Method for Determining, Section after Section, a Parameter-Dependent Correction
Value Approximation Course and Sensor Arrangement
Embodiments of the present invention relate to a method for determining a correction
value approximation course of sensor arrangements, as are exemplarily used in many fields
of technology.
In many sensors or sensor arrangements, corruptions of the measuring values detected
using same occur due to effects caused by manufacturing, the environment, operation or
other effects. Depending on the sensor, sensor type or effect, the respective corruptions
may have different effects on the measuring values established. Apart from a simple offset,
i.e. a shift of the respective measuring values by a constant or parameter-dependent value,
more complex corruptions may also occur. Exemplarily, a ratio between a measuring
quantity acting on the sensor and the respective measuring value detected by the sensor
may exhibit a parameter dependence. Furthermore, a parameter-dependent non-linear
characteristic curve may result between the measuring quantity acting on the sensor and
the measuring value detected by the sensor.
Departing from this, there is demand for an improvement in the measuring precision by
implementing an improved correction value approximation course which, at the same time,
allows simplified sensor manufacturing.
The underlying problem is overcome by embodiments of the present invention, such as, for
example, by a method in accordance with one of claims 1 or 12, a sensor arrangement in
accordance with claim 13, a Hall sensor arrangement in accordance with claim 21 or a
program in accordance with claim 22.
Embodiments of the present invention are based on the finding that an improvement in
measuring precision can be achieved by taking into consideration an improved correction
approximation course, wherein such an improved correction approximation course may be
established on the basis of a single initial correction value and a first parameter coefficient.
In embodiments of the present invention, this is achieved by determining a correction
approximation course section after section, wherein a first sub-section of the correction
approximation course in a first parameter range is preset by a predetermined initial
correction value and a first parameter coefficient relative to an initial parameter value.

If a predetermined condition of a first parameter value associated to the sensor
arrangement or another triggering condition is fulfilled, at first a first measuring signal
value which corresponds to the measuring value of the sensor arrangement and, at the same
time, to a first measuring signal of a sensor element of the sensor arrangement will be
determined. By altering the first parameter value associated to the sensor arrangement,
wherein a second parameter value associated to the sensor arrangement is obtained, a
second measuring signal value can be determined with this second parameter value. This
allows establishing a second sub-section of the correction approximation course for a
second parameter range based on a functional association describing the second sub
section, the first parameter value, the second parameter value, the first measuring signal
value, the second measuring signal value and the initial correction value. In embodiments
of the present invention, the first parameter value is in the second parameter range
underlying the second sub-section of the correction value approximation course.
In contrast to a measuring value or a measuring signal value, a correction value generally is
only accessible for measuring technology under certain circumstances. Generally, such a
correction value basically will no longer be accessible if the sensor or the sensor
arrangement, for example, is already exposed to an influence to which the sensor or the
sensor arrangement reacts by a change in its measuring signals or measuring values. This
applies, in many a case, to sensors which are employed in assemblies or other technical
devices. Additionally, depending on the sensor, type of the sensor and sensitivity of the
sensor, the result may be that, using such a sensor, a correction value cannot be established
outside a specially shielded or specially stabilized space. In order to determine a
corresponding correction value, it is inevitable in many a case to measure the sensor in a
space which is shielded relative to that influence to which the sensor is sensitive, or a
specially stabilized space. Exemplarily, a magnetic field sensor in which, depending on the
sensitivity of the sensor, determining such a correction value, such as, for example, an
offset value, can only be performed in a magnetically sufficiently shielded space, since a
corruption or alteration of the measuring value might be expected already due to the earth's
magnetic field is to be mentioned here. Of course, corresponding corruptions may occur
when measuring the absolute correction values when these are not performed in
correspondingly shielded or stabilized spaces.
Embodiments of the present invention will be detailed subsequently referring to the
appended drawings.
Fig. 1 a shows a flowchart of an embodiment of a method for determining, section
after section, a parameter-dependent correction value approximation course;

Fig. 1b shows an example of a parameter-dependent correction value approximation
course as may be determined using an embodiment of a method for
determining, section after section, a parameter-dependent correction value
approximation course;
Fig. 2 shows a block diagram of an embodiment of a sensor arrangement;
Fig. 3 shows a block diagram of an embodiment of a Hall sensor arrangement; and
Fig. 4 exemplarily shows a comparison between a temperature-dependent
correction value course and a correction approximation course determined
section after section.
In many sensors allowing determining an influence in the form of a measuring value on a
corresponding measuring quantity, the measuring values are frequently corrupted by
effects which make taking correction values or correction value approximations into
consideration for improving the measuring precision obtainable by the sensor advisable.
The different effects resulting in a corruption of the measuring values compared to the
measuring quantity acting on the sensor may result in different corruptions of the
measuring values relative to the underlying measuring quantities. Apart from a simple,
maybe parameter-dependent, offset, i.e. a shift of the measuring values relative to the
measuring quantity, more complex corruptions may also occur. Apart from a parameter-
dependent or measuring value-dependent change in a gradient of the measuring values
relative to a change in the measuring quantities, more complex, such as, for example, non-
linear, corruptions may also occur.
In order to counteract corruptions of this kind, it is advisable in many cases to take
corresponding correction values or correction value approximations into consideration
when measuring using a corresponding sensor. Correction values or correction value
approximations may exemplarily be realized as additive, multiplicative or more complex
corrections of the measuring values of the sensor, also referred to as sensor arrangement.
The procedure described below for determining, section after section, a parameter-
dependent correction value approximation course for correcting a measuring signal of a
sensor arrangement may exemplarily be employed in order to get a grip on the
temperature-dependent spinning current offset of Hall sensors. The subsequent
explanations, however, will make clear that the inventive procedure may be applied to all

