetic field component Bz4.

[0107] In one embodiment, the distance ΔY is equal to the distance ΔX, in which case the four sensor locations are preferably located on a circle and the reference point “Pref” is preferably located at the center of this circle.

[0108] In another embodiment, the distance ΔY is different from ΔX, for example, at least 5% larger or smaller than ΔX, in which case the four sensor locations are preferably located on an ellipse and the reference point “Pref” is preferably located at the center of this ellipse. Using such an embodiment, the size of the semiconductor substrate can be reduced, thus enhancing compactness and reducing costs. This can be particularly suitable for joystick applications where the “handle” is movable over a larger range parallel to the YZ plane (e.g., having at least three or four positions) compared to a range parallel to the XZ plane (e.g., having only two positions).

[0109] In the example of FIG. 5, each of the four sensors S1 to S4 includes an integrated magnetic concentrator (IMC) and two horizontal Hall elements arranged at 180° intervals near the periphery of the IMC.

[0110] More specifically, the first sensor S1 includes a first integrated magnetic concentrator IMC1 and first and second horizontal Hall elements H1 and H2 located on the opposite side of the first IMC on a first virtual line oriented in the first direction X. The second sensor S2 includes a second integrated magnetic concentrator IMC2 and third and fourth horizontal Hall elements H3 and H4 located on the first virtual line on the opposite side of the second IMC. The third sensor S3 includes a third integrated magnetic concentrator IMC3 and fifth and sixth horizontal Hall elements H5 and H6 located on the opposite side of the third IMC on a second virtual line oriented in the second direction Y. The fourth sensor S4 includes a fourth integrated magnetic concentrator IMC4 and seventh and eighth horizontal Hall elements H7 and H8 located on the second virtual line on the opposite side of the fourth IMC.

[0111] The integrated magnetic concentrator (also known as an "integrated flux concentrator") may have a disk shape with a diameter in the range of 150 μm to 250 μm, for example, in the range of 170 μm to 230 μm, for example, equal to about 200 μm.

[0112] When h1 to h8 are the signals provided by the horizontal Hall elements H1 to H8 respectively, four gradient values may be calculated according to the following formula.

[0113] gr1 = (dBx / dx) = Bx2 - Bx1 = (h4 - h3) - (h2 - h1)

[11] gr2 = (dBz / dx) = Bz2 - Bz1 = (h4 + h3) - (h2 + h1)

[12] gr3 = (dBy / dy) = By4 - By3 = (h8 - h7) - (h6 - h5)

[13] gr4 = (dBz / dy) = Bz4 - Bz3 = (h8 + h7) - (h6 + h5)

[14]

[0114] The inventors have surprisingly found that the first angle α can be very well approximated by the following extremely simple formula.

[0115] α = K1 * atan2(gr2, gr1) [15a]

[0116] Furthermore, the second angle β can be very well approximated by the following very simple formula.

[0117] β = K2 * atan2(gr4, gr3) [16a]

[0118] Since both angles α and β are calculated as functions of the magnetic gradient, these angles are very insensitive to the external disturbance field. Furthermore, since the angles are calculated based on the ratio of the two gradients, these angles are also very insensitive to aging effects such as temperature changes and / or demagnetization of the magnet.

[0119] The values of K1 and K2 may be determined by simulation or by calibration, and may be stored in the non-volatile memory of the sensor device. The values of K1 and K2 may depend on the size of the magnet (diameter, height), the distances Δx and Δy between the sensors, and the distance "g" between the magnet and the reference point "Pref".

[0120] However, the present invention is not limited thereto, and the following formula may be used.

[0121] α = K1 * atan2(K3 * gr2, gr1) [15b] β = K2 * atan2(K4 * gr4, gr3) [16b]

[0122] In the formula, K3 and K4 are predetermined constants further described in FIGS. 7(c) and 8(c). Formulas [15b] and [16b] may provide more accurate results when Δx is different from Δy. Of course, many variations of the formula are possible. For example,

[0123] α = K1 * atan2(gr2 / K5, gr1) [15c], or α = K1 * atan2(gr2, K6 * gr1) [15d], or α = K1 * atan2(gr2, gr1 / K7) [15e] may also be used,

[0124] In the formula, K5, K6, and K7 are predetermined constants. A similar modification is also possible for formula [16b].

