Abstract:
A magneto-resistive resistor for use in sensors for determining alignment of the sensor relative to a homogeneous magnetic field include an anisotropic magnetoresistive (AMR) strip having a longitudinal extent and a first and second edge along the longitudinal extent. The first and second edge have a shape along the longitudinal extent such that the direction of current flowing through the strip varies continuously along the longitudinal extent of the strip. The shape of the first and second edges produce a resistance determining angle with respect to the homogeneous magnetic field, the angle varying throughout the length of the strip and filtering out harmonics. A sensor bridge comprising at least one AMR resistor pair, each resistor electrically connected to the other resistor, a positive input contact and a negative input, and an output voltage tap electrically connected between the resistors in each resistor pair.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation application which claims priority to co-pending U.S. patent application Ser. No. 10/547,431, filed Oct. 4, 2006, which is a 371 of and claims priority to International Application No. PCT/EP04/01791, filed Feb. 24, 2004, the contents of this entire chain of applications are herein incorporated by reference for all purposes. 
    
    
     FIELD OF THE INVENTION 
     The invention relates to magneto-resistive sensors for determining angles which a rotatable magnet assumes with respect to the sensor, or of positions with the sensor being opposite a magnetic scale and having a periodic magnetic pattern. Such angle and position measurement arrangements are used in large numbers, for example in machine construction, in motor vehicle engineering and in precision mechanics. 
     BACKGROUND 
     Magneto-resistive sensors for determination of angles or positions are known. The document WO 02/06845 A1 provides a summary of the prior art relating to analog determination of angles by means of magneto-resistive sensors on the basis of the anisotropic magneto-resistive (AMR) effect, the gigantic magneto-resistive (GMR) effect and the tunnel effect between magneto-resistive layers (TMR). In the case of the AMR effect, the resistance of a layer strip is governed by the angle a between the current direction and the direction of magnetization. This can be defined by the relationship:
 
 R ( )= R   0 +(□ R/ 2)(1−cos(2))  Equation (1)
 
     As can be seen from this, the resistance change passes through one complete period after a change in the angle through 180°. If the direction of magnetization matches the direction of the field, acting on the layer strip, of a permanent magnet which is mounted such that it can rotate in the vicinity, then two complete period cycles of the resistance change are produced for one complete revolution of the permanent magnet. This can be measured as a voltage change when current flows through the layer strip. 
     In the case of the GMR effect and TMR effect, the resistance of a layer strip or of a tunnel transition is dependent on the angle □ between the directions of the magnetization of two layers or layer components of magneto-resistive material. If the magnetization direction in the one layer component is fixed by means of a natural or artificial anti-ferromagnet which is in direct contact and only the magnetization direction of the second component follows the applied field of the permanent magnet which can rotate, then the resistance change is defined by the relationship:
 
 R (□)= R   0 +(□ R/ 2)(1−cos(□))  Equation (2)
 
     In this case, this results in only one full period of the resistance change for one revolution of the permanent magnet, or of the voltage, which can be used as a signal, on the layer strip or tunnel junction. 
     In accordance with the stated formulae, this results in ideal conversion of an angle to a cosine function. In practice, however, it has been found that this conversion cannot be carried out without errors. Harmonics of the respective fundamental occur in the signals and their period lengths are an integer fraction of the 180° or 360° mentioned above. The reason for the errors is that the assumed match between the direction of the magnetization of the layers and the direction of the applied magnetic field is not sufficiently accurate. In the case of AMR angle sensors, the match between the stated directions can be improved by high permanent magnetic field strengths. However, this can be achieved only by using expensive high-coercivity permanent magnet materials, or by mechanically complex fitting of the permanent magnet in the very immediate proximity of the sensor. In the case of GMR or TMR sensors, the use of ever higher magnetic strengths does not lead to an improvement in the sinusoid nature of the signal, since these field strengths result in rotation of the magnetization of the magneto-resistive layer which is coupled to the anti-ferromagnet. 
     There are two possible reasons for the discrepancy in the direction of the magnetization of the free and AMR layer strips from the direction of the applied magnetic field. The first is fundamentally of a physical nature and has already been mentioned in Laid-Open Specification DE 198 39 450 A1 with the equation which the angle (1) between the direction of the magnetization and the strip longitudinal direction must satisfy, and which is given by
 
