Magnetic sensor device, system and method, and force sensor

Abstract

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

Description

[Technical field]

[0001] The present invention relates generally 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 is indicative of at least two physical quantities, such as, for example, a force component, or a tilt angle of a joystick, or a lateral position of a thumbstick. [Background technology]

[0002] Magnetic sensors, such as current sensors, proximity sensors, position sensors, etc., are known in the art. They are based on measuring magnetic field characteristics at one or more sensor locations. Depending on the application, the measured magnetic field characteristics can be used to subtract other quantities, such as, for example, current strength, the so-called target proximity, the relative position of the sensor device to a magnet, etc. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] European Patent Application Publication No. 4113085 [Patent Document 2] European Patent Application Publication No. 3885779 [Patent Document 3] European Patent Application Publication No. 3885778 [Patent Document 4] Specification of U.S. Patent Application Publication No. 2022 / 099709 Summary of the Invention [Problem to be solved by the invention]

[0004] Many variations of magnetic sensor devices, systems and methods exist, addressing one or more of the following requirements: using simple or inexpensive magnetic structures, using simple or inexpensive sensor devices, being able to measure over a relatively large range, being able to measure very accurately, requiring only simple arithmetic, being able to measure at high speed, being robust to positioning errors, being robust to disturbance 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 are often in conflict with one another, so trade-offs must be made.

[0005] The present invention relates to a type of magnetic sensor system comprising a permanent magnet flexibly or resiliently mounted to a semiconductor substrate, the position of the magnet indicating a 2D or 3D physical quantity, such as a force vector or a displacement vector, caused by a force applied to a surface or caused by the movement of a joystick or thumbstick or the like.

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

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

[0008] It is an object of embodiments of the present invention to provide a system and method that is less sensitive to external disturbance fields, and / or less sensitive to temperature variations, and / or less sensitive to magnet demagnetization, and preferably two or all of these.

[0009] It is an objective of embodiments of the present invention to provide such systems and methods that use algorithms that do not require explicit analytical or mathematical formulas or expressions.

[0010] For purposes of this embodiment of the present invention, the magnets are embedded in the elastomer above or on top of the semiconductor circuitry.

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

[0012] It is an object of embodiments of the present invention to provide a magnetic sensor system and method in which the magnetic field is measured at at least four sensor locations or at least five sensor locations.

[0013] It is an object of an embodiment of the present invention to provide a magnetic sensor system and method in which the magnet is an axially magnetized two-pole magnet.

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

[0015] It is an object of embodiments of the present invention to provide a magnetic sensor system and method in which the time required to determine the at least two physical quantities is 50 ms or less, or 40 ms or less, or 30 ms or less, or 20 ms or less, or 10 ms or less.

[0016] It is also an object of embodiments of the present invention to provide a semiconductor device (i.e., a single chip) comprising at least a plurality of sensors for measuring magnetic fields, and optionally also comprising processing circuitry for determining said at least two physical quantities.

[0017] It is also an object of an embodiment of the present invention to provide a force sensor system.

[0018] It is an aim of certain embodiments of the present invention to provide a force sensor system capable of measuring two or three force components (i.e. 2D or 3D force vectors) using such a magnetic sensor system.

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

[0020] It is also an object of embodiments of the present invention to provide a joystick system with two degrees of freedom (eg, two tilt movements) or with three degrees of freedom (two tilt movements and a down movement).

[0021] It is also an object of embodiments of the present invention to provide a thumbstick system having two degrees of freedom (e.g., two lateral movements) or three degrees of freedom (two lateral movements and a downward movement). [Means for solving the problem]

[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 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 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 with respect to the integrated circuit and configured to generate a magnetic field, and a (integrated circuit) and a processing circuit (internal or external to the circuit) configured to determine at least two physical quantities related to the position of the magnet (e.g., a 2D or 3D force vector, a 2D or 3D displacement vector, a 2D or 3D position of the joystick, a 2D or 3D position of the thumbstick) using a predefined algorithm that is based on the measured first and second magnetic field components (Bx1, Bx2; Bz1, Bz2) or values ​​derived therefrom as input and that uses a plurality of at least eight (or at least twelve, or at least eighteen) constants (or coefficients or parameters) determined using machine learning.

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

[0025] The inventors have discovered that even when a magnet moves in a highly nonlinear manner, e.g., due to a particular mechanical mounting arrangement, e.g., using an elastomer with a nonlinear stress-strain curve, it is not necessary to find an explicit analytical formula, or a mathematical model with a minimum number of variables, to express the relationship between the physical quantities and the magnet's motion.

[0026] It has been discovered that it is possible to determine physical quantities with great accuracy by implementing a predefined algorithm that uses a number of constants (or parameters) determined by machine learning (ML). It has been found that this approach makes it possible to determine or approximate the desired physical quantities in a manageable manner.

[0027] Those skilled in the art, having the benefit of this disclosure, will be able to readily find suitable algorithms that meet their needs by simply applying the teachings of the present invention.

[0028] Such a magnetic sensor system may be particularly suitable for applications where small errors in absolute accuracy are not detrimental to the application in which the system is used.

[0029] In an embodiment, the processing circuitry is configured to determine the at least two physical quantities using a predefined algorithm that uses as input 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, and that uses 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 may be calculated as a magnetic field gradient or by subtracting an average magnetic field component oriented in the same direction as the original magnetic field component.

[0031] In an embodiment, the integrated circuit comprises a first programmable processor as part of said processing circuitry configured to execute at least a portion of said algorithm.

[0032] The processing circuitry may be implemented on the same semiconductor die that contains the magnetic sensor, or may be implemented on a second semiconductor die connected to the first semiconductor die and also embedded in the same package.

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

[0034] In this embodiment, the integrated circuit preferably includes outputs configured to provide at least two or three physical values ​​(eg, a force value, an angle value, etc.).

[0035] In an embodiment, the magnetic sensor system further comprises a second programmable processor as part of the processing circuitry communicatively connected to, but external to, the integrated circuit, 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 embodiments, the integrated circuit includes a plastic molded package, and the elastomer is disposed on top of and in direct contact with the molded package. In some embodiments, the elastomer does not extend laterally beyond the package (i.e., is supported only by the package). In other embodiments, the elastomer may extend laterally beyond the package, for example, to contact a printed circuit board to which the packaged device is mounted and / or soldered.

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

[0038] As a rule of thumb, a larger number of coefficients results in greater accuracy for a given measurement range, but at the expense of larger circuitry (if implemented in hardware) or more calculations (if implemented in software). However, the inventors have discovered that the number of constants not only affects the amount of calculations and accuracy, but also the type of function used in the algorithm.

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

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

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

[0042] For example, in some embodiments, the measured temperature is used to correct the sensitivity of the sensor elements. In some embodiments, the temperature is taken into account as an additional input (e.g., of a neural network). In some embodiments, for example, when elastomers are used, the measured temperature can 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, the sensors are configured to measure magnetic field components (e.g., the first and second magnetic field components 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 (eg, X) and the second direction (eg, 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 implemented using vertical Hall elements, MR elements, horizontal Hall elements + IMC, or a combination of these.

[0046] In an embodiment, the first direction (eg, X) is parallel to the semiconductor substrate, and the second direction (eg, 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 components (e.g., Bz). This can be implemented using a combination of horizontal and vertical Hall elements, or using a combination of MR elements and horizontal Hall elements, or using horizontal Hall elements and integrated flux concentrators (IMCs).

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

[0049] In this embodiment, the sensor may be 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 may be implemented using a combination of horizontal and vertical Hall elements, or using a combination of MR elements and horizontal Hall elements, or using a horizontal Hall element and an IMC.

[0050] In an embodiment, the plurality of sensors comprises at least one sensor (preferably at least two, at least three, or at least four sensors) comprising 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 apart by multiples of 120°.

[0051] In an embodiment, the plurality of sensors comprises at least one sensor (preferably at least two, or at least three, or at least four sensors) comprising an integrated magnetic concentrator disk and four pairs of horizontal Hall elements positioned about the periphery of the disk and angularly spaced apart by multiples of 45°. Examples of such sensors are shown in Figures 20 and 21.

[0052] In an embodiment, the semiconductor substrate comprises a plurality of magnetic sensors located at the intersections of a 2x2 grid (i.e. the four corners of an imaginary square), or at the intersections of a 3x3 grid, or at the intersections of a 4x4 grid. Preferably, the columns and rows of the grid are equally spaced.

[0053] In an embodiment, a semiconductor substrate comprises a plurality of magnetic sensors arranged in an irregular pattern, for example at pseudo-random locations.

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

[0055] The imaginary circle may have a diameter in the range of 1.0 mm to 3.0 mm, or in the range of 1.5 mm to 2.5 mm, or in the range of 1.7 to 2.3 mm, for example a diameter equal to about 1.8 mm, or equal to about 2.0 mm, or equal to about 2.2 mm.

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

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

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

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

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

[0061] In an embodiment, the magnet is a two-pole magnet, for example a two-pole bar magnet, or a diametrically magnetized ring or disk magnet. 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, for example an axially magnetized ring or disk magnet. The magnetization direction of the magnet may be oriented substantially perpendicular to the semiconductor substrate or substantially parallel to the semiconductor substrate.

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

[0064] In an embodiment, the sensor system comprises three magnets arranged on an imaginary circle above the semiconductor substrate and angularly spaced 120° apart.

[0065] In an embodiment, the sensor system comprises four magnets arranged on an imaginary circle above the semiconductor substrate and angularly spaced 90° apart.

[0066] In an embodiment, the sensor system comprises six magnets arranged on an imaginary circle above the semiconductor substrate and angularly spaced 60° apart.

[0067] In an embodiment, the magnets are (a) two-pole disk magnets each having an outer diameter or maximum diagonal that is smaller than the diameter of the imaginary circle mentioned above in which at least three of the magnetic sensors are located.

[0068] In an embodiment, the magnet is (a) a two-pole disk magnet having an outer diameter or maximum diagonal substantially equal (within ±20%) to the diameter of the imaginary circle described above on which at least three of the magnetic sensors are located.

[0069] In an embodiment, the magnet is (a) a two-pole disk magnet having an outer diameter or maximum diagonal that is greater than the diameter of the imaginary circle mentioned above in which at least three of the magnetic sensors are located.

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

[0071] In an embodiment, the magnet has a central axis that intersects the semiconductor substrate at a location that is offset from the central location of the magnetic sensor ("off-axis placement"). If the sensor is placed on an NxN grid, the offset may be half the distance between two adjacent grid lines.

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

[0073] The use of such magnets is advantageous because the magnetic field generated by them is rotation invariant, meaning that it is independent of rotation of the magnet about its axis, and 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 difference values ​​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 difference values ​​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 at least three, or at least four) physical values ​​(e.g., force components, or angles, or displacements) based on the at least two (or at least three, or at least four) first difference values ​​and the at least two (or at least three, or at least four) second difference values.

