Magnetic sensor device, system and method and force sensor

Abstract

A magnetic sensor system comprising: an integrated circuit comprising a semiconductor substrate comprising a plurality of magnetic sensors configured for measuring at least two first magnetic field components (Bx1, Bx2) oriented in a first direction (X) and for measuring at least two second magnetic field components (Bx1, Bx2) oriented in a second direction (Y; at least two second magnetic field components (Bz1, Bz2) oriented to the first magnetic field component (Bz1, Bz2); a permanent magnet movable relative to the integrated circuit and configured to generate a magnetic field; a processing circuit configured for determining at least two physical quantities (Fx, Fy, Fz) related to the position of the magnet using a predefined algorithm based on the measured first and second magnetic field components (Bx1, Bx2; bz1, Bz2) or values derived therefrom are used as inputs, and a plurality of at least eight constants determined using machine learning are used. A force sensor system. A joystick or thumb joystick system. A method.

Description

[0001] This divisional patent application is a divisional application of the patent application with the application date of September 8, 2022, application number 202280061243.9, and title "Magnetic Sensor Devices, Systems and Methods and Force Sensors". Technical Field

[0002] The present invention generally relates to the field of magnetic sensor devices, systems and methods, and more particularly to magnetic sensor devices, systems and methods in which the position of a magnet relative to a semiconductor substrate indicates at least two physical quantities, such as force components, or the tilt angle of a joystick, or the lateral position of a thumb joystick, etc. Background Art

[0003] Magnetic sensors (e.g., current sensors, proximity sensors, position sensors, etc.) are known in the art. They are based on measuring the magnetic field characteristics at one or more sensor positions. Depending on the application, the measured magnetic field characteristic(s) can be used to infer another quantity (such as, for example, current intensity, the proximity of a so-called target, the relative position of the sensor device and the magnet, etc.).

[0004] There are many variants of magnetic sensor devices, systems and methods that address one or more of the following requirements: using simple or inexpensive magnetic structures, using simple or inexpensive sensor devices, being able to make measurements over a relatively large range, being able to make measurements with high accuracy, requiring only simple arithmetic, being able to make measurements at high speed, being highly robust to positioning errors, being highly robust to external interference fields, providing redundancy, being able to detect errors, being able to detect and correct errors, having a good signal-to-noise ratio (SNR), etc. Two or more of these requirements often conflict with each other, so trade-offs need to be made.

[0005] The present invention relates to a class of magnetic sensor systems that include a permanent magnet flexibly or elastically mounted relative to a semiconductor substrate, and in which the position of the magnet indicates a 2D or 3D physical quantity, such as a force vector or displacement vector caused by a force applied to a surface or by the movement of a joystick or thumb joystick, etc.

[0006] There is always room for improvement or alternatives. Summary of the Invention

[0007] An object of embodiments of the present invention is to provide a magnetic sensor system and method for determining at least two physical quantities related to the position of a permanent magnet that can move relative to a semiconductor circuit.

[0008] An object of embodiments of the present invention is to provide such a system and method that is insensitive to an external interference field, and / or insensitive to temperature changes, and / or insensitive to demagnetization of a magnet, and preferably two or all of these.

[0009] An object of embodiments of the present invention is to provide such a system and method that uses an algorithm that does not require explicit analysis or mathematical formulas or expressions.

[0010] An object of embodiments of the present invention is that a magnet is embedded in an elastomer above or on top of a semiconductor circuit.

[0011] An object of embodiments of the present invention is to provide such a magnetic sensor system that uses only 2D magnetic sensors, or only 3D magnetic sensors, or a combination of 2D magnetic sensors and 3D magnetic sensors.

[0012] An object of embodiments of the present invention is to provide such a magnetic sensor system and method that a magnetic field is measured at at least four sensor positions or at least five sensor positions.

[0013] An object of embodiments of the present invention is to provide such a magnetic sensor system and method that a magnet is an axially magnetized two-pole magnet.

[0014] An object of embodiments of the present invention is to provide such a magnetic sensor system and method that a physical quantity is calculated by an integrated circuit.

[0015] An object of embodiments of the present invention is to provide such a magnetic sensor system and method that a time required to determine the at least two physical quantities is at most 50 ms, or at most 40 ms, or at most 30 ms, or at most 20 ms, or at most 10 ms.

[0016] An object of embodiments of the present invention is also to provide a semiconductor device (i.e., a single chip) that includes at least a plurality of sensors for measuring a magnetic field, and optionally further includes a processing circuitry for determining the at least two physical quantities.

[0017] An object of embodiments of the present invention is also to provide a force sensor system.

[0018] An object of a specific embodiment of the present invention is to provide a force sensor system that can measure two or three force components (i.e., a 2D or 3D force vector) using such a magnetic sensor system.

[0019] An object of embodiments of the present invention is also to provide a robotic finger including at least one force sensor system, and a robotic arm including at least one robotic finger.

[0020] An object of embodiments of the present invention is also to provide a joystick system having two degrees of freedom (e.g., two tilting movements), or having three degrees of freedom (two tilting movements and a downward movement).

[0021] An object of embodiments of the present invention is also to provide a thumb joystick system having two degrees of freedom (e.g., two lateral movements), or having three degrees of freedom (two lateral movements and a downward movement).

[0022] These and other objects are achieved by embodiments of the present invention.

[0023] According to a first aspect, the present invention provides a magnetic sensor system, the magnetic sensor system comprising: an integrated circuit, the integrated circuit comprising a semiconductor substrate, the semiconductor substrate comprising a plurality of magnetic sensors configured to measure at least two (or at least three, or at least four) first magnetic field components (Bx1, Bx2) oriented in a first direction (X), and to measure at least two (or at least three, or at least four) second magnetic field components (Bz1, Bz2) oriented in a second direction (Y; Z) (e.g., perpendicular to the first direction (X)); a permanent magnet movable relative to the integrated circuit and configured to generate a magnetic field; a processing circuit (inside or outside the integrated circuit), the processing circuit being configured to use a predefined algorithm to determine at least two physical quantities (e.g., 2D or 3D force vectors, 2D or 3D displacement vectors, 2D or 3D position of a joystick, 2D or 3D position of a thumb joystick) related to the position of the magnet, the predefined algorithm taking as input the measured first and second magnetic field components (Bx1, Bx2; Bz1, Bz2) or values derived therefrom, and using a plurality of at least eight (or at least twelve, or at least eighteen) constants (or coefficients or parameters) determined by machine learning.

[0024] The "magnetic sensor system" can be, for example, a force sensor system, or a joystick, or a thumb joystick.

[0025] The inventors have found that even if the magnet moves in a highly non-linear manner, for example due to a specific mechanical mounting arrangement (e.g., using an elastomer with a non-linear stress-strain curve), it is not necessary to find an explicit analytical expression or mathematical model that expresses the relationship between the physical quantity and the movement of the magnet with the minimum number of variables.

[0026] It has been found that it is possible to very accurately determine the physical quantity by performing a predefined algorithm using a plurality of constants (or parameters) determined by machine learning (ML). It has been found that this method allows the required physical quantity to be determined or approximated in a manageable manner.

[0027] Those skilled in the art who benefit from the present disclosure can easily find a suitable algorithm that meets their needs by merely applying the teachings of the present invention.

[0028] Such magnetic sensor systems may be particularly suitable for applications where small errors in absolute accuracy do not adversely affect the applications in which the magnetic sensor systems are used.

[0029] In an embodiment, the processing circuit is configured to use a predefined algorithm to determine the at least two physical quantities, the predefined algorithm using at least three or at least four magnetic field differences derived from the at least two first magnetic field components and the at least two second magnetic field components as inputs, and using the plurality of at least eight (or at least twelve, or at least eighteen) constants.

[0030] As will be further explained, the magnetic field difference can be calculated as a magnetic field gradient, or can be calculated by subtracting the mean or average magnetic field components oriented in the same direction as the original magnetic field components.

[0031] In an embodiment, the integrated circuit includes a first programmable processor, which is part of the processing circuit and is configured to execute at least a part of the algorithm.

[0032] The processing circuit can be implemented on the same semiconductor die as a semiconductor die including a magnetic sensor, or can be implemented on a second semiconductor die connected to the first semiconductor die and also embedded in the same package as the first semiconductor die.

[0033] The integrated circuit can include analog processing circuitry, or can include digital processing circuitry using a programmable DSP (Digital Signal Processor) core with MAC (Multiply-Accumulate) instructions.

[0034] In this embodiment, the integrated circuit preferably includes an output configured to provide at least two or three physical values (e.g., force values, angle values, etc.).

[0035] In an embodiment, the magnetic sensor system further includes a second programmable processor, which is part of the processing circuit, communicatively connected to the integrated circuit but located outside of it; and the integrated circuit is configured to provide the at least three first and second magnetic field components (e.g., Bx1, Bx2, Bx3; Bz1, Bz2, Bz3) or values derived therefrom to the second programmable processor.

[0036] In an embodiment, the integrated circuit includes a plastic molded package, and an elastomer is disposed on top of the molded package and in direct contact with the molded package. In some embodiments, the elastomer does not laterally extend beyond the package (i.e., is only supported by the package). In other embodiments, the elastomer may laterally extend beyond the package and may contact, for example, a printed circuit board on which the device of the package is mounted and / or soldered.

[0037] In an embodiment, the number of constants (also referred to as "coefficients") is a value in the range from 12 to 100, or in the range from 12 to 80, or in the range from 18 to 64, or in the range from 25 to 45.

[0038] Empirically, the greater the number of coefficients, the higher the accuracy for a given measurement range, but the larger the circuit system (if implemented in hardware) or the greater the number of calculations (if implemented in software). However, the inventors have found that not only does the number of constants affect the computational workload and accuracy, but also the type of functions used in the algorithm affects the computational workload and accuracy.

[0039] In an embodiment, the semiconductor substrate further includes a temperature sensor for measuring the temperature of the semiconductor substrate, and the semiconductor substrate is configured to correct the measured first magnetic field component and second magnetic field component based on the measured temperature.

[0040] In an embodiment, the semiconductor substrate further includes a temperature sensor for measuring the temperature of the semiconductor substrate, and a predefined algorithm takes the measured temperature as an additional input.

[0041] In an embodiment, the semiconductor substrate further includes a temperature sensor for measuring the temperature of the semiconductor substrate, and the measured temperature is used in a post-processing step.

[0042] For example, in some embodiments, the measured temperature is used to correct the sensitivity of the sensor element. In some embodiments, the temperature is considered as an additional input (e.g., to a neural network). In some embodiments, for example, in the case of using an elastomer, the measured temperature may be used in a post-processing step, for example, to compensate for temperature-dependent material properties (e.g., lower or higher stiffness).

[0043] In an embodiment, a plurality of sensors are configured to measure magnetic field components (e.g., the first magnetic field component and the second magnetic field component described above) in only two orthogonal directions (e.g., the first direction and the second direction).

[0044] In an embodiment, each of the first direction (e.g., X) and the second direction (e.g., Y) is parallel to the semiconductor substrate.

[0045] In this embodiment, the sensor is configured to measure (or only measure) the so-called "in-plane" magnetic field components (e.g., Bx and By). This can be achieved using a vertical Hall element, an MR element, a horizontal Hall element + IMC, or a combination thereof.

[0046] In an embodiment, a first direction (e.g., X) is parallel to the semiconductor substrate, and a second direction (e.g., Z) is perpendicular to the semiconductor substrate.

[0047] In this embodiment, the sensor is configured to measure (or only measure) the so-called "in-plane" magnetic field components (e.g., Bx or By) and the so-called "out-of-plane" magnetic field component (e.g., Bz). This can be achieved using a combination of a horizontal Hall element and a vertical Hall element, or using a combination of an MR element and a horizontal Hall element, or using a horizontal Hall element and an Integrated Magnetic Flux Concentrator (IMC).

[0048] In an embodiment, the plurality of magnetic sensors are further configured to measure at least three third magnetic field components oriented in a third direction perpendicular to the first direction and perpendicular to the second direction.

[0049] In this embodiment, the sensor is configured to measure two "in-plane" magnetic field components (e.g., Bx and By) and one "out-of-plane" magnetic field component (e.g., Bz). This can be achieved using a combination of a horizontal Hall element and a vertical Hall element, or using a combination of an MR element and a horizontal Hall element, or using a horizontal Hall element and an IMC.

[0050] In an embodiment, the plurality of sensors includes at least one sensor (preferably, at least two, or at least three, or at least four sensors), the at least one sensor including an integrated magnetic concentrator disk, and three pairs of horizontal Hall elements disposed near the periphery of the disk, the Hall elements being angularly spaced by a multiple of 120°.