[0125] FIG. 6 is a schematic diagram of another sensor device 600 proposed by the present invention, which can be regarded as a modification of the sensor device in FIG. 5. The main difference is that each sensor includes one horizontal Hall element and one vertical Hall element. Other than the above, those applicable here are also applicable as necessary.

[0126] More specifically, in the example of FIG. 6, the first sensor S1 includes a first horizontal Hall element H1 and a first vertical Hall element V1, the second sensor S2 includes a second horizontal Hall element H2 and a second vertical Hall element V2, and each of the first and second vertical Hall elements V1 and V2 has an axis of maximum sensitivity oriented in the first direction X. Similarly, the third sensor S3 includes a third horizontal Hall element H3 and a third vertical Hall element V3, the fourth sensor S4 includes a fourth horizontal Hall element H4 and a fourth vertical Hall element V4, and each of the third and fourth vertical Hall elements V3 and V4 has an axis of maximum sensitivity oriented in the second direction Y.

[0127] When h1 to h4 are the signals provided by the horizontal Hall elements H1 to H4 and v1 to v4 are the signals provided by the vertical Hall elements V1 to V4, the first and second angles α and β may be calculated according to the following series of formulas.

[0128] gr1 = (dBx / dx) = Bx2 - Bx1 = (v2 - v1)

[17] gr2 = (dBz / dx) = Bz2 - Bz1 = (h2 - h1)

[18] gr3 = (dBy / dy) = By4 - By3 = (v4 - v3)

[19] gr4 = (dBz / dy) = Bz4 - Bz3 = (h4 - h3)

[20] α = K1 * atan2(gr2, gr1) [21a] β = K2 * atan2(gr4, gr3) [22a]

[0129] Alternatively, the following equation is used.

[0130] α = K1 * atan2(K3 * gr2, gr1) [21b] β = K2 * atan2(K4 * gr4, gr3) [22b]

[0131] This can result in a more accurate result when Δx is different from Δy.

[0132] In the modification of FIG. 6, the sensor device does not include a vertical Hall element, but instead includes a magnetoresistive element.

[0133] In another modification, since the vertical Hall element of FIG. 6 is omitted, the sensor device of FIG. 6 includes only four horizontal Hall elements.

[0134] FIG. 7(a) shows an exemplary sensor system 700 comprising a cylindrical magnet having a diameter D = 4 mm and a height H = 4 mm, attached at a distance g = 3 mm from a reference point located on a semiconductor substrate, between two sensors spaced approximately 1.7 mm apart, each having an IMC with a diameter of approximately 190 μm and two horizontal Hall elements (e.g., as illustrated in FIG. 3 or FIG. 5).

[0135] FIGS. 7(b) - 7(e) show the simulation results of this sensor system.

[0136] FIG. 7(b) shows a plot of the waveforms of the magnetic field components Bx, Bz as a function of the mechanical angle α (as shown in FIG. 2) measured by the sensor located at the reference position "Pref", as shown in FIGS. 4(a) and 4(b). This plot also shows the waveform of the magnitude of the magnetic field |B| calculated as the sum of the squares of these components sqr(Bx) + sqr(Bz). As can be seen, this value is substantially constant.

[0137] As shown in FIGS. 4(c) and 4(d), FIG. 7(c) shows plots of the waveforms of the magnetic field gradients gr2 = dBz / dx and gr1 = dBx / dx as functions of the mechanical angle α, which can be derived from the signals measured by two sensors located on the opposite side of the reference position “Pref”, and thus, as shown in FIGS. 5 or 6, can be determined by the sensor device. The plot in FIG. 7(b) also shows the waveform of |dB| calculated as the sum of squares of these gradients sqr(dBx / dx)+sqr(dBz / dx). As can be seen, this value is rather constant but not completely constant, that is, the gradient signals gr1 and gr2 are not perfect orthogonal signals. Equations [15b], [16b], [21b], and [22b] can take this difference into account by selecting values of K3 and K4 different from 1.00, for example, in the range of 0.80 to 0.98 or in the range of 1.02 to 1.20.