[0075] It is explicitly pointed out that this part of the algorithm may be implemented inside an integrated circuit including the magnetic sensor, or outside the integrated circuit including the magnetic sensor (e.g. in an electronic control unit connected to the sensor device), or partly implemented inside the sensor device (e.g. for some difference values) and partly implemented outside the sensor device (e.g. for some other difference values).

[0076] A major advantage of using the difference value is that the result is very insensitive to disturbance fields. To the inventors' knowledge, there is no force sensor in the prior art that is immune to stray magnetic fields.

[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. This embodiment is not theoretically 100% immune to stray magnetic fields, but may still have a relatively wide range of stray magnetic field rejection.

[0078] In an embodiment, each of the at least three first difference values ​​is determined as a pairwise difference between two first magnetic field components, and each of the at least three second difference values ​​is determined as a pairwise difference-to-difference between two second magnetic field components. This may be referred to as a "magnetic field gradient" and may be described in mathematical terms as, for example, dx1=Bx1-Bx2; dx2=Bx1-Bx3, dx3=Bx2-Bx3, and dz1=Bz1-Bz2; dz2=Bz1-Bz3, dz3=Bz2-Bz3.

[0079] In an embodiment, each of the at least three first difference values ​​is determined as a difference between a first magnetic field component and a first common value, and each of the at least three second difference values ​​is determined as a difference between a second magnetic field component and a second common value.

[0080] The first common value may be the first magnetic field component measured at a fourth sensor location (preferably the central sensor location) or may be the average of at least three first magnetic field components. This may be referred to as "average removal" and may be described in mathematical terms, for example, as follows (assuming that the semiconductor substrate has only three 2D sensors measuring Bx and Bz, respectively): 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.

[0081] In an embodiment, the predefined algorithm is configured to calculate each of the physical values ​​as a sum of at least twelve terms, each of which is a function of one or more of the differences.

[0082] In an embodiment, each of the sums includes a constant value determined by machine learning.

[0083] Machine learning is typically applied on a batch basis, rather than on an individual product basis.

[0084] 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 including a linear expression of only one of the differences and at least two terms including a non-linear expression of one or more of the differences.

[0085] Thus, at least two of the terms are scaled versions of only one of the differences, e.g., (K1*dx1) or (K2*dx1+K3), where the constants K1, K2, K3 are determined by machine learning.

[0086] In an embodiment, each of the terms is one or more constants or algebraic functions of the difference.

[0087] An "algebraic function" is a class of functions that includes: "polynomial functions" (e.g., constants, linear functions, quadratic functions, cubic functions) and "rational functions" (i.e., the ratio of two polynomial functions). Algebraic functions also include "piecewise functions" such as absolute value functions, floor functions, ceiling functions, and sign functions. Algebraic functions do not include the so-called "transcendental functions", which are a group of functions whose independent variables appear as exponents, exponents of power roots, logarithmic ratios, or trigonometric ratios.

[0088] In other words, in this embodiment, none of the terms are or include exponential functions, logarithmic functions, or trigonometric functions (e.g., sine, cosine, tangent, cosecant, secant, cotangent), or inverse trigonometric functions (e.g., arctangent).

[0089] Using "only" algebraic functions and excluding transcendental functions is advantageous because algebraic functions are cheaper in terms of processing power or processing time and can be implemented on embedded processors.

[0090] In an embodiment, at least two terms or each sum is or includes a quadratic expression or quadratic polynomial in only one of the differences.

[0091] For example, K1*sqr(dx1), or K2*sqr(dx1-K3), or K4+(K5*dx1)+K6*(dx1)2, where K1 to K6 are constants.

[0092] In an embodiment, some of the terms are third order or fourth order polynomials.

[0093] In a preferred embodiment, none of the terms are polynomials greater than a fourth order polynomial. Using polynomials of fourth order or less, or third order or less, or second order or less, is advantageous as it requires less processing time and power.

[0094] In an embodiment, each sum includes at least one term that is the product of two differences (eg, K7*dx1*dz1).

[0095] It has been discovered that using products of the difference signals is very useful in improving the accuracy of the results. Although the inventors do not wish to be bound by any theory, certain products of the differences appear to have a good correlation with the physical motion of the magnet, although the correlation is not immediately apparent to a human observer.

[0096] In an embodiment, each sum includes at least one term that is a division of two differences (eg, K8*dx1 / dz1).

[0097] Using a ratio of two magnetic field values ​​(eg, the difference) is advantageous because such a ratio is more robust to temperature variations and demagnetization effects.

[0098] In an embodiment, the predefined algorithm is executed by a trained neural network that uses 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 provides at least two (or at least three) physical values ​​as output values.

[0099] The predefined algorithm may include a neural network having multiple layers, each layer including multiple nodes.

[0100] In an embodiment, the neural network includes only one layer having between 12 and 100 nodes.

[0101] In an embodiment, the neural network includes only two layers, each having between 10 and 100 nodes, or between 20 and 60 nodes.

[0102] In an embodiment, the neural network includes only three layers, each having between 10 and 100 nodes, or each having between 5 and 50 nodes.

[0103] In an embodiment, the neural network is a recurrent neural network (RNN).

[0104] In an embodiment, the neural network is an artificial neural network (ANN).

[0105] In an embodiment, the neural network is a convolutional neural network (CNN).

[0106] In an embodiment, the predefined algorithm further includes a post-processing step configured to adjust the determined physical quantity (e.g., determined by the proprietary algorithm described above or determined by a neural network) by adding or subtracting an offset value determined by an individual calibration test.

[0107] "Individual calibration testing" means that this testing is performed individually for each magnetic sensor system, as opposed to machine learning, which is typically performed on a batch basis.

[0108] This "individual calibration test" is preferably performed as an EOL test (end of line test) or may be performed by the OEM customer.

[0109] In the case of a force sensor system or force sensor device or joystick or the like, this calibration test may include: (i) performing a force measurement while applying zero force using a predefined algorithm that uses multiple constants or parameters determined by machine learning (typically determined on a batch basis), typically resulting in two or three force or position values ​​that are slightly offset from zero, and (ii) storing these values ​​in a non-volatile memory of the system, for example in an integrated circuit.

[0110] During normal use of the sensor device, a correction is applied by first providing two or more measurements based on parameters determined by machine learning using a predefined algorithm, and then subtracting the values ​​measured during the calibration step mentioned above.

[0111] Combining the best of both worlds, i.e., a very good approximation of the physical value measured using a predefined algorithm, with multiple constants determined on a batch basis by machine learning, but then corrected so that the "zero force" or "neutral position" of a joystick etc. is offset corrected for each individual product, is a major advantage of this embodiment.

[0112] In an embodiment, the magnet is flexibly mounted to the integrated circuit by a flexible material.

[0113] The flexible material may be a single layer of isotropic material with no voids or hollow areas. The material and magnet may be shaped and sized such that the magnet can move in three directions, X, Y, and Z, but does not rotate significantly about its center (e.g., less than ±10°, or less than ±5° over the measurement range of the force sensor system).

[0114] In an embodiment, the flexible material is a polymer.

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

[0116] The elastomer may be placed above or on top of the integrated circuit, and in a preferred embodiment, the elastomer may be in direct contact with the package of the integrated circuit.

[0117] In an embodiment, the elastomer is or includes a silicone, e.g., a silicone rubber, e.g., a natural rubber.

[0118] In an embodiment, the flexible material has a non-linear stress-strain characteristic, and a linear regression coefficient of a 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.

[0119] In other words, in these embodiments, the curve showing strain as a function of stress for this material is a highly non-linear function.

[0120] In an embodiment, the predefined algorithm further comprises a post-processing step in which the temperature of the flexible material is measured or estimated and the determined physical quantity is corrected to reduce temperature dependent material properties.

[0121] The correction may use predefined correction functions for each of the determined physical quantities individually.

[0122] The compensation function may be, for example, a temperature dependent scaling. The function f(.) may be stored in the form of a look-up table, or as a piecewise linear approximation, or as an analytical function, for example as a polynomial expression.

[0123] A temperature sensor may be integrated inside the integrated circuit, and the temperature of the temperature sensor may be used as an estimate of the elastomer.

[0124] In an embodiment, the predefined algorithm further comprises a post-processing step, or if already present, the post-processing step further comprises an offset correction for each of the output values ​​by subtracting a predefined value stored in the non-volatile memory during the calibration procedure.

[0125] The present invention also provides a force sensor system comprising a magnetic sensor system according to a first aspect, wherein the at least two or three physical quantities to be determined are two or three force components (Fx, Fy, Fz) of a mechanical force exerted on a contact surface of said flexible material.

[0126] The magnetic sensor system may be referred to as a "force sensor system" and the integrated circuit may be referred to as a "force sensor device."

[0127] The force components Fx and Fy are typically referred to as shear or lateral forces. The force component Fz is typically referred to as the downward pressure.

[0128] In an embodiment, the flexible material is located above or on top of the integrated circuit, for example as a layer deposited on the package, and the magnet is at least partially or completely embedded within the flexible material.

[0129] The constants (or parameters or coefficients) may be determined by applying a series of tests in which a number of known forces having only an Fx component are applied, followed by another series of tests in which a number of known forces having only an Fy component are applied, followed by another series of tests in which a number of known forces having only an Fz component are applied, with each component value taking a value within a respective predefined measurement range.

[0130] Alternatively, multiple constants (or parameters or coefficients) may be determined by applying a series of tests in which three-dimensional forces are applied and have Fx, Fy, Fz components within their respective measurement ranges.

[0131] In an embodiment, the multiple constants are determined by applying a series of known forces, with each of the Fx, Fy, and Fz values ​​"sweeping" their respective measurement ranges, for example, every 5 steps, i.e., 5 x 5 x 5 = 125 different combinations, or every 6 steps, i.e., 6 x 6 x 6 = 216 different combinations, or every 7 steps, i.e., 343 combinations, or every 8 steps, i.e., 512 combinations, or every 9 steps, i.e., 729 combinations, or every 10 steps, i.e., 1000 different combinations.

[0132] In an embodiment, no disturbance fields are applied during these steps, and it goes without saying that it is a great advantage that the influence of disturbance fields is substantially eliminated by design (by considering gradient or average correction values).

[0133] In another embodiment, a disturbance field is applied during these steps, which may take pseudo-random values ​​for each step.

[0134] The present invention also provides a robotic finger comprising at least one force sensor system.

[0135] The present invention also provides a robotic hand comprising at least two robotic fingers.

