Method and apparatus for sensing a desired component of an incident magnetic field using magneto resistive elements biased in different directions

A method and apparatus for sensing a desired component of a magnetic field using an isotropic magnetoresistive material. This is preferably accomplished by providing a bias field that is parallel to the desired component of the applied magnetic field. The bias field is applied in a first direction relative to a first set of magnetoresistive sensor elements, and in an opposite direction relative to a second set of magnetoresistive sensor elements. In this configuration, the desired component of the incident magnetic field adds to the bias field incident on the first set of magnetoresistive sensor elements, and subtracts from the bias field incident on the second set of magnetoresistive sensor elements. The magnetic field sensor may then sense the desired component of the incident magnetic field by simply sensing the difference in resistance of the first set of magnetoresistive sensor elements and the second set of magnetoresistive sensor elements.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention generally relates to magnetic field sensor devices 
and more particularly relates to such devices that measure a selected 
component of an incident magnetic field. 
2. Description of the Prior Art 
Magnetometers and other magnetic sensing devices have many diverse 
applications including automobile detection, proximity sensors, magnetic 
disk memories, magnetic tape storage systems, magnetic strip readers, etc. 
Such devices typically provide one or more output signals that represent 
the magnetic field sensed by the magnetic sensing device. 
Magnetic sensor devices typically include one or more sensor element that 
is formed from a magnetoresistive material. The resistance of a 
magnetoresistive material typically changes when exposed to an incident 
magnetic field. Thus, to detect an incident magnetic field, most magnetic 
sensor devices simply sense the change in the resistance of the 
magnetoresistive material, and provide an output signal that indicates the 
presence of, or has an amplitude that is a function of, the incident 
magnetic field. 
Common magnetoresistive materials include Anisotropic Magnetoresistive 
(AMR) materials, Giant Magnetoresistive (GMR) materials, and Colossal 
Magnetoresistive (CMR) materials. The resistance of AMR materials 
typically only changes a few percent change when exposed to an incident 
magnetic field. AMR materials are typically anisotropic with respect to 
the supplied current direction and incident field direction. Under limited 
conditions, however, AMR materials can be isotropic with respect to the 
incident field direction. 
The resistance of GMR materials can change several hundred percent when 
exposed to an incident field. GMR materials are typically formed using 
multilayer films to produce a giant magnetoresistive effect. GMR materials 
are typically isotropic with respect to current direction, but can be 
anisotropic or isotropic with respect to the incident field direction 
depending on the type of crystal and shape structure. AMR and GMR 
materials are further discussed in U.S. Pat. No. 5,569,544 to Daughton. 
CMR materials have the greatest magnetoresistive effect in response to an 
incident magnetic field. The resistance of a CMR material can change up to 
a 10.sup.6 percent. Most CMR materials are intrinsically isotropic in 
nature with respect to the supplied current and the incident magnetic 
field direction. 
The response curve for a magnetoresistive material is often defined with 
the amplitude of the incident magnetic field along the X-axis, and the 
resulting resistance of the magnetoresistive material along the Y-axis. 
CMR and some GMR magnetoresistive materials often have both a symmetrical 
and isotropic response curve. A symmetrical response curve is one that is 
symmetrical about the Y-Axis. That is, the magnetoresistive material 
satisfies the equation R(H)=R(-H), where H is the incident magnetic field. 
For CMR and some GMR magnetoresistive materials, the response curve is not 
perfectly symmetrical because of a hysteresis effects. FIG. 1 shows a 
response curve for a typical CMR magnetoresistive material. The response 
curve is nearly symmetrical (R(H).apprxeq.R(-H)) about H=0, with some 
hysteresis shown. For CMR and some GMR magnetoresistive materials, the 
hysteresis effects are small and can be effectively ignored except in the 
most sensitive magnetic sensor applications. As indicated above, CMR and 
some GMR magnetoresistive materials also have an isotropic response curve. 
An isotropic response curve is one that is independent of the direction of 
the incident magnetic field, usually within a sensor plane. 