[0138] However, as described above, surprisingly, it has been found that these signals closely resemble orthogonal signals even without the K factor.

[0139] Actually, FIG. 7(d) shows the curve obtained by the formula atan2(gr2, gr1). As can be seen, this curve is almost linear and has a slope equal to about 2.5. Such a high linearity was completely unexpected.

[0140] FIG. 7(e) shows the difference (or error) between the mechanical angle α and the value calculated as (0.4)*atan2(gr2, gr1) by applying Equation [15a] with K1 = 0.4. The error is less than ±4° for the mechanical angle α that varies from about 60° to about 120°. Such a small error for such a simple equation is not predictable.

[0141] Figures 7(a) to 7(e) show only the simulation of angle α, but these simulations also represent the second angle β. However, in this case, the labels of the curves are "By" instead of "Bx" in Figure 7(b), "dBz / dy" instead of "dBz / dx", and "dBy / dy" instead of "dBx / dx" in Figure 7(c).

[0142] As described above, the inventors have also found that this error can be further reduced to a value of less than ±5°, or less than ±3°, or less than ±1.0°, or less than ±0.5°, or even less than ±0.2°, or less than ±0.1° by a known "post - processing technique" based on remapping the curve in Figure 7(d) using, for example, piece - wise linear approximation, where the parameters may be determined during a calibration step and stored in the non - volatile memory of the sensor device.

[0143] It can be understood from Figure 7(c) that the signal dBz / dx alone can be used as a measure of the first angle, and similarly, the signal dBz / dy alone can be used as a measure of the second angle. Depending on the application (such as a game console, an excavator, etc.), this measure may be sufficient in some cases or not in others. The measure may be further improved by using a look - up table or piece - wise linear correction.

[0144] Figure 8(a) shows an exemplary sensor system 800 comprising a cylindrical magnet having a diameter D = 8 mm and a height H = 4 mm, attached at a distance g = 3 mm from a reference point "Pref" located between two sensors spaced approximately 1.7 mm apart, each having an IMC with a diameter of approximately 190 μm and two horizontal hole elements (e.g., as illustrated in Figure 3 or Figure 5).

[0145] Figures 8(b) to 8(e) show the simulation results of this sensor system.

[0146] The curves in FIGS. 8(b) to 8(e) are very similar to the curves in FIGS. 7(b) to 7(e), but the inherent linearity of the curve shown in FIG. 8(d) is improved, and the inherent error shown in FIG. 8(e) is reduced to a value within the range of ±3° (the "inherent linearity" means the linearity of the curve without "post-processing"). As described above, the inherent linearity may be improved using any of equations [15b], [16b], [21b], and [22b] with K3 and K4 different from 1.00.

[0147] However, naturally, the present invention is not limited to the sensor system having the specific dimensions shown in the examples of FIGS. 7(a) and 8(a), and functions for systems having, for example, the following combinations of parameters.

[0148] [Table 1]

[0149] Those skilled in the art having the benefits of the present disclosure can easily find the optimal values of K1, K2, and optionally K3 and K4 by, for example, performing simulations and / or calibration tests. The values of K1 to K4 can be stored in the non-volatile memory 931 of the sensor device (see, for example, FIG. 9).

[0150] FIG. 9 shows an electrical block diagram of a circuit 910 that can be used in the above-described position sensor device. The circuit 910 includes a plurality of magnetic sensor elements M1 to M8 (e.g., horizontal Hall elements, vertical Hall elements, MR elements, etc.), a processing unit 930 (including, for example, analog components and / or digital components), and a non-volatile memory 931 (e.g., EEPROM or flash). The biasing and reading of a circuit including a Hall sensor or an MR element are well known in the art and thus need not be described in further detail here.