[0136] The present invention also provides a joystick system or joystick assembly for determining a 2D or 3D position of a joystick, comprising a magnetic sensor system according to the first aspect and a joystick movable relative to an integrated circuit in at least two degrees of freedom, wherein a magnet is fixedly connected to the joystick.

[0137] For example, the joystick system may determine two angle values ​​to indicate the position of the joystick, for example, as shown in Fig. 25. The joystick may be rotatable about a pivot point. The pivot point may be located above a magnet. In other words, the magnet may be located between the pivot point and the semiconductor substrate.

[0138] Joysticks may be used in consumer electronics applications (eg, for gaming) or for agricultural vehicles.

[0139] An exemplary embodiment of the joystick includes a bearing whereby a control lever is mounted for movement with at least two degrees of freedom relative to the housing. The control lever has a portion movable by a user and an inner portion that are opposed to one another on different sides of the bearing in a longitudinal direction. A magnet is disposed on the control lever. A semiconductor substrate having a plurality of magnetic sensors is disposed in a fixed location relative to the housing.

[0140] The present invention also provides a thumbstick system or assembly for determining the 2D or 3D position of a thumbstick, comprising a magnetic sensor system according to the first aspect and a thumbstick movable relative to an integrated circuit in two or three degrees of freedom, wherein a magnet is fixedly connected to the thumbstick.

[0141] The thumbstick system may, for example, determine two lateral displacement values ​​to indicate the position of the joystick and, optionally, may also indicate whether a drumstick is pressed down (or depressed).

[0142] According to another aspect, the invention also provides a method for measuring at least two physical quantities (e.g., a 2D or 3D force vector, a 2D or 3D displacement vector, a 2D or 3D position of a joystick, a 2D or 3D position of a thumbstick) related to the position of a permanent magnet 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); and b) measuring at least two (or at least three) first magnetic field components (e.g., Bx1, Bx2; Bx1, Bx2, Bx3) perpendicular to the 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 direction (e.g., Y or Z); and c) determining the at least two physical quantities using a predefined algorithm using the measured first and second magnetic field components (e.g., Bx1, Bx2, Bx3; Bz1, Bz2, Bz3) as input and a plurality of at least eight (or at least twelve, or at least sixteen) constants (or coefficients or parameters) determined using machine learning.

[0143] In an embodiment, the method has one or more of the features described above.

[0144] According to another aspect, the present invention also provides an integrated semiconductor device comprising a plurality of sensors having a topology as shown in any of Figures 3(a) to 21, or a variation thereof as described in the [Description of Embodiments], comprising block 2222 (sensitivity correction) and one or both of blocks 2224 (average removal) and 2232 (slope calculation) as shown in Figures 22(a) and 22(b), and configured to output values ​​provided by blocks 2223 or 2232, e.g., via a serial bus, e.g. using an I2C or SPI or SENT protocol.

[0145] According to another aspect, the present invention also provides a force sensor device or system comprising an 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 (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), e.g. 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 (internal or external to 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.

[0146] According to another aspect, the present invention also provides a force sensor device comprising an integrated circuit comprising a semiconductor substrate, the semiconductor substrate being configured to measure at least three or at least four magnetic field components oriented in a first direction, or configured to measure at least a first magnetic field component and a second magnetic field component oriented in a first direction and configured to measure at least a third magnetic field component and a fourth magnetic field component oriented in a second direction; a permanent magnet flexibly attached to the integrated circuit by a flexible material and 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 exerted on the flexible material based on pairwise differences of at least two or at least three of the magnetic field components.

[0147] In an embodiment, the processing circuitry is implemented on the same semiconductor substrate as the magnetic sensors. In another embodiment, the processing circuitry 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 next to, on top of, or below the first semiconductor substrate.

[0148] In an embodiment, the second direction is the same as the first direction, hi another embodiment, the second direction is different from the first direction, for example, perpendicular to the first direction.

[0149] The force sensor device may be configured to determine said physical quantity using one or more predefined functions. This function or these functions may be stored in the non-volatile memory of the processing circuit, for example in the form of a mathematical formula, for example as a polynomial with a number of coefficients (for example with 3 to 30 coefficients, for example with 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 with 3 to 15 terms (for example with 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), or in the form of a look-up table. Some of the terms may be the square of the magnetic field difference, or may be the cross product of two magnetic field differences obtained from a pair of sensors spaced apart in the same direction, or may be the cross product of two magnetic field differences obtained from a pair of sensors spaced apart in different directions.

[0150] The coefficients or parameters may be determined using machine learning. Alternatively, the coefficients or parameters are determined using classical techniques, such as, for example, using curve fitting techniques, linear or non-linear regression techniques, or linear or non-linear models.

[0151] 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.

[0152] In an embodiment, at least two pairwise differences are determined, or at least three pairwise differences are determined, or at least four pairwise differences, or at least six pairwise differences, or at least eight pairwise differences are determined, and an output value is determined based on these pairwise differences.

[0153] Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features from the dependent claims may be combined with features of the independent claims and with features of other dependent claims as appropriate and not merely as explicitly set out in the claims.

[0154] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. [Brief description of the drawings]

[0155] [Figure 1] FIG. 1 is a schematic block diagram of a sensor circuit known in the art. [Diagram 2] FIG. 1 is a schematic block diagram of a sensor circuit known in the art. [Figure 3(a)] 1 is a schematic diagram of an exemplary embodiment of a magnetic sensor system comprising a permanent magnet that is movable relative to a semiconductor substrate; [Figure 3(b)] FIG. 2 is a schematic diagram of another exemplary embodiment of a magnetic sensor system comprising a permanent magnet movable relative to two semiconductor substrates arranged side by side; [Figure 4] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Diagram 5] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 6] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 7(a)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 7(b)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 8] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 9] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 10] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 11(a)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 11(b)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 11(c)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 11(d)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 12] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 13] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 14(a)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 14(b)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 15(a)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 15(b)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 16] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 17(a)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 17(b)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 18] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 19(a)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 19(b)] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 20] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 21] FIG. 2 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. [Figure 22(a)] FIG. 1 shows a schematic block diagram of a magnetic sensor system proposed by the present invention. [Figure 22(b)] 3 shows a schematic block diagram of another magnetic sensor system proposed by the present invention; [Figure 23(a)] 1 illustrates an example of a mechanical device or sensor assembly that may be used in an embodiment of the present invention. [Figure 23(b)] 1 illustrates an example of a mechanical device or sensor assembly that may be used in an embodiment of the present invention. [Figure 23(c)] 1 illustrates an example of a mechanical device or sensor assembly that may be used in an embodiment of the present invention. [Figure 23(d)]1 illustrates an example of a mechanical device or sensor assembly that may be used in an embodiment of the present invention. [Figure 23(e)] 1 illustrates an example of a mechanical device or sensor assembly that may be used in an embodiment of the present invention. [Figure 24(a)] An image of the prototype force sensor system is shown. [Figure 24(b)] An image of the prototype force sensor system is shown. [Figure 24(c)] 1 shows an image of the mechanical setup used to apply a known force. [Figure 25(a)] The results of measurements of Bx and Bz are shown when a force Fz oriented in a direction perpendicular to the semiconductor substrate is applied. [Figure 25(b)] The results of measurements of Bx and Bz are shown when a force Fz oriented in a direction perpendicular to the semiconductor substrate is applied. [Figure 26] 1 illustrates a computer model of a mechanical device that can be used to simulate an embodiment of the present invention that includes an elastomer. [Figure 27(a)] 13 shows the correspondence between the forces measured with the calibration setup and those predicted by the force sensor algorithm. [Figure 27(b)] 13 shows the correspondence between the forces measured with the calibration setup and those predicted by the force sensor algorithm. [Figure 27(c)] A "force error histogram" is shown. [Figure 27(d)] A "force error histogram" is shown. [Figure 28] 13 is a graph illustrating the error in the measured shear force Fx as a function of an applied disturbance field in the X direction with and without the use of an averaging block. [Figure 29] 1 shows a graph illustrating the magnitude of a force Fz oriented in a direction towards the semiconductor substrate versus the displacement of the magnet. [Diagram 30] FIG. 30 is a schematic block diagram of a sensor device 3010 as may be used in embodiments of the present invention. [Diagram 31]It is used to show that the principles of the present invention can also be used to determine the tilt angles φ and ψ of a joystick assembly. [Diagram 32] 32 shows a flow chart of a method 3200 for measuring at least two physical quantities related to the position of a permanent magnet as proposed by the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0156] The drawings are only schematic and non-limiting. In the drawings, the size of some of the elements may be exaggerated and not drawn to scale for illustrative purposes. Any reference signs in the claims should not be construed as limiting the scope. In different drawings, the same reference signs refer to the same or similar elements.

[0157] The present invention will be described with respect to particular embodiments and with reference to certain drawings but the invention is not limited thereto but only by the claims.

[0158] Terms such as first, second, etc. in this specification and claims are used to distinguish between similar elements and are not necessarily used to describe an order, temporally, spatially, sequentially, or in any other manner. It will be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operating in orders other than those described or illustrated herein.

[0159] Terms such as up, down, and the like in this specification and claims are used for purposes of explanation and not necessarily to describe relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in orientations other than those described or illustrated herein.

[0160] It should be noted that the term "comprising" used in the claims should not be interpreted as being limited to the means listed thereafter, and does not exclude other elements or steps. Thus, when mentioned, it should be interpreted as specifying the presence of the stated features, elements, steps or components, but without excluding the presence or addition of one or more other features, elements, steps, components, or groups thereof. Thus, the scope of the expression "a device comprising means A and means B" should not be limited to a device consisting of only components A and B. This means that in the context of the present invention, the only relevant components of the device are A and B.

[0161] References throughout this specification to "one embodiment" or "an embodiment" mean that a particular feature, structure, or characteristic described in connection with an embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase "in one embodiment" or "in an embodiment" in various places throughout this specification do not necessarily all refer to the same embodiment, although they may. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, as would be apparent to one of ordinary skill in the art from this disclosure.

[0162] Similarly, in describing exemplary embodiments of the invention, it should be understood that various features of the invention may be grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and facilitating understanding of one or more of the various inventive aspects. However, this method of disclosure should not be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the Detailed Description are expressly incorporated into this Detailed Description, with each claim standing on its own as a separate embodiment of the invention.

[0163] Furthermore, although some embodiments described herein include some but not others features that are included in other embodiments, as will be understood by those skilled in the art, combinations of features of different embodiments are meant to be within the scope of the invention and form different embodiments. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0164] In the description provided herein, numerous specific details are set forth. However, it is 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 in order not to obscure an understanding of this description.

[0165] In this document, unless expressly stated otherwise, the term "magnetic sensor device" or "sensor device" preferably refers to a device comprising at least two magnetic sensor elements integrated in a semiconductor substrate. The sensor device may be included in a package also called a "chip", although this is not absolutely necessary.