[0051] In an embodiment, the plurality of sensors includes at least one sensor (preferably, at least two, or at least three, or at least four sensors), the at least one sensor including an integrated magnetic concentrator disk, and four pairs of horizontal Hall elements disposed near the periphery of the disk, the Hall elements being angularly spaced by a multiple of 45°. Figure 20 and Figure 21 Examples of such sensors are illustrated in

[0052] In an embodiment, the semiconductor substrate includes a plurality of magnetic sensors located at the intersections of a 2×2 grid (i.e., at the corners of a hypothetical square), or at the intersections of a 3×3 grid, or at the intersections of a 4×4 grid. Preferably, the columns and rows of the grid are equally spaced.

[0053] In an embodiment, the semiconductor substrate includes a plurality of magnetic sensors arranged in an irregular pattern (e.g., at pseudo-random positions).

[0054] In an embodiment, at least three of the magnetic sensors are located on a virtual circle.

[0055] The virtual circle can have a diameter in the range from 1.0 mm to 3.0 mm, or in the range from 1.5 mm to 2.5 mm, or in the range from 1.7 mm to 2.3 mm, for example, a diameter equal to approximately 1.8 mm, or equal to approximately 2.0 mm, or equal to approximately 2.2 mm.

[0056] In an embodiment, the semiconductor substrate includes three magnetic sensors located on the virtual circle and angularly spaced by multiples of 120°.

[0057] In an embodiment, the semiconductor substrate includes four magnetic sensors located on the virtual circle and angularly spaced by multiples of 90°.

[0058] In an embodiment, the semiconductor substrate includes five magnetic sensors located on the virtual circle and angularly spaced by multiples of 72°.

[0059] In an embodiment, the semiconductor substrate includes six magnetic sensors located on the virtual circle and angularly spaced by multiples of 60°.

[0060] In an embodiment, the semiconductor substrate further includes one magnetic sensor located at the center of the virtual circle.

[0061] In an embodiment, the magnet is a two-pole magnet (e.g., a two-pole bar magnet, or an annular or disk-shaped magnet magnetized in the diameter direction). The magnetization direction of the magnet can be oriented substantially perpendicular to the semiconductor substrate, or substantially parallel to the semiconductor substrate.

[0062] In an embodiment, the magnet is an axially magnetized magnet (e.g., an axially magnetized annular or disk-shaped magnet). The magnetization direction of the magnet can be oriented substantially perpendicular to the semiconductor substrate, or substantially parallel to the semiconductor substrate.

[0063] In an embodiment, the sensor system includes only one magnet.

[0064] In an embodiment, the sensor system includes three magnets arranged on a virtual circle above the semiconductor substrate and angularly spaced by 120°.

[0065] In an embodiment, the sensor system includes four magnets that are arranged on a virtual circle above a semiconductor substrate and are angularly spaced by 90°.

[0066] In an embodiment, the sensor system includes six magnets that are arranged on a virtual circle above a semiconductor substrate and are angularly spaced by 60°.

[0067] In an embodiment, the (one or more) magnets are (one or more) two-pole disk-shaped magnets, and the outer diameter or the maximum diagonal of each magnet is less than the diameter of the virtual circle on which at least three of the magnetic sensors in the magnetic sensor are located.

[0068] In an embodiment, the (one or more) magnets are (one or more) two-pole disk-shaped magnets: the outer diameter or the maximum diagonal of each magnet is substantially equal to the diameter of the virtual circle on which at least three of the magnetic sensors in the magnetic sensor are located (within ±20% of the diameter of the virtual circle).

[0069] In an embodiment, the (one or more) magnets are (one or more) two-pole disk-shaped magnets: the outer diameter or the maximum diagonal of each magnet is greater than the diameter of the virtual circle on which at least three of the magnetic sensors in the magnetic sensor are located.

[0070] In an embodiment, the magnet has a central axis that intersects the semiconductor substrate at the central position of the magnetic sensor (“on-axis arrangement”).

[0071] In an embodiment, the magnet has a central axis that intersects the semiconductor substrate at a position offset from the central position of the magnetic sensor (“off-axis arrangement”). In the case where the sensors are arranged on an N×N grid, the offset can be half of the distance between two adjacent grid lines.

[0072] In an embodiment, the magnet is an axially magnetized two-pole ring-shaped or disk-shaped magnet.

[0073] The advantage of using such magnets is that the magnetic field generated by such magnets is rotationally invariant, which means that the magnetic field is independent of the rotation of the magnet about its axis. Therefore, the magnetic sensor system is insensitive to torque about an axis perpendicular to the semiconductor substrate.

[0074] In an embodiment, the predefined algorithm is configured to derive at least two (or at least three, or at least four) first differences from the at least two (or at least three, or at least four) first magnetic field components, and to derive at least two (or at least three, or at least four) second differences from the at least two (or at least three, or at least four) second magnetic field components; and to calculate the at least two (or three, or four) physical values (e.g., force components, angles or displacements) based on the at least two (or at least three, or four) first differences and the at least two (or at least three, or four) second differences.

[0075] It is explicitly stated that this part of the algorithm can be implemented within the integrated circuit containing the magnetic sensor, or outside the integrated circuit containing the magnetic sensor (e.g., in an electronic control unit connected to the sensor device), or partially within the sensor device (e.g., for some of the differences) and partially outside the sensor device (e.g., for some other differences).

[0076] The main advantage of using differences is that the result is highly insensitive to external interference fields. To the inventors' knowledge, there is no force sensor resistant to stray fields in the prior art.

[0077] In an embodiment, the predefined algorithm further takes into account at least one first magnetic field component, or at least one second magnetic field component. Although this embodiment is not 100% immune to stray fields in theory, it may still have a relatively large stray field suppression.

[0078] In an embodiment, each of the at least three first differences is determined as a pairwise difference between two first magnetic field components, and wherein each of the at least three second differences is determined as a pairwise difference between two second magnetic field components; or

[0079] This can be referred to as a "magnetic field gradient" and can be written in mathematical terms, for example, as: dx1 = Bx1 - Bx2; dx2 = Bx1 - Bx3, dx3 = Bx2 - Bx3, and dz1 = Bz1 - Bz2; dz2 = Bz1 - Bz3, dz3 = Bz2 - Bz3.

[0080] In an embodiment, each of the at least three first differences is determined as the difference between a first magnetic field component and a first common value, and wherein each of the at least three second differences is determined as the difference between a second magnetic field component and a second common value.

[0081] The first common value can be the first magnetic field component measured at the fourth sensor position (preferably, the central sensor position), or can be the average of at least three first magnetic field components. This can be referred to as "mean removal" and can be written in mathematical terms, for example, as follows (assuming the semiconductor substrate has only three 2D sensors, each measuring Bx and Bz): Bx_avg = (Bx1 + Bx2 + Bx3), Bz_avg = (Bz1 + Bz2 + Bz3); dx1 = Bx1 - Bx_avg, dx2 = Bx2 - Bx_avg, dx3 = Bx3 - Bx_avg, dz1 = Bz1 - Bz_avg, dz2 = Bz2 - Bz_avg, dz3 = Bz3 - Bz_avg.

[0082] In an embodiment, the predefined algorithm is configured to calculate each of the physical values as a sum of at least twelve terms, where each of the at least twelve terms is a function of one or more of the differences.

[0083] In an embodiment, each of these sums includes a constant value determined by machine learning.

[0084] Machine learning is typically applied on a batch basis rather than on an individual product basis.

[0085] In an embodiment, the predefined algorithm is configured to calculate each of the physical values as a sum of at least twelve terms; at least two terms contain a linear expression of only one of the differences; and at least two terms contain a non - linear expression of one or more of the differences.

[0086] Thus, at least two of these terms are scaled versions of only one of the differences, for example: (K1*dx1) or (K2*dx1 + K3), where the constants K1, K2, K3 are determined by machine learning.

[0087] In an embodiment, each of these terms is a constant or an algebraic function of one or more of the differences.

[0088] "Algebraic function" is a class of functions that includes: "polynomial functions" (e.g., constant, linear, quadratic, cubic power functions) and "rational functions" (i.e., the ratio of two polynomial functions). Algebraic functions also include "piece - wise functions" such as the absolute value function, the floor function, the ceiling function, and the sign function. Algebraic functions do not include the so - called "transcendental functions", which are a group of functions where the independent variable appears as an exponent, a radical index, a logarithm, or a trigonometric ratio.

[0089] In other words, in this embodiment, none of the terms is or includes an exponential function, a logarithmic function, a trigonometric function (e.g., sine, cosine, tangent, cosecant, secant, cotangent), or an inverse trigonometric function (e.g., arctangent).

[0090] The fact that only algebraic functions are used and transcendental functions are excluded is an advantage because algebraic functions are cheaper in terms of processing power or processing time and can be implemented in an embedded processor.

[0091] In an embodiment, at least two terms or each sum is or includes a quadratic expression or a second-order polynomial of only one of the differences in the said differences.

[0092] For example: K1*sqr(dx1), or K2*sqr(dx1 - K3), or K4+(K5*dx1)+K6*(dx1)2, where K1 to K6 are constants.

[0093] In an embodiment, some of the terms are third-order or fourth-order polynomial expressions.

[0094] In a preferred embodiment, none of the terms is a polynomial expression of higher than four. Using a polynomial order of at most four, or at most three, or at most two is advantageous because it requires less processing time and less processing power.

[0095] In an embodiment, each sum includes at least one term that is a product of two differences (e.g., K7*dx1*dz1).

[0096] It has been found that using the product of difference signals does contribute to improving the accuracy of the results. Although the inventors do not wish to be bound by any theory, it seems that certain products of differences have a good correlation with the physical movement of the magnet, although this correlation is not immediately obvious to a human observer.

[0097] In an embodiment, each sum includes at least one term that is a division of two differences (e.g., K8*dx1 / dz1).

[0098] Using the ratio of two magnetic field values (e.g., differences) is advantageous because such ratios are highly robust with respect to temperature variations and demagnetization effects.

[0099] In an embodiment, a predefined algorithm is performed by a trained neural network using at least three first magnetic field components (e.g., Bx1, Bx2, Bx3) and at least three second magnetic field components (e.g., Bz1, Bz2, Bz3) as input signals and providing at least two (or at least three) physical values as output values.

[0100] The predefined algorithm may include a neural network having multiple layers, where each layer includes multiple nodes.

[0101] In an embodiment, the neural network comprises only one layer, and this layer has 12 to 100 nodes.

[0102] In an embodiment, the neural network comprises only two layers, and each layer has 10 to 100 nodes, or has 20 to 60 nodes.

[0103] In an embodiment, the neural network comprises only three layers, and each layer has 10 to 100 nodes, or each layer has 5 to 50 nodes.

[0104] In an embodiment, the neural network is a Recurrent Neural Network (RNN).

[0105] In an embodiment, the neural network is an Artificial Neural Network (ANN).

[0106] In an embodiment, the neural network is a Convolutional Neural Network (CNN).

[0107] In an embodiment, the predefined algorithm further includes a post-processing step; and the post-processing step is configured to adjust the determined physical quantity (e.g., determined using the above proprietary algorithm, or determined using a neural network) by adding or subtracting an offset value determined by a separate calibration test.

[0108] "Separate calibration test" means that this test is performed separately for each magnetic sensor system, which is contrary to machine learning, where machine learning is not performed on an individual basis but is typically performed on a batch-by-batch basis.

[0109] This "separate calibration test" is preferably performed as an EOL test (End-of-Line test), or it can be performed by the OEM customer.

[0110] In the case of a force sensor system or a force sensor device or a joystick, etc., this calibration test may include: (i) performing a force measurement using the predefined algorithm while applying zero force by using a plurality of constants or parameters determined by machine learning (which are typically determined on a batch basis), thereby generating two or three force values or position values that are usually slightly deviated from zero; and (ii) storing these values in the non-volatile memory of the system (e.g., the non-volatile memory of an integrated circuit).

[0111] During the normal use of the sensor device, first the predefined algorithm is used to provide two or more measurement values based on the parameters determined by machine learning, and then a correction is applied by subtracting the values measured during the calibration step explained above.

[0112] The main advantage of this embodiment is that it combines the advantages of two aspects, namely: a very good approximation of a physical value that is to be measured using a predefined algorithm that utilizes multiple constants determined on a batch basis by machine learning, but is subsequently corrected, such that an offset correction of the "zero force" or "neutral position" of a joystick or the like is performed for each individual product.

[0113] In an embodiment, the magnet is flexibly mounted relative to the integrated circuit by means of a flexible material.

[0114] The flexible material can be a single layer composed of an isotropic material without any voids or hollow regions. The shape and size of this material and the magnet can be designed such that the magnet can move in three directions X, Y, Z, but will not rotate significantly about its center (e.g., will rotate less than ±10°, or less than ±5° within the measurement range of the force sensor system).