sensor arrangements infested by offset, measuring errors or error signals, wherein apart
from temperature changes, pressure changes and any changing environmental influences
may be considered as a sensor parameter influencing or interfering in the measuring value.
Before the embodiments of the present invention and their mode of functioning will be
detailed, it is pointed out that, in order to simplify the presentation, elements, circuits and
other objects having similar functions or equal functions are referred to by same or similar
reference numerals. Additionally, it is pointed out here that corresponding sections of the
description referring to elements, objects and circuits having similar functions or same
functions, are mutually exchangeable, unless explicitly indicated otherwise. Furthermore,
in order to simplify the presentation, summarizing reference numerals will be used in the
further course for components occurring several times in one embodiment, unless reference
is made to individual elements or objects. This also serves simplification and clearer
structuring of the description.
When referring to Figs, la, lb and 2 to 4, a first embodiment of a method for determining,
section after section, a parameter-dependent correction value approximation course is
described, Fig. la showing a flowchart of an embodiment of this method and Fig. lb
showing an example of a corresponding parameter-dependent correction value
approximation course, whereas Fig. 2 shows a corresponding sensor or corresponding
sensor arrangement as a block diagram. However, at first an embodiment of an inventive
method will be discussed referring to Figs, la and lb.
The embodiment of a method for determining, section after section, a parameter-dependent
correction value approximation course, which is illustrated in Fig. la as a flowchart, is
based on the fact that an initial correction value AW and a first parameter coefficient pK1
relative to an initial parameter value p0 which generally is in a first parameter range 215-1
are preset, i.e. exemplarily measured in a series test and stored in the sensor. A first sub-
section 240-1 of the sectioned correction value approximation course 240 is given on the
basis of the first parameter coefficient pKl and the initial correction value AW.
Fig. lb illustrates this using a corresponding plotting of the correction value and the
correction value approximation value based on the embodiment in dependence on the
parameter p. Thus, Fig. lb shows a correction value course 200, which normally is no
longer accessible during measuring operation, which at the initial parameter value po
exhibits the initial correction value AW (absolute value). The initial parameter value p0 is
in the first parameter range 215-1 which, with regard to the parameter values p in the

situation schematically shown in Fig. 1b, extends in the parameter interval between p0 - ∆p
and p0 + ∆p.
In the situation shown in Fig. lb, a second parameter range 215-2 over which a second
sub-section 240-2 of the correction value approximation course 240 is to be established by
the embodiment of the present invention is abutting on the first parameter range 215-1 over
which the first sub-section 240-1 of the correction value approximation course 240 is
defined.
In the example of the present invention described here, the first and second parameter
ranges 215-1, 215-2 are mutually abutting so that, potentially taking a measuring resolution
with regard to the parameter values, a quantizing resolution or another resolution limit
inherent to the respective sensor into consideration, there are no parameter values between
the first and second parameter ranges 215-1,215-2.
When, after starting the method (step S100), it is found out in a step S110 that a first
parameter value p1 associated to the sensor arrangement fulfills a predetermined condition
or a triggering condition is fulfilled, in a step S120 a first measuring signal value MW1 at
the first parameter value p1 will be determined. Subsequently, in a step S130, the first
parameter value p1 associated to the sensor is changed such that a second parameter value
P2 will be obtained. In a step S140, a second measuring signal value MW2 is determined at
the second parameter value p2, whereupon in a step S150 a second sub-section 240-2 of the
correction value approximation course 240 is established on the basis of a functional
association describing the second sub-section 240-2, taking into consideration the first and
second parameter values p1 and p2, the first and second measuring signal values MW1 and
MW2 and the initial correction value AW, before the method ends in a step S160. If,
however, it is found out in step S110 that the first parameter value does not fulfill the
predetermined condition, nor is the triggering condition fulfilled, step S160 is entered
directly.
Using the measuring signal values MW1 (first measuring signal value) and MW2 (second
measuring signal value) determined at the parameter values p1 (first parameter value) and
p2 (second parameter value), on the basis of the following relation:


a parameter coefficient pK2 in the second parameter range 215-2 in which there is at least
he parameter value p1 can be established. A description of the second sub-section 240-2 of
the correction value approximation course 240 which in the situation shown in Fig. lb
follows the first sub-section 240-1 of the correction value approximation course 240
continuously may be done on the basis of this parameter coefficient pK2.
In the situation shown in Fig. 1b, in the case of the two abutting parameter ranges 215-1,
215-2, the first and second sub-sections 240-1, 240-2 of the correction approximation
course 240 are continuous to each other, wherein again the resolution limits already
mentioned with regard to the measuring values or measuring signal may have to be taken
into consideration. As will be explained later on, the parameter-dependent correction
approximation course 240 determined section after section may additionally comprise one
or several further or additional sub-sections with regard to one or several additional
parameter ranges.
Fig. 2 shows an embodiment of the present invention implemented as a sensor 100. The
sensor 100 includes a first sensor element 110 for providing measuring signals
corresponding to respective measuring values. The first sensor element 110 here is coupled
to a processing circuit 120 which is configured to detect the respective measuring signals.
Additionally, the processing circuit 120 is coupled to a second sensor element for
providing parameter signals which correspond to parameter values.
The processing circuit 120 is additionally configured to perform, based on the measuring
signals, the measuring values contained therein, the parameter signals and the parameter
values contained therein, the method described before for determining, section after
section, a parameter-dependent correction value approximation course. Depending on the
specific implementation, the sensor 100 additionally includes parameter value changing
means 140 as an optional component (indicated in Fig. 2 in broken lines) capable of
changing the parameter values of the first sensor element 110 which is used for the actual
measuring value detection. Changing the corresponding parameter or actually determining
the parameter value of the sensor 100 (or the first sensor element 110) is performed by the
second sensor element 130 which in embodiments of the present invention is, for this
purpose, spatially arranged to be as close as possible to the first sensor element 110, ideally
directly neighboring thereto. In order to provoke, if applicable, a most locally limited
change in the parameter value, this similarly also applies for the optional parameter
changing means 140, if implemented.