[0166] 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 magnetoresistance element (eg a GMR element or an XMR element).

[0167] In this document, the terms "magnetic sensor" or "magnetic sensor structure" may refer to a group of components or sub-circuits or structures capable of measuring a magnetic quantity, such as, for example, a group of at least two magnetic sensor elements, or a Wheatstone bridge including four MR elements.

[0168] In certain embodiments of the invention, the terms "magnetic sensor" or "magnetic sensor structure" may refer to a configuration that includes one or more integrated magnetic concentrators (IMCs), also known as integrated magnetic flux concentrators, and two, four, or eight horizontal Hall elements arranged near the periphery of the IMCs.

[0169] 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" mean the same thing. If the sensor device is or includes a semiconductor substrate, this also means "magnetic field component parallel to the semiconductor substrate".

[0170] In this document, the expressions "out-of-plane component of a vector" and "Z component of a vector" and "orthogonal projection of a vector on an axis perpendicular to the sensor plane" mean the same thing.

[0171] Embodiments of the present invention are typically described using a Cartesian coordinate system having three axes X, Y, Z fixed to the sensor device, with the X and Y axes parallel to the substrate and the Z axis perpendicular to the substrate.

[0172] In this document, the expressions "spatial differential" or "derivative" or "spatial gradient" or "gradient" are used synonymously. In the context of the present invention, the gradient is determined as the difference between two values ​​measured at two different locations, which may be separated by a distance ranging from 1.0 mm to 3.0 mm. In theory, the gradient is calculated as the difference between the two values ​​divided by the distance "dx" between the sensor locations, but in practice the division by "dx" is often omitted since the measured signal needs to be scaled anyway.

[0173] In this document, horizontal Hall plates are typically referred to as H1, H2, etc., and 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 signals from these vertical Hall plates are typically referred to as v1, v2, etc.

[0174] In this document, when referring to machine learning or deep learning, the terms "coefficients", or "parameters", or "constants" mean the same thing regardless of whether these values ​​are used as coefficients in a matrix, or as offset values, or as scaling factors.

[0175] The present invention relates generally 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 is indicative of at least two physical quantities, such as, for example, a force component, or a tilt angle of a joystick, or a lateral position of a thumbstick.

[0176] Referring to the drawings: FIG. 1 is a schematic block diagram of a sensor circuit known in the art. The sensor circuit comprises a first sensor (or sensor structure) at a first sensor location X1 and a second sensor (or sensor structure) at a second sensor location X2 along the X-axis, each sensor structure comprising an integrated magnetic concentrator (IMC) and two horizontal Hall elements arranged on either side of the IMC, also referred to herein as "2D magnetic pixels". Each of these 2D magnetic pixels can measure the Bx and Bz magnetic field components at the center of the IMC disk. The sensor circuit of FIG. 1 with two 2D pixels can be used to determine two magnetic field gradients dBx / dx and dBz / dx along the X-axis.

[0177] Fig. 2 is a schematic block diagram of a sensor circuit known in the art, which is a variation of Fig. 1. The sensor circuit comprises a first sensor structure at a first sensor location X1 and a second sensor structure at a second sensor location X2 along the X-axis, each sensor structure comprising an integrated magnetic concentrator (IMC) and four horizontal Hall elements arranged around the IMC, 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. The sensor circuit of Fig. 2 with two 3D pixels can be used to determine three magnetic field gradients along the X-axis: dBx / dx, dBy / dx, and dBz / dx.

[0178] 3(a) is a schematic diagram of an exemplary embodiment of a magnetic sensor system comprising a permanent magnet movable relative to a semiconductor substrate. The semiconductor substrate comprises a plurality of magnetic sensors. Although not explicitly shown in FIG. 3(a), the semiconductor substrate may be embedded in a 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 magnet.

[0179] 3(b) is a schematic diagram of another exemplary embodiment of a magnetic sensor system comprising a permanent magnet movable relative to two semiconductor substrates arranged side by side, each of which comprises a plurality of magnetic sensors. Although not explicitly shown in FIG. 3(b), the semiconductor substrates may be embedded in a single packaged device, and the magnets may be embedded in an elastomer located above or on top of the packaged device. The magnets may be axially magnetized two-pole disk magnets.

[0180] FIG. 4 is a schematic block diagram of a sensor circuit as may be used in an embodiment of the present invention. The sensor circuit comprises three 2D magnetic pixels located on an imaginary circle. In the illustrated example, the three sensors are angularly spaced apart by multiples of 120°. Each sensor can measure a Bx magnetic field component parallel to the semiconductor surface (also referred to as an "in-plane magnetic field component") and a Bz magnetic field component perpendicular to the semiconductor surface (also referred to as an "out-of-plane magnetic field component"). The sensor circuit can measure six magnetic field components of the magnetic field generated by the magnet, which may be referred to herein as (Bx1, Bz1) at a first sensor location, (Bx2, Bz2) at a second sensor location, and (Bx3, Bz3) at a third sensor location. When the sensor circuit is used in the magnetic sensor system of FIG. 3(a) or FIG. 3(b) or variations thereof, the magnet is preferably located substantially above the center of the imaginary circle.

[0181] FIG. 5 is a schematic block diagram of a sensor circuit as may be used in an embodiment of the present invention. The sensor circuit comprises four 2D magnetic pixels, three of which are located on an imaginary circle, one of which is located at the center of the imaginary circle. The sensor circuit of FIG. 5 may be considered as a variation of the sensor circuit of FIG. 4 with an additional 2D magnetic pixel locator at the center. The sensor circuit may measure eight magnetic field components of the magnetic field generated by the magnet, which may be referred to herein as (Bx1, Bz1) at the first sensor location, (Bx2, Bz2) at the second sensor location, (Bx3, Bz3) at the third sensor location, and (Bx4, Bz4) at the fourth sensor location. When this sensor circuit is used in the magnetic sensor system of FIG. 3(a) or FIG. 3(b) or variations thereof, the magnet is preferably located substantially above the center of the imaginary circle.

[0182] In a variation of Figure 5 (not shown), the centrally located sensor is a 3D magnetic pixel instead of a 2D magnetic pixel (e.g. as in Figures 13 and 15) and is configured to measure three orthogonal magnetic field components Bx4, By4, Bz4 at a fourth sensor location.

[0183] FIG. 6 is a schematic block diagram of a sensor circuit as may be used in an embodiment of the present invention. The sensor circuit comprises four 1D magnetic pixels, three of which are located on an imaginary circle, one of which is located at the center of the imaginary circle. In the illustrated example, each sensor is a horizontal Hall element. The sensor circuit can measure four magnetic field components of the magnetic field generated by a magnet, which may be referred to herein as (Bz1) at a first sensor location, (Bz2) at a second sensor location, (Bz3) at a third sensor location, and (Bz4) at a fourth sensor location. When the sensor circuit is used in the magnetic sensor system of FIG. 3(a) or FIG. 3(b) or a variation thereof, the magnet is preferably located substantially above the center of the imaginary circle.

[0184] The inventors have reached the 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 disturbance field, since only Bz_ext is unknown (Bx_ext and By_ext are inconsequential in this case).

[0185] In a variation of Fig. 6 (not shown), the sensor circuit includes five horizontal Hall elements, four of which are located on an imaginary circle and angularly spaced apart by multiples of 90°, one of which is located at the center of the imaginary circle. This sensor circuit can measure Bz1 to Bz5.

[0186] In a variation of Fig. 6 (not shown), the sensor circuit includes four vertical Hall elements, each having an axis of maximum sensitivity oriented in a single direction parallel to the semiconductor substrate, e.g., the X direction. This sensor circuit can measure Bx1 to Bx4. In a further variation, the sensor circuit includes a fifth vertical Hall element located at the center of an imaginary circle.

[0187] In a variation of Fig. 6 (not shown), the sensor circuit includes four magnetoresistance (MR) elements, each having an axis of maximum sensitivity oriented in a single direction parallel to the semiconductor substrate, e.g., the X-direction. This sensor circuit can measure Bx1 to Bx4. In a further variation, the sensor circuit includes a fifth MR element located at the centre of an imaginary circle.

[0188] In a variation of FIG. 6 (not shown), the sensor circuit includes an array of horizontal Hall elements (without IMC), each configured to measure Bz in a direction perpendicular to the semiconductor substrate, the semiconductor substrate being, for example, located on an N×M grid, where N and M are integer values ​​ranging from 2 to 5, for example a 2×4 grid, a 3×3 grid, a 3×4 grid, a 3×5 grid, a 4×4 grid, etc. The grid lines may be perpendicular, but that is not absolutely necessary. The distance between parallel grid lines may be constant, but that is also not absolutely necessary. Not all locations in the array need be occupied by a Hall element.

[0189] In another variation of FIG. 6 (not shown), the sensor circuit includes a plurality of at least four magnetic sensors, located at random or pseudo-random locations, e.g., not located on a circle, or square, or grid, and / or not equally spaced from one another, each with only horizontal Hall elements (no IMC) configured to measure Bz in a direction perpendicular to the semiconductor substrate. FIG. 7(a) is a schematic block diagram of a sensor circuit as may be used in an embodiment of the present invention. The sensor circuit comprises four 2D magnetic pixels located on an imaginary circle and angularly spaced apart by multiples of 90°. The sensor circuit is capable of measuring eight magnetic field components of the magnetic field generated by a magnet, which may be referred to herein as (Bx1, Bz1) at the first sensor location, (Bx2, Bz2) at the second sensor location, (Bx3, Bz3) at the third sensor location, and (Bx4, Bz4) at the fourth sensor location. When this sensor circuit is used in the magnetic sensor system of FIG. 3(a) or FIG. 3(b) or variations thereof, the magnet is preferably located substantially above the center of the imaginary circle.

[0190] FIG. 7(b) shows a variation of FIG. 7(a) where all 2D pixels are rotated by 45°.

[0191] FIG. 8 is a schematic block diagram of a sensor circuit as may be used in an embodiment of the present invention. The sensor circuit comprises five 2D magnetic pixels, four of which are located on an imaginary circle and angularly spaced apart by multiples of 90°, one of which is located at the center of the imaginary circle. The sensor circuit of FIG. 8 may be considered as a variation of the sensor circuit of FIG. 7 with an additional 2D magnetic pixel locator at the center. The sensor circuit may measure ten magnetic field components of the magnetic field generated by the magnet, which may be referred to herein as (Bx1, Bz1) at the first sensor location, (Bx2, Bz2) at the second sensor location, (Bx3, Bz3) at the third sensor location, (Bx4, Bz4) at the fourth sensor location, and (Bx5, Bz5) at the fifth sensor location. When this sensor circuit is used in the magnetic sensor system of FIG. 3(a) or FIG. 3(b) or variations thereof, the magnet is preferably located substantially above the center of the imaginary circle.

