Methods for compensating angular errors

Abstract

Method for compensating angular errors in the determination of angular values ​​by an arrangement with a permanent magnet and at least two magnetic field sensors, with a distance formed between the permanent magnet and the magnetic field sensors, in which a sinusoidal signal and a cosine signal are generated in the magnetic field sensors, and from the two signals an evaluation signal corresponding to the angular values ​​is formed by means of an arctangent function, wherein arrangement errors and errors of a measuring and evaluation unit change the shape of the evaluation signal and lead to an angular deviation in the evaluation signal, and in order to minimize the angular deviation, values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors are changed from the signals and values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors are determined.in which a second harmonic is determined for the evaluation signal and / or a third harmonic is determined for the signals and / or density differences of measurement points of a Lissajous plot.

Description

[0001] The invention relates to a method for compensating angular errors.

[0002] DE 10 2014 109 693 A1 discloses a method in which the angular position of a magnetic device with a rotational axis is determined by a non-contact measurement. The magnetic device comprises a magnet and at least three magnetic field sensors, and a sinusoidal and a cosinusoidal output signal is calculated from the signals of the magnetic field sensors using a transformation.

[0003] From the two output signals, or from the instantaneous values ​​of the two output signals, the angle of rotation, i.e. the angular position of the magnet or sensor arranged on the axis of rotation, is calculated directly in an evaluation device using an arctangent function.

[0004] By using at least three magnetic field sensors, magnetic interference fields can be compensated, which are particularly common in automotive electronics applications. The device and method are not limited to three magnetic field sensors. Using more than three sensors allows for more precise calculation of the angular position.

[0005] However, such methods are not suitable for compensating for errors due to positioning and position inaccuracies. For example, both the magnet and the sensor device may be axially offset from each other due to tolerances, or exhibit an inclination or tilt.

[0006] Further errors in the signals and, consequently, in the angle determination, are caused by non-ideal magnetic properties, particularly temperature changes and aging. Basically, the errors can be divided into three classes: - offset errors that cause DC components of the signals, and - amplification errors causing deviations in the peak values ​​of the amplitudes of the signals, and - Orthogonality errors, which cause deviations in the phase shift of the two signals.

[0007] Further methods for compensating these errors are known from "Application Note APN000202_001EN." The underlying devices have means for implementing compensation methods.

[0008] However, due to the variety of error sources and the superposition of error sources, such as an axial misalignment between the magnet and sensor device in conjunction with a tilting of the magnet, effects occur that cannot be corrected with the compensation methods mentioned.

[0009] Against this background, the object of the invention is to provide a method which further develops the state of the art.

[0010] The object is achieved by a method for compensating angular errors with the features of patent claim 1. Advantageous embodiments of the invention are the subject of subclaims.

[0011] According to the subject matter, a method for compensating angular errors is provided.

[0012] The method is used to determine angle values ​​from an arrangement with a permanent magnet and at least two magnetic field sensors.

[0013] The two magnetic field sensors are connected to a measuring and evaluation device.

[0014] A gap is formed between the permanent magnet and the magnetic field sensors.

[0015] By means of a forced mechanical movement, a sinusoidal signal and a cosinusoidal signal are generated in the magnetic field sensors or the sinusoidal signal and the cosinusoidal signal are generated by means of a transformation.

[0016] From the two signals, an evaluation signal corresponding to the angle values ​​is formed using an arctangent function, whereby arrangement errors and errors from the measuring and evaluation unit change the shape of the evaluation signal.

[0017] In the evaluation signal, the errors lead to an angular deviation, whereby in order to minimize the angular deviation, values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors in the signals are changed.

[0018] In one process step, the correction values ​​for amplification and / or orthogonality are determined by determining a second harmonic in the evaluation signal and / or a third harmonic in the signals and / or density differences of measuring points of a Lissajous plot.

[0019] It should be noted that the measurement and evaluation unit generally does not determine the gain error correction values ​​and / or orthogonality error correction values, but rather applies gain error correction values ​​and / or orthogonality error correction values ​​that have already been determined, for example, during calibration. The latter usually takes place outside the measurement and evaluation unit and is generally stored.