 H   x   /H   0  tan(□)+sin(□)− H   y   /H   0 =0  Equation (3)
 
     H x  is in this case the magnetic field component in the strip longitudinal direction, and H y  is the component at right angles to this. The match between the angle □ and the angle stated above for which the equation:
 
tan( )= H   y   /H   x   Equation (4)
 
     applies is achieved only in the situation in which H x /H 0 , and H y /H 0  assume very large values, which corresponds to the stated condition of the need to use high field strengths. The second reason is that, in limited angle ranges and with relatively weak fields from the permanent magnet, the magnetization direction is split into domains, particular at strip ends and edges, and this leads to resistances which differ from the ideal behavior and to hysteresis in the angle ranges. 
     The two cited documents WO 02/06845 A1 and DE 198 39 450 A1 have specified arrangements of layer strips, which each form magneto-resistive resistors, in order to improve the measurement accuracy which can be achieved by means of magneto-resistive angle sensors, and these arrangements are suitable for filtering out the harmonics from the output signals from the sensors. This filtering is also effective at relatively low magnetic field strengths. This is achieved in that, in the case of AMR sensors, two or more groups of parallel straight strips with precisely defined angles between the longitudinal directions of the strips are used instead of long straight magneto-resistive strips whose longitudinal directions are parallel to one another in sensors without harmonic filtering. The greater the number of groups of strips that are used, the higher is the order of harmonics up to which the harmonics are filtered out of the signal. However, one disadvantage is that each new group of strips with a new fixed inclination angle with respect to the already existing strips also results in new angle ranges of the applied magnetic field, whose angle must be measured, and in which splitting into domains and thus hysteresis occurs. This applies in particular to field strengths which are not very much greater than the anisotropic field strength of the strips. 
     It is admittedly normally possible to use parallel long magneto-resistive strips in the case of GMR and TMR sensors. However, the directions of the magnetization of the layers which are coupled to the respective anti-ferromagnet in the various groups of strips must form precisely defined angles between them. It is thus fundamentally impossible to avoid magnetization components which are aligned at right angles to the strip longitudinal direction, and, in this case as well, this results in the formation of a number of angle ranges, which increases with the number of groups of strips in which hysteresis occurs, particularly in the case of the relatively weak field strengths which can be produced economically. 
     Magneto-resistive sensors for determination of positions, which are arranged close to the surface of magnetic scales such that they can move in the measurement direction, determine the respective position value from the angle which the magnetic field forms with a strip direction at the location of the sensor. If the magnetic scale is composed of a permanent magnet material which is magnetized periodically in alternate directions, then this angle varies approximately linearly with progress in the measurement direction. The problems which have to be solved in order to achieve high measurement accuracies correspond essentially to those in the case of angle sensors. This applies primarily to use for filtering of harmonics. 
     SUMMARY 
     In accordance with the invention, position and angle sensors magneto-resistive effects are provided whose measurement accuracy is increased by filtering out harmonic components from the signals without hysteresis, which would corrupt the measured values, in relatively weak magnetic field strengths. 
     In accordance with the invention, sensor resistors are formed without sudden changes in the resistance-determining angle in the magneto-resistive strips from which the sensor resistors are formed. When the AMR effect is being used, the angle between the current direction and the direction of the magnetization is the resistance-determining angle. In order to achieve harmonic filtering in the magneto-resistive resistors, different resistance-determining angles are required in the strips. These can be achieved without any sudden change in the resistance-determining angle by the shape of the edges of the strips. If, by way of example, both strip edges can be represented as parallel running sinusoidal curves, then the current direction in the strips will be matched to this shape, and the angle of the current direction with respect to the longitudinal direction of the strip, which is formed by the straight-line connection between its end points, likewise runs in the form of a sine function. The direction of the magnetization of the magneto-resistive material of the strips when the magnetic field strengths are relatively weak is governed by the field strength of the magnetic field applied to the strips, by the crystal anisotropy field strength of the material, and by the shape anisotropy field strength. The crystal anisotropy of the material has the same strength and direction in all places in the area of the sensor chip. The shape anisotropy likewise runs parallel to the edge in the quoted example. The direction of the magnetization along the strip thus also changes only continuously. There are therefore no sudden changes in the direction of the magnetization, and this avoids one reason for the splitting into domains. 