[0192] In a variation of Figure 8 (not shown), the centrally located sensor S5 is a 3D magnetic pixel instead of a 2D magnetic pixel (e.g. as in Figures 13 and 15) and is configured to measure three orthogonal magnetic field components Bx5, By5, Bz5 at a fifth sensor location.

[0193] Fig. 9 is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. The sensor circuit comprises an array of 3x3 = 9 2D magnetic pixels located on a grid with 3 rows and 3 columns. The sensor circuit can measure 9 sets of 2 magnetic field components each (Bx, Bz), thus a total of 2x9 = 18 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 a variant thereof, the magnet is preferably located substantially above the central sensor location (its initial position).

[0194] FIG. 10 is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. The sensor circuit includes an array of 3×3=9 2D magnetic pixels located on a grid with three rows and three columns. The sensor circuit can measure nine sets of two magnetic field components each (Bu, Bz), thus a total of 2×9=18 magnetic field components. If the X direction is chosen parallel to the row direction and the Y direction parallel to the column direction, the U direction forms an angle of 45° with the X direction. The sensor circuit of FIG. 10 can be considered as a variation of the sensor circuit of FIG. 9, where each of the sensors is rotated 45° around the Z axis. When this sensor circuit is used in the magnetic sensor system of FIG. 3(a) or FIG. 3(b) or its variations, the magnet (when in its initial position) is preferably located substantially above the location of the central sensor.

[0195] Figure 11 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. The sensor circuit includes eight 2D magnetic pixels located on a grid having three rows and three columns. This sensor circuit can be considered as a variation of the sensor circuit of Figure 9, where the central sensor is omitted and the two Hall elements of each sensor are located on an imaginary line passing through the central position.

[0196] In a variation of Figure 11 (not shown), the sensor circuit further comprises a 3D magnetic pixel having only four horizontal Hall elements located on an imaginary line parallel to the row and column directions, as depicted in Figure 11(b).

[0197] In a variation of Figure 11 (not shown), the sensor circuit further comprises a 3D magnetic pixel having only four horizontal Hall elements located on an imaginary line forming a 45° angle with the row and column direction, as depicted in Figure 11(c).

[0198] In a variation of FIG. 11 (not shown), the sensor circuit further comprises a 3D magnetic pixel having eight horizontal Hall elements spaced apart by multiples of 45°, two of which are located in a row and two of which are located in a column, as depicted in FIG. 11(d).

[0199] FIG. 12 is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. The sensor circuit comprises four 2D magnetic pixels located on an imaginary circle. The two Hall elements of each sensor are located on radially oriented segments. The sensor structure can measure (Bx1, Bz1) at the first sensor location, (Bx2, Bz2) at the second sensor location, (By3, Bz3) at the third sensor location, and (By4, Bz4) at the fourth sensor location, thus measuring eight magnetic field components in total.

[0200] Figure 13 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. This sensor circuit may be considered as a variation of the sensor circuit of Figure 12, further comprising a 3D magnetic pixel at the center of an imaginary circle. This sensor circuit is capable of measuring (4x2)+(1x3)=8+3=11 magnetic field components.

[0201] FIG. 14(a) is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. The sensor circuit comprises four 3D magnetic pixels located on an imaginary circle and spaced apart by multiples of 90°. In this example, each sensor comprises an IMC disk with four horizontal Hall elements, two of which are located on an imaginary line parallel to the X direction and two of which are located on an imaginary line parallel to the Y direction. The sensor circuit can measure two in-plane magnetic field components (Bx, By) at four sensor locations and an out-of-plane magnetic field component Bz at four sensor locations, thus measuring a total of 16 magnetic field components. In other words, the sensor circuit can measure four magnetic field components tangent to the imaginary circle, four magnetic field components oriented radially with respect to the imaginary circle, and four magnetic field components oriented axially.

[0202] Figure 14(b) is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention, which can be viewed as a variation of the sensor circuit of Figure 14(a) in which each sensor is rotated by 45° with respect to a Z-axis perpendicular to the semiconductor substrate.

[0203] Fig. 15(a) is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. This sensor circuit can be considered as a variation of the sensor circuit of Fig. 14(a) further comprising a 3D magnetic pixel located at the center of an imaginary circle. This sensor circuit can measure (5 x 3) = 15 magnetic field components.

[0204] Figure 15(b) is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention, which can be viewed as a variation of the sensor circuit of Figure 15(a) in which each sensor is rotated by 45° with respect to a Z-axis perpendicular to the semiconductor substrate.

[0205] Figure 16 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention. The sensor circuit comprises an array of 3x3 = 9 3D magnetic pixels located on a grid with 3 rows and 3 columns. The sensor circuit is capable of measuring 9 sets of 3 orthogonal magnetic field components each (Bx, By, Bz), thus a total of 3x9 = 27 magnetic field components. The sensor circuit may be considered as a modification of the sensor circuit of Figure 9, where each 2D magnetic pixel is replaced by a 3D magnetic pixel.

[0206] In a variation of Fig. 16 (not shown), each sensor is rotated 45° around the Z axis perpendicular to the semiconductor substrate and is capable of measuring nine sets of 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.

[0207] Figure 17(a) is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention, which may be viewed as a variation of the sensor circuit of Figure 12, with each sensor comprising a horizontal Hall element (without IMC) configured to measure the out-of-plane magnetic field component Bz, and one (or at least one) vertical Hall element with its axis of maximum sensitivity oriented in the radial direction.

[0208] In a variation of Figure 17 (not shown), each sensor has two vertical Hall elements oriented in the same direction but spaced radially apart, e.g., one vertical Hall element on either side of the horizontal Hall element, one in the larger imaginary circle and one in the smaller imaginary circle. The signals from the two corresponding vertical Hall elements may be added or averaged.

[0209] FIG. 17(b) shows a variation of FIG. 17(a) where all 2D pixels are rotated by 45°.

[0210] Figure 18 is a schematic block diagram of a sensor circuit such as may be used in an embodiment of the present invention, which may be viewed as a variation of the sensor circuit of Figure 7, with each sensor comprising a horizontal Hall element (without IMC) configured to measure the out-of-plane magnetic field component Bz, and one (or at least one) vertical Hall element with its axis of maximum sensitivity oriented in the X-direction.

[0211] In a variation of FIG. 18 (not shown), the sensor circuit further includes a fifth sensor located at the center of the imaginary circle and having a horizontal Hall element without an IMC for measuring the Bz component and at least one vertical Hall element at the center of the imaginary circle for measuring the Bx component.

[0212] Fig. 19(a) is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. This sensor circuit can be considered as a variant of the sensor circuit of Fig. 14(a), where each sensor comprises a horizontal Hall element (without IMC) configured to measure the out-of-plane magnetic field component Bz, with an axis of maximum sensitivity oriented in the X direction, two vertical Hall elements located on either side of the horizontal Hall element, and two vertical Hall elements with an axis of maximum sensitivity oriented in the Y direction, located on either side of the horizontal Hall element. In other words, the horizontal Hall element is surrounded by four vertical Hall elements located on the sides of a square. Each of these sensors forms a 3D magnetic pixel capable of measuring three orthogonal magnetic field components (Bx, By, Bz).

[0213] In a variant of Fig. 19(a) (not shown), the sensor circuit further comprises a fifth 3D magnetic pixel located at the centre of an imaginary circle, which is capable of measuring five sets of three orthogonal magnetic field components (Bx, By, Bz), thus a total of 5 x 3 = 15 magnetic field components.

[0214] Fig. 19(b) is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. This sensor circuit can be considered as a variation of the sensor circuit of Fig. 19(a) where each sensor is rotated 45° around the Z axis perpendicular to the semiconductor substrate. This sensor circuit comprises four 3D magnetic pixels, each capable of measuring an out-of-plane magnetic field component Bz oriented in the Z direction perpendicular to the semiconductor substrate, and further each capable of measuring two in-plane magnetic field components (Bu, Bv) oriented in the U and V directions.

[0215] In a variant of Fig. 19(b) (not shown), the sensor circuit further comprises a fifth 3D magnetic pixel located at the centre of the imaginary circle, which is capable of measuring five sets of three orthogonal magnetic field components (Bu, Bv, Bz), thus a total of 5 x 3 = 15 magnetic field components.

[0216] Fig. 20 is a schematic block diagram of a sensor circuit as can be used in an embodiment of the present invention. This sensor circuit can be considered as a variation of the sensor circuit of Fig. 14(a) or 14(b) and comprises four sensors, each comprising 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. This sensor circuit can measure 4 x 5 = 20 magnetic field components.

[0217] Figure 21 is a schematic block diagram of a sensor circuit as may be used in an embodiment of the present invention. This sensor circuit may be considered as a variation of the sensor circuit of Figure 20, further comprising a fifth 3D magnetic pixel located at the center of an imaginary circle. This sensor circuit is capable of measuring five sets of five magnetic field components (Bx, By, Bu, Bv, Bz), thus a total of 5 x 5 = 25 magnetic field components.

[0218] In all of the above embodiments (FIGS. 1-21) in which one or more integrated magnetic concentrators IMC are used, the IMC preferably has a disk shape with a height of approximately 17-23 μm and a diameter of approximately 170-230 μm.

[0219] In all the above embodiments where the magnetic sensors (also referred to herein as 2D magnetic pixels or 3D magnetic pixels) are located on an imaginary circle, the diameter of this imaginary circle is preferably between 1.7 and 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 embodiment where the sensors are located on a 3x3 grid, the distance between the grid lines is preferably on the order of about 0.7 mm to about 1.5 mm, or on the order of about 0.9 mm to about 1.3 mm.

[0220] The horizontal Hall plate typically has a square shape with an area equal to 15 μm×15 μm to 25 μm×25 μm, for example, about 20 μm×20 μm.

[0221] 22(a) shows a schematic block diagram of a magnetic sensor system 2200 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, the three orthogonal components of a force vector applied to the sensor system. The system may further be subjected to disturbance fields (also called stray magnetic fields) and changing temperatures.

[0222] The sensor system 2200 comprises one or more semiconductor substrates comprising a plurality of magnetic sensors 2210. The one or more semiconductor substrates are preferably integrated into a semiconductor package (also known as a sensor chip) (see, for example, FIG. 23(d)). In a preferred embodiment, the plurality of magnetic sensors are integrated into a single semiconductor substrate smaller than 3.0×3.0 cm, preferably smaller than 2.5×2.5 mm.

[0223] The sensor system further comprises a permanent magnet that is flexibly or resiliently mounted to the semiconductor substrate, for example by means of an elastic material.

