WO2005054784A1

WO2005054784A1 - Angle sensor for measuring the angle of a magnetic angle transmitter

Info

Publication number: WO2005054784A1
Application number: PCT/EP2003/050885
Authority: WO
Inventors: Christian Schott
Original assignee: Sentron Ag
Priority date: 2003-11-24
Filing date: 2003-11-24
Publication date: 2005-06-16
Also published as: AU2003298316A1

Abstract

The invention relates to an angle sensor for measuring the angle of a magnetic angle transmitter producing a plane magnetic field and comprising a first magnetic field sensor (6) whose output signal is quantitatively maximum when the direction of the magnetic field produced in the field of angle sensor is parallel to a first measuring axis (9), and a second magnetic field sensor (7) whose output signal is quantitatively maximum when the direction of the magnetic field produced in the field of angle sensor is parallel to a second measuring axis (10). The first measuring axis (9) is characterised by a first angle Ψ1 and a second measuring axis (10) is characterised by a second angle Ψ2. Said angle sensor also comprises an evaluation circuit for forming an output angle U2. The inventive angle sensor is characterised in that the difference | Ψ2-Ψ1 | of the angles of the two measuring axes (9, 10) is less than 90° and the formation of the output angle U2 by the evaluation circuit comprises the division of the output signals of the two magnetic field sensors (6, 7) into a quantitatively smallest of two output signals in a numerator and the quantitatively largest of two output signals in a division quotient denominator.

Description

Angle sensor for measuring the angle of a magnetic encoder

The invention relates to an angle sensor for measuring the angle of a magnetic angle encoder of the type mentioned in the preamble of claim 1.

For the contactless measurement of an absolute angular position are magnetic increasingly for reasons of low cost and high reliability and robustness

Angle encoder used. Such an angle encoder consists of a magnet which is mounted on a rotatable body and a sensor which is mounted on a non-rotating body. If the magnet turns, the magnetic field turns at the location of the sensor. The sensor determines the direction of the magnetic field, which is defined by the specification of an angle α, by measuring two components of the magnetic field, which lie in the plane perpendicular to the axis of rotation and are orthogonal to one another, and calculates the angle from the two measured values. For this purpose, the sensor contains two magnetic field sensors, the first magnetic field sensor providing an electrical signal that is proportional to the size B * sinα, and the second magnetic field sensor providing an electrical signal that is proportional to the size B * cosα, where B is the strength of the magnetic field designated. The two signals are then further processed by appropriate electronics to form a signal which corresponds to the absolute angle α. This measuring principle has the advantage that only the direction but not the absolute strength of the magnetic field is included in the angle calculation. With this e.g. Temperature drifts of the sensitivity of the sensor or the strength of the magnet largely suppressed. The signal processing is usually carried out in digital form by a microcontroller using a suitable algorithm such as the CORDIC algorithm. The magnetic field sensors are based on the Hall effect or on the magnetoresistive effect. However, the technology of magnetoresistive sensors is not compatible with the semiconductor technology. The implementation of Hall-effect based sensors in the widespread CMOS technology, which are sensitive parallel to the chip surface, can be done in two ways: either by using a ferromagnetic flux concentrator, which locally deflects the magnetic field lines running parallel to the chip surface into vertical field lines, so that they can be measured by conventional horizontal Hall elements that are integrated in the semiconductor chip, or by using so-called vertical Hall elements that are sensitive to a magnetic field that runs parallel to the surface of the semiconductor chip.

In order to calculate the angle α from the voltages measured by the Hall elements when the magnet rotates, the two measured values are usually digitized. After the conversion, either the angle value corresponding to the measured value is read from a table or an iterative algorithm is used to calculate the angle. The first method requires a large and expensive memory, the second method takes a lot of time, so that the measurement rate is very limited. This is a disadvantage if the sensor is used in closed applications Control loop should be used. One such application is the regulation of the throttle valve position in the intake manifold of an internal combustion engine.

A sensor for the detection of the direction of a magnetic field with a magnetic field concentrator and with horizontal or vertical Hall elements is known from the European patent application EP 1182461. This sensor can be used as an angle sensor. The information about the angle of the magnetic angle encoder must be determined according to one of the methods described above.

The invention has for its object to develop an angle sensor in which the determination of the angle is possible without complex operations and which is therefore also suitable for applications with a closed control loop.