     In addition to the configuration of the strip edge, there is a second possible way to change the direction of the current in strips composed of AMR material. This is to use the barber&#39;s pole structure, which has already been described in Laid-Open Specification DE 35 14 457, but without any reference to harmonic filtering for angle and length measurement. In the case of the barber&#39;s pole structure, there are a large number of conductive layer strips on the strips of magneto-resistive material, at a distance which is of the same order of magnitude as the width of the magneto-resistive strips, with the longitudinal directions of the conductive layer strips forming intermediate angles with those of the magneto-resistive strips. Owing to the comparatively high conductivity of the conductive layer strips, the current direction is approximately at right angles to their longitudinal direction. Different current directions can thus be set in magneto-resistive strips with straight and parallel edges by choosing different intermediate angles, so that the required different resistance-determining angles can be achieved with the same magnetization direction. There is therefore no need for a relatively large number of magneto-resistive strips inclined at different angles to one another, and this precludes any increase in the occurrence of areas subject to hysteresis in the angle measurement. 
     In the case of the GMR effect, layer systems whose first component has a magnetization whose direction can essentially follow the magnetic field of a magnet which can be rotated with respect to the sensor and in which the magnetization of the second component remains essentially independent of the direction of the magnetic field acting there by coupling to a further magnetic component are particularly suitable for angle measurement. The resistance determining angle is that between the directions of the magnetizations of the first and of the second component. Different resistance-determining angles are required for harmonic filtering. According to the invention, this is achieved in that the direction of the magnetization of the second component is varied continuously along the longitudinal direction of the magneto-resistive strips. Such continuous variation is achieved, for example, in such a way that the opposite strip edges can be represented by identical continuously varying functions, such that the further component is an anti-ferromagnet to whose axial direction the magnetization of the second component is coupled, and such that the axial direction is adjusted by means of the magnetic field of a current through the magneto-resistive strips. In consequence, the direction of the magnetization of the second component is always at right angles to the edge, and changes continuously in the longitudinal direction of the strips. The continuous variation in the direction of the magnetization of the second component avoids the formation of domains both in the second component and (owing to unavoidably weaker coupling between the first component and the second component) in the first component, and thus increased occurrence of hysteresis areas. The magnetization direction of the second component can advantageously be adjusted by the use of a constant magnetic field in conjunction with the field of a current through the strips. It is thus possible to produce different continuous functions for the profile of the resistance-determining angle along the longitudinal direction. 
     Specific functions for the profile of the edges of the magneto-resistive strips for the use of both AMR sensors and GMR sensors may be used. The choice of the optimum relationship between the period length and the amplitude of the periodic edge functions is made as a result of a calculation which assesses harmonic components and the amplitude of the signals. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be explained further with reference to exemplary embodiments. A better understanding may be had with reference to the accompanying drawings in which: 
         FIG. 1 : shows resistance-determining angles for the AMR effect, 
         FIG. 2 : shows resistance-determining angles for the GMR effect, 
         FIG. 3 : shows the current direction set by the strip edges for AMR sensors, 
         FIG. 4 : shows an AMR length sensor bridge according to the invention, 
         FIG. 5 : shows an AMR angle sensor bridge according to the invention, 
         FIG. 6 : shows a current direction set by means of a barber&#39;s pole structure for AMR sensors, 
         FIG. 7 : shows an AMR length sensor according to the invention with a barber&#39;s pole structure, 
         FIG. 8 : shows a continuously varying profile of the field-independent magnetization direction for GMR sensors, and 
         FIG. 9 : shows a GMR angle sensor bridge according to the invention. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates the x-y layer plane of an AMR strip. The strip longitudinal direction is intended to coincide with the x axis in this case. The direction of the current (I) for a point on the strip is shown. In general, this direction does not match the strip longitudinal direction x. Under the influence of an external magnetic field, the magnetization (M) at the point under consideration points in the direction shown. The angle between the direction of the current I and the direction of the magnetization M is. The resistivity □ a  of the magneto-resistive layer is governed by this angle:
 