[0224] The permanent magnet 390, 2390 is preferably a single axially magnetized ring or disk magnet having an outer diameter equal to about 1.2 mm to about 1.8 mm, for example about 1.5 mm, and an (axial) height equal to about 0.3 to about 0.7 mm, or 0.4 to 0.6 mm, for example about 0.5 mm. In a preferred embodiment, the permanent magnet has an outer diameter smaller than the diameter of an imaginary circle in which the sensor elements are located.

[0225] The permanent magnet may typically be mounted by a lever and bearing or the like, as in the case of a joystick, or may be mounted by one or more springs, or may be embedded in a flexible material, such as an elastomer, as suggested in, for example, FIG. 3(a) and FIG. 3(b), or as shown in FIG. 23(a)-FIG. 23(e), or as shown in the prototype in FIG. 24(a) and FIG. 24(b), or as shown in the simulation model shown in FIG. 25, or as described in co-pending US Pat. No. 6,399,414, filed on June 28, 2021 by the same applicant and entitled “Force sensor with target on semiconductor package” (the document is incorporated herein by reference in its entirety, and specifically in FIGS. 1-5 and the corresponding description, which show and describe the assembly of a force sensor with an elastomer), or in any other suitable manner. Elastomers may have highly nonlinear stress-strain characteristics, making it extremely difficult or nearly impossible to find explicit analytical expressions for determining the components of the mechanical force exerted on the magnet based on the signal obtained from the magnetic sensor. A further problem encountered by the inventors is that the mechanical properties of the elastic material may also depend on temperature. For example, in the expected temperature range, the elastic material may become harder as the temperature decreases. Although the permanent magnet and the mechanical attachment of the magnet are represented diagrammatically by block 2204, which generates a magnetic field that depends on the applied mechanical force, it can also be said that the magnetic field generated by the permanent magnet is "modulated" by the mechanical force.

[0226] The influence from an (unknown) disturbance field is typically added to the magnetic field generated by a magnet.

[0227] In the example of FIG. 22(a), a mechanical force 2202 is applied to a magnet and the physical quantities measured are force components in the X, Y and Z directions; although the invention is primarily described with respect to a force sensor system for relative simplicity of explanation, the invention is not limited thereto and also functions to determine other physical quantities, such as for example to determine the position of a joystick (e.g. two tilt angles) or to determine the position (e.g. two lateral displacements and / or downward displacement of a thumbstick), etc.

[0228] The mechanical force to be measured may be applied directly or indirectly to the magnet, for example to the contact surface of an elastomer sealing the permanent magnet. The latter may be preferred, for example, to avoid slippage. The magnetic field generated by the permanent magnet may be measured by a sensor circuit comprising a plurality of magnetic sensors 2210, for example using any of the sensor circuits shown in Figs. 3(a) to 21, the invention being not limited thereto, since sensor circuits having a plurality of sensor elements, for example located on a 4x4 grid or located at pseudo-random locations, also work. In practice, the magnetic sensor is typically biased with a current or voltage source, and the signal provided by the sensor element is typically amplified and digitized in a so-called "bias and readout circuit" (such circuits are not explicitly shown in Fig. 22, since they are very well known in the art, are not the focus of the invention, and therefore do not need to be described in more detail here). It can be said that techniques such as "rotating current", chopping, etc. may also be used.

[0229] The signal processing will be described primarily with reference to a prototype that has been constructed, evaluated and simulated, as shown in Figures 3(b) and 7(b), but it will be appreciated that the invention is not limited to this example and will also work with other systems using the same principles.

[0230] The sensor circuit of FIG. 7(b) provides eight magnetic field component signals: Bx1, Bz1, Bx2, Bz2, Bx3, Bz3, Bx4, Bz4, and therefore in the prototype example, block 2210 provides these eight signals.

[0231] In block 2222, these eight magnetic field component signals are preferably amplified, offset corrected, and sensitivity corrected in a known manner, for example as a function of temperature. For this purpose, the sensor circuit preferably further comprises a temperature sensor 2208. For completeness, it should be noted that this block may not only correct for temperature changes, but also for mechanical stresses applied to the silicon substrate in a known manner, for example as described in co-pending US Pat. No. 6,233,933 and / or as described in co-pending US Pat. No. 6,233,933 (both documents are incorporated herein by reference in their entirety), or in any other suitable manner. Block 2222 may also digitize the signals using one or more analog-to-digital converters ADC, not explicitly shown.

[0232] In the example of FIG. 22(a), four sensitivity-corrected Bx signals are input to block 2224, the average of these four sensitivity-corrected Bx signals is calculated, and the average is then subtracted from each of the sensitivity-corrected Bx signals. Similarly, four sensitivity-corrected Bz signals are input to block 2224, the average of these four sensitivity-corrected Bz signals is calculated, and the average is then subtracted from each of the sensitivity-corrected Bz signals. When implemented in this way, block 2224 outputs four "average-corrected" Bx-related signals and four "average-corrected" Bz-related signals, thus a total of eight signals. It is also possible to perform the "average removal" in the analog domain and digitize the average-corrected Bx and average-corrected Bz values.

[0233] In the example of Fig. 22(a), the processing circuit further comprises a "feature and polynomial growth" block 2226 configured to receive four average corrected Bx values ​​and four average corrected Bz values, and configured to calculate one or more of the following: a sum of two values, a difference of two values, a product of two values, a ratio of two values, a square of a value, a sign of a value multiplied by a square of a value, a cube of a value, an absolute value of a value, a sum of two (e.g., orthogonal) squares of values ​​(related to a "norm"), a sum of three (orthogonal) squares of values ​​(related to a "norm"), and configured to output the (original) average corrected Bx and Bz values ​​and the additionally generated values ​​as output signals. In a preferred embodiment, the total number of values ​​"Ntot" provided by block 2226 is a value in the range of 12 to 100, or a value in the range of 12 to 80, or a value in the range of 16 to 64.

[0234] It should be noted that the distinction between "feature augmentation" and "polynomial augmentation" is somewhat arbitrary and irrelevant to the present invention. What is important is that block 2226 takes a certain number of input values ​​and generates some (e.g., the same number, or preferably, a larger number) of output values ​​derived therefrom. Surprisingly, we have found that by increasing the number of values, the accuracy of the final output (e.g., force components) is significantly improved. These values ​​are counterintuitive because they do not add "new information". In particular, we have found that adding additional values ​​in the form of squares of input values ​​and / or in the form of products of similar input values ​​(e.g., Bx1*Bx2) and / or in the form of different input values ​​(e.g., Bx1*Bz1) is highly advantageous.

[0235] In block 2230, the physical quantity to be determined is calculated as a function of these values, more specifically, as a weighted sum of these values, each biased with an offset.

[0236] For example, if block 2226 outputs values ​​v1, v2, ..., v64, block 2230 may calculate one or more of the components (Fx, Fy, Fy) of the force vector according to the following formula: Fx=A1*(v1-B1)+A2*(v2-B2)+...+A64*(v64-B64)[1] Fy=C1*(v1-D1)+C2*(v2-D2)+...+C64*(v64-D64)[2] Fz=E1*(v1-F1)+E2*(v2-F2)+...+E64*(v64-F64)[3] In the formula, the values ​​A1 to A64, B1 to B64, C1 to C64, D1 to D64, E1 to D64, and F1 to F64 are constants determined by machine learning or deep learning.

[0237] It should be noted that the "training" or "learning" was done over a relatively wide range of three-dimensional force values, i.e., a sufficient number of different combinations of 3D force components were selected to represent the 3D space of possibilities. In other words, many combinations of forces (Fx, Fy, Fz) were used to train the coefficients (e.g., at least 2 times, or at least 5 times, e.g., about 10 times more measurements than the number of parameters to be determined).

[0238] As will be further explained when considering Figure 29, there is an optional "temperature correction block" 2225. If temperature is used as an addition to block 2226 (representing a feature augmentation and / or polynomial augmentation block, or a neural network), then "training" or "learning" should be performed using various combinations of (T, Fx, Fy, Fz).

[0239] Fig. 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, the three orthogonal components of a force vector applied to the sensor system. This system can be considered as a modification of the system of Fig. 22(a), in which the mean removal block 2224 is replaced by a gradient calculator block 2232.

[0240] If the sensor circuit 2210 includes multiple sensors, as depicted in FIG. 7(b), the slope calculator block may calculate one or more of the following Bx-related slope signals: g1=(Bx1-Bx3),g2=(Bx1-Bx4),g3=(Bx1-Bx2), g4=(Bx3-Bx4),g5=(Bx3-Bx2),g6=(Bx4-Bx2) And one or more of the following Bz-related gradient signals may be calculated: g7=(Bz1-Bz3),g8=(Bz1-Bz4),g9=(Bz1-Bz2) g10=(Bz3-Bz4),g11=(Bz3-Bz2),g12=(Bz4-Bz2) Also, everything else mentioned above for the system of FIG. 22(a) is applicable here too.

[0241] It should be noted that in contrast to many prior art magnetic sensor systems in which analytical expressions are used, in the present invention the signals entering block 2226 do not need to behave like sine and cosine functions of the physical quantity being determined.

[0242] In an embodiment (not shown), the predefined algorithm is executed by a trained neural network that uses 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 provides at least two (or at least three) physical values ​​as output values.

[0243] The neural network may replace blocks 2226 and 2230 in Figures 22(a) and 22(b). Optionally, block 2224 (remove mean) and block 2232 (gradient calculator) may be omitted in this case.

[0244] The predefined algorithm may include a neural network having multiple layers, each layer including multiple nodes. In an embodiment, the neural network includes only one layer having 12-100 nodes. In an embodiment, the neural network includes only two layers, each having 10-100 nodes, or having 20-60 nodes. In an embodiment, the neural network includes only three layers, each having 10-100 nodes, or having 5-50 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 convolutional neural network (CNN).

[0245] 23(a)-23(e) show an example of a mechanical device comprising a sensor device or sensor assembly 2300 comprising a sensor device 2392, e.g., a packaged chip comprising a semiconductor substrate encapsulated in a molding compound, 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" (typically referred to as an "air gap") from the sensor device. The sensor device may be mounted on a printed circuit board (PCB) 2393. The elastomer 2391 may be supported only by the semiconductor device, e.g., as illustrated in Figs. 23(c)-23(e). Alternatively, a portion of the elastomer may be supported by the printed circuit board, e.g., as illustrated in Figs. 23(a) and 23(b). Optionally, there may be an intermediate layer, e.g., an adhesive layer, between the sensor chip 2392 and the elastomer 2391, e.g., as illustrated in Fig. 23(d).

[0246] The magnet 2390 is preferably an axially magnetized ring or disk magnet. The outer diameter of the magnet may have a dimension corresponding to that of the sensor device, e.g., equal to, greater than, or less than the diameter of an imaginary circle in which the magnetic sensors are located. However, preferably, the outer diameter of the magnet 2390 is smaller than the maximum distance between the magnetic sensor elements.