FIG. 2 shows a schematic of a typical resistance measurement of a 
magnetoresistive film 20. Only a portion of the magnetoresistive film 20 
is shown. Input current terminals 22 and 24 are electrically connected to 
the magnetoresistive field 20, as shown. A current source 26 is then 
connected between input current terminals 22 and 24 to provide a current 
through the magnetoresistive film 20. Output voltage terminals 28 and 30 
are also electrically connected to the magnetoresistive field 20, as 
shown. A volt meter 32 measures the voltage generated between the output 
voltage terminals 28 and 30. The voltage measured by volt meter 32 is 
proportional to the resistance of the magnetoresistive film 20. 
To measure the response curve of a magnetoresistive material, an incident 
magnetic field H 38 is provided to the film 20 at an angle .theta. 34 
relative to a reference direction 36 in the sensor plane. As indicated 
above, CMR and some GMR magnetoresistive materials are typically 
isotropic, exhibiting the same response curve regardless of the direction 
.theta. 34 of the incident magnetic field in the sensor plane. 
For many applications, it is desirable to sense only one component of an 
incident magnetic field. AMR materials provide this function 
intrinsically. However, and as indicated above, AMR materials are have a 
much smaller magneto-resistive effect than materials such as CMR materials 
and some GMR materials. CMR and some GMR materials, while having a higher 
magneto-resistive effect, typically exhibit the same response curve 
regardless of the direction of the incident magnetic field in the sensor 
plane. Thus, it would be desirable to provide a magnetic field sensor that 
uses an isotropic material with a higher magneto-resistive effect, but 
anisotropic in that only a desired component of the incident magnetic 
field is sensed thereby. 
SUMMARY OF THE INVENTION 
The present invention overcomes many of the disadvantages of the prior art 
by providing a magnetic field sensor that uses an isotropic material, but 
senses only a desired component of the incident magnetic field. This is 
preferably accomplished by providing a bias field that is parallel to the 
desired component of the applied magnetic field. The bias field is applied 
in a first direction relative to a first set of magnetoresistive sensor 
elements, and in an opposite direction relative to a second set of 
magnetoresistive sensor elements. In this configuration, the desired 
component of the incident magnetic field adds to the bias field incident 
on the first set of magnetoresistive sensor elements, and subtracts from 
the bias field incident on the second set of magnetoresistive sensor 
elements. The magnetic field sensor may then sense the desired component 
of the incident magnetic field by simply sensing the difference in 
resistance of the first set of magnetoresistive sensor elements and the 
second set of magnetoresistive sensor elements. 
In a first illustrative embodiment, the magnetic field sensor includes a 
bias field generator means for generating a bias field that is parallel to 
the desired component of the incident magnetic field. Also provided are a 
first leg incorporating an isotropic magnetoresistive material that 
connects an output net to a first power supply, and a second leg 
incorporating an isotropic magnetoresistive material that connects the 
output net to a second power supply. Thus, the first leg and the second 
leg are in a voltage divider configuration. 
The first leg is preferably oriented in a first direction relative to the 
bias field, and the second leg is preferably oriented in a second 
direction relative to the bias field. Although not necessary, the first 
and second legs are preferably substantially identical in size and shape, 
and thus provide the same resistance when an identical magnetic field is 
applied thereto. 
Absent a bias field, each component of an incident magnetic field changes 
the resistance of the first and second legs equally, regardless of the 
direction of the incident magnetic field. Accordingly, the output net 
remains at a relatively fixed value. When the bias field is applied, the 
component of the incident magnetic field adds to the bias field in the 
first leg, and subtracts from the bias field in the second leg. Thus, and 
referring to FIG. 1, a first change in resistance is produced in the first 
leg and a second change in resistance is produced in the second leg. This 
produces a voltage change at the output net. 
The amplitude of the voltage change at the output net is a function of the 
amplitude of the desired component of the incident magnetic field. The 
direction of the voltage change at the output net indicates the direction 
of the desired component of the magnetic field relative to the bias field. 
It is contemplated that the bias field may be a DC bias field or an AC 
bias field. 