[0115] In an embodiment, the flexible material is a polymer.

[0116] In an embodiment, the flexible material is an elastomer.

[0117] The elastomer can be disposed above or on top of the integrated circuit. In a preferred embodiment, the elastomer can directly contact the package of the integrated circuit.

[0118] In an embodiment, the elastomer is or comprises silicone (e.g., silicone rubber (e.g., natural rubber)).

[0119] In an embodiment, the flexible material has a non-linear stress-strain characteristic; and the linear regression coefficient of the portion of the non-linear stress-strain characteristic corresponding to the measurement range of the magnetic sensor system is less than 0.90, or less than 0.85, or less than 0.80, or less than 0.75, or less than 0.70.

[0120] In other words, in these embodiments, the curve showing strain as a function of the stress of the material is a highly non-linear function.

[0121] In an embodiment, the predefined algorithm further includes a post-processing step in which the temperature of the flexible material is measured or estimated, and wherein the determined physical quantity is corrected to reduce temperature-dependent material properties.

[0122] The correction can use a predefined correction function separately for each determined physical quantity.

[0123] The compensation function can be, for example, temperature-dependent scaling. The function f(.) can be stored in the form of a look-up table, or as a piecewise linear approximation, or as an analytical function (e.g., as a polynomial expression).

[0124] A temperature sensor can be integrated inside an integrated circuit, and the temperature of the temperature sensor can be used as an estimate of the elastomer.

[0125] In an embodiment, the predefined algorithm further includes a post-processing step, or if it already exists, the post-processing step further includes: for each output value, performing an offset correction by subtracting a predefined value stored in the non-volatile memory during the calibration process.

[0126] The present invention also provides a force sensor system, including a magnetic sensor system according to the first aspect, wherein at least two or three physical quantities to be determined are two or three force components (Fx, Fy, Fz) of a mechanical force applied to a contact surface of the flexible material.

[0127] The magnetic sensor system can be referred to as a "force sensor system", and the integrated circuit can be referred to as a "force sensor device".

[0128] The force components Fx and Fy are generally referred to as shear forces or lateral forces. The force component Fz is generally referred to as a downward pressure.

[0129] In an embodiment, the flexible material is located above or on top of the integrated circuit (e.g., as a layer deposited on the package), and the magnet is at least partially or completely embedded inside the flexible material.

[0130] A plurality of constants (or parameters or coefficients) can be determined by applying a series of tests, where a plurality of known forces having only the Fx component are applied, followed by another series of tests where a plurality of known forces having only the Fy component are applied, and then another series of tests where a plurality of known forces having only the Fz component are applied. In each series of tests, the respective component values are assumed to be values within their respective predefined measurement ranges.

[0131] Alternatively, a plurality of constants (or parameters or coefficients) can be determined by applying a series of tests in which three-dimensional forces are applied, the three-dimensional forces having Fx, Fy, and Fz components within their respective measurement ranges.

[0132] In an embodiment, a plurality of constants are determined by applying a series of known forces, where each of the Fx, Fy, and Fz values "sweeps" through their respective measurement ranges, for example, each in 5 steps, i.e., 5 * 5 * 5 = 125 different combinations; or each in 6 steps, i.e., 6 * 6 * 6 = 216 different combinations; or each in 7 steps, i.e., 343 combinations; or each in 8 steps, i.e., 512 combinations; or each in 9 steps, i.e., 729 combinations; or each in 10 steps, i.e., 1000 different combinations.

[0133] In an embodiment, no external interference field is applied during these steps. Needless to say, this is a great advantage, and by design (by considering gradient or mean correction values), the influence of the external interference field is substantially eliminated.

[0134] In another embodiment, an external interference field is applied during these steps. The external interference field can assume pseudo-random values for each step.

[0135] The present invention also provides a robotic finger including at least one force sensor system.

[0136] The present invention also provides a robotic hand including at least two robotic fingers.

[0137] The present invention also provides a joystick system or joystick assembly for determining the 2D or 3D position of a joystick, the joystick system or joystick assembly including: a magnetic sensor system according to the first aspect; and a joystick movable relative to the integrated circuit with at least two degrees of freedom; wherein, a magnet is fixedly connected to the joystick.

[0138] The joystick system can determine, for example, two angular values for indicating the position of the joystick, for example, as Figure 31 illustrated. The joystick can be rotatable about a pivot point. The pivot point can be located above the magnet. In other words, the magnet can be located between the pivot point and the semiconductor substrate.

[0139] The joystick can be used in consumer electronic applications (for example, for gaming) or for agricultural vehicles.

[0140] Exemplary embodiments of the joystick include bearings by means of which the control rod is mounted to move relative to the housing with at least two degrees of freedom. The control rod has a portion movable by the user and an internal portion, which are opposite to each other on different sides of the bearing in the longitudinal direction. The magnet is arranged on the control rod. A semiconductor substrate having a plurality of magnetic sensors is arranged at a fixed position relative to the housing.

[0141] The present invention also provides a thumb joystick system or thumb joystick assembly for determining the 2D or 3D position of a thumb joystick, the thumb joystick system or thumb joystick assembly including: a magnetic sensor system according to the first aspect; and a thumb joystick movable relative to the integrated circuit with at least two or three degrees of freedom; wherein, a magnet is fixedly connected to the thumb joystick.

[0142] The thumb joystick system can determine, for example, two lateral displacement values for indicating the position of the joystick, and optionally also gives an indication of whether the drumstick is pressed (or pushed down).

[0143] According to another aspect, the present invention also provides a method for measuring at least two physical quantities related to the position of a permanent magnet (e.g., 2D or 3D force vector, 2D or 3D displacement vector, 2D or 3D position of a joystick, 2D or 3D position of a thumb joystick), the permanent magnet being movable relative to an integrated circuit and configured to generate a magnetic field, the method comprising the steps of: a) measuring at least two (or at least three) first magnetic field components (e.g., Bx1, Bx2; Bx1, Bx2, Bx3) oriented in a first direction (e.g., X); b) measuring at least two (or at least three) second magnetic field components (e.g., Bz1, Bz2; Bz1, Bz2, Bz3) oriented in a second direction (e.g., Y or Z) perpendicular to the first direction (e.g., X); c) using a predefined algorithm to determine the at least two physical quantities, the predefined algorithm using the measured first magnetic field components and second magnetic field components (e.g., Bx1, Bx2, Bx3; Bz1, Bz2, Bz3) as inputs and using a plurality of at least eight (or at least twelve, or at least sixteen) constants (or coefficients or parameters) determined using machine learning.

[0144] In an embodiment, the method has one or more of the above features.

[0145] According to another aspect, the present invention also provides an integrated semiconductor device, comprising: a plurality of sensors having a topology as illustrated in any of Figures 3(a) to 21 or a variant thereof as described in the detailed description, and having a block 2222 (sensitivity correction); and one or both of the blocks 2224 (mean removal) and 2232 (gradient calculation) illustrated in FIGS. 22(a) and 22(b), and configured to output values provided by block 2223 or 2232 via an output interface (e.g., using a serial bus such as the I2C or SPI or SENT protocol).

[0146] According to another aspect, the present invention also provides a force sensor device or system, comprising: an integrated circuit including a semiconductor substrate having a plurality of magnetic sensors configured to measure at least two (or at least three, or at least four) first magnetic field components (e.g., Bx1, Bx2) oriented in a first direction (e.g., X), and to measure at least two (or at least three, or at least four) second magnetic field components (e.g., Bz1, Bz2) oriented in a second direction (e.g., Y or Z) perpendicular to the first direction (e.g., X); a permanent magnet movable relative to the integrated circuit and configured to generate a magnetic field; and a processing circuit (inside or outside the integrated circuit) configured to determine at least two magnetic field gradients (e.g., dBx / dx, dBz / dx) derived from the magnetic field components, and to determine one or two or three force components (e.g., Fx, Fy, Fz) based on the at least two magnetic field gradients.

[0147] According to another aspect, the present invention also provides a force sensor device, comprising: an integrated circuit including a semiconductor substrate having a plurality of magnetic sensors configured to measure at least three or at least four magnetic field components oriented in a first direction, or configured to measure at least first and second magnetic field components oriented in a first direction and to measure at least third and fourth magnetic field components oriented in a second direction; a permanent magnet flexibly mounted to the integrated circuit by means of a flexible material, the permanent magnet generating a magnetic field; and a processing circuit configured to determine at least one physical quantity or at least two physical quantities related to the position of the magnet relative to the sensor device, or related to a force or pressure applied to the flexible material, based on at least two or at least three paired differences of the magnetic field components.

[0148] In an embodiment, the processing circuit is implemented on the same semiconductor substrate as the magnetic sensors. In another embodiment, the processing circuit is implemented on a first semiconductor substrate (e.g., a CMOS substrate), and the magnetic sensors are implemented on one or more sensor substrates (e.g., CMOS, Ga-As, Ga-In, or In-Sb) mounted beside or on top of or beneath the first semiconductor substrate.

[0149] In an embodiment, the second direction is the same as the first direction. In another embodiment, the second direction is different from the first direction (e.g., the second direction is orthogonal to the first direction).

[0150] The force sensor device may be configured to determine the physical quantity using one or more predefined functions. The function or functions may be stored, for example, in the non-volatile memory of the processing circuit in the form of a mathematical formula (e.g., as a polynomial expression having a plurality of coefficients (e.g., having 3 to 30 coefficients (e.g., having at least 3 or at least 4 or at least 6 or at least 8 or at least 12 coefficients))); or in the form of a sum having 3 to 15 terms (e.g., having at least 3 terms, or at least 4 terms, or at least 6 terms, or at least 8 terms, or at least 10 terms, or at least 12 terms) in the non-volatile memory of the processing circuit; or in the form of a look-up table in the non-volatile memory of the processing circuit. Some terms may be the square of the magnetic field difference, or may be the cross product of two magnetic field differences obtained from sensor pairs spaced apart in the same direction, or may be the cross product of two magnetic field differences obtained from sensor pairs spaced apart in different directions.

[0151] The coefficients or parameters may be determined using machine learning. Alternatively, the coefficients or parameters may be determined using classical techniques such as, for example, using curve fitting techniques, linear regression or non-linear regression techniques, or linear or non-linear models.

[0152] The force sensor device may have three 1D pixels, or four 1D pixels, or three 2D pixels, or four 2D pixels, or five 2D pixels, or six 2D pixels, or seven 2D pixels, or eight 2D pixels, or nine 2D pixels, or four 2D pixels and one 3D pixel, or four 3D pixels, or five 3D pixels, or nine 3D pixels.

[0153] In an embodiment, at least two pairwise differences are determined, or at least three pairwise differences are determined, or at least four pairwise differences are determined, or at least six pairwise differences are determined, or at least eight pairwise differences are determined, and the (one or more) output values are determined based on these pairwise differences.

[0154] Specific and preferred aspects of the invention are set out in the appended independent and dependent claims. Features from the dependent claims may be combined appropriately with the features of the independent claims and with the features of other dependent claims, not only as explicitly set out in the claims.

[0155] These and other aspects of the invention will be apparent with reference to the (one or more) embodiments described hereinafter, and these and other aspects of the invention are elucidated with reference to the (one or more) embodiments described hereinafter. Description of the Drawings

[0156] Figure 1 is a schematic block diagram of a sensor circuit known in the art.

[0157] Figure 2 It is a schematic block diagram of a sensor circuit known in the art.

[0158] Figure 3(a) is a schematic representation of an illustrative example of a magnetic sensor system including a permanent magnet movable relative to a semiconductor substrate.

[0159] Figure 3(b) is a schematic representation of another illustrative example of a magnetic sensor system including a permanent magnet movable relative to two semiconductor substrates arranged side by side.

[0160] Figures 4 to 21 It is a schematic block diagram of a sensor circuit that can be used in embodiments of the present invention.

[0161] Figure 22(a) shows a schematic block diagram of a magnetic sensor system proposed by the present invention.

[0162] Figure 22(b) shows a schematic block diagram of another magnetic sensor system proposed by the present invention.

[0163] Figures 23(a) to 23(e) It shows an example of a mechanical arrangement or sensor assembly that can be used in embodiments of the present invention.

[0164] Figures 24(a) and 24(b) show pictures of a force sensor system prototype.

[0165] Figure 24(c) shows a picture of a mechanical setup for applying a known force.

[0166] Figures 25(a) and 25(b) show the results of measured values of Bx and Bz when a force Fz oriented in a direction perpendicular to the semiconductor substrate is applied.

[0167] Figure 26 It shows a computer model of a mechanical arrangement that can be used to simulate embodiments of the present invention including an elastomer.