[0247] In the example of FIG. 23(a), the magnet may have a height (in the vertical direction perpendicular to the semiconductor substrate) of about 8 mm, and a diameter (parallel to the semiconductor substrate) of about 12 mm.

[0248] In the sensor assembly shown in Figures 23(b) and 23(c), the magnet may have a diameter in the range of 5mm to 10mm, and a height of approximately 3.5mm.

[0249] 23(d), the magnet may have a diameter less than 2.5 mm or less than 2.0 mm, for example equal to about 1.5 mm, and a height of about 0.5 mm to about 1.0 mm. The elastomer 2391 may have a thickness in the range of 2.0 mm to 5.0 mm, or in the range of 2.5 mm to 4.0 mm, for example equal to about 3.0 mm.

[0250] One of ordinary skill in the art having the benefit of this disclosure can easily find suitable dimensions by considering the following rules of thumb: the larger the magnet and / or the closer it is to the semiconductor substrate and the softer the elastomeric material, the larger the signal obtained from the magnetic sensor element.

[0251] FIGS. 24(a) and 24(b) show images of a prototype of a force sensor system as described herein that was used to develop and evaluate the algorithms described in FIGS. 22(a) and 22(b).

[0252] Figure 24(c) shows an image of the mechanical setup used to apply known forces (Fx, Fy, Fz) to the force sensor assembly. Machine learning (ML) was used to determine the parameters (e.g., A1-F64) by applying a series of tests at various force values ​​and measuring the corresponding magnetic field components.

[0253] 25(a) shows the results of measurements of Bx1 to Bx4, which are oriented in a direction perpendicular to the semiconductor substrate and have a magnitude in the range of 0.0 Newtons to 12.5 Newtons, when a force Fz is applied, and FIG. 25(b) shows the results of measurements of Bz1 to Bz4. As shown in the figure, there is a certain value range between the curves, and the curves are not completely linear.

[0254] The inventors have surprisingly found that the values ​​of Bx1-Bx4 show a very good correlation with the applied force and thus provide a very good indication of the force component Fz, despite their relatively small values ​​(on the order of about 5-15 mT), respectively. The inventors have also surprisingly found that the values ​​Bz1-Bz4 have a very large spread between them, despite the fact that their signals are typically about twice as large as the signals of Bx1-Bx4. This was not expected. We demonstrate that applying analytical expressions to any of the individual signals Bx1-Bx4 and Bz1-Bz4 will likely not lead to a reliable measurement of the applied force component Fz, but as will be further demonstrated, combinations of these signals, more specifically polynomial combinations of these signals (e.g., quadratic polynomials), and algebraic combinations of these signals with a sufficient number of parameters (e.g., products or ratios), can provide good results.

[0255] 26 shows a computer model of a mechanical device that can be used to simulate how an elastomer deforms and how a magnet moves when subjected to a force with normal force component Fz and / or shear force components Fx, Fy. This computer model can be simulated, for example, using a commercially available tool known as "Comsol."

[0256] For a given set of parameters (e.g., A1-F64) determined by machine learning, using the mechanical setup shown in FIG. 24, the computer model of FIG. 25 can then be used to validate the algorithm of FIG. 22(a) or FIG. 22(b) with those parameters.

[0257] Figures 27(a) and 27(b) show the performance profile of the forces measured by the calibration setup (see Figure 24(c)) of the prototype implementation and predicted by the force sensor algorithm (see Figure 22(a)). Figure 27(a) is for a "downwards" directed force oriented in the negative Z direction perpendicular to the semiconductor substrate. Figure 27(b) is for a shear force. As can be seen, there is a very good linear fit between these values.

[0258] It is surprising that it is indeed possible to measure the force applied in the Y direction, despite the fact that minor components are not measured.

[0259] It should be noted that these results are obtained using the sensor circuit of FIG. 7(b) having only four 2D magnetic pixels, which may not be oriented in the most optimal direction.

[0260] It is contemplated that sensor circuits in which 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 the number of sensors and / or the number of parameters required to achieve a certain accuracy, or what the most cost-effective solution to achieve a certain accuracy would be. Nevertheless, the present invention discloses many solutions that provide practical, and even very good, results, even though they are not perfect.

[0261] Figure 27(c) shows a "force error histogram" when measuring (or determining) a force oriented in the negative Z direction (denoted as Fz) using the sensor system of Figure 22(a). As can be seen, the majority of measurements (>97%) are accurate within a maximum error of ±0.25N (corresponding to an error of about ±25 grams of weight), 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.

[0262] 27(d) shows a "force error histogram" when measuring shear forces (i.e., oriented parallel to the semiconductor substrate). As can be seen, the majority of measurements (>97%) are accurate to within a maximum error of ±0.15 N, which corresponds to an error of approximately ±15 grams of weight.

[0263] Figure 28 is a graph showing the error in Fx as a function of the applied disturbance field in the X direction with and without the use of the mean removal block 2224 of Figure 22(a). The graph clearly shows that "mean removal" is a very effective way of removing the effects of stray magnetic fields. Similar results are expected when using the gradient calculation block 2232 of Figure 22(b).

[0264] 29 shows a graph showing the magnitude (in arbitrary units) of the "normal force" Fz oriented towards the semiconductor substrate versus the magnet displacement (in arbitrary units). As can be seen, the behavior is not completely linear, likely due to the fact that the stiffness of the elastomer typically increases as more pressure is applied to the elastomer.

[0265] Although not explicitly shown in Figure 29, the inventors have also found that the stiffness of the elastomer also depends on temperature. Testing has shown that this effect can be taken into account by a post-processing step in which the values ​​of Fx, Fy, Fz are corrected as a function of temperature, for example according to the following equation: Fx_corr=Fx(using formula [1])*[1+K(Tchip-35)][4] Fy_corr=Fy(using formula [2])*[1+K(Tchip-35)][5] Fz_corr=Fz(using formula [3])*[1+K(Tchip-35)][6] where Tchip is the temperature measured by the on-chip temperature sensor, expressed in degrees Celsius, and K is a constant that can be determined during a calibration step.

[0266] This effect may also be taken into account in the optional “Temperature Compensation” block 2225, for example, according to the following formula: Scorr=Sraw.[1+α(Tchip-35)]+β(Tchip-35)[7] where Tchip is the temperature measured by the on-chip temperature sensor, expressed in degrees Celsius, Sraw is the raw signal value (e.g., average correction value or slope value) obtained from the previous block 2226 or 2232, Scorr is the temperature corrected signal value, and α and β are two constants that can be determined by simulation or in a calibration step.

[0267] Figure 30 is a schematic block diagram of a sensor device 3010 as may be used in embodiments of the present invention. This block diagram is provided merely for completeness.

[0268] The sensor device 3010 comprises a semiconductor substrate comprising a plurality of magnetic sensors, only five of which are shown as M1-M5 (eg, any of the circuits shown in FIGS. 4-21).

[0269] The sensor device further comprises bias and readout circuitry, e.g. as part of the processing circuitry 3030, configured to receive signals m1, m2, etc. from the magnetic sensors. The signals are typically amplified and offset corrected. Preferably, the sensor device further comprises a temperature sensor, and the magnetic sensitivity of the sensor element is preferably corrected (in the analog or digital domain) based on the base temperature. The processing circuitry may further comprise at least one analog-to-digital converter (ADC) for converting analog signals to digital signals.

[0270] Depending on the implementation, the processing circuit 3030 may be further configured to perform one or more of the functions of blocks 2224 (mean removal), 2232 (gradient calculation), 2226 (feature growth and polynomial growth), 2230 (weighting and biasing) described above (see Fig. 22(a) and Fig. 22(b)). In this case, the sensor device 3010 may output force component values ​​Fx, Fy, Fz. To be able to measure applied forces at a reasonably 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 least 40 Hz), the number of growth values ​​may be limited, the complexity of the functions used in the (polynomial) growth block 2226 may be limited to algebraic functions (e.g., including square functions and products, but excluding division), and the number of terms added to block 2230 may be limited to 50 terms or less, or 40 terms or less, or 36 terms or less. Such algorithms may be executed by a programmable signal processor (DSP) and a number of constants may be stored in non-volatile memory 3031. Although not explicitly shown, it is also possible to use analog processing circuits, such as analog or digital accelerators, or analog or digital co-processors.

[0271] However, in other embodiments, the processing circuit measures the magnetic field values ​​(block 2210), implements sensitivity correction (block 2222), and optionally implements mean removal (2224) or gradient calculation (2232), but does not implement feature growth (block 2226) and does not calculate the weighted sum (block 2230). In this case, the sensor device 3010 may output the values ​​of blocks 2222, or 2224, or 2232, preferably as digital values, and provide these values ​​to the external processor. The external processor then performs feature and / or polynomial growth (block 2226) and calculates the weighted sum (block 2230). It is an advantage of this implementation that the external processor 3040 may be much more powerful, for example, may have a clock frequency higher than 1.0 GHz, and / or may have multiple processor cores, and / or may have much more random access memory (RAM), for example at least 1 GB of RAM.

[0272] The sensor device 3010 may also output the measured temperature T to an external processor to enable the external processor to perform post-processing corrections to take into account the temperature dependence of the stiffness of the elastomer.

[0273] FIG. 31 is provided for completeness and shows that the principles of the invention may also be used to determine the tilt angles φ and ψ of a joystick assembly, where a magnet is rotatable about a pivot point 3101 by a handle or lever 3102.

[0274] It is a major advantage of embodiments of the present invention that no explicit equations are required to determine the tilt angle and the solution is highly insensitive to disturbance fields. It should be noted that in this case, an elastomeric material is not required, but instead a mechanical assembly is typically used to hold the magnet and allow for magnet movement. Those skilled in the art will appreciate that the sensor circuits shown in Figures 3(a)-21 and the algorithms described above in Figures 22(a) and 22(b) can also be used to determine the tilt angle (a physical quantity related to the position of the magnet) of the handle of a joystick assembly.

[0275] Although not explicitly shown, the principles of the present invention can also be used to determine the position of a thumbstick. In this case, the magnet can be moved in a plane parallel to the semiconductor substrate by moving the thumbstick in a plane parallel to the semiconductor substrate. Optionally, one or more springs can be involved. Those skilled in the art will appreciate that the sensor circuitry shown in Figures 3(a)-21 and the algorithms described above in Figures 22(a) and 22(b) can also be used to determine at least the lateral displacement, and optionally the downward push-down displacement, of a thumbstick of a thumbstick assembly (i.e., a physical quantity related to the position of the magnet).