In another illustrative embodiment, the magnetic field sensor includes a 
bias field generator means for generating a bias field that is parallel to 
the desired component of the applied magnetic field. The magnetic field 
sensor also includes a first, a second, a third and a fourth leg. The 
first and second legs are preferably connected between a first output net 
and a second output net, respectively, and a first power supply. The third 
and fourth legs are preferably connected between the first output net and 
the second output net, respectively, and a second power supply. The first, 
second, third and fourth legs preferably incorporate an isotropic 
magnetoresistive material to produce an isotropic change in the resistance 
in the corresponding leg in response to a magnetic field. 
The first leg and the fourth leg are preferable oriented in a first 
direction relative to the bias field, and the second and third legs are 
preferably oriented in a second direction relative to the bias field. 
Although not necessary, the first, second, third and fourth legs are 
preferably substantially identical in size and shape. 
Absent a bias field, each component of an incident magnetic field changes 
the resistance of the first, second, third and fourth legs equally, 
regardless of the direction of the incident magnetic field. Thus, the 
first output net and the second output net remain at a relatively fixed 
value. When the bias field is applied, the component of the incident 
magnetic field adds to the bias field at the first leg and fourth legs, 
and subtracts from the bias field at the second and third legs. Thus, and 
referring to FIG. 1, a first change in resistance is produced in the first 
and fourth legs and a second change in resistance is produced in the 
second and third legs. This produces a first voltage change at the first 
output net and an opposite voltage change at the second output net. 
Accordingly, the difference in voltage between the first output net and the 
second output net changes, and the amplitude of the change is a function 
of the amplitude of the desired component of the incident magnetic field. 
In this embodiment, the change in voltage between the first output net and 
the second output net may be twice that of the embodiment of FIG. 3. 
It is contemplated that the bias field may be a DC bias field or an AC bias 
field. When a DC bias field is applied, the direction of the voltage 
change between the first output net and the second output net indicates 
the direction of the desired component of the magnetic field. When an AC 
bias field is applied, the phase of the voltage change between the first 
output net and the second output net indicates the direction of the 
desired component of the magnetic field. 
In accordance with the above, a method for sensing a desired component of 
an incident magnetic field is contemplated. The illustrative method 
comprises the steps of: providing a bias field that is parallel to the 
desired component of the applied magnetic field, wherein the bias field is 
applied in a first direction relative to a first set of the two or more 
magnetoresistive sensor elements and in a second direction relative to a 
second set of the two or more magnetoresistive sensor elements; and 
receiving the incident magnetic field, wherein the desired component of 
the incident magnetic field adds to the bias field incident on the first 
set of magnetoresistive sensor elements, and subtracts from the bias field 
incident on the second set of magnetoresistive sensor elements. The terms 
"add" and "subtract" are used herein in the vector sense, particularly 
when an AC bias field is applied. The sensor device then senses the 
desired component of the incident magnetic field by sensing a difference 
in resistance caused by the difference in the magnetic fields that are 
incident on the first set of magnetoresistive sensor elements and the 
second set of magnetoresistive sensor elements.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Other objects of the present invention and many of the attendant advantages 
of the present invention will be readily appreciated as the same becomes 
better understood by reference to the following detailed description when 
considered in connection with the accompanying drawings, in which like 
reference numerals designate like parts throughout the figures thereof and 
wherein: 
FIG. 3 is a schematic diagram of a first illustrative embodiment of the 
present invention. In this embodiment, the magnetic field sensor includes 
a first leg 50 and a second leg 52. The first leg 50 is connected between 
an output net V.sub.out 54 and a first power supply terminal 56. The 
second leg 52 is connected between the output net V.sub.out 54 and a 
second power supply terminal 58. The first power supply terminal 56 is 
preferably connected to a first power supply voltage (Vs), and the second 
power supply terminal 58 is preferably connected to ground (GND). 
The first leg preferably has a first resistance R1, and the second leg 
preferably has a second resistance R2. In this configuration, the output 
voltage at the output net V.sub.out 54 is given by the expression: 
##EQU1## 
To sense an incident magnetic field, the first leg 50 and the second leg 52 
each preferably incorporate an isotropic magnetoresistive material. 