Should a corresponding implementation of parameter changing means 140 not be
necessary, the processing circuit 120 may also cause a corresponding parameter change of
the first sensor element 110 indirectly, exemplarily by changing a supply power, such as,
for example, by increasing or reducing same.
Embodiments of the present invention are thus based on the basic idea that an
improvement in the measuring results of a sensor 100, while at the same time simplifying
the manufacturing method or calibration method of the sensor 100, can be achieved by
being able to limit the complex series tests for determining absolute correction values to a
single initial correction value at an initial parameter value. A correction value
approximation course is, with regard to at least first and second parameter ranges,
determined or established section after section having at least a first sub-section and a
second sub-section, the first sub-section being based on the predetermined initial correction
value and an also predetermined first parameter coefficient. For the second parameter
range and the respective second sub-section of the correction value approximation course
which may, with regard to the parameter values, exemplarily follow the first parameter
range of the first sub-section or abut thereon, the second sub-section can be established by
determining a first measuring signal value at a first parameter value and a second
measuring signal value at a second parameter value. Here, the second parameter value
emerges from the first parameter value by changing the respective parameter value. Since,
as has been explained, there is a substantial difference between correction values and
correction value approximations on the one hand, and measuring values and measuring
signal values on the other hand, the second sub-section is established indirectly or directly
based on the predetermined initial correction value.
The resulting advantage is that in embodiments of the present invention both a simplified
calibration method for determining the initial correction value and the first parameter
coefficient can be done in the works, wherein compared to a correction value
approximation course which is based only on these two values determined in the
calibration test, a significantly improved measuring precision can be achieved.
Additionally, embodiments of the present invention also allow improved compensation
relative to great parameter ranges, as exemplarily occur with regard to sensors in the
automobile sector, in the nautical sector, in the aviation sector and in many other
technological applications. Using an embodiment of the present invention implemented as
a method for determining, section after section, a parameter-dependent correction value
approximation course and the respective sensors, the measuring precision can also be
improved significantly in ranges relative to the operating parameters which are only
accessible using an extrapolation.

Expressed differently, embodiments of the present invention allow using sensors in an
operating parameter range for which no initial correction values and parameter coefficients
are determined in a series test or corresponding calibration and test measurements. Another
advantage of embodiments of the present invention is that compensation of aging effects as
may occur in sensors can be done by correspondingly determining a sectioned parameter-
dependent correction value approximation course regularly, such as, for example, after a
certain time interval elapsing, responsive to a corresponding CPU (central processing unit)
instruction or another processor-based instruction, when switching the sensor on. The
parameter coefficients established in this way, or the sub-sections of the correction value
approximation course determined in this manner can be saved in a storage for further
usage. Thus, embodiments of the present invention allow, if necessary, regularly
performing monitoring and optionally correcting the correction value approximation
courses or sub-portions thereof.
Even when in the embodiments of the present invention, which will follow in Figs. 3 and
4, Hall sensors or Hall sensor arrangements will be described exemplarily, this only is a
single embodiment of the present invention which is not to be interpreted as being limiting.
The embodiments shown in the following Figs. 3 and 4 are about a magnetic field sensor in
which the temperature or temperature values are used as parameter values in an offset
compensation as a correction value approximation. Embodiments of the present invention
are of course not limited to Hall sensors and the temperature dependence of the offset
values thereof, but may be applied to a plurality of different sensors and corresponding
parameters.
Hall sensors may exemplarily exhibit a mostly great and additionally strongly temperature-
dependent offset. Such an offset may fundamentally be reduced using the so-called
spinning current principle (SC), however, what frequently remains is a temperature
dependence of the spinning current offset. The spinning current principle is continually
cyclically turning (exemplarily by 90°) at a certain clock frequency the measuring direction
for detecting the Hall voltage at the Hall sensor element of the sensor and summing up
over all the measuring signals of a complete turn by 360°.
Fig. 3 shows a block diagram of a Hall sensor 100 comprising a Hall sensor element as a
first sensor element 110. In the embodiment of the present invention shown in Fig. 3, the
Hall sensor element 110 is exemplarily coupled to a processing circuit 120 for controlling
and for evaluating the sensor signals of the Hall sensor element 110 via four terminals each
offset by 90°. In the present invention, two components coupled to each other are meant to

be components which are connected to each other directly or indirectly via another
component (such as, for example, a resistor, amplifier).
The Hall sensor 100 additionally comprises a temperature sensor element 130 as second
sensor element, which in the embodiment shown in Fig. 3 is a resistor element. Depending
on the specific implementation, the temperature sensor element may be a PTC (positive
temperature coefficient) resistor element, an NTC (negative temperature coefficient)
resistor element or another respective resistor element, exemplarily on the basis of a
semiconductor compound. Additionally, the Hall sensor 100 comprises, as parameter
changing means 140, a heating element 140 as a switchable heat source. Such a heating
element may exemplarily be implemented as a resistor element having a corresponding
electrical resistance.
It is thus characteristic of embodiments of the present invention that an offset temperature
coefficient TK (parameter coefficient) and an absolute value AW of the offset (initial
correction value) are established only at one temperature TO (initial parameter value) on
the chip in the series test using the temperature sensor element 130. Additional
measurements at different temperatures during the series test are no longer required and
may thus be saved. Starting from this first test measurement in the series test calibration,
calibration over the complete operating temperature range will only be done during
operation of the sensor 100.
The following mode of functioning already described will be employed here. Starting from
the known values AW and TK of the offset, the sensor 100 operates with practically no
offset close to the series test temperature. Using the temperature sensor element 130, the
operating temperature can be monitored during operation by the processing circuit 120.
Should same change by a certain magnitude AT, another offset temperature coefficient,
namely the second parameter coefficient, will be established on the chip. In this way, the
offset course relative to the temperature may in principle be simulated or approximated
over any number of straight lines or other functional associations.
Fig. 4 shows a schematic comparison between an offset course (correction value course) of
a sensor 100 and an offset course simulated by three straight lines as a correction value
approximation course determined section after section. More explicitly, Fig. .4 shows
plotting of correction values and correction value approximations in dependence on a
temperature T. Here, a course 200 shown in Fig. 4 represents the actual offset course of the
Hall sensor 100, which usually is no longer accessible during operation. Apart from this
real offset course of the Hall sensor 100, a first approximation straight line 210 the course