□ a ( )=□ a0 +(□□ a /2)(1−cos(2))  Equation (5)
 
where □ a0  is the non-field-dependent component and □□ a  is the amplitude of the field-dependent change in the resistivity. The resistance-determining angle at any point on the strip is. The resistivity is likewise a function of x when the direction of the current I and of the magnetization M varies in the strip longitudinal direction x.
 
       FIG. 2  shows a GMR layer system at a point on the x-y layer plane. The longitudinal direction of a strip formed from the layer system is intended to match the x axis. The GMR layer system contains two components, whose magnetizations M, and M 2  can be set in different directions independently of one another. M, is in this case the magnetization of the first component, whose direction essentially matches that of the applied external magnetic field, at the point under consideration. M 2  is the magnetization of the second component, which in this case is essentially coupled to the alignment of a third anti-ferromagnetic component. The angle between the directions of the magnetizations M, and M 2  is □. The resistivity □ g  of the GMR layer at the point under consideration is given by:
 
□ g (□)=□ g0 +(□□ g /2)(1−cos(□))  Equation (6)
 
where □ is the resistance-determining angle at any point on the strip. The resistivity is likewise a function of x when the direction of the magnetization M, and of the magnetization M 2  vary in the strip longitudinal direction x.
 
       FIG. 3  shows an AMR strip  1  whose longitudinal extent extends in the x direction. The AMR strip  1  is bounded by a first edge  2  and a second edge  3 . In general, it is possible to represent the edges  2  and  3 , in accordance with the invention, by any desired functions which vary continuously in the x direction. In the illustrated case, both edges  2 ;  3  run parallel and are sinusoidal. The period length  13  of the sine function is considerably greater than the width  14  of the AMR strip  1 . The current I in the AMR strip thus flows parallel everywhere to the edges  2 ;  3 , and its direction varies continuously as x progresses. A homogeneous magnetic field H h , acts on the plane of the AMR strip  1  with a field strength which is greater than the anisotropy field strength of the AMR strip  1 . The direction of the magnetization M at any point on the AMR strip  1  is thus given essentially by the direction of the homogeneous magnetic field H h , and the resistance-determining angle likewise varies continuously with progress in the x direction. When using AMR strips  1  for angle, position or length determination, the homogeneous magnetic field H h , that is shown rotates on the x-y plane. The resistance of the AMR strip  1  as a function of the angle which the homogeneous magnetic field H h , forms with the x axis in this case has a minimal proportion of harmonics. For this purpose, the angle range which the current direction includes with the x axis should include values between 0° and at least 15°. The upper limit for the magnitude of the greater angle between the current and the x direction is 45°. 
     The stated values for this angle should also be complied with for situations in which the edges of the AMR strips cannot be represented by sinusoidal curves. The edges  2 ,  3  can advantageously be formed by curves in the form of circular arcs or by sums of second and fourth order parabolic curves. 
     A sensor bridge formed on the basis of the AMR strip  1  shown in  FIG. 3  on a chip surface  4  for determination of the position with respect to a scale  9  is illustrated in  FIG. 4 . The scale  9  is illustrated in the form of a section, and the plane of the chip surface  4  matches the section surface. The scale  9  is magnetized periodically upwards and downwards, alternately on the section surface, with constant pole lengths  10 . The size relationships in the drawing are not to scale. For example, the strip widths have been illustrated enlarged. Two AMR strips  1  in each case form one branch of the Wheatstone bridge. The AMR strips  1  are electrically connected to one another via non-magnetic conductive layer strips. The positive pole of the operating voltage of the bridge is connected to the connecting contacts  6 , and the negative pole is connected to the connecting contact  5 . The output voltage of the bridge can be tapped off at the output contacts  7  and  8 . As can be seen from  FIG. 4 , the AMR strips  1  are arranged at a distance of half the pole length  10  alongside one another. The directions of the current I and of the magnetization M, as they occur under the influence of the magnetic field of the magnetic scale  9  in the illustrated position, are in each case indicated at a point which is at an equal distance from the lower strip end for all of the AMR strips. The suppression of harmonic components as a function of the resistances of the AMR strips  1  from that position means that the output signal from the bridge is a voltage which varies periodically with the position, with the period length corresponding to the pole length  10 . This voltage can essentially be represented by a simple sinusoidal function. 