Further, the first leg 50 and the second leg 52 are preferably 
substantially identical in size and shape. Because an isotropic 
magnetoresistive material is used, the first leg 50 and the second leg 52 
provide the same resistance in response to an incident magnetic field, 
regardless of the direction of the incident magnetic field. Therefore, 
without a bias field applied, the above expression for V.sub.out reduces 
to; 
##EQU2## 
Thus, the output net V.sub.out 54 remains relatively constant when an 
incident magnetic field is applied to the magnetic field sensor. 
The incident magnetic field may have an x-component 62, a y-component 64 
and/or a z-component 66. Preferably, the isotropic magnetoresistive 
material incorporated into the first leg 52 and the second leg 54 is 
applied as a film. In this configuration, the z-component 66 of the 
incident magnetic field may not produce a significant change in the 
resistance of the magnetoresistive material because of relatively large 
demagnetizing fields along the thickness of the film. 
To sense only one component of the incident magnetic field, the present 
invention contemplates providing a bias field that is parallel to the 
desired component of the incident magnetic field. This may be accomplished 
using a bias field generator 74. The bias field generator may be an 
external coil, an electromagnet, an integrated on-chip coil, or any other 
means for generating a bias field. 
In the embodiment shown, the bias field is applied parallel to the 
x-component 62 of the incident magnetic field. The bias field is 
preferably applied in a first direction 70 relative to the first leg 50, 
and in an opposite direction 72 relative to the second leg 52. 
Accordingly, the x-component 62 of the incident magnetic field adds to the 
bias field incident on the first leg 50, and subtracts from the bias field 
incident on the second leg 52. The magnetic field sensor may then senses 
the x-component 62 of the incident magnetic field by simply sensing the 
difference in resistance of the first leg 50 and the second leg 52 by 
examining the voltage at the output net V.sub.out 54. 
Absent a bias field, both the x-component 62 and the y-component 64 of the 
incident magnetic field change the resistance of the first leg 50 and 
second leg 52 equally, as described above. However, when the bias field is 
applied in parallel with the x-component of the incident magnetic field, 
an imbalance is created. The bias field adds to the x-component of the 
incident magnetic field to produce a first change in resistance in the 
first leg 50. Likewise, the bias field subtracts from the x-component of 
the incident magnetic field to produce a second change in resistance in 
the second leg 52. 
Accordingly, the voltage at the output net V.sub.out 54 changes. The 
amplitude of the voltage change at the output net V.sub.out 54 may be a 
function of the amplitude of the desired component of the incident 
magnetic field. The direction of the voltage change may indicate the 
direction of the desired component of the incident magnetic field relative 
to the applied bias field. 
It is contemplated that the bias field may be a DC bias field or an AC bias 
field. FIG. 4 is a diagram showing the voltage V.sub.out versus time, with 
a DC bias field applied. Line 100 represents the voltage of V.sub.out with 
only the bias field applied. Even though the bias field is applied to the 
first leg 50 in an opposite direction to the second leg 52, both the first 
leg 50 and the second leg 52 produce the same change in resistance. This 
is because the magnetoresistive material incorporated into the first leg 
50 and the second leg 52 is preferably isotropic. Thus, the output net 
V.sub.out 54 remains at a relatively fixed value, as shown. 
Line 100 also represents the voltage of V.sub.out with an incident magnetic 
field is present, absent a bias field. As indicated above, both the 
x-component 62 and the y-component 64 of the incident magnetic field 
change the resistance of the first leg 50 and second leg 52 equally, 
regardless of the direction of the incident magnetic field. Accordingly, 
the output net V.sub.out 54 remains at a relatively fixed value, as shown. 
Line 102 shows the value of V.sub.out with a bias field applied in a first 
direction parallel to the x-component of an incident magnetic field. When 
the bias field is applied in the manner, the x-component of the incident 
magnetic field produces a first change in resistance in the first leg 50 
and a second change in resistance in the second leg 52. Thus, the voltage 
at the output net V.sub.out 54 changes in first direction, as shown. The 
amplitude of the change is a function of the amplitude of the x-component 
of the incident magnetic field. 
Line 104 shows the value of V.sub.out with a bias field applied in a second 
direction parallel to the x-component of the incident magnetic field. 