of which has been determined by the absolute value AW and the temperature coefficient
TK in the series test at the temperature TO is additionally indicated in Fig. 4. The
approximation straight line 210 thus represents the first sub-section 240-1 of the
approximation correction value course 240 in a first temperature range 215-1. With the
foundation of this starting point of the known or predetermined absolute value AW and the
temperature coefficient TK, further temperature coefficients TK2, TK3, ... can then be
determined at different temperatures so as to simulate or approximate the offset course
200.
When the temperature exemplarily exceeds a threshold temperature Tg = TO + AT and thus
leaves the first temperature range 215-1, a first measuring signal value MW1 of the Hall
sensor 100 may be determined at first at a corresponding temperature value T1 (first
parameter value) in the method described before. Subsequently, by controlling the heating
element 140, the temperature can be increased by another value which exemplarily is small
compared to the temperature value AT in order to detect a second (measuring) signal value
MW2 at this temperature value T2 serving as the second parameter value. With the first
measuring value MW1 at the temperature Tl and the measuring value MW2 at the
temperature T2, the result will be a second temperature coefficient in a second temperature
range 215-2 at temperatures of greater than (TO + AT) in accordance with:

as the gradient of a corresponding approximation straight line as sub-section 240-2 of the
correction value approximation course 240.
Thus, a second sub-section 240-2 of the correction value approximation course can be
determined on the basis of the second temperature coefficient TK2 by exemplarily
continuously continuing the approximation straight line 210 and a second approximation
straight line 220 at the temperature Tg = (TO + AT), as is also illustrated in Fig. 4. By
dealing analogously with a third temperature range 215-3 (third parameter range or another
parameter range) at temperatures T below the temperature TO - AT, a third sub-section
240-3 of the correction value approximation course 240 determined section after section
which is indicated in Fig. 4 as the third approximation straight line 230 can be established
or determined. Here, the temperature range between the temperatures TO - AT and TO +
AT represents the first temperature range or the first parameter range, whereas the
temperature ranges below the first mentioned temperature value or temperature range
above the second mentioned temperature value represent the second and third temperature

ranges, respectively, using which the offset of the Hall sensor 100 is simulated. In Fig. 4,
this offset simulation is emphasized in bold type using three straight lines as the sectioned
correction value approximation course 240.
Additionally, Fig. 4 shows a course 250 of a residual offset after calibration using the
method described before on the basis of an offset simulation 240 which illustrates the
improvement achieved in the temperature ranges above the temperature TO + AT and
below the temperature TO - AT. Thus, in these two regions, the residual offset course 250
snaps off clearly compared to the course within the first temperature range between TO -
AT and TO + AT, which illustrates the improvement in the precision of the sensor 100.
The basis for this on-chip calibration of the temperature coefficients TK, here of the
temperature coefficient TK1, is the switchable heat source 140. Using same, the Hall
sensor can be heated during operation. When the temperature difference ATEMP and the
measuring value difference AMW are known, the temperature coefficient can be
determined.
A considerable advantage as has already been mentioned is the fact that only the absolute
value AW has to be measured in the field-free space in the embodiment of the present
invention described in connection with Fig. 4. The temperature coefficients TK, TK1, TK2
can, in contrast to the absolute value AW, also be measured with a magnetic field applying,
since they are, in a good approximation, independent of the respective current measuring
value. Depending on the specific implementation and application of a Hall sensor 100, it
may be advisable here for the sensor 100 to be exposed to a constant magnetic field or a
magnetic field which at least on average does not change, during a change in temperature
by the heating element 140. Thus, in the case of a magnetic field changing periodically
around a constant magnetic field value for example, integration over a period of such a
changing magnetic field may also be made the basis for determining the first and second
measuring signal values.
As has already been illustrated in the embodiment shown in Fig. 4, more than two
temperature ranges or parameter ranges including the respective sub-sections may of
course be employed for simulating the correction value course. Basically, the more
temperature coefficients TK are measured or determined, the more precise the simulation
and the lower a potentially occurring residual offset.
The embodiments of the present invention described in connection with Figs. 3 and 4 thus
represents an automatic calibration of the temperature-dependent offset in Hall sensors 100

using an on-chip determination of the respective temperature coefficients TK. Apart from
using a heating element 140, as has been the case in the embodiment of the present
invention shown in Fig. 3, any other circuit part, i.e. even the first sensor element 110 or
the Hall sensor 110 itself, may be used as switchable heat source. The higher the dissipated
power in the Hall sensor element 110, the faster the heating in the respective Hall sensor,
for example. One or several temperature coefficients can be determined correspondingly
faster. Basically, it is possible to reduce the temperature of the Hall sensor element
compared to a temperature value during normal operation (normal operation mode or state)
by switching circuit parts off for example. In such a case, it must be kept in mind with
regard to using equation (2) or determining the temperature coefficients, that in this case
the respective sign of the temperature change is taken into consideration. This means that,
in this case, it must be provided for that there is a negative temperature change. Apart from
using heating elements, like, for example, electrical resistors or other switchable heat
sources, a temperature change may also be caused by increasing or reducing the power of
the sensor, sensor arrangement, sensor elements or other parts of the circuit. Of course,
cooling elements, such as, for example, a Peltier element, may also be used here.
As has already been discussed, different parameters than the temperature may be employed
when correcting the measuring value or determining a parameter-dependent correction
value approximation course section after section. Apart from temperature, pressure,
mechanical deformations or other parameters depending on the environment or operation
may exemplarily be used. Examples of this are electrical voltages, electrical currents, but
also chemical environmental parameters (such as, for example, oxygen contents of the
environment).
When one or several ones of the parameters mentioned before have an influence on the
sensor, the sensor arrangement or the respective sensor element itself, same can be
determined by a corresponding sensor element 120 and potentially be influenced directly
or indirectly via another parameter, a corresponding determination, section after section, of
a parameter-dependent correction value approximation course can be performed using
embodiments of the present invention. In the case of pressure or another mechanical
influence on the sensor, the sensor arrangement or the sensor element itself, a piezo-
element may exemplarily be used as parameter changing means 140.
Apart from using approximation straight lines as described in Fig. 4, other functional
associations may also be used for formally describing parameter dependencies of the
correction value approximation course. As has been discussed before, the absolute
correction values are generally not accessible, however,it is possible to establish, using