[0151] This block diagram can be used, for example, in a sensor device having the sensor structure illustrated in FIG. 5 or FIG. 6 or a modification thereof.

[0152] The sensor device may be configured to measure magnetic field components Bx1 and Bz1 at a first sensor location, Bx2 and Bz2 at a second sensor location, By1 and Bz3 at a third sensor location, and By2 and Bz4 at a fourth sensor location. The first sensor location and the second sensor location are located on the X-axis, the third sensor location and the fourth sensor location are located on the Y-axis perpendicular to the X-axis. The sensor device is configured to determine an in-plane gradient dBx / dx and an out-of-plane gradient dBz / dx along the X direction, an in-plane gradient dBy / dy and an out-of-plane gradient dBz / dy along the Y direction, and two angular values α and β based on these magnetic field gradients.

[0153] The first angle α and the second angle β may be determined by the above-described method, for example, by using the above-described mathematical formulas [15a] and [15b], or [21a] and [21b], and / or optionally by using a look-up table with interpolation. Optionally, for example, piecewise linear correction is used for α, piecewise linear correction is used for β, and the correction steps are also applied. The piecewise linear correction of α may be independent of the piecewise linear correction of β.

[0154] The subtraction of signals for determining magnetic field components (e.g., h2 - h1 in FIG. 5) and / or for determining magnetic field gradients (e.g., Bx2 - Bx1 in FIG. 5, or v4 - v3 in FIG. 6) may be performed in the analog domain before or after amplification, or in the digital domain.

[0155] The processing unit 930 may optionally include a non-volatile memory 931 (e.g., NVRAM or EEPROM or flash) or be connected thereto, and may include a digital processor. This memory may be configured to store one or more constants, e.g., K1, K2, and also, when used, K3, K4, and optionally, when applied, the values or coefficients of the corrected steps. The digital processor 930 may be, for example, an 8-bit processor or a 16-bit processor.

[0156] Although not explicitly shown, the sensor device 910 may further include one or more components or sub-circuits selected from the group consisting of an amplifier, a differential amplifier, an analog-to-digital converter (ADC), a multiplexer, etc. The ADC may have a resolution of at least 8 bits, or at least 10 bits, or at least 12 bits, or at least 14 bits, or at least 16 bits.

[0157] It is a great advantage that the processing circuit does not need to perform a fast Fourier transform (FFT) or implement a neural network with hundreds of nodes.

[0158] FIG. 10 shows a flowchart of a method 1000 for determining the orientation (α, β) of a cylindrical magnet having an axis (A) with respect to a reference point "Pref" located on a semiconductor substrate. The method is based on at least two of the above magnetic field gradients. a) Determining 1001 the first magnetic field gradient dBx / dx of the first magnetic field component Bx oriented in the first direction X parallel to the semiconductor substrate along the first direction X. b) Determining 1002 the second magnetic field gradient dBy / dy of the second magnetic field component By oriented in the second direction Y parallel to the semiconductor substrate and perpendicular to the first direction X along the second direction Y. c) Determining 1003 the third magnetic field gradient dBz / dx of the third magnetic field component Bz oriented in the third direction Z perpendicular to the semiconductor substrate along the first direction X. d) determining a fourth magnetic field gradient dBz / dy of a third magnetic field component Bz oriented in a third direction Z along a second direction Y; 1004 e) determining a first angle α formed between a positive projection of an axis "A" of a magnet on a first virtual plane XZ parallel to a first direction X and the third direction Z based on at least two of the magnetic field gradients; 1005 f) determining a second angle β formed between a positive projection of the axis "A" of the magnet on a second virtual plane YZ parallel to the second direction Y and the third direction Z based on at least two of the magnetic field gradients; 1006 including.

[0159] Step e) may include determining the first angle α based only on a first magnetic field gradient dBx / dx and a third magnetic field gradient dBz / dx.

[0160] Step f) may include determining the second angle β based only on a second magnetic field gradient dBy / dy and a fourth magnetic field gradient dBz / dy.