[0168] Figures 27(a) and 27(b) show the correspondence between the force measured by a calibration setup and the force predicted by a force sensor algorithm.

[0169] Figures 27(c) and 27(d) show a "force error histogram".

[0170] Figure 28 It is a graph showing the error of the measured shear force Fx according to an external interference field applied in the X direction, with and without a mean removal block.

[0171] Figure 29 It shows a graph showing the magnitude of the force Fz oriented in a direction towards the semiconductor substrate relative to the displacement of the magnet.

[0172] Figure 30 is a schematic block diagram of a sensor device 3010 that can be used in embodiments of the present invention.

[0173] Figure 31 The principle used to illustrate the present invention can also be used to determine the tilt angles θ and ψ of the joystick assembly.

[0174] Figure 32 shows a flowchart of a method 3200 for measuring at least two physical quantities related to the position of a permanent magnet proposed by the present invention.

[0175] These drawings are merely schematic and not restrictive. In the drawings, for illustrative purposes, the sizes of some of the elements may be enlarged and not drawn to scale. Any reference numerals in the claims should not be construed as limiting the scope. In different drawings, the same reference numerals refer to the same or similar elements. Detailed Description of the Invention

[0176] The present invention will be described with reference to specific embodiments and specific drawings, but the present invention is not limited thereto and is only defined by the claims.

[0177] The terms first, second, etc. in the specification and claims are used to distinguish between similar elements and are not necessarily used to describe an order in terms of time, space, rank, or in any other way. It should be understood that such terms are interchangeable under appropriate circumstances, and the embodiments of the present invention described herein can operate in an order different from the order described or illustrated herein.

[0178] The terms top, bottom, etc. in the specification and claims are used for descriptive purposes and are not necessarily used to describe a relative position. It should be understood that such terms are interchangeable under appropriate circumstances, and the embodiments of the present invention described herein can operate in an orientation different from the orientation described or illustrated herein.

[0179] It should be noted that the term "comprising" used in the claims should not be construed as being limited to the means listed thereafter; it does not exclude other elements or steps. Thus, this term should be interpreted as specifying the presence of the stated features, integers, steps, or components as mentioned, 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. It means that for the present invention, the only relevant components of the device are A and B.

[0180] References to "one embodiment" or "an embodiment" in the present specification mean that the specific features, structures, or characteristics described in connection with the embodiment are included in at least one embodiment of the present invention. Thus, the appearances of the phrases "in one embodiment" or "in an embodiment" throughout the present specification do not necessarily all refer to the same embodiment, but may. Additionally, in one or more embodiments, as will be apparent to those of ordinary skill in the art from the present disclosure, the specific features, structures, or characteristics may be combined in any suitable manner.

[0181] Similarly, it should be appreciated that in the description of the exemplary embodiments of the present invention, for the purpose of streamlining the present disclosure and facilitating the understanding of one or more of the inventive aspects, the various features of the present invention are sometimes grouped together in a single embodiment, drawing, or description thereof. However, such a 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 reflected in the appended claims, the inventive aspects lie in less than all of the features of a single foregoing disclosed embodiment. Thus, the appended claims of the detailed description are hereby expressly incorporated into the detailed description, where each claim itself represents a separate embodiment of the present invention.

[0182] Furthermore, although some of the embodiments described herein include some features included in other embodiments but not other features included in those other embodiments, it will be understood by those skilled in the art that combinations of features of different embodiments are intended to fall within the scope of the present invention and form different embodiments. For example, in the appended claims, any of the claimed embodiments may be used in any combination.

[0183] In the specification provided herein, numerous specific details are set forth. However, it should be understood that embodiments of the present 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 the present specification.

[0184] In this document, unless otherwise expressly stated, the term "magnetic sensor device" or "sensor device" refers to a device including at least two magnetic sensor elements, which device is preferably integrated in a semiconductor substrate. The sensor device may be included in a package (also referred to as a "chip"), but that is not absolutely necessary.

[0185] In this document, the term "sensor element" or "magnetic sensor element" refers to a single vertical Hall element or a single horizontal Hall element or a single magnetoresistive element (e.g., a GMR element or an XMR element).

[0186] In this document, the terms "magnetic sensor" or "magnetic sensor structure" may refer to a set of components or sub - circuits or structures capable of measuring a magnetic quantity, such as, for example, a set of at least two magnetic sensor elements, or a Wheatstone bridge containing four MR elements.

[0187] In certain embodiments of the present invention, the terms "magnetic sensor" or "magnetic sensor structure" may refer to an arrangement including one or more integrated magnetic concentrators (IMCs) (also known as integrated flux concentrators), and two or four or eight horizontal Hall elements arranged near the periphery of the IMC.

[0188] In this document, the expressions "in - plane component of the magnetic - field vector" and "orthogonal projection of the magnetic - field vector in the sensor plane" have the same meaning. If the sensor device is or includes a semiconductor substrate, this also means "magnetic - field component parallel to the semiconductor substrate".

[0189] In this document, the expressions "out - of - plane component of the vector" and "Z - component of the vector" and "orthogonal projection of the vector on an axis perpendicular to the sensor plane" have the same meaning.

[0190] Embodiments of the present invention are typically described using an orthogonal coordinate system fixed to the sensor device and having three axes X, Y, Z, where the X - axis and the Y - axis are parallel to the substrate, and the Z - axis is perpendicular to the substrate.

[0191] In this document, the expressions "spatial derivative" or "derivative" or "spatial gradient" or "gradient" are used as synonyms. In the context of the present invention, the gradient is typically determined as the difference between two values measured at two different positions that can be spaced in the range from 1.0 mm to 3.0 mm. Theoretically, the gradient is calculated as the difference between the two values divided by the distance "dx" between the sensor positions, but in practice, dividing by "dx" is often omitted because the measured signal needs to be scaled anyway.

[0192] In this document, horizontal Hall plates are typically referred to as H1, H2, etc., and the signals from these horizontal Hall plates are typically referred to as h1, h2, etc.; vertical Hall plates are typically referred to as V1, V2, etc.; and the signals from these vertical Hall plates are typically referred to as v1, v2, etc.

[0193] In this document, the terms "multiple coefficients", or "multiple parameters" or "multiple constants" have the same meaning when referring to machine learning or deep learning, regardless of whether these values are used as coefficients in a matrix, or as offset values or as scaling factors.

[0194] The present invention generally relates to the field of magnetic sensor devices, systems, and methods, and more particularly to magnetic sensor devices, systems, and methods in which the position of a magnet relative to a semiconductor substrate indicates at least two physical quantities, such as for example a force component, or the tilt angle of a joystick, or the lateral position of a thumb joystick, and the like.

[0195] Refer to the accompanying drawings.

[0196] Figure 1 is a schematic block diagram of a sensor circuit known in the art. The sensor circuit includes a first sensor (or sensor structure) at a first sensor position X1 along the X-axis and a second sensor (or sensor structure) at a second sensor position X2; each sensor structure includes an integrated magnetic concentrator (IMC) and two horizontal Hall elements arranged on opposite sides of the IMC. These sensor structures are also referred to herein as "2D magnetic pixels". Each of these 2D magnetic pixels is capable of measuring the Bx and Bz magnetic field components at the center of the IMC disk. Figure 1 The sensor circuit with two 2D pixels of can be used to determine two magnetic field gradients dBx / dx and dBz / dx along the X-axis.

[0197] Figure 2 is a schematic block diagram of a sensor circuit known in the art, which is Figure 1 a variant of. The sensor circuit includes a first sensor structure at a first sensor position X1 along the X-axis and a second sensor structure at a second sensor position X2; each sensor structure includes an integrated magnetic concentrator (IMC) and four horizontal Hall elements arranged at the periphery of the IMC. These sensor structures are also referred to herein as "3D magnetic pixels". Two of the four horizontal Hall elements are located on the X-axis, and the other two of the four horizontal elements are located on the Y-axis perpendicular to the X-axis. Figure 2 The sensor circuit with two 3D pixels of can be used to determine three magnetic field gradients dBx / dx, dBy / dx, and dBz / dx along the X-axis.

[0198] Figure 3(a) is a schematic representation of an illustrative example of a magnetic sensor system including a permanent magnet that can move relative to a semiconductor substrate. The semiconductor substrate includes a plurality of magnetic sensors. Although not explicitly shown in Figure 3(a), the semiconductor substrate can be embedded in a packaged device, and the magnet can be embedded in an elastomer located above or on top of the packaged device. The magnet can be an axially magnetized two-pole disk-shaped magnet.

[0199] Figure 3(b) is a schematic representation of another illustrative example of a magnetic sensor system including a permanent magnet that is movable relative to two semiconductor substrates arranged side by side, each including a plurality of magnetic sensors. Although not explicitly shown in Figure 3(b), the semiconductor substrates may be embedded in a single packaged device, and the magnet may be embedded in an elastomer located above or on top of the packaged device. The magnet may be an axially magnetized two-pole disk-shaped magnet.

[0200] Figure 4 is a schematic block diagram of a sensor circuit that can be used in embodiments of the present invention. The sensor circuit includes three 2D magnetic pixels located on a virtual circle. In the example shown, the three sensors are angularly spaced by multiples of 120°. Each sensor is capable of measuring the Bx magnetic field component parallel to the semiconductor surface (also referred to as the "in-plane magnetic field component") and the Bz magnetic field component perpendicular to the semiconductor surface (also referred to as the "out-of-plane magnetic field component"). The sensor circuit can measure six magnetic field components of the magnetic field generated by the magnet, which six magnetic field components may be referred to herein as (Bx1, Bz1) at a first sensor position, (Bx2, Bz2) at a second sensor position, and (Bx3, Bz3) at a third sensor position. When the sensor circuit is used in a magnetic sensor system of Figure 3(a) or Figure 3(b) or a variant thereof, the magnet is preferably located substantially above the center of the virtual circle.

[0201] Figure 5 is a schematic block diagram of a sensor circuit that can be used in embodiments of the present invention. The sensor circuit includes four 2D magnetic pixels, three of which are located on a virtual circle and one of which is located at the center of the virtual circle. Figure 5 The sensor circuit of Figure 4 can be considered a variant of the sensor circuit of

[0202] with an additional 2D magnetic pixel located at the center. The sensor circuit can measure eight magnetic field components of the magnetic field generated by the magnet, which eight magnetic field components may be referred to herein as (Bx1, Bz1) at a first sensor position, (Bx2, Bz2) at a second sensor position, (Bx3, Bz3) at a third sensor position, and (Bx4, Bz4) at a fourth sensor position. When the sensor circuit is used in a magnetic sensor system of Figure 3(a) or Figure 3(b) or a variant thereof, the magnet is preferably located substantially above the center of the virtual circle.

[0202] In a variant (not shown) of Figure 5 , the sensor located at the center is a 3D magnetic pixel instead of a 2D magnetic pixel (e.g., as shown in Figure 13 and Figures 15(a) - 15(b) ), and is configured to measure three orthogonal magnetic field components Bx4, By4, Bz4 at the fourth sensor position.

[0203] Figure 6 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit includes four 1D magnetic pixels, three of the four 1D magnetic pixels are located on a virtual circle, and one of the four 1D magnetic pixels is located at the center of the virtual circle. In the example shown, each sensor is a horizontal Hall element. The sensor circuit can measure four magnetic field components of the magnetic field generated by a magnet, and these four magnetic field components can be referred to herein as (Bz1) at a first sensor position, (Bz2) at a second sensor position, (Bz3) at a third sensor position, and (Bz4) at a fourth sensor position. When the sensor circuit is used in a magnetic sensor system such as in Fig. 3(a) or Fig. 3(b) or a variant thereof, the magnet is preferably located substantially above the center of the virtual circle.

[0204] The inventors have come to a surprising insight that, at least in theory, these four sensor signals should be sufficient to uniquely determine the 3D position of the magnet relative to the semiconductor substrate or a physical quantity related to said position even in the presence of a magnetic interference field, because only Bz_ext is unknown (in this case, Bx_ext and By_ext are not relevant).

[0205] In Figure 6 a variant (not shown), the sensor circuit includes five horizontal Hall elements, four of the five horizontal Hall elements are located on the virtual circle and are angularly spaced by multiples of 90°, and one of the five horizontal Hall elements is located at the center of the virtual circle. The sensor circuit is capable of measuring Bz1 to Bz5.

[0206] In Figure 6 a variant (not shown), the sensor circuit includes four vertical Hall elements, each element having a maximum sensitivity axis oriented in a single direction parallel to the semiconductor substrate (e.g., the X direction). The sensor circuit is capable of measuring Bx1 to Bx_{4}. In another variant, the sensor circuit includes a fifth vertical Hall element located at the center of the virtual circle.