parameter coefficients and other correction value approximations determined from sub-
sections, mathematical functions or functional associations which simulate the real
correction value course which cannot be obtained. Corresponding formulae and
mathematical associations can also be used in sub-sections of the correction value
approximation course. Using the measuring signal values MW1 (first measuring signal
value) and MW2 (second measuring signal value) determined using the two parameter
values p1 (first parameter value) and p2 (second parameter value), a parameter coefficient
pK in the respective parameter range 215 in which at least the parameter value p1 is can be
established on the basis of equation (1). On the basis of these parameter coefficients pK,
sub-sections of the correction value approximation course may then be described by means
of polynomial functions, rational functions (quotient of two polynomial expressions),
exponential functions, hyperbolic functions, harmonic functions or other combinations of
corresponding functions.
In the case of a degree N polynomial expression, N being a positive integer, this will be
explained in greater detail. Polynomial expressions are based on an expression in
accordance with:

p being a parameter value, f(p) being a value of the polynomial expression at the parameter
value p, ak being a real-value coefficient and k being an integer in a range between 0 and
N. In the case of describing sub-sections as straight lines (N = 1), two parameters (a0, a1)
must be set for each one of the sub-sections. Consequently, in the case of straight lines,
two conditions are to be made to the respective course of the sub-section. In the case of
parabolae (N = 2), three parameters including three conditions are to be set in
correspondence. Expressed generally, in the case of degree N polynomial expressions, (N
+ 1) conditions are to be made to each of the sub-sections, since the same number of
parameters must be determined for each of the sub-sections. Here, in each parameter range,
at least one condition can be fulfilled by the parameter coefficient in accordance with
equation (1). Depending on the number of the further coefficients of the polynomial
expression to be determined, further conditions are to be made, such as, for example, to the
continuity of the individual sub-sections relative to one another, differentiability of the
individual sub-sections at the respective boundaries of the parameter ranges underlying the
sub-sections and/or relative to the initial correction value as the absolute value for
polynomial courses. It is also possible to demand continuity or differentiability as (further)

boundaries conditions with regard to higher derivatives of the respective polynomials or
functional associations.
In the present description, continuous and differentiable are meant in a mathematical sense,
wherein corresponding jumps which are to be attributed to noise, quantizing effects or
other effects limiting the resolution are not taken into consideration as such. Expressed
differently, this means that in a parameter-dependent correction value approximation
course determined section after section, or even within the individual parameter ranges, the
sub-sections thereof are continuous when there is, for all the parameters of the respective
parameter range or the parameter ranges for each correction value approximation value, for
all (mathematically definable) intervals around this value, there is another (mathematically
definable) interval including the respective parameter value so that, for all the parameter
values within this further interval, the respective correction value approximation values are
within the first interval. Here, the limitation, as explained before, with regard to noise,
resolution, or quantizing, may result in the respective intervals to be limited with regard to
their quantity to small values or to great values. In complete analogy, in the present
description, differentiability here means continuity of a (mathematically definable)
derivative of the correction value approximation course or the sub-sections thereof. When
such a mathematically definable derivative cannot be defined in a practical way, in the
present description, the term of differentiability is extended to corresponding differential
curves wherein differences with regard to the parameter values of neighboring parameter
and correction value approximation values are considered. The remarks discussed before
with regard to noise, resolution and quantizing apply here, too.
In case of the embodiment illustrated in Fig. 4 considering degrees (degree of the
polynomial N = 1), thus for example the first partial section of the correction value
approximation course may be described by an equation

wherein in contrast to the embodiment illustrated in Fig. 4 a parameter p and not a
temperature T is assumed. Here, f1(p) is a value of the first partial section with a parameter
value p, pk1 is the first parameter coefficient and p0 the initial parameter value, wherein the
initial correction value f0 in the calibration measurements and/or test measurements was
determined in a series test for the corresponding sensor 100. If the parameter value p
exceeds a threshold with regard to the parameter values pg and thus changes into a second
parameter range across which a second partial section of the correction value

approximation course is defined or is to be defined, based on the previously discussed
conditions of the two for a parameter to be currently determined the necessity results to
define two boundary conditions regarding the correction value approximation course and
accordingly determine the corresponding parameters. In case of two directly adjacent
parameter ranges with the parameter boundary value pg, a coefficient of the general degree
formula according to equation (3) (with N = 1) may be determined on the basis of the
inclination and/or the parameter coefficient according to a corresponding application of
equation (1) by two measurement values MW1, MW2 with the parameter values p1, p2. As
a second boundary condition regarding the coefficient of the straight line, in addition to
that the continuity of the overall correction value approximation course may be requested.
Based on the polynomial description of the individual partial sections, this request is easily
fulfilled within the individual parameter ranges. Thus, the second coefficient of the straight
line may be determined on the basis of the continuity requirement at the boundary
parameter value pg between the two partial sections of the correction value approximation
course. Thus, for the second partial section the following results