[0161] Step e) may include determining the first angle α according to formula [15a] or [15b].

[0162] Step f) may include determining the second angle β according to formula [21a] or [21b].

[0163] The method may further include a correction step to improve accuracy, for example, to reduce or substantially eliminate the non-linear errors shown in FIGS. 7(e) and 8(e).

[0164] In a variation of this method, steps a) and b) (not explicitly shown) are omitted, step e) includes determining the first angle based on only one magnetic field gradient, i.e., dBz / dx, and step f) includes determining the second angle based on only one magnetic field gradient, i.e., dBz / dy.

[0165] In the above, a system is described in which the magnet is a cylindrical magnet pivotable about a reference point "Pref" located on the semiconductor surface. However, the present invention is not limited to this. The present invention also functions when the magnet is a two-pole magnet of another shape (e.g., spherical or rod-shaped), and / or when the reference point "Pref" is fixed to the semiconductor substrate but is located at a non-zero distance "dref" from the semiconductor substrate.

[0166] FIG. 11 shows a modified example of the sensor system of FIG. 1 in which a magnet 1101 is pivotable about a reference point "Pref" located at a predetermined non-zero distance "dref" above a semiconductor substrate (not explicitly shown but also defined by the XY plane). In this example, the reference point "Pref" is located on the positive Z-axis, which means that the magnet and the reference point are located on the same side of the substrate. However, the present invention is not limited to this, and the reference point may be located on the negative Z-axis, i.e., on the substrate on the opposite side of the magnet.

[0167] The reference point "Pref" of the systems shown in FIGS. 1 and 11 is located outside the space defined by the size of the cylindrical magnet and is located between the semiconductor substrate and the magnet when the magnet is in the neutral position (i.e., when α = 0°, β = 0°).

[0168] However, the present invention is not limited to this. The present invention also functions when a (real or imaginary) reference point "Pref" about which the axis of the magnet is pivotable is located within the space defined by the magnet or above the space defined by the magnet.

[0169] It has been found that in these cases, the same equations as above may be used to calculate α and β. Alternatively, the first angle α and the second angle β may be calculated as the "atan2" function (the arctangent function of two arguments), and each of the first argument and the second argument is a linear combination of two or more magnetic field gradients selected from the group consisting of dBx / dx, dBz / dx, dBy / dy, and dBz / dy.

[0170] Optionally, the sensor device may be further adapted to apply post-processing to these angles in a manner known in the art, for example, by applying a first piecewise linear correction for angle α using a first set of predefined coefficients and by applying a second piecewise linear correction for angle β using a second set of predefined coefficients. These coefficients may be determined during a calibration step and may be stored in the non-volatile memory of the sensor device.

Claims

1. A sensor device for determining the orientation of a magnet having an axis (A), a semiconductor substrate, i) a first magnetic field gradient (dBx / dx) of a first magnetic field component (Bx) oriented in the first direction (X) along a first direction (X) parallel to the semiconductor substrate, ii) a second magnetic field gradient (dBy / dy) of a second magnetic field component (By) oriented in the second direction (Y) along a second direction (Y) parallel to the semiconductor substrate and perpendicular to the first direction (X), iii) a third magnetic field gradient (dBz / dx) of a third magnetic field component (Bz) oriented in a third direction (Z) perpendicular to the semiconductor substrate along the first direction (X), and iv) a semiconductor substrate including a plurality of magnetic sensors configured to determine a fourth magnetic field gradient (dBz / dy) of the third magnetic field component (Bz) oriented in the third direction (Z) along the second direction (Y), a processing circuit (930) configured to determine an angle α or an angle ψ based on the first magnetic field gradient (dBx / dx) and the third magnetic field gradient (dBz / dx), wherein the angle α is an angle of a first orthogonal projection of the axis (A) of the magnet on a first virtual plane (XZ) parallel to the first direction (X) and the third direction (Z) with respect to the first direction (X), and the angle ψ is an angle of the first orthogonal projection of the axis (A) of the magnet on the first virtual plane (XZ) with respect to the third direction (Z), the processing circuit (930), the processing circuit (930) is for determining an angle β or an angle φ based on the second magnetic field gradient (dBy / dy) and the fourth magnetic field gradient (dBz / dy), wherein the angle β is an angle of a second orthogonal projection of the axis (A) of the magnet on a second virtual plane (YZ) parallel to the second direction (Y) and the third direction (Z) with respect to the second direction (Y), and the angle φ is an angle of the second orthogonal projection of the axis (A) of the magnet on the second virtual plane (YZ) with respect to the third direction (Z), a sensor device.