[0276] It goes without saying that the requirements in terms of accuracy and robustness against disturbance signals of a thumbstick assembly, for example as part of a gaming machine for consumer electronics applications, are quite different from those for robotics applications. In other words, it is quite feasible to build an integrated sensor device that performs all of the signal processing steps shown in Figures 22(a) and 22(b), albeit with a limited number of terms and constants and with limited accuracy.

[0277] 32 shows a flow chart of a method 3200 for measuring at least two physical quantities (e.g., a 2D or 3D force vector, a 2D or 3D displacement vector, a 2D or 3D position of a joystick, a 2D or 3D position of a thumbstick) related to the position of a permanent magnet that is movable relative to an integrated circuit and configured to generate a magnetic field. The method 3200 includes the following steps: a) measuring 3201 at least two (or at least three, or at least four) first magnetic field components (Bx1, Bx2; Bx1, Bx2, Bx3; Bx1-Bx4) oriented in a first direction (e.g., X). The first direction may be parallel to the semiconductor substrate ("in-plane").

[0278] b) Optionally, determining 3202 a first gradient (eg, dBx / dx) or a first average correction value of the first magnetic field component. c) measuring 3203 at least two (or at least three, or at least four) second magnetic field components (Bz1, Bz2; Bz1, Bz2, Bz3; Bz1-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 perpendicular to the semiconductor substrate ("out-of-plane").

[0279] d) Optionally, determining 3204 a second gradient (eg, dBz / dx) or a second average correction value of the second magnetic field component. e) determining the at least two physical quantities (e.g., Fx, Fy, Fz) using a predefined algorithm that uses the measured magnetic field components and / or gradients and / or average correction values ​​as input and a plurality of at least 8 (or at least 12, or at least 16) constants (or coefficients or parameters) determined using machine learning (ML) or deep learning.

[0280] Of course, this method can be further improved in the same manner as described above.

[0281] For example, in an embodiment, the at least two physical quantities may be determined using a predefined algorithm that uses as input 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, and that uses the plurality of at least eight constants.

[0282] In another or further embodiment, the method may further include measuring a temperature of the semiconductor substrate and correcting the measured first and second magnetic field components based on the measured temperature, or taking the measured temperature into account as an additional input of a predefined algorithm, or processing the temperature in a post-processing step.

[0283] others It should be noted that for completeness, blocks 2226 (remove mean) and 2232 (calculate gradient) may be omitted and the stray magnetic fields would still be countered by blocks 2226 and 2230, which may be neural networks.

[0284] According to another aspect, the present invention also provides a force sensor device comprising an integrated circuit comprising a plurality of magnetic sensors, a permanent magnet flexibly mounted to the integrated circuit by 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; 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, or Ga-In, or In-Sb) mounted next to, on top of, or below the first semiconductor substrate, for example in a manner similar to that described in US Pat. No. 6,399,323, which is incorporated herein by reference in its entirety.

[0285] 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 a first magnetic field component and a second magnetic field component oriented in a first direction and to measure at least a third magnetic field component and a fourth magnetic field component oriented in a second direction, which may be the same as the first direction or may be different from the first direction, e.g., orthogonal thereto.

[0286] The permanent magnet is configured to generate a magnetic field.

[0287] The processing circuitry is configured to determine at least one pairwise difference, or at least two pairwise differences, or at least three pairwise differences between pairs of 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, e.g. based on a function of the one or more pairwise differences.

[0288] The force sensor device may be configured to determine the at least one or the at least two physical quantities using one or more predefined functions. This function or these functions may be stored in the non-volatile memory of the processing circuit, for example in the form of a mathematical formula, for example as a polynomial with a number of coefficients (for example with 3 to 30 coefficients, for example with 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 with 3 to 15 terms (for example with 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), or in the form of a look-up table. Some of the terms may be the square of the magnetic field difference, or may be the cross product of two magnetic field differences obtained from a pair of sensors spaced apart in the same direction, or may be the cross product of two magnetic field differences obtained from a pair of sensors spaced apart in different directions.

[0289] The coefficients or parameters may be determined using machine learning. Alternatively, the coefficients or parameters are determined using classical techniques, such as using curve fitting techniques, linear or non-linear regression techniques, or linear or non-linear models. It should be noted that "machine learning" or "deep learning" is typically used for "neural networks" that have "hidden layers" and typically require much more computation than classical curve fitting techniques.

[0290] Block diagrams similar to those of Figures 22(a) and 22(b) may be applicable, with blocks 2226 ("Feature Augmentation and Polynomial Augmentation") and 2230 ("Weighting and Biasing") being replaced by the predefined function, e.g., the polynomial, or the lookup table.

[0291] The force sensor device may have an appearance as shown in Figures 23(a) to 23(e), although of course the invention is not limited to this.

[0292] The force sensor device may, for example, have three 1D pixels, or four 1D pixels (e.g., as shown in FIG. 6), or three 2D pixels (e.g., as shown in FIG. 4), or four 2D pixels (e.g., as shown in FIG. 5 or FIG. 7(a) or FIG. 7(b) or FIG. 12 or FIG. 17(a) or FIG. 17(b) or FIG. 18), or five 2D pixels (e.g., as shown in FIG. 8), or nine 2D pixels (e.g., as shown in FIG. 9 or FIG. 10). 13), or 4 2D pixels and 1 3D pixel (e.g., as shown in FIG. 13), or 4 3D pixels (e.g., as shown in FIG. 14(a) or FIG. 14(b) or FIG. 19(a) or FIG. 19(b)), or 5 3D pixels (e.g., as shown in FIG. 15(a) or FIG. 15(b)), or 9 3D pixels (e.g., as shown in FIG. 16).

[0293] 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, or at least six pairwise differences, or at least eight pairwise differences are determined, and an output value is determined based on these pairwise differences.

[0294] Many variations of this force sensor device are envisioned, similar to those described above, for example, the force sensor device may further comprise a temperature sensor, and temperature may be taken into account in the calculations and / or used to compensate for temperature dependent material properties of the elastomer.

Claims

1. A force sensor system, comprising: The force sensor system comprises: an integrated circuit including a semiconductor substrate, the semiconductor substrate including a plurality of magnetic sensors for measuring magnetic fields; a permanent magnet movable relative to the integrated circuit, the permanent magnet configured to generate the magnetic field, the permanent magnet being flexibly fixed to the integrated circuit using a flexible material; a processing circuit configured to determine, based on the measured magnetic field and using a predetermined algorithm, at least two physical quantities related to the position of the permanent magnet, the at least two physical quantities being two or three force components (Fx, Fy, Fz) of a mechanical force acting on a contact surface of the flexible material; the plurality of magnetic sensors are configured to measure at least two first magnetic field components (Bxl, Bx2) arranged in a first direction (X) and at least two second magnetic field components (Bzl, Bz2) arranged in a second direction (Y; Z); the processing circuitry is configured to determine the at least two force components using the predetermined algorithm, the predetermined algorithm using as input at least three or at least four magnetic field differences derived from at least two first magnetic field components and at least two second magnetic field components, and the predetermined algorithm using at least eight constants determined using machine learning. Force sensor system.

2. The semiconductor substrate further comprises a temperature sensor for measuring a temperature of the semiconductor substrate; (A) the semiconductor substrate is configured to compensate for measured first and second magnetic field components based on a measured temperature; (B) the predetermined algorithm considers the measured temperature as an additional input; and (C) the measured temperature is used in a post-processing step; and The force sensor system of claim 1 .

3. (A) each of the first direction (X) and the second direction (Y) is parallel to a semiconductor substrate; (B) the first direction (X) is parallel to the semiconductor substrate, and the second direction (Z) is perpendicular to the semiconductor substrate; Either 3. The force sensor system according to claim 1.

4. (A) the plurality of sensors, at least one of which comprises an integrated magnetic concentrator disk and three pairs of horizontal Hall elements positioned adjacent to the periphery of the disk, the Hall elements being angularly spaced apart in multiples of 120°; (B) the plurality of sensors, at least one of the sensors comprising an integrated magnetic concentrator disk and four pairs of horizontal Hall elements positioned adjacent a periphery of the disk, the Hall elements being angularly spaced at multiples of 45°; (C) the semiconductor substrate includes a plurality of magnetic sensors arranged at intersections of a 2x2 grid, or at intersections of a 3x3 grid, or at intersections of a 4x4 grid; (D) the semiconductor substrate includes a plurality of magnetic sensors arranged in an irregular pattern; and (E) the at least three magnetic sensors are arranged on an imaginary circle; and Either 3. The force sensor system according to claim 1.

5. The semiconductor substrate includes a plurality of magnetic sensors arranged in pseudo-random positions. The force sensor system of claim 4 .

6. The permanent magnet is a two-pole permanent magnet; the permanent magnet is an axially magnetized ring-shaped or disk-shaped permanent magnet; At least one of the following is true:

3. The force sensor system according to claim 1.

7. The predetermined algorithm is configured to derive at least two first difference values from at least two first magnetic field components, derive at least two second difference values from at least two second magnetic field components, and calculate at least two physical values based on the at least two first difference values and the at least two second difference values.

3. The force sensor system according to claim 1.

8. (A) each of the at least three first difference values is determined as a pairwise difference between two first magnetic field components, and each of the at least three second difference values is determined as a pairwise difference between two second magnetic field components; (B) each of the at least three first difference values is determined as a difference between a first magnetic field component and a first common value, and each of the at least three second difference values is determined as a difference between a second magnetic field component and a second common value; Either The force sensor system of claim 7 .

9. The predetermined algorithm is configured to calculate each physical value as a sum of at least 12 terms; each of the at least 12 terms is a function that depends on one or more of the differences; The force sensor system of claim 6 .

10. The method of claim 1, wherein each sum includes a constant value determined by machine learning. The force sensor system of claim 9.

11. The predetermined algorithm is configured to calculate each physical value as a sum of at least 12 terms; the at least two terms include only one linear representation of the difference, and the at least two terms include one or more non-linear representations of the difference; The force sensor system of claim 9.

12. The or each sum of the at least two terms includes a quadratic expression or a quadratic polynomial of only one of the differences; each said sum includes at least one term that is the product of two differences; each said sum includes at least one term that is the division of two differences; At least one of the following is true: The force sensor system of claim 9.

13. The predetermined algorithm is performed by a trained neural network, It is carried out by using at least three first magnetic field components (Bx1, Bx2, Bx3) and at least three second magnetic field components (Bz1, Bz2, Bz3) as input signals and providing at least two or at least three physical values as output values.

3. The force sensor system according to claim 1.

14. The flexible material is an elastomer.

3. The force sensor system according to claim 1.

15. The predetermined algorithm further includes a post-processing step of measuring or estimating a temperature of the flexible material; correcting the determined force components to mitigate temperature-dependent material properties; 3. The force sensor system according to claim 1.

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