wherein pk2 is the second parameter coefficient for the second parameter range determined
according to equation (1) and f2(p) is a value of the second partial section for the parameter
value p in the second parameter range underlying the second partial section.
Alternatively, of course, also in other embodiments of the present invention another second
condition regarding the coefficients of the straight line may be set. There might, for
example, also have been the request that the straight line representing the second partial
section, being extrapolated, also should have passed through the initial correction value f0
with the initial parameter value p0. In this case, instead of equation (5) an equation
basically corresponding to equation (4) would result in which instead of f1(p) the value of
the second partial section f2(p) and instead of the first parameter coefficient pki, the second
parameter coefficient pk2 would have had to be used.
This way it is possible to define not only two partial sections of the parameter-dependent
correction value approximation course which was determined section after section. It is
rather possible, as already indicated in Fig. 4, to introduce many parameter ranges with
underlying partial sections. Depending on the used functional connections underlying the
individual partial sections, thus a traverse and/or a polygonal description (by sections) of
the correction value approximation course as a whole results. In case of the use of

continuous and differentiable correction value approximation courses, analogue to that, if
applicable, also a "smooth" course differentiable at the boundaries of the corresponding
parameter ranges may result. Such an implementation may already be achieved by the use
of parabolic (polynomial degree N =) functional connections.
Depending on the concrete implementation of embodiments of the present invention, it
may, apart from that, be obvious to restrict the number of different parameter ranges and
the associated partial sections of the correction value approximation course. Thus, it may
be advisable, for example, not to classify the maximum admissible operation parameter
range and/or parameter range into more than 50, 30, 20 or 10 parameter ranges, for
example to save memory space, guarantee an efficient implementation or restrict the
number of calibration processes. In other words, in some embodiments of the present
invention a maximum admissible parameter range may maximally be classified into a
predetermined number of individual parameter ranges and associated partial sections of the
correction value approximation course, wherein this predetermined number is typically a
natural number greater than 2.
In embodiments of the present invention there is apart from that the possibility to
compensate aging effects. For this purpose, a trigger condition may be implemented, which
leads to the execution of a corresponding determination, section after section, of a
parameter dependent correction value approximation course. By this, for example in
regular intervals, i.e., e.g., when a predetermined time period elapses, when switching on
the sensor or with every n-th switch-on, the method for a determination of a parameter
dependent correction value approximation course, section after section, may be executed,
wherein n is an integer number greater than or equal to 1. Depending on the parameter
value present at this point in time, then according to the described method, a second partial
section of the correction value approximation course may be determined, which may also
lead to a finer classification of the maximum accessible parameter range by several
parameter ranges. In addition to that, in further embodiments of the present invention, also
the predetermined first parameter coefficient may, if applicable, be adapted or recalibrated,
as far as the same is stored in a memory accordingly included in the sensor 100 which
enables a re-writing and/or storing of this value. Thus, for example the processing circuit
120 may for these values, for example, be stored in a non-volatile memory wherein these
values may be subject to aging and thus be accessible for recalibration. Such non-volatile
memories are, for example, flash memories, EEPROM memories (electrically erasable
programmable read only memories). If, however, the sensor 100 is in its "normal sensor
life" typically not separated from a supply voltage, an implementation of a non-volatile
memory may also be replaced by a volatile memory. If the first parameter coefficient is

newly determined, it may be advisable to again determine also the further partial sections
(as far as necessary) to further fulfill continuity or other boundary conditions, if applicable.
Even if, in particular in connection with Fig. 3 and 4, an embodiment of the present
invention was described in the form of a hall sensor 100 with one single hall sensor
element 110, embodiments of the present invention are of course not limited to sensors or
hall sensors 100 with one single sensor element. In further embodiments, thus also several
hall sensor elements may be used as a replacement for the single hall sensor element 110
illustrated in Fig. 3. The same may, for example, be interconnected in the form of serial,
parallel circuits or more complex circuits. Further, different (hall) sensor types may be
interconnected.
Further, embodiments of the present invention are not limited to hall sensors. Thus, other
magnetic field sensors, for example any magneto-resistive sensors (xMR sensors), i.e., for
example AMR sensors (anisotropic magneto resistance), GMR sensors (giant magneto
resistance), TMR sensors (tunnel magneto resistance) or EMR sensors (extraordinary
magneto resistance) may be used. But also other sensors, like for example pressure sensors,
acceleration sensors or sensors responsive to mechanical, electrical, radiation-conditioned
or physical effects may be used within the scope of embodiments of the present invention.
In addition to that, corresponding sensors 100 may also be ones which respond to chemical
or biological effects and processes.
In different embodiments of the present invention, the sensors 100 may, for example, with
the help of the processing circuit 120, convert a measurement signal received from the first
sensor element 110 into an output signal of the sensor 100, by correcting the output signal
depending on the parameter signal of the second sensor element 130 on the basis of the
correction value approximation course. For this purpose, for example the measurement
value included in the measurement signal of the first measurement element 110 may be
changed by addition and/or subtraction, multiplication or also by division by the value of
the correction value approximation course in the corresponding parameter value of the
parameter signal. Thus, for example, an offset correction and/or a scaling correction may
be executed.
Embodiments of the present invention may, in addition to that, be realized as integrated
circuits (IC), as a discreet implementation using individual, discrete electrical and
electronical circuit elements or in combination of both technologies. In addition to that,
embodiments of the present invention may be executed on the basis of an analogue and/or
a digital signal processing. Depending on the respective implementation, thus for example