[0207] In Figure 6 a variant (not shown), the sensor circuit includes four magneto - resistive (MR) elements, each element having a maximum sensitivity axis oriented in a single direction parallel to the semiconductor substrate (e.g., the X direction). The sensor circuit is capable of measuring Bx1 to Bx_{4}. In another variant, the sensor circuit includes a fifth MR element located at the center of the virtual circle.

[0208] In Figure 6In a variant (not shown), the sensor circuit includes an array of horizontal Hall elements (without IMC), each element being configured to measure Bz in a direction perpendicular to the semiconductor substrate. These elements are located, for example, on an N×M grid, where N and M are integer values in the range from 2 to 5. For example, they are located on a 2×4 grid, 3×3 grid, 3×4 grid, 3×5 grid, 4×4 grid, etc. The grid lines can be vertical, but this is not absolutely necessary. The distance between parallel grid lines can be constant, but this is also not absolutely necessary. Not all positions in the array need to be occupied by Hall elements.

[0209] In Figure 6 In another variant (not shown), the sensor circuit includes a plurality of at least four magnetic sensors, which are only horizontal Hall elements (without IMC), located at random or pseudo-random positions (e.g., not on a circle or square or grid, and / or not equidistantly spaced from each other), each being configured to measure Bz in a direction perpendicular to the semiconductor substrate.

[0210] Figure 7(a) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit includes four 2D magnetic pixels located on a virtual circle and angularly spaced by multiples of 90°. The sensor circuit can measure eight magnetic field components of the magnetic field generated by a magnet, which can be referred to herein as (Bx1, Bz1) at a first sensor position, (Bx2, Bz2) at a second sensor position, (Bx3, Bz3) at a third sensor position, and (Bx4, Bz4) at a fourth sensor position. When the sensor circuit is used in the magnetic sensor system of Figure 3(a) or Figure 3(b) or its variant, the magnet is preferably located substantially above the center of the virtual circle.

[0211] Figure 7(b) shows a variant of Figure 7(a) in which all 2D pixels are rotated by 45°.

[0212] Figure 8 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit includes five 2D magnetic pixels, four of which are located on a virtual circle and angularly spaced by multiples of 90°, and one of which is located at the center of the virtual circle. Figure 8The sensor circuit can be regarded as a variant of the sensor circuit in Fig. 7(a) with an additional 2D magnetic pixel located at the center. This sensor circuit can measure ten magnetic field components of the magnetic field generated by a magnet, which can be referred to as (Bx1, Bz1) at the first sensor position, (Bx2, Bz2) at the second sensor position, (Bx3, Bz3) at the third sensor position, (Bx4, Bz4) at the fourth sensor position, and (Bx5, Bz5) at the fifth sensor position herein. When this sensor circuit is used in the magnetic sensor system of Fig. 3(a) or Fig. 3(b) or its variant, the magnet is preferably located substantially above the center of the virtual circle.

[0213] In Figure 8 a variant (not shown), the sensor S5 located at the center is a 3D magnetic pixel instead of a 2D magnetic pixel (e.g., as shown in Figure 13 and Fig. 15), and is configured to measure three orthogonal magnetic field components Bx5, By5, Bz5 at the fifth sensor position.

[0214] Figure 9 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. This sensor circuit includes an array of 3×3 = 9 (nine) 2D magnetic pixels located on a grid having three rows and three columns. This sensor circuit can measure nine sets each having two magnetic field components (Bx, Bz), thereby measuring a total of 2×9 = 18 (eighteen) magnetic field components. The X direction is parallel to the row direction and orthogonal to the column direction. When this sensor circuit is used in the magnetic sensor system of Fig. 3(a) or Fig. 3(b) or its variant, the magnet is preferably located substantially above the center sensor position (in its default position).

[0215] Figure 10 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. This sensor circuit includes an array of 3×3 = 9 (nine) 2D magnetic pixels located on a grid having three rows and three columns. This sensor circuit can measure nine sets each having two magnetic field components (Bu, Bz), thereby measuring a total of 2×9 = 18 (eighteen) magnetic field components. If the X direction is selected to be parallel to the row direction and the Y direction is selected to be parallel to the column direction, the U direction forms a 45° angle with the X direction. Figure 10 The sensor circuit of Figure 9 can be regarded as a variant of the sensor circuit of

[0216] Figure 11(a) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit includes an array of eight 2D magnetic pixels located on a grid having three rows and three columns. The sensor circuit can be considered as a variant of a sensor circuit in which the central sensor is omitted and in which two Hall elements of each sensor are located on a virtual line passing through the central position. Figure 9 of the sensor circuit.

[0217] In a variant (not shown) of Figure 11(a), the sensor circuit further includes a 3D magnetic pixel having only four horizontal Hall elements located on virtual lines parallel to the row direction and the column direction, as depicted in Figure 11(b).

[0218] In a variant (not shown) of Figure 11(a), the sensor circuit further includes a 3D magnetic pixel having only four horizontal Hall elements located on virtual lines forming a 45° angle with respect to the row direction and the column direction, as depicted in Figure 11(c).

[0219] In a variant (not shown) of Figure 11(a), the sensor circuit further includes a 3D magnetic pixel having eight horizontal Hall elements spaced by multiples of 45° (two of the eight horizontal Hall elements are located on a row and two of the eight horizontal Hall elements are located on a column), as depicted in Figure 11(d).

[0220] Figure 12 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit includes four 2D magnetic pixels located on a virtual circle. Two Hall elements of each sensor are located on a radially oriented segment. The sensor structure is capable of measuring (Bx1, Bz1) at a first sensor position, measuring (Bx2, Bz2) at a second sensor position, measuring (By3, Bz3) at a third sensor position, and measuring (By4, Bz4) at a fourth sensor position, thereby measuring a total of eight magnetic field components.

[0221] Figure 13 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit can be considered as a variant of a sensor circuit that further includes a 3D magnetic pixel located at the center of the virtual circle. Figure 12 of the sensor circuit. The sensor circuit is capable of measuring (4x2)+(1x3) = 8 + 3 = 11 magnetic field components.

[0222] Figure 14(a) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit includes four 3D magnetic pixels located on a virtual circle and spaced by multiples of 90°. In this example, each sensor includes an IMC disk having four horizontal Hall elements, two of the four horizontal Hall elements being located on a virtual line parallel to the X direction, and two of the four horizontal Hall elements being located on a virtual line parallel to the Y direction. The sensor circuit is capable of measuring two in-plane field components (Bx, By) at four sensor positions, and is capable of measuring an out-of-plane field component Bz at four sensor positions, thereby being able to measure a total of sixteen magnetic field components. Or in other words, the sensor circuit is capable of measuring four magnetic field components tangent to the virtual circle, as well as magnetic field components radially oriented with respect to the virtual circle, and four axially oriented magnetic field components.

[0223] Figure 14(b) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit can be regarded as a variant of the sensor circuit of Figure 14(a) in which each sensor is rotated 45° with respect to the Z axis perpendicular to the semiconductor substrate.

[0224] Figure 15(a) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit can be regarded as a variant of the sensor circuit of Figure 14(a) further including a 3D magnetic pixel at the center of the virtual circle. The sensor circuit is capable of measuring (5x3) = 15 magnetic field components.

[0225] Figure 15(b) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit can be regarded as a variant of the sensor circuit of Figure 15(a) in which each sensor is rotated 45° with respect to the Z axis perpendicular to the semiconductor substrate.

[0226] Figure 16 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit includes an array of 3×3 = 9 (nine) 3D magnetic pixels located on a grid having three rows and three columns. The sensor circuit can measure nine sets each having three magnetic field components (Bx, By, Bz), thereby measuring a total of 3×9 = 27 magnetic field components. The sensor circuit can be regarded as a variant of the Figure 9 sensor circuit in which each 2D magnetic pixel is replaced by a 3D magnetic pixel.

[0227] In Figure 16 a variant (not shown) of the, each sensor is rotated 45° about the Z axis perpendicular to the semiconductor substrate. The sensor is capable of measuring nine sets having three orthogonal magnetic field components (Bu, Bv, Bz), nine components oriented in the U direction, nine components oriented in the V direction, and nine components oriented in the Z direction.

[0228] Figure 17(a) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. This sensor circuit can be regarded as Figure 12 such a variant of the sensor circuit: where each sensor includes a horizontal Hall element (without IMC) configured to measure the out-of-plane magnetic field component Bz, and includes one (or at least one) vertical Hall element having a maximum sensitivity axis oriented in the radial direction.

[0229] In a variant (not shown) of Figure 17(a), each sensor has two vertical Hall elements that are oriented in the same direction but radially spaced apart, for example, one vertical Hall element on each side of the horizontal Hall element, one at a larger imaginary circle and one at a smaller imaginary circle. Signals from the two corresponding vertical Hall elements can be added or averaged.

[0230] Figure 17(b) shows a variant of Figure 17(a) in which all 2D pixels are rotated by 45°.

[0231] Figure 18 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. This sensor circuit can be regarded as such a variant of the sensor circuit of Figure 7(a): where each sensor includes a horizontal Hall element (without IMC) configured to measure the out-of-plane magnetic field component Bz, and includes one (or at least one) vertical Hall element having a maximum sensitivity axis oriented in the X direction.

[0232] In Figure 18 a variant (not shown) of, the sensor circuit further includes a fifth sensor located at the center of the virtual circle. This fifth sensor also has a horizontal Hall element (without IMC) for measuring the Bz component and at least one vertical Hall element for measuring the Bx component at the center of the virtual circle.

[0233] Figure 19(a) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. This sensor circuit can be regarded as such a variant of the sensor circuit of Figure 14(a): where each sensor includes a horizontal Hall element (without IMC) configured to measure the out-of-plane magnetic field component Bz, and includes two vertical Hall elements having a maximum sensitivity axis oriented in the X direction and located on opposite sides of the horizontal Hall element, and includes two vertical Hall elements having a maximum sensitivity axis oriented in the Y direction and located on opposite sides of the horizontal Hall element. In other words, the horizontal Hall element is surrounded by four vertical Hall elements located on each side of the square. Each of these sensors is capable of measuring three orthogonal magnetic field components (Bx, By, Bz) to form a 3D magnetic pixel.

[0234] In a variant (not shown) of FIG. 19(a), the sensor circuit further includes a fifth 3D magnetic pixel located at the center of the virtual circle. The sensor circuit can measure five sets having three magnetic field components (Bx, By, Bz), thereby measuring a total of 5×3 = 15 magnetic field components.

[0235] FIG. 19(b) is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit can be regarded as a variant of the sensor circuit of FIG. 19(a) in which each sensor is rotated 45° about the Z axis perpendicular to the semiconductor substrate. The sensor circuit includes four 3D magnetic pixels, each of which can measure an out-of-plane magnetic field component Bz oriented in the Z direction perpendicular to the semiconductor substrate, and in addition each 3D magnetic pixel can measure two in-plane magnetic field components (Bu, Bv) oriented in the U direction and the V direction.

[0236] In a variant (not shown) of FIG. 19(b), the sensor circuit further includes a fifth 3D magnetic pixel located at the center of the virtual circle. The sensor circuit is capable of measuring five sets having three orthogonal magnetic field components (Bx, By, Bz), thereby measuring a total of 5×3 = 15 magnetic field components.

[0237] Figure 20 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit can be regarded as such a variant of the sensor circuit of FIG. 14(a) or FIG. 14(b): the sensor circuit includes four sensors, each of which includes an integrated magnetic concentrator disk IMC and eight horizontal Hall elements located near the periphery of the IMC disk and angularly spaced by multiples of 45°. Each of these sensors can measure four in-plane magnetic field components Bx, By, Bu, Bv and one out-of-plane magnetic field component Bz. The sensor circuit can measure 4×5 = 20 magnetic field components.

[0238] Figure 21 is a schematic block diagram of a sensor circuit that can be used in an embodiment of the present invention. The sensor circuit can be regarded as a variant of the Figure 20 sensor circuit that further includes a fifth 3D magnetic pixel located at the center of the virtual circle. The sensor circuit can measure five sets having five orthogonal magnetic field components (Bx, By, Bu, Bv, Bz), thereby measuring a total of 5×5 = 25 magnetic field components.

[0239] In all of the above embodiments ([[]] Figures 1 to 21 ) in which one or more integrated magnetic concentrators IMC are used, the IMC preferably has a disk shape with a height of about 17 to 23 μm and a diameter of about 170 to 230 μm.