2. The plurality of magnetic sensors includes a first sensor (S1), a second sensor (S2), a third sensor (S3), and a fourth sensor (S4), the first sensor (S1) located at a first sensor location and the second sensor (S2) located at a second sensor location are located on a first imaginary line oriented in the first direction (X) and are spaced apart from each other by a first distance; the first sensor (S1) is configured to measure a first magnetic field component (Bx1) oriented in the first direction (X) and a second magnetic field component (Bz1) oriented in the third direction (Z); the second sensor (S2) is configured to measure a third magnetic field component (Bx2) oriented in the first direction (X) and a fourth magnetic field component (Bz2) oriented in the third direction (Z); the third sensor (S3) located at a third sensor location and the fourth sensor (S4) located at a fourth sensor location are located on a second imaginary line oriented in the second direction (Y) and are spaced apart from each other by a second distance; the third sensor (S3) is configured to measure a fifth magnetic field component (By1) oriented in the second direction (Y) and a sixth magnetic field component (Bz3) oriented in the third direction (Z); 2. The sensor device of claim 1, wherein the fourth sensor (S4) is configured to measure a seventh magnetic field component (By2) oriented in the second direction (Y) and an eighth magnetic field component (Bz4) oriented in the third direction (Z).

3. The angle α is expressed by the formula α=K1*atan2(dBz / dx, dBx / dx) is determined in accordance with where atan2() is the arctangent function of two arguments, dBx / dx is the first magnetic field gradient, dBz / dx is the third magnetic field gradient, and K1 is a first predetermined constant; The angle β is expressed by the formula: β=K2*atan2(dBz / dy, dBy / dy) is determined in accordance with 3. The sensor device of claim 1, wherein atan2( ) is the arctangent function of two arguments, dBy / dy is the second magnetic field gradient, dBz / dy is the fourth magnetic field gradient, and K2 is a second predetermined constant.