an implementation of analogue/digital converters, digital filters and maybe a
digital/analogue converter may be advisable; Also, different embodiments of the present
invention may include analogue preamplifiers, amplifiers, electric filters and other
analogue components.
In addition to that, embodiments of the present invention may be implemented in larger
integrated circuits or also as individual sensor ICs. Also an implementation in so-called
ASICs (application specific integrated circuits) is possible, which include individual
processor circuits or processors depending on the field of application. In such a case, for
example, an embodiment of a method for a determination, section after section, of a
parameter dependent correction value course, or another embodiment of the present
invention may be implemented in software or firmware, which then runs on the processor
or the processing circuit. Examples for this are intelligent sensors which are manufactured
as ASIC or as IC with corresponding sensors, sensor elements and/or sensor arrangements.
Thus, embodiments of the present invention for example enable an offset reduction with
hall sensors, which may for example be of interest in the field of automotives (applications
in the motor vehicle field) with its high temperature requirements. The above described
functioning in particular with hall sensors 100 may, as explained above, of course be
applied to any type of sensor with a temperature-dependent or parameter-dependent offset.
Thus, an automatic calibration of a temperature-dependent or parameter-dependent offset
may take place with any type of sensors with a corresponding offset.
Depending on the conditions, embodiments of the inventive method may be implemented
in hardware or in software. The implementation may be on a digital storage medium, in
particular a floppy disc, CD or DVD having electronically readable control signals which
may cooperate with a programmable computer system so that embodiments of the
inventive method are executed. In general, thus embodiments of the present invention also
consist in a computer program product and/or a software program product and/or a
program product having a program code stored on a machine readable carrier for executing
an embodiment of the inventive method when the software program product runs on a
computer or a processor. In other words, embodiments of the present invention may thus
be realized as a computer program and/or software program and/or program having a
program code for executing an embodiment of a method when the program runs on a
processor. The processor may here be formed by a computer, a chip card (smart card), an
ASIC, an intelligent sensor or another integrated circuit.

We Claim:
A method of determining, section after section, a parameter-dependent correction
value approximation course (240) for a measurement signal correction of a sensor
arrangement (100), wherein with regard to an initial parameter value (AW) an
initial correction value (po) and a first parameter coefficient (PK1) are given, and
wherein the correction value approximation course (240) comprises a first partial
section (240-1) for a first parameter range (215-1) which is based on the initial
correction value (AW) and the first parameter coefficient (PK1), comprising:
determining a first measurement signal value with a first parameter value (P1)
associated with the sensor arrangement (100), when the first parameter value (P1)
fulfils a predetermined condition or a trigger condition is fulfilled;
changing the first parameter value (P1) associated with the sensor arrangement to
obtain a second parameter value (P2) associated with the sensor arrangement;
determining a second measurement signal value with the second parameter value
(P2); and
determining a second partial section (240-2) of the correction value approximation
course (240) for a second parameter range (215-2) based on a functional connection
describing the second partial section considering the first (P1) and the second
parameter value (P2), the first and the second measurement signal value and the
initial correction value (AW),
wherein the second partial section (240-2) of the correction value approximation
course (240) is determined so that the first parameter range (215-1) is adjacent to
the second parameter range (215-2); and
wherein the first partial section (240-1) and the second partial section (240-2) of the
correction value approximation course (240) are continuously adjacent to each
other.
The method according to claim 1, which is executed during the operation of the
sensor arrangement (110).

The method according to one of the preceding claims, wherein a further partial
section (240-3) of the correction value approximation course (240) is determined
for a further parameter range (215-3), so that the further parameter range (215-3) is
adjacent to the first (215-1) or the second parameter range (215-2).
The method according to claim 3, wherein the further partial section (240-3) of the
correction approximation course (240) is determined so that the further parameter
range (215-3) is adjacent to the first parameter range (215-1) and which further
includes the following steps:
determining a further first measurement signal for a further first parameter value of
the further parameter range (215-3);
changing the further first parameter value to obtain a further second parameter
value;
determining a further second measurements signal with the further second
parameter value; and
determining the further partial section (240-3) of the correction value
approximation course (240) for the further parameter range (215-3) based on a
functional connection describing the further partial section (240-3) considering the
further first and the further second parameter value, the further first and the further
second measurement value and the first partial section (240-1),
wherein the determination is executed so that the further partial section (240-3) of
the correction value approximation course is continuously adjacent to the first
partial section (240-1).
The method according to claim 3, wherein the further partial section (240-3) of the
correction approximation course (240) is determined so that the further parameter
range (215-3) is adjacent to the second parameter range (215-2) and further
includes the following steps:
determining a further first measurement signal for a further first parameter value of
the further parameter range (215-3);

changing the further first parameter value to obtain a further second parameter
value;
determining a further second measurement signal in the further second parameter
value; and
determining the further partial section (240-3) of the correction value
approximation course (240) for the further parameter range (215-3) based on a
functional connection describing the further partial section (240-3) considering the
further first and the further second parameter value, the further first and the further
second measurement signal value and the second partial section (240-2),
wherein the determination is executed so that the further partial section (240-3) of
the correction value approximation course (240) is continuously adjacent to the
second partial section (240-2).
The method according to one of the preceding claims, wherein as a parameter value
a temperature value or a pressure value is used.
The method according to one of the preceding claims, wherein the predetermined
condition is fulfilled when the first parameter value is not in the first parameter
range.
The method according to one of the preceding claims, wherein the trigger condition
is fulfilled by switching on or after switching on the sensor arrangement (100).
The method according to one of the preceding claims, wherein the first (240-1) or
the second partial section (240-2) of the correction approximation course (240) is
described based on the functional connection

wherein p is a parameter value, f(p) is a value of the first or the second section of
the correction approximation course with the parameter value p, N is a positive
integer number indicating an order of a polynomial, ak is a real constant depending
on k and k is an integer number between 0 and N.