[0240] In all of the above embodiments in which the magnetic sensors (also referred to herein as 2D magnetic pixels or 3D magnetic pixels) are located on a virtual circle, the diameter of the virtual circle is preferably from 1.7 to 2.3 mm, for example, equal to about 1.9 mm, or equal to about 2.0 mm, or equal to about 2.1 mm. In the embodiments in which the sensors are located on a 3×3 grid, the distance between the grid lines is preferably from about 0.7 mm to about 1.5 mm, or from about 0.9 mm to about 1.3 mm.

[0241] The horizontal Hall plates generally have a square shape with an area from 15 μm×15 μm to 25 μm×25 μm, for example equal to about 20 μm×20 μm.

[0242] FIG. 22(a) shows a schematic block diagram of a magnetic sensor system 2200 proposed by the present invention. The magnetic sensor system 2200 can be used to measure one or two or three physical quantities related to the position of a permanent magnet, such as, for example, three orthogonal components of a force vector applied to the sensor system. The system may further be affected by an external interference field (also referred to as a stray field) and by a varying temperature.

[0243] The sensor system 2200 includes one or more semiconductor substrates that include a plurality of magnetic sensors 2210. The one or more semiconductor substrates are preferably incorporated into a semiconductor package (also referred to as a sensor chip), see, for example, FIG. 23(d). In a preferred embodiment, the plurality of magnetic sensors are incorporated into a single semiconductor substrate having dimensions less than 3.0 cm×3.0 cm (preferably, less than 2.5 mm×2.5 mm).

[0244] The sensor system further includes a permanent magnet that is mounted flexibly or elastically relative to the (one or more) semiconductor substrates, for example, by means of an elastic material.

[0245] The permanent magnets 390, 2390 are preferably single axially magnetized ring-shaped or disk-shaped magnets having an outer diameter of about 1.2 mm to about 1.8 mm (for example, equal to about 1.5 mm); and a height (in the axial direction) of about 0.3 mm to about 0.7 mm, or from 0.4 mm to 0.6 mm (for example, equal to about 0.5 mm). In a preferred embodiment, the outer diameter of the permanent magnet is less than the diameter of the virtual circle on which the sensor elements are located.

[0246] The permanent magnet can be mounted by means of a rod and bearings, etc. (as is usually the case in a joystick), or can be mounted by means of one or more springs, or can be embedded in a flexible material (for example, in an elastomer), for example, as shown in FIGS. 3(a) and 3(b), or as Figures 23(a) to 23(e) illustrated, or as illustrated in the prototypes of FIGS. 24(a) and 24(b), or as in Figure 26As illustrated in the simulation model shown, or as described in the co-pending EP application No. EP21182116.0, titled "Force Sensor with Target on a Semiconductor Package", filed by the same applicant on June 28, 2021, which document is incorporated herein by reference in its entirety (especially Figures 1 to 5 and the corresponding description, which illustrates and describes the assembly of the force sensor and the elastomer), or is included herein in any other suitable manner. The elastomer may have highly non-linear stress-versus-strain characteristics, thus making it extremely difficult or almost impossible to find an explicit analytical formula for determining the component of the mechanical force applied to the magnet based on the signal obtained from the magnetic sensor. An additional problem encountered by the inventors is that the mechanical properties of the elastic material may also be temperature-dependent. For example, in the envisioned temperature range, the elastic material may become harder as the temperature decreases. The permanent magnet and the mechanical mounting of the magnet are schematically represented by block 2204, which generates a magnetic field that depends on the applied mechanical force, but it can also be said that the magnetic field generated by the permanent magnet is "modulated" by the mechanical force.

[0247] The influence from an (unknown) external interference field is typically added to the magnetic field generated by the magnet.

[0248] In the example of FIG. 22(a), a mechanical force 2202 is applied to the magnet, and the physical quantities to be measured are the force components in the X, Y, and Z directions. The present invention will be mainly explained with respect to the force sensor, keeping the description relatively simple, but the present invention is not limited thereto and is also applicable to determining other physical quantities, such as, for example, determining the position of a joystick (e.g., two tilt angles), or determining the position of a thumb joystick (e.g., two lateral displacements, and / or a downward displacement), etc.

[0249] The mechanical force to be measured can be applied directly or indirectly to the magnet, for example, directly or indirectly to the contact surface of the elastomer enclosing the permanent magnet. The latter may be preferred, for example, to avoid slipping. The magnetic field generated by the permanent magnet can be measured by a sensor circuit including a plurality of magnetic sensors 2210 (e.g., using Figures 3(a) to 21 any of the sensor circuits shown in the sensor circuit), the present invention is not limited thereto, because, for example, a sensor circuit having a plurality of sensor elements located on a 4×4 grid or at pseudo-random positions will also work. In fact, magnetic sensors are typically biased with a current or voltage source, and the signals provided by the sensor elements are typically amplified and digitized, etc. in a so-called "bias and readout circuit", which is not explicitly shown in FIG. 22(a) because such circuits are well known in the art and are not the focus of the present invention and thus do not need to be explained in more detail herein. It can be said that techniques such as "spin current", chopping, etc. can also be used.

[0250] The processing of the signals will be explained mainly with reference to the prototypes illustrated in FIGS. 3(b) and 7(b), which have been constructed, evaluated, and simulated. Of course, the present invention is not limited to this example, but also applies to other systems using the same principle.

[0251] The sensor circuit of FIG. 7(b) provides eight magnetic field component signals: Bx1, Bz1, Bx2, Bz2, Bx3, Bz3, Bx4, Bz4, whereby in the example of the prototype, block 2210 provides these eight signals.

[0252] In block 2222, the eight magnetic field component signals are preferably amplified, offset corrected, and sensitivity corrected in a known manner, for example, according to temperature. For this purpose, the sensor circuit preferably further includes a temperature sensor 2208. For completeness, it should be noted that this block can be corrected not only for temperature variations, but also for mechanical stress applied to the silicon substrate in a known manner, for example, as described in co-pending patent application EP21161150.4 (publication number: EP3885779), and / or as described in co-pending patent application EP21161151.2 (publication number: EP3885778), both of which are incorporated herein by reference in their entirety, or in any other suitable manner. Block 2222 can also digitize the signals using one or more analog-to-digital converters ADCs (not explicitly shown).

[0253] In the example of FIG. 22(a), four sensitivity-corrected Bx signals are input to block 2224, where the mean or average value of these four sensitivity-corrected Bx signals is calculated, and then this mean or average value is subtracted from each of the sensitivity-corrected Bx signals. Similarly, four sensitivity-corrected Bz signals are input to block 2224, where the mean or average value of these four sensitivity-corrected Bz signals is calculated, and then this mean or average value is subtracted from each of the sensitivity-corrected Bz signals. If implemented in this way, block 2224 outputs four "mean-corrected" Bx-related signals and four "mean-corrected" Bz-related signals, thereby a total of eight signals. It is also possible to perform "mean removal" in the analog domain and digitize the mean-corrected Bx values and mean-corrected Bz values.

[0254] In the example of FIG. 22(a), the processing circuit further includes a "feature expansion and polynomial expansion" block 2226, which is configured to receive four mean-corrected Bx values and four mean-corrected Bz values, and is configured to calculate one or more of the following: the sum of two values, the difference of two values, the product of two values, the ratio of two values, the square of a value, the sign of a value multiplied by the square of the value, the cube of a value, the absolute value of a value, the sum of the squares of two (e.g., orthogonal) values (related to "norm"), the sum of the squares of three (e.g., orthogonal) values (related to "norm"); and to output the (original) mean-corrected Bx and Bz values and additionally the generated values as output signals. In a preferred embodiment, the total number "Ntot" of values provided by block 2226 is a value in the range from 12 to 100, or in the range from 12 to 80, or from 16 to 64.

[0255] It should be noted that the difference between "feature expansion" and "polynomial expansion" is somewhat arbitrary and not relevant to the present invention. What is important is that block 2226 obtains a certain number of input values and generates a plurality of output values (e.g., the same number, or preferably a larger number) based on the values derived from them. It has surprisingly been found that by expanding the number of values, the accuracy of the final output (e.g., force components) is greatly improved, which is counterintuitive since these values do not add "new information". In particular, it has been found that it is very advantageous to add additional values in the form of the square of the input values, and / or in the form of the product of similar input values (e.g., Bx1*Bx2), and / or in the form of different input values (e.g., Bx1*Bz1).

[0256] In block 2230, the physical quantity to be determined is calculated based on these values, more specifically, as a weighted sum of these values each offset by an offset.

[0257] For example, if block 2226 outputs values v1, v2,... v64, then block 2230 can calculate one or more components (Fx, Fy, Fz) of the force vector according to the following formulas:

[0258] Fx = A1*(v1 - B1)+A2*(v2 - B2)+...+A64*(v64 - B64)[1]

[0259] Fy = C1*(v1 - D1)+C2*(v2 - D2)+...+C64*(v64 - D64)[2]

[0260] Fz = E1*(v1 - F1)+E2*(v2 - F2)+...+E64*(v64 - F64)[3]

[0261] Among them, the values A1 to A64, B1 to B64, C1 to C64, D1 to D64, E1 to D64, and F1 to F64 are constants, and these constants are determined by machine learning or by deep learning.

[0262] It should be noted that "training" or "learning" is done over a relatively wide range of three-dimensional force values, that is, a sufficient number of various combinations of 3D force components are selected to represent the 3D space of possibilities. In other words, many combinations of forces (Fx, Fy, Fz) are used to train the coefficients, for example, the number of measurements is at least 2 times or at least 5 times (such as about 10 times) the number of parameters to be determined.

[0263] There is an optional "temperature correction box" 2225, as will be further explained when discussing Figure 29 as follows. In the case where temperature is used as an additional part of box 2226 (representing a feature enhancement and / or polynomial enhancement box, or a neural network), "training" or "learning" should be performed using various combinations of (T, Fx, Fy, Fz).

[0264] Figure 22(b) shows a schematic block diagram of another magnetic sensor system 2250 proposed by the present invention, which can be used to measure one or two or three physical quantities related to the position of a permanent magnet, such as, for example, three orthogonal components of the force vector applied to the sensor system. This system can be regarded as a variant of the system of Figure 22(a) in which the mean removal box 2224 is replaced by a gradient calculator box 2232.

[0265] If the sensor circuit 2210 contains multiple sensors as depicted in Figure 7(b), the gradient calculator box can calculate one or more of the following Bx-related gradient signals:

[0266] g1 = (Bx1 - Bx3), g2 = (Bx1 - Bx4), g3 = (Bx1 - Bx2),

[0267] g4 = (Bx3 - Bx4), g5 = (Bx3 - Bx2), g6 = (Bx4 - Bx2)

[0268] And it can calculate one or more of the following Bz-related gradient signals:

[0269] g7 = (Bz1 - Bz3), g8 = (Bz1 - Bz4), g9 = (Bz1 - Bz2)

[0270] g10 = (Bz3 - Bz4), g11 = (Bz3 - Bz2), g12 = (Bz4 - Bz2)

[0271] All other things mentioned above for the system of Figure 22(a) also apply here.

[0272] It should be noted that, compared with many prior art magnetic sensor systems that use analytical formulas therein, in the present invention, it is not required that the signals entering block 2226 behave like sine and cosine functions of the physical quantity to be determined.

[0273] In an embodiment (not shown), a predefined algorithm is performed by using at least three first magnetic field components (e.g., Bx1, Bx2, Bx3) and at least three second magnetic field components (e.g., Bz1, Bz2, Bz3) as input signals through a trained neural network, and providing at least two (or at least three) physical values as output values.

[0274] The neural network can replace blocks 2226 and 2230 in FIGS. 22(a) and 22(b). Optionally, in this case, blocks 2224 (mean removal) and 2232 (gradient calculator) can be omitted.

[0275] The predefined algorithm can include a neural network having multiple layers, where each layer includes multiple nodes. In an embodiment, the neural network includes only one layer having 12 to 100 nodes. In an embodiment, the neural network includes only two layers, each having 10 to 100 nodes, or having 20 to 60 nodes. In an embodiment, the neural network includes only three layers, each having 10 to 100 nodes, or each having 5 to 50 nodes. In an embodiment, the neural network is a Recurrent Neural Network (RNN). In an embodiment, the neural network is an Artificial Neural Network (ANN). In an embodiment, the neural network is a Convolution Neural Network (CNN).

[0276] Figures 23(a) to 23(e) An example of a mechanical arrangement including a sensor device or including a sensor assembly 2300 is shown, including a sensor device 2392, which is, for example, a packaged chip that includes a semiconductor substrate enclosed in a molding compound; and an elastomer 2391 above or on top of the sensor device 2392; and a magnet 2390 embedded in the elastomer and located at a distance “d” (commonly referred to as an “air gap”) from the sensor device. The sensor device can be mounted on a printed circuit board (PCB) 2393. The elastomer 2391 can be supported only by semiconductor devices, for example, as Figures 23(c) to 23(e)As illustrated. Alternatively, a portion of the elastomer may be supported by a printed circuit board, e.g., as illustrated in FIGS. 23(a) and 23(b). Optionally, an intermediate layer (e.g., an adhesive layer) may be present between the sensor chip 2392 and the elastomer 2391, e.g., as illustrated in FIG. 23(d).