[0020] In other words, in particular amplification errors, ie differences in the amplitude of the signals, and / or orthogonality errors, ie a deviation of the phase relationship of 90 degrees between the two signals, are known before the method is carried out and are taken into account by the measuring and evaluation unit, ie the signals are corrected accordingly.

[0021] It should be noted that, in contrast to the prior art, in which, for example, the minimum and maximum values ​​of the signals are considered, whereby the resulting angular deviation is in some cases even increased instead of reduced, in the present invention the values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors are determined using a different method in order to reliably correct second-order angular deviations.

[0022] It is understood that the term "magnetic field sensors" includes, in particular, vertical Hall sensors and / or lateral Hall sensors and / or TMR and / or AMR and / or other types of sensors. Furthermore, different types of magnetic field sensors can also be used in the arrangement.

[0023] It should be noted that even in a design with just two sensors, the sinusoidal signal and the cosinusoidal signal are either directly obtained as a measurement signal from the two magnetic field sensors or can only be derived by transforming the measurement signals. Particularly with more than two magnetic field sensors, the sinusoidal signal and the cosinusoidal signal can generally only be generated by transforming them. Even with exactly two magnetic field sensors, a transformation may be necessary depending on the arrangement of the two magnetic field sensors and / or when using different types of magnetic field sensors (e.g., one of the two magnetic field sensors is designed as a TMR and the other as a Hall sensor).

[0024] It should be noted that when scanning from 0° to 360°, the measurement points in the Lissajous plot generally lie on a closed curve. If the setup is undisturbed, the curve has a constant radius and the measurement points are evenly distributed along the circumference. In other words, the curve is a circle.

[0025] If there is a disturbance, the radius is no longer constant and the curve deviates from a circle and / or the distribution of the points on the Lissajous plot is different.

[0026] It should be noted that, in general terms, the method minimizes the third harmonic in the signals by changing values ​​for correcting gain errors and / or values ​​for correcting orthogonality errors.

[0027] The determination of the third harmonic can be determined directly in the signals or in the resulting effects, such as the resulting angular deviation of the evaluation signals as a second harmonic or the density differences of the Lissajous plot of the two signals.

[0028] It should be noted that in an alternative approach, the angular deviation in the evaluation signals should be minimized, which occurs there as the second harmonic. In other words, the second harmonic is minimized.

[0029] In another alternative, the density differences are compensated during the evaluation using the Lissajous plot.

[0030] It should be noted that the approaches described above for reducing errors are equivalent to each other in terms of their effect.

[0031] It is understood that error values ​​can be determined and adjusted directly in the signals and only then are the values ​​for correcting the amplification errors and / or values ​​for correcting the orthogonality errors determined by means of the method according to the invention.

[0032] An advantage of the method is that errors resulting from axial misalignment between the magnet and sensor device or from tilting of the magnet and other error causes that cause higher-order effects in the signals can be compensated.

[0033] In particular, a third harmonic can be determined in the sinusoidal and cosinusoidal signals, which appears as a second harmonic in the resulting deviation of the rotation angle. It is understood that it is advantageous to consider at least one 360° sweep.

[0034] Furthermore, it should be noted that the method significantly extends the compensation of angular errors, which occur in the form of the third harmonic of the signals.

[0035] This increases the achievable precision of angle measurement, while also reducing manufacturing tolerance requirements and reducing the yield and effort required to assemble the fixture. In other words, manufacturing costs can be reduced.

[0036] It goes without saying that the method is not limited to angle measurement. The method can be used for all forms of contactless displacement measurement in which at least one permanent magnet, in combination with at least two magnetic field sensors, generates a sine and cosine signal. This particularly includes any type of linear movement whose magnetic structure is designed accordingly.

[0037] In one embodiment, after calculating the angle values ​​using the arctangent function, the values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors are determined from the second harmonic of the resulting angular deviation of a 360° rotation.

[0038] In one embodiment, in order to determine the values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors from the density differences of the Lissajous plot, the measurement points are recorded at a more constant period speed / frequency or rotation speed with a fixed sampling rate.

[0039] In another embodiment, the values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors are determined from the component of the second harmonic calculated by means of DFT or FFT in the resulting course of the error of the rotation angle of a 360° revolution.