[0006] According to the invention, the stated object is achieved by the features of claim 1.

[0007] The angle sensors according to the invention are designed for an angle transmitter with a predetermined measuring range. The measuring range is defined as an angular range with end values of ßi and ß2. For the sake of simplicity, the measuring range is based on a measuring range from 0 ° to ß, ie ßi = 0 ° and ß ₂ = ß. Typical measuring ranges are 0 ° to 30 °, 0 ° to 60 °, 0 ° to 120 °, under certain circumstances 0 ° to 150 °. The angle β is therefore typically> 30 ° and <180 °. The angle sensor comprises a semiconductor chip with two magnetic field sensors, logic, amplifier and evaluation circuits. The amplitudes of the output signals of the magnetic field sensors depend on the direction of the external magnetic field. Hall elements integrated in the semiconductor chip are preferably used as magnetic field sensors, but magnetoresistive or other magnetic field sensitive sensors can also be used. In a preferred embodiment, a flat, circular or disk-shaped magnetic field concentrator made of ferromagnetic material is applied to the surface of the semiconductor chip. The angle sensor serves to determine the direction of the magnetic field generated by an external magnetic angle transmitter in the plane defined by the surface of the semiconductor chip or the flat magnetic field concentrator. The direction of the magnetic field in this plane can be characterized by a polar angle α. The sensor is characterized by two measuring axes that intersect at a common point. The measuring axes are each defined by a polar angle ψi or ψ ₂ . A magnetic field sensor is assigned to each measuring axis. The assignment of a magnetic field sensor to a measuring axis is defined such that the output signal of the magnetic field sensor is always greatest when the external magnetic field runs parallel to its measuring axis. According to the invention, the two measuring axes are not orthogonal to one another, but instead form an angle different from 90 °, ie it is ψi - ψ ₂ 1 ≠ 90 °. The angle α is obtained from the output signals Ui and U _{2 of} the two magnetic field sensors, wherein this includes a division of the two output signals Uj and U ₂ , ie the division - - or the "ι

Division - -, the smaller of the two output signals in the numerator and the larger of the two U ₂ output signals in the denominator of the division quotient.

The invention proposes two solutions for the determination of the angles ψi and ψ _{2 of} the two measuring axes and the determination of the angle α as a function of the angle β, which defines the size of the measuring range.

In the first solution, the angles ψi and ψ _{2 are} given by ψi = + ß / 2 + δ and ψ ₂ = 3ß / 2-δ, the angle δ representing a correction angle. In this solution, the angle ψi of the first measuring axis (9) is smaller than the angle β, while the angle ψ _{2 of} the second measuring axis (10) is larger than the angle β. The angle α is determined by dividing the output signals of the magnetic field sensors assigned to the two measuring axes:

The resulting systematic measurement error is the smallest and thus the linearity of the angle sensor 1 is greatest when the correction angle is δ = 0 °. The first solution is suitable for relatively small measuring ranges in the range ß = 15 ° to ß = 45 °, but in exceptional cases up to ß = 60 ° or ß <90 °, otherwise the systematic measurement error will be large.

In the second solution, the angles ψi and ψ _{2 are} given by ψi = + ß / 4 + δ and ψ ₂ = 3ß / 4-δ, the angle δ representing a correction angle. In this solution, the angles ψi and ψ _{2 of} the two measuring axes 9 and 10 are smaller than the angle ß. The resulting systematic measurement error is the smallest and thus the linearity of the angle sensor 1 is greatest when the correction angle δ is approximately δ = 0.0135 * ß at small angles ß and approximately δ = 0.012 * ß at larger angles ß. The following Table 1 contains some values for the optimal angle δ as a function of the angle ß for achieving the greatest possible accuracy.

The angle α is formed from the output signals as follows: = - U, - * - ß forUι <U ₂ U ₂ 2 α = forUi> U ₂ . (2)

The advantage of the second solution over the first solution is that for a given measuring range the deviation of the determined angle α from the actual angle α ', i.e. the mistake is smaller.