4. The angle α is determined by the formula: α=K1*atan2(K3*dBz / dx, dBx / dx) is determined in accordance with where atan2() is the arctangent function of two arguments, dBx / dx is the first magnetic field gradient, dBz / dx is the third magnetic field gradient, K1 and K3 are predetermined constants, The angle β is expressed by the formula: β = K2 * atan2(K4 * dBz / dy, dBy / dy) is determined according to where atan2() is the arc tangent function of two arguments, dBy / dy is the second magnetic field gradient, dBz / dy is the fourth magnetic field gradient, and K2 and K4 are predetermined constants, the sensor device according to claim 1 or 2. **Claim 5** The magnet is movable such that the axis (A) of the magnet is pivotable about a reference point having a predetermined position with respect to the semiconductor substrate. The sensor device according to claim 1. **Claim 6** The first distance (ΔX) between the first sensor location and the second sensor location is substantially equal to the second distance (ΔY) between the third sensor location and the fourth sensor location, or the first distance (ΔX) between the first sensor location and the second sensor location is at least 5% greater than or at least 5% less than the second distance (ΔY) between the third sensor location and the fourth sensor location. The sensor device according to claim 2. **Claim 7** Each of the four sensors (S1 to S4) includes integrated magnetic concentrators (IMC1 to IMC4) and two horizontal Hall elements (H1 to H8). The sensor device according to claim 2. **Claim 8** Each of the four sensors (S1 to S4) includes a horizontal Hall element and a vertical Hall element, or each of the four sensors (S1 to S4) includes a horizontal Hall element and at least one magnetoresistive sensor element. The sensor device according to claim 2. **Claim 9** The processing circuit is integrated with the semiconductor substrate. The sensor device according to claim 1. **Claim 10** A position sensor system (100; 700; 800; 1100) comprising a sensor device according to claim 1 or 2, comprising a semiconductor substrate, and a magnet pivotable about a reference point having a predetermined position with respect to the semiconductor substrate. **Claim 11** The system further comprises a joystick connected to the magnet, the position sensor system according to claim 10. **Claim 12** A method (1000) for determining the orientation of a magnet pivotable about a reference point having a predetermined position with respect to a semiconductor substrate, the method (1000) comprising The method (1000) is a) determining a first magnetic field gradient (dBx / dx) of a first magnetic field component (Bx) oriented in the first direction (X) along a first direction (X) parallel to the semiconductor substrate (1001); b) determining a second magnetic field gradient (dBy / dy) of a second magnetic field component (By) oriented in the second direction (Y) along a second direction (Y) parallel to the semiconductor substrate and perpendicular to the first direction (X) (1002); c) determining a third magnetic field gradient (dBz / dx) of a third magnetic field component (Bz) oriented in a third direction (Z) perpendicular to the semiconductor substrate along the first direction (X) (1003); d) determining a fourth magnetic field gradient (dBz / dy) of the third magnetic field component (Bz) oriented in the third direction (Z) along the second direction (Y) (1004); e) determining an angle α or an angle ψ based at least on the first magnetic field gradient (dBx / dx) and the third magnetic field gradient (dBz / dx) (1005), wherein the angle α is an angle of a first orthogonal projection of an axis (A) of a magnet on a first virtual plane (XZ) parallel to the first direction (X) and the third direction (Z) with respect to the first direction (X), and the angle ψ is an angle of the first orthogonal projection of the axis (A) of the magnet on the first virtual plane (XZ) with respect to the third direction (Z); f) determining an angle β or an angle φ based at least on the second magnetic field gradient (dBy / dy) and the fourth magnetic field gradient (dBz / dy) (1006), wherein the angle β is an angle of a second orthogonal projection of the axis (A) of the magnet on a second virtual plane (YZ) parallel to the second direction (Y) and the third direction (Z) with respect to the second direction (Y), and the angle φ is an angle of the second orthogonal projection of the axis (A) of the magnet on the second virtual plane (YZ) with respect to the third direction (Z), comprising a method (1000). **Claim 13** wherein the angle α is determined according to the formula: α = K1 * atan2(dBz / dx, dBx / dx) wherein atan2() is the arctangent function of two arguments, dBx / dx is the first magnetic field gradient, dBz / dx is the third magnetic field gradient, and K1 is a first predetermined constant; wherein the angle β is determined according to the formula: β = K2 * atan2(dBz / dy, dBy / dy) wherein atan2() is the arctangent function of two arguments, dBz / dy is the fourth magnetic field gradient, dBy / dy is the second magnetic field gradient, and K2 is a second predetermined constant; and is determined according to the following formula: where atan2() is the arc tangent function of two arguments, dB y / dy is the second magnetic field gradient, dB z / dy is the fourth magnetic field gradient, and K2 is a second predetermined constant. The method (1000) according to claim 12. **Claim 14** The angle α is given by the formula: α = K1 * atan2(K3 * dB z / dx, dB x / dx) and is determined according to: where atan2() is the arc tangent function of two arguments, dB x / dx is the first magnetic field gradient, dB z / dx is the third magnetic field gradient, and K1 and K3 are predetermined constants. The angle β is given by the formula: β = K2 * atan2(K4 * dB z / dy, dB y / dy) and is determined according to: where atan2() is the arc tangent function of two arguments, dB y / dy is the second magnetic field gradient, dB z / dy is the fourth magnetic field gradient, and K2 and K4 are predetermined constants. The method (1000) according to claim 12.

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