[0277] The magnet 2390 is preferably an axially magnetized toroidal or disc-shaped magnet. The outer diameter of the magnet may have a size comparable to the size of the sensor device (e.g., equal to, or greater than, or less than the diameter of the virtual circle on which the magnetic sensor is located). However, preferably, the outer diameter of the magnet 2390 is less than the maximum distance between the magnetic sensor elements.

[0278] In the example of FIG. 23(a), the magnet may have a height of approximately 8 mm (in the vertical direction, perpendicular to the semiconductor substrate) and a diameter of approximately 12 mm (parallel to the semiconductor substrate).

[0279] In the sensor assemblies illustrated in FIGS. 23(b) and 23(c), the magnet may have a diameter in the range of 5 mm to 10 mm and a height of approximately 3.5 mm.

[0280] In the sensor assembly illustrated in FIG. 23(d), the magnet may have a diameter less than 2.5 mm or less than 2.0 mm (e.g., equal to approximately 1.5 mm); and may have a height of approximately 0.5 mm to approximately 1.0 mm. The thickness of the elastomer 2391 may be in the range from 2.0 mm to 5.0 mm, or in the range from 2.5 mm to 4.0 mm (e.g., equal to approximately 3.0 mm).

[0281] Those skilled in the art benefiting from this disclosure can consider the following rule of thumb to easily find suitable dimensions: the larger the magnet, and / or the closer the magnet is to the semiconductor substrate; and the softer the elastomer material, the larger the signal obtained from the magnetic sensor elements.

[0282] FIGS. 24(a) and 24(b) show pictures of a prototype of a force sensor system as described herein and used to develop and evaluate the algorithms described in FIGS. 22(a) and 22(b).

[0283] FIG. 24(c) shows a picture of a mechanical setup for applying known forces (Fx, Fy, Fz) to the force sensor assembly. By applying a series of tests with different force values and by measuring the corresponding magnetic field components, the parameters (e.g., A1 to F64) are determined using machine learning (ML).

[0284] Figure 25(a) shows the results of the measured values of Bx1 to Bx4 when a force Fz is applied that is oriented in a direction perpendicular to the semiconductor substrate and has an amplitude in the range from 0.0 Newton to 12.5 Newtons, and Figure 25(b) shows the results of the measured values of Bz1 to Bz4 when a force Fz is applied that is oriented in a direction perpendicular to the semiconductor substrate and has an amplitude in the range from 0.0 Newton to 12.5 Newtons. It can be seen that there is a certain spread between the curves, and the curves are not perfectly linear.

[0285] Surprisingly, the inventors found that the values of Bx1 to Bx4 show a very good correlation with the applied force and are thus very good indicators for the force component Fz, even though their values are relatively small (about 5 to 15 mT). Surprisingly, the inventors also found that, despite the fact that the signals of the values Bz1 to Bz4 are typically about twice the signals of Bx1 to Bx4, the spread between the values Bz1 to Bz4 is very large. This was not expected. It shows that applying an analytical formula to any of the signals Bx1 to Bx4 and Bz1 to Bz4 will likely not result in a reliable measurement of the applied force component Fz, but as will be shown further, a combination of these signals (more specifically, a polynomial combination of these signals (e.g., a second-order polynomial) and an algebraic combination of these signals (e.g., a product or a ratio)) with a sufficient number of parameters can yield good results.

[0286] Figure 26 A computer model of the mechanical arrangement is shown, which can be used to simulate how an elastic body will deform and how a magnet will move when a force with a normal force component Fz and / or with shear force components Fx, Fy is applied. The computer model can be simulated using, for example, a commercially available tool called "Comsol".

[0287] Using Figures 14(a) - 14(b) the mechanical setup shown, for a given set of parameters (e.g., A1 to F64) determined by machine learning, Figure 26 the computer model can then be used to verify the algorithm of Figure 22(a) or Figure 22(b) using these parameters.

[0288] Figures 27(a) and 27(b) show how well the force measured by the calibration setup (see Figure 24(c)) and the force predicted by the force sensor algorithm of the prototype implementation (see Figure 22(a)) work. Figure 27(a) relates to a force in the "downward" direction, which is oriented in the negative Z direction, perpendicular to the semiconductor substrate. Figure 27(b) relates to a shear force. It can be seen that there is a very good linear fit between these values.

[0289] Surprisingly, it is possible to measure the force applied in the Y direction even though no By component is measured.

[0290] It should be noted that these results were obtained using the sensor circuit of Fig. 7(b), which has only four 2D magnetic pixels that may not be oriented in the optimal direction.

[0291] It is envisioned that sensor circuits in which the 2D pixels are oriented in different directions, and / or have more than four magnetic pixels, and / or have 3D magnetic pixels, and / or use algorithms with more parameters may provide more accurate results. However, it is not easy to predict how many sensors and / or how many parameters are required to achieve a certain accuracy or to predict the most cost-effective solution for achieving a certain accuracy. Even so, the present invention discloses a large number of solutions that produce viable and even very good results, even if they are not perfect.

[0292] Fig. 27(c) shows a "force error histogram" when measuring (or determining) a force (denoted as Fz) oriented in the negative Z direction using the sensor system of Fig. 22(a). It can be appreciated that the vast majority of the measurements (>97%) are accurate, with a maximum error within ±0.25 N (corresponding to a weight error of approximately ±25 grams), which is good enough for many applications, including many robotic applications where a robotic arm with robotic fingers needs to gently grasp an object without damaging it.

[0293] Fig. 27(d) shows a "force error histogram" when measuring a shear force (i.e., oriented parallel to the semiconductor substrate). It can be appreciated that the vast majority of the measurements (>97%) are accurate, with a maximum error within ±0.15 N (corresponding to a weight error of approximately ±15 grams).

[0294] Figure 28 Fig. shows a graph of the error of Fx according to an external interference field applied in the X direction, with and without the mean removal box 2224 of Fig. 22(a). The graph clearly shows that "mean removal" is a very effective method for removing the influence of stray fields. Similar results are expected when using the gradient calculation box 2232 of Fig. 22(b).

[0295] Figure 29 Fig. shows a graph of the magnitude (in arbitrary units) of the "normal force" Fz oriented in the direction towards the semiconductor substrate versus the displacement (in arbitrary units) of the magnet. It can be seen that the performance is not completely linear, which may be due to the fact that the stiffness of the elastomer generally increases as the pressure applied to the elastomer increases.

[0296] Although Figure 29Although not explicitly shown in the figure, the inventors have also found that the stiffness of the elastomer also depends on temperature. Tests have shown that this effect can be taken into account by a post-processing step in which the values of Fx, Fy, and Fz are corrected according to temperature, for example, according to the following formula:

[0297] Fx_corr = Fx (using Equation [1]) * [1 + K(Tchip - 35)][4]

[0298] Fy_corr = Fy (using Equation [2]) * [1 + K(Tchip - 35)][5]

[0299] Fz_corr = Fz (using Equation [3]) * [1 + K(Tchip - 35)][6]

[0300] where Tchip (T 芯片 ) is the temperature in degrees Celsius measured by the on-chip temperature sensor, and K is a constant that can be determined during the calibration step.

[0301] This effect can also be taken into account, for example, according to the following formula, in the optional "temperature correction" box 2225:

[0302] Scorr = Sraw.[1 + α(Tchip - 35)] + β(Tchip - 35)[7]

[0303] where Tchip is the temperature in degrees Celsius measured by the on-chip temperature sensor, Sraw (S 原始 ) is the raw signal value (e.g., the mean-corrected value or the gradient value) obtained from the previous box 2226 or 2232, Scorr (S 校正 ) is the temperature-corrected signal value, and α and β are two constants that can be determined by simulation or during the calibration step.

[0304] Figure 30 is a schematic block diagram of the sensor device 3010 that can be used in the embodiments of the present invention. This block diagram is provided only for completeness.

[0305] The sensor device 3010 includes a semiconductor substrate that includes a plurality of magnetic sensors, and only five of the plurality of magnetic sensors are shown as M1 to M5, for example, Figures 4 to 21 any of the circuits shown in the figure.

[0306] The sensor device further includes a bias and readout circuit (e.g., as part of the processing circuit 3030), which is configured to receive signals m1, m2, etc. from the magnetic sensors. The signals are typically amplified and offset corrected. Preferably, the sensor device further includes a temperature sensor, and the magnetic sensitivity of the sensor element is preferably corrected based on the temperature (in the analog or digital domain). The processing circuit may further include at least one analogue to digital converter (ADC) for converting the analog signals into digital signals.

[0307] Depending on the implementation, the processing circuit 3030 may further be configured to perform one or more of the functions of block 2224 (mean removal), 2232 (gradient calculation), 2226 (feature augmentation and polynomial augmentation), 2230 (weights and biases) as described above, see FIGS. 22(a) and 22(b). In this case, the sensor device 3010 may output force component values Fx, Fy, Fz. In order to be able to measure the applied force at a relatively high rate (e.g., at a frequency of at least 20 Hz, or at a frequency of at least 25 Hz, or at a frequency of at least 30 Hz, or at a frequency of at least 40 Hz), the number of augmented values may be limited, and the complexity of the functions used in the (polynomial) augmentation block 2226 may be limited to algebraic functions (e.g., including square functions and products, but excluding division), and the number of terms to be added in block 2230 may be limited to at most 50 terms, or at most 40 terms, or at most 36 terms. Such algorithms may be executed by a programmable signal processor (DSP), and a plurality of constants may be stored in the non-volatile memory 3031. Although not explicitly shown, it is also possible to use an analog processing circuit system (e.g., an analog or digital accelerator, or an analog or digital coprocessor).

[0308] However, in other embodiments, the processing circuit will measure the magnetic field value (block 2210), and will implement sensitivity correction (block 2222), and may also optionally implement mean removal (2224) or gradient calculation (2232), but will not implement feature augmentation (block 2226), and will not calculate the weighted sum (block 2230). In this case, the sensor device 3010 may output the value of block 2222, or 2224 or 2232 (preferably, output as a digital value), and provide these values to an external processor. Then, the external processor will perform feature and / or polynomial augmentation (block 2226) and calculate the weighted sum (block 2230). The advantage of this implementation is that the external processor 3040 can be much more powerful, for example, having a clock frequency higher than 1.0 GHz, and / or can have multiple processor cores, and / or can have much more random access memory (RAM) (e.g., at least 1 GB of RAM).

[0309] To allow the external processor to perform post-processing correction to account for the temperature dependence of the stiffness of the elastomer, the sensor device 3010 may also output the measured temperature T to the external processor.

[0310] Figure 31 is provided for completeness to illustrate that the principles of the present invention can also be used to determine the tilt angles of the joystick assembly and ψ, where the magnet can rotate about the pivot point 3101 by means of the handle or rod 3102.

[0311] A major advantage of the embodiments of the present invention is that no explicit formula is required to determine the tilt angles, and the solution is highly insensitive to external interference fields. It should be noted that in this case, no elastomer material is required, but mechanical components will conventionally be used to hold the magnet and allow the magnet to move. Those skilled in the art will understand Figures 3(a) to 21 that the sensor circuit shown in and the algorithms described above in FIGS. 22(a) and 22(b) can also be used to determine the tilt angle of the handle of the joystick assembly (a physical quantity related to the position of the magnet).

[0312] Although not explicitly shown, the principles of the present invention can also be used to determine the position of the thumb joystick. In this case, by moving the thumb joystick in a plane parallel to the semiconductor substrate, the magnet can be movable in a plane parallel to the semiconductor substrate. Optionally, one or more springs may be involved. Those skilled in the art will understand Figures 3(a) to 21 that the sensor circuit shown in and the algorithms described above in FIGS. 22(a) and 22(b) can also be used to at least determine the lateral displacement of the thumb joystick of the thumb joystick assembly, and optionally, also determine the displacement of the downward squeeze (i.e., a physical quantity related to the position of the magnet).

[0313] Needless to say, the requirements for the accuracy and robustness of a thumb joystick assembly (e.g., as part of a game console for consumer electronic applications) with respect to interference signals are completely different from those for robotic applications. In other words, it is very feasible to construct an integrated sensor device that performs all the signal processing steps shown in FIGS. 22(a) and 22(b), although the number of terms and constants is limited and the accuracy is limited.