In the first solution, the choice of the correction angle δ to δ = 0 ° results in the smallest systematic error. In the second solution, the choice of the correction angle δ according to Table 1 results in the smallest systematic error. However, the size of the correction angle δ has a comparatively large influence on the sensitivity of the angle sensor. In applications in which the maximum permissible error may be greater than the maximum systematic error achieved with the value δ according to Table 1, it is therefore advantageous to increase the sensitivity at the expense of accuracy. That the correction angle δ is chosen so that the maximum error within the measuring range reaches the maximum permissible systematic error. With a measuring range of ß = 60 °, the second solution with δ = 0.79 ° gives the highest accuracy, namely a maximum systematic error of 0.2% of the measured value, but the sensitivity is only 0.84% / °. With δ = -11 ° you get a smaller accuracy, namely a maximum systematic error of 1% of the measured value, but a significantly higher sensitivity of 1.5% / °.

The determination of the angle α according to equation (1) or equations (2) is preferably carried out using analog circuitry. This will be explained later using the detailed description. The angle signal is then continuously available, which is advantageous when using the angle sensor in a closed control loop. However, the determination of the angle α can also be carried out digitally by digitizing the two output signals Ui and U ₂ and then calculating the angle α according to equation (1) or equations (2).

The accuracy of the determined angle α can be increased if the value determined according to equation (1) or equations (2) is corrected by means of a characteristic curve. The characteristic curve is preferably present in the form of a table with pairs of values (α, α "), with each value α determined from the output signals being associated with the corresponding correct value α ' This is interesting for both the first and the second solution. Hall elements are particularly suitable as magnetic field sensors, since they can be integrated into the semiconductor chip. Hall elements that are sensitive to a magnetic field running parallel to the surface of the semiconductor chip are referred to as "vertical" Hall elements. Hall elements that are sensitive to a magnetic field running perpendicular to the surface of the semiconductor chip are referred to as "horizontal" Hall elements.

[0016] The angle sensor can be designed with or without a magnetic field concentrator. If the angle sensor is designed without a magnetic field concentrator, then the magnetic field sensors must be sensitive to a magnetic field which is directed parallel to the surface of the semiconductor chip. The magnetic field sensors that belong to different measuring axes then differ in their alignment in the semiconductor chip. In this case, vertical Hall elements are used. If the

If the angle sensor is provided with a flat, ring-shaped or disk-shaped magnetic field concentrator, then the magnetic field sensors are to be arranged along the edge of the magnetic field concentrator, where the field strength of the magnetic field is greatest. In this case, both horizontal and vertical Hall elements can be used. Horizontal Hall elements are to be arranged below the outer edge of the magnetic field concentrator. The orientation of a horizontal Hall element with respect to the measuring axis assigned to it does not matter. Vertical Hall elements are to be arranged outside the outer edge of the magnetic field concentrator. The vertical Hall element must be aligned with the measuring axis assigned to it.

As already explained above, the angle sensor contains two magnetic field sensors, each of which is assigned a measuring axis according to the proviso that the output signal of the first

The magnitude of the magnetic field sensor is greatest when the direction of the magnetic field generated by the angle encoder in the plane runs parallel to the first measuring axis, and that the output signal of the second magnetic field sensor is largest in terms of amount when the direction of the magnetic field generated by the angle encoder in the plane is parallel to the second measuring axis runs. Such a magnetic field sensor can consist of one or more sensor elements which lie on the assigned measuring axis. However, such a magnetic field sensor can also consist of several sensor elements which are arranged symmetrically around the measuring axis and from whose individual output signals the output signal of the magnetic field sensor is formed. For example, if the position of the measuring axis is defined by the angle ψ = 60 °, then, for example, a sensor element on an axis, which is defined by the angle ψ = 50 °, and a second sensor element on an axis, which is defined by the angle ψ = 70 ° is defined.

The invention is explained in more detail below using exemplary embodiments and the drawing.

1 shows an angle sensor according to a first exemplary embodiment, 2 shows a diagram, FIG. 3 shows an angle sensor according to a second exemplary embodiment, FIG. 4 shows a circuit for forming the ratio of the output voltages of two Hall elements, and FIG. 5 shows another circuit.