[0040] In a further development, the values ​​for correcting the gain errors and / or the orthogonality errors are determined from the modification of correction values ​​already generated by other methods in conjunction with the third harmonic of the sinusoidal and cosinusoidal signals calculated using DFT or FFT. In other words, using the method according to the invention, after the correction from the determination of the third harmonic of the signals, the gain errors and / or the values ​​for correcting the orthogonality errors are calculated from the determination of the second harmonic.

[0041] In a further development, the DFT calculation is performed using a Goertzel algorithm, or, alternatively, the second harmonic or third harmonic is directly determined using a sinusoidal fitting function. In other words, no FFT or DFT calculation is performed in this alternative. One advantage is that the computing power is reduced.

[0042] In one embodiment, it is preferred that the values ​​for correcting the gain errors and / or the values ​​for correcting the orthogonality errors be determined multiple times, iteratively. This allows the accuracy of the angle calculation to be further increased.

[0043] According to another further development, after correction values ​​have already been determined, a third harmonic is determined directly at the signals from a comparison of the signal curve with an ideal sine curve and from a comparison of the signal curve with an ideal cosine curve.

[0044] From the correction values ​​already determined and the deviation from the ideal curves, the values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors are then determined.

[0045] In one embodiment, the method is used to determine the rotational angle position in an arrangement with permanent magnets and magnetic field sensors.

[0046] The arrangement has an axis with an end face and at least one permanent magnet arranged on the end face or laterally on the axis.

[0047] Magnetic field sensors are arranged along an imaginary extension of the axis. Alternatively, the magnetic field sensors are arranged laterally, i.e., spaced apart from the imaginary extension of the axis.

[0048] It is understood that there is a distance between the axis and the magnetic field sensors.

[0049] A measuring and evaluation device is connected to the magnetic field sensors, whereby when the axis rotates, a sinusoidal signal or a cosinusoidal signal is generated at an output of the respective magnetic field sensor or is only obtained by means of a transformation.

[0050] In a further development, the magnetic field sensors are spaced along an X-direction.

[0051] In another embodiment, the magnetic field sensors are arranged directly next to one another in the X-direction and / or are arranged partially or completely next to one another in a Z-direction.

[0052] In a further embodiment, three magnetic field sensors are arranged in the form of a pixel cell, with the three magnetic field sensors measuring three different directions of a magnetic field. In a further development, several magnetic field sensors are arranged in an XY plane, preferably linearly or in a circle.

[0053] The measuring and evaluation device is designed to calculate an evaluation signal corresponding to the angle of rotation values ​​from the signals using an arctangent function.

[0054] Furthermore, the measuring and evaluation device is configured to calculate values ​​for correcting the amplification errors and / or values ​​for correcting the orthogonality errors for a change in the evaluation signal in order to minimize the angular deviation.

[0055] In an alternative embodiment, the method is applied to a different arrangement for determining angle values ​​of a translational movement path.

[0056] Here, the other arrangement comprises a plurality of permanent magnet pairs arranged along the translational path and at least two magnetic field sensors arranged along the translational movement path.

[0057] It is understood that the magnetic field sensors are arranged at a distance from the permanent magnet pairs, relative to each other and movable along the translational movement path.

[0058] Furthermore, a measuring and evaluation device connected to the magnetic field sensors is provided.

[0059] During a translational movement of the permanent magnet pairs or the magnetic field sensors along the path, a sinusoidal signal or a cosinusoidal signal is present at an output of the respective magnetic field sensor or these are obtained by means of a transformation.

[0060] The measuring and evaluation device is designed to calculate an evaluation signal corresponding to the angle values ​​from the signals using an arctangent function.

[0061] Furthermore, the measuring and evaluation device is configured to calculate values ​​for correcting the amplification errors and / or values ​​for correcting the orthogonality errors for a change in the evaluation signal in order to minimize the angular deviation.

[0062] In a preferred embodiment, the measuring and evaluation device is configured to determine values ​​for correcting the gain errors and / or values ​​for correcting the orthogonality errors by means of a DFT or FFT evaluation.