     A complete position sensor contains two of the illustrated Wheatstone bridges which are offset with respect to one another through (n+¼) times the pole length  10 , where n is an integer (n=0; 1; 2; 3; . . . ). The position is determined in a known manner from the number of pole lengths  10  which have already been traveled over and the fraction which results from the quotient of the two bridge signals by the use of arctangent interpolation. Because of the suppression of the harmonic component in the bridge signals, the position indication error is small. 
     In order to increase the resistance of the bridges for the position sensor and in order to make better use of the chip area  4 , a greater number of identically designed AMR strips can be arranged parallel and connected in a meandering shape, instead of each individual AMR strip  1 . 
     As another embodiment of the invention,  FIG. 5  shows a bridge arrangement on a chip surface  4  which is part of an angle sensor. The use of the connecting contacts  5 ;  6  and of the output contacts  7 ;  8  corresponds to that shown in  FIG. 4 . The AMR strips  1  are in this case bounded by edges  2 ;  3 , which originates from one another by mirror-imaging. The current direction matches its direction only directly on the longitudinal axis of the AMR strips  1 . However, it will run increasingly parallel to the direction of the edge  2 ;  3  the closer the point under consideration is to the respective edge  2  or  3 . Thus, in this case as well, the current direction changes continuously in the longitudinal direction of the AMR strips  1 . If the direction of the magnetization of the AMR strips  1  is essentially the same in a homogeneous magnetic field H h , then the resistance-determining angle is likewise subject to a continuous change. Different resistance-determining angles are a precondition for harmonic filtering in the AMR strips  1 . The continuous change of these angles prevents the occurrence of hysteresis. The resistance-determining angles are shown in  FIG. 5  at points which are at equal distances from the end of the AMR strips  1  and from the longitudinal axis thereof. The longitudinal directions of the two AMR strips  1  which each form one bridge arm are at right angles to one another. The resistance changes in opposite sensors in the AMR strips  1  in each bridge arm during rotation of the homogeneous magnetic field H h  whose direction is intended to be determined by the angle sensor is thus ensured. When the homogeneous magnetic field H h  is rotated through 180°, the sinusoidal output voltage produced as the output signal changes through one entire period. In addition to the illustrated bridge, the complete angle sensor also contains an identical bridge which is rotated through 45° with respect to that illustrated. The angle value is determined from the quotient of the output signals from the two bridges using the known arctangent interpolation process. 
     A greater number of identical AMR strips can be arranged parallel and can be connected in a meandering shape, instead of each individual AMR strip  1 , in order to increase the resistance of the bridges in the angle sensor, and in order to make better use of the chip area  4 . 
       FIG. 6  illustrates a further implementation option for different current directions in AMR strips  1 . The AMR strip  1  has straight and parallel edges  2 ;  3 . Conductive layer strips  11 , which are inclined with respect to the longitudinal direction, are arranged on the AMR strip  1 . Their conductivity is several orders of magnitude higher than that of the AMR layer. The current therefore flows on the shortest route from one conductive layer strip  11  to the next, and the current direction is at right angles to the longitudinal direction of the conductive layer strips  11 . The direction of the current I may be adjusted in this way by the inclination of the conductive layer strips  11 .  