1 shows in top view and schematically an angle sensor 1 which is designed for a measuring range from 0 ° to β = 60 °. The angle sensor 1 consists of a semiconductor chip 2, on the surface of which a flat, disk-shaped magnetic field concentrator 3 is applied. The angle sensor 1 is used to measure the direction of a magnetic field generated by a magnet 4 in the plane defined by the magnetic field concentrator 3. In this example, the magnet 4 is magnetized in the direction of its long axis. The magnet 4 is arranged such that it can be rotated relative to the angle sensor about an axis 5 perpendicularly penetrating the center of the magnetic field concentrator 3, the rotational position of the magnet 4 being defined by the angle α. The angle sensor 1 and the magnet 4 together form an angle sensor. The semiconductor chip 2 has two magnetic field sensors 6 and 7, which are arranged in the region of the edge 8 of the magnetic field concentrator 3. The position of the two magnetic field sensors 6 and 7 with respect to the measuring range is given by the two angles ψi = + ß / 2 = 30 ° and ψ ₂ = 3ß / 2 = 90 °. The two magnetic field sensors 6 and 7 define two measuring axes 9 and 10, which intersect on the axis 5 and their position by the angle ψibzw. ψ _{2 is} defined. The strength of the magnetic field at the location of the two magnetic field sensors 6 and 7 is given by:

B ₂ = ki * B * cos (ψ ₂ - α) (4), the size ki denoting a constant dependent on the geometry of the magnetic field concentrator 3 and the size B the strength of the magnetic field. If there is no magnetic field concentrator, then ki = 1. The output signals Ui and U _{2 of} the first and second magnetic field sensors 6 and 7 are given by: Uι = k ₂ * B _j (5) U ₂ = k ₂ * B ₂ (6), the size k _{2 being} a constant dependent on the properties of the magnetic field sensors. The magnitude of the output signal of the first magnetic field sensor 6 is greatest when the magnetic field generated by the magnet 4 runs parallel to the measuring axis 9. The amount of the output signal of the second magnetic field sensor 7 is greatest when the magnetic field runs parallel to the measuring axis 10. The angle α is an approximately linear function of the ratio B2 B1. The information about the angle α can therefore be obtained by dividing the output signals Uj and U _{2 of} the two magnetic field sensors 6 and 7: _{α =} _ ² - * ß (7). U, 2 shows measured values 11 of the angle α as a function of the angle α 'actually occupied by the magnet 4 in the measuring range from 0 ° to β = 60 °. The measured values 11 are approximately on a straight line 12. The following table 2 gives an overview of the achievable accuracy. The absolute error of the greatest difference between the measured angle α and the actual angle α 'within the measuring range is referred to as the maximum error or maximum non-hearance.

In the example shown in FIG. 1, the two magnetic field sensors 6 and 7 are so-called horizontal housings 13 and 14, the sensitive zone of which is arranged below the edge 8 of the disk-shaped magnetic field concentrator 3. The magnetic field sensors 6 and 7 can also be arranged on their measuring axis 9 or 10 on the diametrically opposite side below the edge 8 of the magnetic field concentrator 3, similarly as horizontal housing elements 15 and 16. Since the direction of the magnetic field is opposite in opposite diametrically opposite positions is, the housing elements 13 and 15 have the same output voltage in terms of amount, but with different signs. The same is good for the housing elements 14 and 16. The magnetic field sensor 6 therefore preferably consists of the two housing elements 13 and 15, the output signal of the magnetic field sensor 6 being composed of the difference in the output voltages of the two housing elements 13 and 15, and the magnetic field sensor 7 preferably exists from the two housing elements 14 and 16 and its output signal is composed of the difference in the output voltages of the two housing elements 14 and 16.

3 shows in top view and schematically an angle sensor 1, which is also designed for a measuring range from 0 ° to β = 60 ° and which is constructed in the same way as the angle sensor 1 shown in FIG. 1. The difference exists in the selection of the position of the two measuring axes 9 and 10 on which the magnetic field sensors 6 and 7 are arranged, and in the method for calculating the angle α from the output signals Ui and U _{2 of} the two magnetic field sensors 6 and 7. The position of the two measuring axes 9 and 10 is given by the two angles ψi = + ß / 4 + δ = 15 ° + δ and ψ ₂ ⁼ 3ß / 4-δ = 45 ° -δ. The optimal value of the correction angle δ in this example is δ = 0.0132 * 60 ° = 0.79 °. This gives ψi = 15.79 ° and ψ ₂ = 44.21 °. The output signals Ui and U _{2 of} the first and second magnetic field sensors 6 and 7 are again given by: Ui = kj * k ₂ * B * cos (ψι - α) (8) U ₂ = ki * k ₂ * B * cos (ψ ₂ - α) (9). The information about the angle α is now obtained from the output signals Ui and U _{2 of} the two magnetic field sensors 6 and 7 according to the following rule: = forU ₂ <Uι U _: 2

The following TabeUe 3 gives an overview of the achievable accuracy.