[0063] In a further development, the measuring and evaluation device comprises a Goertzel filter or the measuring and evaluation device is configured to perform a sinusoidal adaptation function.

[0064] In an alternative development, the measuring and evaluation device is set up to determine the density differences of a Lissajous plot.

[0065] In a preferred embodiment, the measuring and evaluation device with the magnetic field sensors is integrated monolithically or as a multi-chip solution in an IC housing.

[0066] The invention will be explained in more detail below with reference to the drawings. Similar parts are labeled with identical designations. The illustrated embodiments are highly schematic, ie the distances and the lateral and vertical extensions are not to scale and, unless otherwise stated, do not have any deducible geometric relationships to one another. Fig. 1 third harmonic erroneous sinusoidal signals and cosinusoidal signals Fig. 2 a spectrum of signals, Fig. 3 a representation of the resulting angular error of the evaluation signal, Fig. 4 a spectrum of the evaluation signal, Fig. 5 a representation of erroneous sinusoidal and cosinusoidal signals in a Lissajous plot with density differences of the measuring points, Fig. 6 faulty sinusoidal and cosinusoidal signals Fig. 7 a Goertzel filter, Fig. 8 a rotating device, Fig. 9 a linear device, Fig. 10 a representation of ideal sinusoidal and cosinusoidal signals.

[0067] It should be noted that in the following figures, the sinusoidal and cosinusoidal signals from the two magnetic field sensors S1 and S2 are either directly available as measurement signals or only after a transformation.

[0068] The illustration of the Fig. Figure 1 shows an ideal sinusoidal signal 10 and an ideal cosinusoidal signal 20, each representing the first harmonic of the two signals 10 and 20. The abscissa represents the applied angle value in degrees, and the ordinate represents the magnitude of the output signal, with the maximum amplitude normalized to the value 1.

[0069] A sinusoidal error signal 30 and a cosinusoidal error signal 40 occur at three times the frequency and thus each represent a third harmonic with respect to the two ideal signals 10 and 20.

[0070] The curves 50 and 60 show the actual signals, whereby the actual signals are distorted by a superposition of the ideal signals 10 and 20 with the error signals 30 and 40.

[0071] The illustration of the Fig. Figure 2 shows a spectrum of signals 50 and 60.

[0072] The frequency is plotted on the abscissa. The logarithmically scaled amplitude of the signals is plotted on the ordinate.

[0073] The amplitude of the first harmonic 70, which is also called the fundamental wave, and the amplitude of the third harmonic 80, which is also called the second harmonic, are correspondingly strong.

[0074] The inventive application of the method results in a reduction 90 of the third harmonic 80 to a significantly lower level 100.

[0075] The illustration of the Fig. 3 shows the curve of the resulting angular error delta Phi, which appears as the second harmonic 110.

[0076] The abscissa represents the actual angle value in degrees of the magnet arrangement. The ordinate represents the resulting angle error in degrees.

[0077] In this case, the error occurs as a second harmonic oscillation. The characteristic shown requires a deviation of the signals in the form of a pronounced third harmonic.

[0078] The illustration of the Fig. Figure 4 shows a spectral representation of the resulting angle error Delta Phi. The amplitude of the second harmonic 120 is clearly visible.

[0079] The inventive application of the method results in a reduction 130 of the second harmonic 120 to a significantly lower level 140.

[0080] In the illustration of the Fig. Figure 5 shows a Lissajous plot of the sinusoidal and cosinusoidal measurement signals.

[0081] The plot is not further deformed, which means that the three errors in question are already perfectly aligned. However, the plot does not show any equidistant measurement points.

[0082] The density distribution indicates the presence of a second harmonic in the signals. Changing the gain error correction values ​​and / or the orthogonality error correction values ​​distorts the plot but homogenizes the density distribution and thus reduces the resulting angular error, delta phi.

[0083] The illustration of the Fig. 6 shows the curve of the uncompensated sinusoidal and cosinusoidal signals as a function of the actual rotation angle value applied by the magnetic device.

[0084] The signals exhibit three types of errors, the compensation of which represents the state of the art. A DC component 170, often referred to as offset, causes one or both signals to be biased in a positive or negative direction.

[0085] A gain error of 180 results in a difference in the peak values ​​of the two signals without any DC component.