The method according to claim 9, wherein N = 1, 2 or 3.
The method according to one of the proceeding claims, wherein the first section of
the correction value approximation course is described based on the functional
connection
fi(p) = pk1-(p-p0) + f0
f1(p) = pk1-(p-po) + fo
and the second section of the correction approximation course is described on the
functional connection
f2(p) = pk2 -(p-pg) + pk, .(pg -po) + fo
f2(p) = pk2 -(p-pg) + pk1 .(pg -po) + fo
wherein p is a parameter value, f1(P) a value of the first section of the correction
approximation course with the parameter value p, f2(p) is a value of the second
section of the correction approximation course with the parameter value p, pk1 is
the first parameter coefficient, f0 the initial correction value, pk2 a second parameter
coefficient based on the first parameter value, the second parameter value, the first
measurement signal value and the second measurement signal value, and pg is a
threshold parameter value, wherein a parameter range underlying the first section of
the correction approximation course is adjacent to a second section of the correction
value approximation courser underlying the second section of the correction value
approximation course underlying the second section of the correction value
approximation course.
The method according to one of the preceding claims, wherein the step of changing
the first parameter value includes controlling a heating element (140), controlling a
cooling element (140), controlling a pressure element (140), increasing a supply
power of the sensor arrangement, a sensor element (110) of the sensor arrangement
(100) or a part of the sensor arrangement (100) or reducing the supply power of the
sensor arrangement (100), the sensor element (110) of the sensor arrangement (100)
or a part of the sensor arrangement (100).
13. The method according to one of the preceding claims, wherein the
parameter is a temperature, the sensor arrangement is a hall sensor arrangement
(100), the initial correction value (po) is an initial temperature value T0, the first
parameter coefficient (PK1) is a first temperature coefficient (TK), the first

parameter range (215-1) is a first temperature range (215-1), the second parameter
range (215-2) is a second temperature range (215-2), the first parameter value (PI)
is a first temperature value and the second parameter value (P2) is a second
temperature value
A sensor arrangement (100), comprising:
a first sensor element (110) for providing measurement signals;
a second sensor element (130) for providing parameter signals; and
a processing circuit (120) coupled to the first (110) and the second sensor element
(120) and implemented to detect measurement signals from the first sensor element
(110) and parameter signals from the second sensor element (120) and further
implemented,
wherein the processing circuit (120) is further implemented to determine a first
measurement signal with a first parameter value associated with the sensor
arrangement (100) and corresponding to a first parameter signal, when the first
parameter value fulfils a predetermined condition or a trigger condition is fulfilled;
wherein the processing circuit (120) is further implemented to change the first
parameter value associated with the sensor arrangement (100) to obtain a second
parameter value associated with the sensor arrangement (100) and corresponding to
a second parameter signal;
wherein the processing circuit (120) is further implemented to determine a second
measurement signal value with the second parameter value; and
wherein the processing circuit (120) is further implemented to determine a second
partial section of the correction approximation course in a second parameter range
which is based on a functional connection describing the second partial section
(240-2), considering the first and the second parameter value, the first and the
second measurement signal value an initial correction value (AW),
wherein a first partial section (240-1) of the correction value approximation course
(240) in a first parameter range (215-1) is based on the predetermined initial
correction value (AW) and the first predetermined parameter coefficient (TK);

wherein the second partial section (240-2) of the correction value approximation
course (240) is determined so that the first parameter range (215-1) is adjacent to
the second parameter range (215-2); and
wherein the first partial section (240-1) and the second partial section (240-2) of the
correction value approximation course (240) are continuously adjacent.
The sensor arrangement (100) according to claim 14, wherein the processing circuit
(120) is implemented to cause the change of the first parameter value by increasing
a supply power of the sensor arrangement (100), the first sensor element (110), the
second sensor element (130) or a part of the sensor arrangement (100) or by
reducing the supply power of the sensor arrangement (100), the first sensor element
(110), the second sensor element (130) or a part of the sensor arrangement (100).
The sensor arrangement (100) according to one of claims 14 or 15, further
comprising an additional parameter changing means (140) which is coupled the
processing circuit (120), and wherein the processing circuit (140) is further
implemented to provide a signal to the parameter changing means to cause a change
of the first parameter value.
The sensor arrangement (100) according to claim 16, wherein the parameter
changing means (140) is arranged adjacent to the first sensor element (110) to make
a parameter change with regard to the first sensor element (110) produceable.
The sensor arrangement (100) according to one of claims 16 or 17, wherein the
parameter changing means (114) includes a heating element, a piezo element, a
cooling element or a Peltier element.
The sensor arrangement (100) according to one of claims 14 to 18, wherein the first
sensor element (110) includes a Hall sensor.
The sensor arrangement (100) according to one of claims 14 to 19, wherein the
second sensor element (130) includes a temperature sensor, a PTC resistance
element, an NTC resistance element, a pressure sensor element or a piezo element.
The sensor arrangement (100) according to one of claims 14 to 20, wherein the
processing circuit (120) is further implemented to output an output signal based on

a measurement signal, wherein the output signal is corrected depending on a
parameter value included in a parameter signal depending on the correction value
approximation course.
22. The sensor arrangement according to one of claims 14 to 21, wherein the
sensor arrangement (100) is a Hall sensor arrangement (100), the first sensor
element (110) is a Hall sensor element (110), the second sensor element (130) is a
temperature sensor element (130) and the processing circuit (120) is implemented
so that the parameter is a temperature, the initial correction value (po) is an initial
temperature value (T0), the first parameter coefficient (PK1) is a first temperature
coefficient (TK), the first parameter range (215-1) is a first temperature range (215-
1), the second parameter range (215-2) is a second temperature range (215-2), the
first parameter value (P1) is a first temperature value and the second parameter
value (P2) is a second temperature value
A program having a program code for executing a method according to claim 1
when the program is executed on a processor.

An embodiment of a method for a determination, section after section, of a parameter-
dependent correction value approximation course includes determining a first measurement
signal value with a first parameter value associated with a sensor arrangement when the
first parameter value fulfils a predetermined condition or a trigger condition is fulfilled,
changing the first parameter value to obtain a second parameter value, determining a
second signal value with the second parameter value and determining a second partial
section of the correction value approximation course for a second parameter range based
on a functional connection describing the second partial section, the first parameter value,
the second parameter value, the first measurement signal value, the second measurement
signal value and an initial correction value.