The achievable accuracy is greatest when the angles ψi and ψ _{2 of} the measuring axes 9 and 10 are determined on the basis of the values for the correction angle δ given in the table. However, the improvement in accuracy compared to the version with δ = 0 ° is relatively modest. The angles ψi = + ß / 4 and ψ ₂ = 3ß / 4 can therefore be used for the two measuring axes 9 and 10 without a great reduction in accuracy. Although the optimal value of the correction angle is approximately δ = 0.013 * ß, the conical angle δ can also be chosen somewhat larger or smaller.

The two measuring axes 9 and 10 are arranged symmetrically with respect to the axis defined by the angle β / 2. From this symmetry it follows that for U ₂ <Uι the ratio U: _ / Uι gives an approximately linear output signal, while for U ₂ > Ui the ratio U] / U ₂ gives an approximately linear output signal. The rule defined in equations (10) generates an approximately linear and continuous output signal in the entire measuring range.

The ratio U ₂ / U ₁ can be built with analog circuitry if the two magnetic field sensors 6 and 7 are Hall elements. An electronic circuit for the operation of the two HaU elements, which generates an output signal U _a , which is proportional to the ratio WUi, is described in the European patent application EP 1243897.

4 shows such an electronic circuit, which has the first housing element 13 for measuring the component Bi and the second housing element 14 for measuring the component B ₂ . The measurement of the measured components of the magnetic field is carried out analogously, since in this circuit the housing voltage of the first housing element 13 is regulated to a constant value and the current I ₂ flowing through the second housing element 14 is proportional to the current Ii flowing through the first Hall element 13. The circuit Hefert an output signal U _a according to equation (7). A mass Potential of the circuit is denoted by m. The circuit includes:

a first operational amplifier 17, which taps the Hall voltage differentieU established between the two voltage contacts of the first housing element 13 and references it with respect to the ground potential m. Good for the output voltage Vi of the first operational amplifier 17 with an amplification factor of one: Vi = Sι * Iι * Bι, where Si denotes the sensitivity of the first housing element 13.

- A second operational amplifier 18, which taps, amplifies the reference voltage which occurs between the two voltage contacts of the second housing element 14, and references it with respect to the ground potential m. With an amplification factor of one, the following applies to the output voltage V _{2 of} the second operational amplifier 18: V ₂ = S ₂ * I ₂ * B ₂ , where S ₂ denotes the sensitivity of the second housing element 14. The output voltage V _{2 of} the second operational amplifier 18 serves as the output signal U _{a of} the circuit: U _a = V ₂ . Since the two housing elements 13 and 14 are connected, the current It is proportional to the current I ₂ . Since the two housing elements 13 and 14 have the same properties, Si = S _{2 is} good. - A PI controller built up from a third operational amplifier 19, a resistor R ₂ and a capacitor C, the inverting input of which is a reference voltage -V _Ref via a first resistor Ri and the output voltage Vi of the first operational amplifier 17 via a second resistor Ri of the same size is supplied and its non-inverting input is connected to ground m. The output of the third operational amplifier 19 feeds one current contact each of the first and second housing elements 13 and 14, while the other current contacts of the two housing elements 13 and 14 are electrically connected and connected to a voltage source 20 with a supply voltage m negative in relation to ground. Vi = V _R ^ is controlled via the controlled system composed of the first housing element 13 and the first operational amplifier 17. By transforming the equations one obtains U _a = Vit _s f * B ^ i = ω- * WUi.