[0086] An orthogonality error of 190° results in a phase shift of other than 90° in the signals. The orthogonality error describes the deviation of the two measured magnetic field vector components from an ideal 90° orientation.

[0087] The application of the method according to the invention reduces the amplitude of the third harmonic in the measured values ​​by correcting the values ​​for compensating gain errors and / or the values ​​for compensating orthogonality errors and thereby also minimizes the resulting angle error Delta Phi.

[0088] It is inherent in the method that in the case of a third harmonic present in the signals, an increased gain error and / or an increased orthogonality error leads to a smaller resulting angular error than one according to the known compensation, in which a gain error and / or an orthogonality error in the signals is directly compensated.

[0089] This can be described as overcompensation. In other words, using the method according to the invention, the overcompensation of the gain error and / or the orthogonality error from the first harmonic in the signals leads to an increase in the accuracy of the angle calculation.

[0090] In the illustration of the Fig. Figure 7 shows an example of a second-order Görtzel filter. The use of the Görtzel filter allows the targeted determination of individual spectral components of a signal. The Görtzel filter is particularly suitable for determining the third harmonic of signals according to the invention.

[0091] In the illustration of the Fig. 8 depicts a rotating device DV, wherein the rotating device DV has a rotation axis DA formed in a Z direction and a permanent magnet PM arranged on an end face of the rotation axis DA in an XY plane. The permanent magnet PM has a north pole N and a south pole S. A first magnetic field sensor S1 and a second magnetic field sensor S2 are arranged on a carrier board TR along an imaginary extension of the rotation axis DA.

[0092] The two magnetic field sensors S1, S2 are spaced apart in the X-direction by a distance x1. Both magnetic field sensors S1, S2 are also spaced apart from the head end of the rotation axis DA. If the carrier board with the two magnetic field sensors S1, S2 is tilted relative to the front end and / or if the magnetic field sensors S1, S2 are misaligned, the signals will be subject to different errors.

[0093] In an embodiment not shown, the distance x1 between the two magnetic field sensors S1 and S2 is zero or very small, so that the two magnetic field sensors S1 and S2 are arranged one above the other in the Z direction, wherein in the arrangement one above the other the two magnetic field sensors preferably measure different components of the magnetic field.

[0094] In the illustration of the Fig. Figure 9 shows an arrangement of pairs of permanent magnets along a straight line.

[0095] Using the linearly movable permanent magnet PM, which has the pole pairs M1-M7 arranged in a row, a sine-shaped and a cosine-shaped signal can be generated by the spaced magnetic field sensors S1 and S2, respectively. The inventive compensation of angular errors due to third-order deviations in the signals can also be applied to linear motion, including translational displacement / position measurement.

[0096] The illustration of the Fig. 10 shows an ideal course of the two signals with a sinusoidal signal 200 and a cosinusoidal signal 210 depending on the actual rotation angle value applied by the magnetic device.

[0097] By evaluating the arctangent function, the angle of rotation value is determined from the quotient of the signals.

[0098] Both the sinusoidal signal and the cosinusoidal signal are ideal, i.e. error-free. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] DE 10 2014 109 693 A1

[0002]