FIG. 6  shows only two different current directions. However, it is clear that a continuous change in the current direction can be achieved by variation of the inclination angle of each subsequent conductive layer strip  11  with respect to its predecessor. The length of an AMR strip is frequently about 1000 times greater than the width. The distance between the conductive layer strips should be of the same order of magnitude as this width. With the large number of conductive layer strips  11  which are thus required, the change in the inclination angle which is required from one conductive layer strip  11  to the next is sufficiently small that continuous variation can be assumed. The magnetization then also points in this direction. The resultant resistance-determining angles a for the two inclination angles of the conductive layer strips are shown. 
       FIG. 7  shows a Wheatstone bridge on a chip surface  4  which is formed from four identical AMR strips  1  with conductive layer strips  11 , and is used for position measurement. The chip surface  4  is vertically above the surface of the scale  9  whose section surface is illustrated in the drawing. The scale  9  is magnetized in alternate directions in pole lengths  10  of equal length. The position of the AMR strips  1  and their connection and circuitry correspond to those described in  FIG. 4 . In the specific illustrated case, the conductive layer strips  11  are applied to the AMR strips  1  such that the current I flows in the same direction in each case four length elements, of equal length, of the AMR strips  11 . The angles which the current directions form with the longitudinal direction of the AMR strips  1  are ±6° and ±24°. The third and fifth order harmonics have thus been eliminated from the position dependency of the resistances of the AMR strips  1 . Even-order harmonics are cancelled out by subtraction in the bridge. All the harmonics up to the seventh order are thus removed from the bridge output signal. In this case as well, two bridges which are offset through (1+¼) times the pole length  10  are once again required for the complete position sensor. In this case as well, each AMR strip  1  may be replaced by a plurality of parallel, identical AMR strips connected in a meandering shape, in order to increase the bridge resistance. 
     In contrast to the situation illustrated in  FIG. 7 , the angle of the current direction with respect to the longitudinal direction of the AMR strips  1  can also be varied continuously from one distance between the conductive layer strips  11  to the next. Optimum matching to the required measurement accuracy for the position value is possible by calculation of the bridge output signals. 
     According to the invention, angle sensors can also be formed from AMR strips  1  with conductive layer strips  11  arranged on them. In this case, by suitable choice of the angles between the longitudinal direction of the conductive layer strips  11  and the longitudinal direction of the AMR strips, it is possible for the longitudinal directions of the AMR strips  1  in both resistors in one bridge arm to be aligned parallel to one another or to be inclined at 90° to one another, or to include any angle value between 0° and 90° between them. 
     In all magneto-resistive sensor arrangements with harmonic filtering, it is impossible to avoid a reduction in the amplitude of the output signal as a function of the angle or of the position, in comparison to those without such harmonic filtering. In the case of the AMR strips  1  with conductive layer strips  11 , this reduction has the least value. This is because, in this case, averaging need be carried out only over different current angles in each resistance in the strips, and not also over different angles of the magnetization in the respective AMR strips  1 . The magnetization direction in the straight AMR strips is the same everywhere. 
     The use of the invention for GMR sensors is explained using a further example in  FIG. 8  and  FIG. 9 .  