This circuit can be expanded in a simple manner, so that the information about the angle α according to equation (10) can be combined with analog circuitry. An example of such an extended circuit is shown in FIG. 5. It has six switches, three of which are designated by the letter A and three by the letter B and whose switching state "open" or "closed" depends on the ratio Vι / V ₂ , and a circuit with a fourth operational amplifier 21 and two of the same Resistors R ₃ . The non-inverting input of the fourth operational amplifier 21 is connected to ground m. If V2 / V1 <1, the switches marked A are closed and the switches marked B are open. The circuit with the fourth operational amplifier 21 is bypassed. The voltage U _a = V _Re f * V ₂ Vι = V _R ^ * WU _{I is present} at the output of the circuit. If V2 / V1> 1, the switches marked B are closed and the switches marked A are open. The circuit with the fourth operational amplifier 21 is now between the output of the second operational amplifier 18 and the Output switched. At the output of the circuit is the voltage U _a = V _RCΓ * (2-Vι / V ₂ ) =

V _Ref * (2-Uι / U ₂ ). The output signal U _a is approximately linear in the measuring range from 0 ° to ß

Function of the angle ct .: U _a = a + b * α (11), whereby the constants a and b are to be determined by a calibration measurement. The control signals for controlling the control of the switches are generated, for example, by means of a comparator 22, the output signal of which depends on which of the two voltages Vi and V _{2 is} the larger. A logic inverter 23 ensures that the control signals for switches A and B are inverse to one another. The outputs of the comparator 22 and the logical inverter 23, designated A 'and B', carry the control signals for the switches A and B. The output signal U _a can be digitized if necessary by means of an A / D converter, the reference voltage V _Ref serves as a voltage reference.

Claims

1. Angle sensor for measuring the angle of an angle encoder, which generates a magnetic field in one plane, with a first magnetic field sensor (6), the output signal of which is greatest in terms of magnitude, if the direction of the magnetic field generated by the angle encoder in the plane is parallel to a first measuring axis (9), and a second magnetic field sensor (7), the output signal of which is the largest in terms of magnitude if the direction of the magnetic field paraUel generated by the angle encoder in the plane runs to a second measuring axis (10), the first measuring axis (9) being marked by a first angle ψi and the second measuring axis (10) is characterized by a second angle ψ ₂ , and with an evaluation circuit for the formation of an output signal U _a , characterized in that the difference | ψ ₂ - ψi | the angle of the two measuring axes (9, 10) is less than 90 ° and that the loading of the output signal U _a by the evaluation circuit comprises a division of the output signals of the two magnetic field sensors (6, 7), the smaller of the two output signals in the counter and the is larger in magnitude of the two output signals in the denominator of the division quotient.

2. Angle sensor according to claim 1, characterized in that based on a measuring range from 0 ° to ß, the angle ß being less than 90 °, the angle ψi of the first measuring axis (9) being smaller than the angle ß and the angle ψ ₂ the second measuring axis (10) is greater than the angle β.

3. Angle sensor according to claim 2, characterized in that the angles ψi and ψ _{2 are} given by ψi = ß / 2 + δ and ψ ₂ = 3ß / 2-δ, where δ is a correction angle.

4. Angle sensor according to claim 2, characterized in that the angles ψi and ψ _{2 are} given by ψi = ß / 2 and ψ ₂ = 3 ß / 2.

5. Angle sensor according to claim 1, characterized in that based on a measuring range from 0 ° to ß, the angle ß being less than 180 °, the angles ψi and ψ _{2 of} the two measuring axes (9 and 10) smaller than the angle are and that the output signal U _a by the evaluation circuit comprises a division of the output signal of the second magnetic field sensor (7) by the output signal of the first magnetic field sensor (6), provided that the output signal of the first magnetic field sensor (6) is greater than the output signal of the second Magnetic field sensor (7), and that the output signal U _a comprises a division of the output signal of the first magnetic field sensor (6) by the output signal of the second magnetic field sensor (7), provided that the output signal of the first magnetic field sensor (6) is smaller than the output signal of the second Magnetic field sensor (7).

6. Angle sensor according to claim 5, characterized in that the angles ψi and ψ _{2 are} given by ψi = ß / 4 + δ and ψ ₂ = 3ß / 4-δ, where δ is a correction angle.

7. Angle sensor according to claim 5, characterized in that the angles ψi and ψ _{2 are} given by ψi = ß / 4 and ψ ₂ = 3ß / 4.

8. Angle sensor according to claim 6, characterized in that the correction angle δ has a value which is calculated according to the measuring range ß by interpolation from the following table:

9. Angle sensor according to claim 6, characterized in that to increase the sensitivity of the angle sensor, the correction angle δ is selected such that the maximum error within the measuring range reaches a predetermined value.

10. Angle sensor according to one of claims 1 to 9, characterized in that the output signal U _a is corrected on the basis of a characteristic curve stored in a table.