[0314] Figure 32 A flowchart of a method 3200 for measuring at least two physical quantities related to the position of a permanent magnet (e.g., a 2D or 3D force vector, a 2D or 3D displacement vector, the 2D or 3D position of a joystick, the 2D or 3D position of a thumb joystick) is shown, where the permanent magnet can move relative to an integrated circuit and is configured to generate a magnetic field. Method 3200 includes the following steps:

[0315] a) Measuring (3201) at least two (or at least three, or at least four) first magnetic field components (Bx1, Bx2; Bx1, Bx2, Bx3; Bx1 to Bx4) oriented in a first direction (e.g., X); the first direction can be parallel to the semiconductor substrate ("in-plane").

[0316] b) Optionally determining (3202) a first gradient (e.g., dBx / dx) or a first mean-corrected value of the first magnetic field component;

[0317] c) Measuring (3203) at least two (or at least three, or at least four) second magnetic field components (e.g., Bz1, Bz2; Bz1, Bz2, Bz3; Bz1 to Bz4) oriented in a second direction (e.g., Y or Z) perpendicular to the first direction (X). The second direction can be parallel to the semiconductor substrate ("in-plane") or can be perpendicular to the semiconductor substrate ("out-of-plane").

[0318] d) Optionally determining (3204) a second gradient (e.g., dBz / dx) or a second mean-corrected value of the second magnetic field component;

[0319] e) Using a predefined algorithm to determine the at least two physical quantities (e.g., Fx, Fy, Fz), the predefined algorithm using the measured magnetic field components and / or gradients and / or mean-corrected values as inputs, and using a plurality of at least eight (or at least twelve, or at least sixteen) constants (or coefficients or parameters) determined using machine learning (ML) or deep learning.

[0320] Of course, the method can be further refined in the same manner as described above.

[0321] For example, in an embodiment, the at least two physical quantities may be determined using such a predefined algorithm: the predefined algorithm uses at least three or at least four magnetic field differences derived from the at least two first magnetic field components and the at least two second magnetic field components as inputs, and uses the plurality of at least eight constants.

[0322] In another or further embodiment, the method may further include measuring the temperature of the semiconductor substrate; and correcting the measured first and second magnetic field components based on the measured temperature, or considering the measured temperature as an additional input to the predefined algorithm, or processing the temperature in a post-processing step.

[0323] And so on.

[0324] For completeness, it should be noted that blocks 2226 (mean removal) and 2232 (calculate gradient) may be omitted, and the stray field is still eliminated by blocks 2226 and 2230 (which may be a neural network).

[0325] According to another aspect, the present invention also provides a force sensor device, comprising: an integrated circuit including a plurality of magnetic sensors; a permanent magnet flexibly mounted to the integrated circuit by means of a flexible material (e.g., an elastomer); and a processing circuit. The processing circuit may be implemented on the same semiconductor substrate as the magnetic sensors, but this is not absolutely necessary, and the processing circuit may be implemented on a first semiconductor substrate (e.g., a CMOS substrate), and the magnetic sensors may be implemented on one or more sensor substrates (e.g., CMOS, or Ga-As, Ga-In or In-Sb) mounted beside, on top of, or below the first semiconductor substrate, and the one or more sensor substrates are mounted beside, above, or below the first semiconductor substrate in a manner similar to that described in US2022099709(A1), which is incorporated herein by reference in its entirety.

[0326] The plurality of magnetic sensors may be configured to measure at least three or at least four magnetic field components oriented in a first direction, or may be configured to measure at least first and second magnetic field components oriented in a first direction and to measure at least third and fourth magnetic field components oriented in a second direction. The second direction may be the same as the first direction, or may be different from the first direction (e.g., orthogonal thereto).

[0327] The permanent magnet is configured to generate a magnetic field.

[0328] The processing circuit is configured to determine at least one pairwise difference, or at least two pairwise differences, or at least three pairwise differences between the magnetic field components, and to determine and output at least one value, or at least two values, or at least three values related to the position of the magnet relative to the sensor device, or related to the force or pressure applied to the flexible material, based on the one or more pairwise differences (e.g., according to the one or more pairwise differences).

[0329] The force sensor device may be configured to determine the at least one physical quantity or the at least two physical quantities using one or more predefined functions. The function or functions may be stored, for example, in the non-volatile memory of the processing circuit in the form of a mathematical formula (e.g., as a polynomial expression having a plurality of coefficients (e.g., having 3 to 30 coefficients (e.g., having at least 3 or at least 4 or at least 6 or at least 8 or at least 12 coefficients))); or in the form of a sum having 3 to 15 terms (e.g., having at least 3 terms, or at least 4 terms, or at least 6 terms, or at least 8 terms, or at least 10 terms, or at least 12 terms) in the non-volatile memory of the processing circuit; or in the form of a look-up table in the non-volatile memory of the processing circuit. Some terms may be the square of the magnetic field difference, or may be the cross product of two magnetic field differences obtained from sensor pairs spaced apart in the same direction, or may be the cross product of two magnetic field differences obtained from sensor pairs spaced apart in different directions.

[0330] The coefficients or parameters may be determined using machine learning. Alternatively, the coefficients or parameters may be determined using classical techniques (such as, for example, using curve fitting techniques, linear or non-linear regression techniques, or linear or non-linear models). It is noted that "machine learning" or "deep learning" is typically used for "neural networks" having "hidden layers" and generally requires much more computation than classical curve fitting techniques.

[0331] A block diagram similar to the block diagrams of FIGS. 22(a) and 22(b) may be applicable, where blocks 2226 ("feature augmentation and polynomial augmentation") and 2230 ("weights and biases") would be replaced by the predefined function (e.g., the polynomial, or the look-up table).

[0332] The force sensor device may have an appearance as shown in Figures 23(a) to 23(e) but of course, the present invention is not limited thereto.

[0333] The force sensor device may have, for example, three 1D pixels, or four 1D pixels (e.g., as illustrated in Figure 6 ), or three 2D pixels (e.g., as illustrated in Figure 4 ), or four 2D pixels (e.g., as illustrated in Figure 5or Figure 7(a) or Figure 7(b) or Figure 12 or Figure 17(a) or Figure 17(b) or Figure 18 as illustrated therein), or five 2D pixels (e.g., as Figure 8 as illustrated therein), or nine 2D pixels (e.g., as Figure 9 or Figure 10 as illustrated therein), or eight 2D pixels (e.g., as illustrated in Figure 11(a)), or four 2D pixels and one 3D pixel (e.g., as Figure 13 as illustrated therein), or four 3D pixels (e.g., as illustrated in Figure 14(a) or Figure 14(b) or Figure 19(a) or Figure 19(b)), or five 3D pixels (e.g., as illustrated in Figure 15(a) or Figure 15(b)), or nine 3D pixels (e.g., as Figure 16 as illustrated therein).

[0334] In a preferred embodiment, at least two pairwise differences are determined, or at least three pairwise differences are determined, or at least four pairwise differences are determined, or at least six pairwise differences are determined, or at least eight pairwise differences are determined, and the (one or more) output values are determined based on these pairwise differences.

[0335] Many variations of the force sensor device are envisioned, similar to those described above. For example, the force sensor device may further include a temperature sensor, and the temperature may be considered in the calculations, and / or may be used to correct the temperature-dependent material properties of the elastomer.

Claims

1. A magnetic sensor system, comprising: an integrated circuit including a semiconductor substrate having a plurality of magnetic sensors configured to measure at least two first magnetic field components oriented in a first direction and at least two second magnetic field components oriented in a second direction; wherein the semiconductor substrate further includes a temperature sensor for measuring the temperature of the semiconductor substrate; a permanent magnet movable relative to the integrated circuit and configured to generate a magnetic field; a processing circuit configured to determine at least two physical quantities related to the position of the magnet using a predefined algorithm that takes as input the measured first and second magnetic field components or values derived therefrom, and uses a plurality of at least eight constants determined using machine learning, and wherein the predefined algorithm takes the measured temperature into account as an additional input.

2. The magnetic sensor system according to claim 1, Among them, wherein the predefined algorithm uses at least three or at least four magnetic field differences derived from the at least two first magnetic field components and the at least two second magnetic field components as input, and uses the plurality of at least eight constants.

3. The magnetic sensor system according to claim 1, Among them, wherein each of the first direction and the second direction is parallel to the semiconductor substrate; or wherein the first direction is parallel to the semiconductor substrate and the second direction is perpendicular to the semiconductor substrate.

4. The magnetic sensor system according to claim 1, Among them, wherein the plurality of sensors includes at least one sensor including an integrated magnetic concentrator disk and three pairs of horizontal Hall elements arranged near the periphery of the disk, the Hall elements being angularly spaced by a multiple of 120°; or wherein the plurality of sensors includes at least one sensor including an integrated magnetic concentrator disk and four pairs of horizontal Hall elements arranged near the periphery of the disk, the Hall elements being angularly spaced by a multiple of 45°; or wherein the semiconductor substrate includes a plurality of magnetic sensors located at the intersections of a 2×2 grid, or at the intersections of a 3×3 grid, or at the intersections of a 4×4 grid; or wherein the semiconductor substrate includes a plurality of magnetic sensors arranged in an irregular pattern; or wherein at least three of the magnetic sensors are located on a virtual circle.

5. The magnetic sensor system according to claim 1, Among them, wherein the semiconductor substrate includes a plurality of magnetic sensors arranged at pseudo-random positions.

6. The magnetic sensor system according to claim 1, Among them, wherein the magnet is a two-pole magnet; and / or wherein the magnet is an axially magnetized ring-shaped or disk-shaped magnet.

7. The magnetic sensor system according to claim 1, Among them, wherein the predefined algorithm is configured to derive at least two first differences from the at least two first magnetic field components and at least two second differences from the at least two second magnetic field components; and for calculating the at least two physical values based on the at least two first differences and the at least two second differences.

8. The magnetic sensor system according to claim 7, Among them, each of the at least three first differences is determined as a pairwise difference between two first magnetic field components, and wherein each of the at least three second differences is determined as a pairwise difference between two second magnetic field components; or wherein each of the at least three first differences is determined as a difference between a first magnetic field component and a first common value, and wherein each of the at least three second differences is determined as a difference between a second magnetic field component and a second common value.

9. The magnetic sensor system according to claim 7, Among them, the predefined algorithm is configured to calculate each of the physical values as a sum of at least twelve terms, and wherein each of the at least twelve terms is a function of one or more of the differences.

10. The magnetic sensor system according to claim 9, Among them, each of the sums includes a constant value determined by machine learning.

11. The magnetic sensor system according to claim 9, Among them, the predefined algorithm is configured to calculate each of the physical values as a sum of at least twelve terms, wherein at least two terms contain a linear expression of only one of the differences; and wherein at least two terms contain a non - linear expression of one or more of the differences.

12. The magnetic sensor system according to claim 9, Among them, at least two or each sum is a quadratic expression or a second - order polynomial of only one of the differences, or at least two or each sum contains a quadratic expression or a second - order polynomial of only one of the differences; and / or wherein each sum contains at least one term that is a product of two differences; and / or wherein each sum contains at least one term that is a quotient of two differences.

13. The magnetic sensor system according to claim 1, Among them, the predefined algorithm is performed by a trained neural network.

14. The magnetic sensor system according to claim 1, Among them, the magnet is mounted flexibly relative to the integrated circuit by means of a flexible material.

15. The magnetic sensor system according to claim 14, Among them, the flexible material is an elastomer.

16. The magnetic sensor system according to claim 14, Among them, the predefined algorithm further includes a post - processing step in which the temperature of the flexible material is measured or estimated, and wherein the determined physical quantity is corrected to reduce temperature - related material properties.

17. A force sensor system, comprising the magnetic sensor system according to claim 14, Among them, the at least two or at least three physical quantities to be determined are two or three force components (Fx, Fy, Fz) of a mechanical force applied to a contact surface of the flexible material.

18. A rod system for determining the 2D or 3D position of a rod, the rod system comprising: the magnetic sensor system according to claim 1; a rod that can move relative to the integrated circuit with at least two degrees of freedom; wherein the rod is a joystick or a thumb - stick; Wherein, the magnet is fixedly connected to the rod.

19. A method for measuring at least two physical quantities related to the position of a permanent magnet, the permanent magnet being movable relative to an integrated circuit and configured to generate a magnetic field, the method comprising the steps of: a) Measuring at least two first magnetic field components oriented in a first direction; b) Measuring at least two second magnetic field components oriented in a second direction perpendicular to the first direction; c) Measuring the temperature of the semiconductor substrate; d) Using a predefined algorithm to determine the at least two physical quantities, the predefined algorithm using the measured first and second magnetic field components and the measured temperature as inputs, and using a plurality of at least eight constants determined using machine learning.

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