Claims

[1] Method for compensating angular errors when determining angular values from an arrangement with a permanent magnet (PM) and at least two magnetic field sensors (S1, S2), - a measuring and evaluation device connected to the magnetic field sensors (S1, S2), - a distance formed between the permanent magnet and the magnetic field sensors (S1, S2), - a sinusoidal signal and a cosinusoidal signal are generated by means of a forced mechanical movement in the magnetic field sensors (S1, S2) or the sinusoidal signal and the cosinusoidal signal are generated by means of a transformation, and an evaluation signal corresponding to the angle values is formed from the two signals by means of an arctangent function, whereby - Arrangement errors and errors from the measuring and evaluation unit change the shape of the evaluation signal and lead to an angular deviation in the evaluation signal, and - Amplification values and orthogonality values of the signals are changed to minimize the angular deviation, characterized by that the values for correcting the amplification errors and / or values for correcting the orthogonality errors are determined by determining a second harmonic in the evaluation signal and / or a third harmonic in the signals and / or density differences of measuring points of a Lissajous plot. [2] Method according to claim 1, characterized by that after calculating the angle values using the arctangent function, the values for correcting the gain errors and / or values for correcting the orthogonality errors are determined from the amplitude and phase of the second harmonic of the resulting angular deviation of a 360° rotation. [3] Method according to claim 1, characterized bythat in order to determine the values of the amplification error and / or values for correcting the orthogonality errors from the density differences of the measuring points of the Lissajous plot, the measuring points are recorded at a constant rotation speed with a fixed sampling rate. [4] Method according to claim 1, characterized by that the values for correcting the gain errors and / or values for correcting the orthogonality errors are determined from the component, calculated by means of DFT or FFT, of the second harmonic in the resulting course of the error of the angle of rotation of a 360° revolution. [5] Method according to claim 1, characterized by that the values for correcting the gain errors and / or values for correcting the orthogonality errors are determined by changing correction values already generated by other methods and the third harmonics of the sinusoidal and cosinusoidal signals calculated by DFT or FFT. [6] Method according to claim 4 or 5, characterized by that the DFT calculation is carried out using a Goertzel algorithm or the second harmonic or the third harmonic is determined directly using a sinusoidal fitting function. [7] Method according to one of the preceding claims, characterized by that a determination of values for correcting the gain errors and / or values for correcting the orthogonality errors is carried out several times, in an iterative manner. [8] Method according to one of the preceding claims, characterized bythat after determining correction values, a third harmonic is determined directly at the signals from a comparison of the signal curve with an ideal sine curve and from a comparison of the signal curve with an ideal cosine curve, and the values to be set to correct the gain errors and / or values to correct the orthogonality errors are determined from the correction values already determined and the deviation from the ideal curves. [9] Method according to one of the preceding claims, characterized by that the magnetic field sensors (S1, S2) are spaced apart along an X-direction or the magnetic field sensors (S1, S2) are arranged one above the other in a Z-direction. [10] Use of the method according to one of the preceding claims for determining angle of rotation values, comprising - an axle with an end face and at least one permanent magnet arranged on the end face or laterally on the axle, - at least two magnetic field sensors (S1, S2) arranged along an imaginary extension of the axis or magnetic field sensors arranged laterally to the axis, wherein a distance is formed between the axis and the magnetic field sensors (S1, S2), - a measuring and evaluation device connected to the magnetic field sensors (S1, S2), wherein - when the axis rotates, a sinusoidal signal or a cosinusoidal signal is present at an output of the respective magnetic field sensor, the measuring and evaluation device is set up to calculate an evaluation signal corresponding to the rotation angle values from the signals by means of an arctangent function in order to minimize the angular deviation. [11] Use of the method according to one of the preceding claims 1 to 8 for determining angle values of a translational movement path comprising - a plurality of permanent magnet pairs arranged along the translational path, - at least two magnetic field sensors arranged along the translational movement path, which are spaced apart from the permanent magnet pairs and are arranged to be movable along the translational movement path, - a measuring and evaluation device connected to the magnetic field sensors (S1, S2), wherein - during a translational movement of the permanent magnet pairs or the magnetic field sensors (S1, S2) along the path, a sinusoidal signal or a cosinusoidal signal is present at an output of the magnetic field sensors (S1, S2), the measuring and evaluation device is designed to calculate an evaluation signal corresponding to the angle values from the signals by means of an arctangent function in order to minimize the angular deviation. [12] Use of the method according to claim 10 or claim 11, characterized by that the measuring and evaluation device is set up to determine values for correcting the gain errors and / or values for correcting the orthogonality errors by means of a DFT or FFT evaluation. [13] Use of the method according to any one of claims 10 to 12, characterized bythat the measuring and evaluation device comprises a Goertzel filter or the measuring and evaluation device is designed to perform a sinusoidal adaptation function. [14] Use of the method according to claim 10 or claim 11, characterized by that the measuring and evaluation device is set up to determine density differences between the measuring points of a Lissajous plot. [15] Use of the method according to one of the preceding claims, characterized by that the measuring and evaluation device with the magnetic field sensors is integrated monolithically or as a multi-chip solution in an IC housing.

Images