FIG. 8  shows a GMR strip  12  whose layer plane is defined on the x-y plane and whose longitudinal direction matches the x direction. The direction of the magnetization M, (shown in  FIG. 2 ) of the first component of the GMR layer, which essentially follows the direction of the external magnetic field, is not shown here. The GMR strip  12  is bounded by the edges  2  and  3 . The edges  2 ;  3  can be represented in the drawing by identical sinusoidal curves, and run parallel for each x value. As can be seen from the drawing, the direction of the magnetization M 2  of the second component of the GMR layer is at right angles to the edges  2 ;  3  in all cases. This distribution of the magnetization M 2  is the result of the field of a current through the GMR strip which was fed in at a time at which the GMR strip  12  was cooling down from a higher temperature to below its Neel temperature. The details of this magnetization setting process are known and are not the subject matter of the present invention. The continuous variation of the magnetization M 2  as the x value progresses results in continuous variation of the resistance determining angle □ when an external field is applied and the direction of the magnetization M, of the first component is thus essentially constant (as shown in  FIG. 2 ). 
       FIG. 9  shows an angle sensor bridge which is formed from GMR strips as shown in  FIG. 8 . Four GMR strips  12  are located on a chip surface  4  and have been supplemented by conductive, non-magnetic connections and connecting contacts corresponding to the description relating to  FIG. 4  to form a Wheatstone bridge. The chip surface  4  is subject to a homogeneous magnetic field H h  whose direction can rotate on the plane of the chip surface  4  and whose angle with respect to the lower edge of the chip surface  4  is intended to be determined. The longitudinal directions of the four GMR strips  12  are parallel, and the two GMR strips in each bridge arm originate from one another by mirror-imaging. This also applies to the directions of the magnetization M 2  of the second component of the GMR layer. This ensures that the resistance of the resistors in each bridge arm changes in opposite senses during rotation of the magnetic field H h . The magnetization of the first component of the GMR layer M 1  essentially points in the direction of the magnetic field H h . The resistance-determining angle □ thus varies continuously along each GMR strip  12  for any applied magnetic field H h  thus making it more difficult for hysteresis areas to form. The use of different resistance determining angles in each bridge resistor results in harmonic filtering. In order to achieve a level of suppression of the harmonic component that is significant in practice, the magnitude of the maximum gradient angle of the edge curves should be chosen to be in the range between 30° and 90°. The choice of the optimum relationship between the period length and the maximum gradient angle of the edge curves is made by calculation of the bridge output signal. 
     In this case as well, the complete angle sensor contains a second bridge of identical design, but which is arranged rotated through 90° with respect to that shown. The angle value to be determined is obtained from the quotient of the two bridge signals by use of the arctangent interpolation process. 
     The edges  2 ;  3  of the GMR strips can be reproduced by different curves with a continuous profile. Curve sections in the form of circular arcs or sums of second and fourth order parabolas are advantageous. 
     The values of the resistances in the bridge can be increased by using parallel GMR strips, which are identical to one another, with a meandering connection instead of each individual GMR strip  12 . 
     The direction of the magnetization M 2  of the second component of the GMR layer is advantageously aligned by combination of fields from currents through the GMR strips and from externally applied magnetic fields while the GMR strips  12  are being cooled down below the Neel temperature. 
     The configuration of position sensors based on GMR strips  12  is not shown in detail here, but is part of the present invention and can easily be derived from the exemplary embodiments described. 
     LIST OF REFERENCE SYMBOLS 
     
         
           1  AMR strip 
           2  First edge 
           3  Second edge 
           4  Chip surface 
           5  Operating voltage contact 
           6  Operating voltage contact 
           7  Bridge output voltage contact 
           8  Bridge output voltage contact 
           9  Scale 
           10  Pole length of the scale 
           11  Conductive layer strip 
           12  GMR strip 
           13  Period length of the edge curve 
           14  Width of the strip 
         Resistance-determining angle 
         □ Resistance-determining angle 
         H h  Homogeneous magnetic field 
         M Magnetization of the AMR layer 
         M, Magnetization of the first component of the GMR layer 
         M 2  Magnetization of the second component of the GMR layer 
         I Current 
         x,y Coordinates of the layer plane