Under this scenario, the x-component of the incident magnetic field 
produces the first change in resistance in the second leg 52 and the 
second change in resistance in the first leg 50. Accordingly, the voltage 
at the output net V.sub.out 54 changes in a second direction, as shown. 
Again, the amplitude of the change is a function of the amplitude of the 
x-component of the incident magnetic field. As can be seen from lines 102 
and 104 of FIG. 4, the direction of the voltage change of V.sub.out 
indicates the direction of the desired component of the magnetic field 
relative to the direction of the bias field. 
FIG. 5 is a diagram showing the value of V.sub.out versus time when a 
square wave AC bias field is applied to the embodiment shown in FIG. 3. In 
this embodiment, the imbalance in resistance between the first leg 50 and 
the second leg 52 is time dependent. The result is a square wave output, 
with the amplitude of the square wave being a function of the amplitude of 
the x-component of the incident magnetic field. The phase of the square 
wave output indicates the direction of the incident magnetic field 
relative to the bias field. 
FIG. 6 is a diagram showing the value of V.sub.out versus time when a sine 
wave AC bias field is applied to the embodiment shown in FIG. 3. In this 
embodiment, the imbalance in resistance between the first leg 50 and the 
second leg 52 is also time dependent. The result is a modified square wave 
output, with the amplitude of the modified square wave output being a 
function of the amplitude of the x-component of the incident magnetic 
field. The phase of the modified square wave output indicates the 
direction of the incident magnetic field relative to the bias field. 
To maximize the output signal of the magnetic sensor device, the first leg 
50 and the second leg 52 preferably incorporate a Colossal 
magnetoresistive (CMR) material. Colossal magnetoresistive materials are 
known to have an isotropic and symmetrical response curve. Other isotropic 
magnetoresistive materials may also be used, including certain isotropic 
GMR materials. 
Illustrative Colossal magnetoresistive materials are those generally 
described by the formula (LnA)MnO.sub.3, wherein Ln=La, Nd, or Pr and 
A=Ca, Sr, Ba or Pb. Preferably, the Colossal magnetoresistive material is 
LaCaMnO, having concentrations of La between 26-32 at %, Ca between 9-20 
at %, and Mn between 47-64 at %. More preferably, the Colossal 
magnetoresistive material is LaCaMnO, having a 28.4 at % concentration of 
La, a 11.6 at % concentration of Ca, and a 60 at % concentration of Mn. 
FIG. 7 is a schematic diagram of a second illustrative embodiment of the 
present invention. This embodiment includes a first leg 122, a second leg 
124, a third leg 126 and a fourth leg 128. The first leg 122 connects a 
first output net 130 to a first power supply 132. The second leg 124 
connects a second output net 134 to the first power supply 132. The third 
leg 126 connects the first output net 130 to a second power supply 138. 
The fourth leg 128 connects the second output net 134 to the second power 
supply 138. 
The first, second, third and fourth legs preferably incorporate an 
isotropic magnetoresistive material to produce an isotropic change in the 
resistance in the corresponding leg in response to a magnetic field. The 
first leg 122 and the fourth leg 128 are preferable oriented in a first 
direction relative to the bias field, and the second leg 124 and the third 
leg 126 are preferably oriented in a second direction relative to the bias 
field. The first leg 122, second leg 124, third leg 126 and fourth leg 128 
are preferably substantially identical in size and shape. 
To maximize the output signal of the magnetic sensor device, the first leg 
122, second leg 124, third leg 126, and fourth leg 128 each preferably 
incorporate a Colossal magnetoresistive material. Colossal 
magnetoresistive materials are known to have an isotropic and symmetrical 
response curve. As indicated above, however, other isotropic materials may 
also be used, including certain isotropic GMR materials. 
Absent a bias field, each component of an incident magnetic field changes 
the resistance of the first leg 122, second leg 124, third leg 126 and 
fourth leg 128 equally, regardless of the direction of the incident 
magnetic field. Accordingly, the first output net 130 and the second 
output net 134 remain at a relatively fixed value. When the bias field is 
applied, however, the component of the incident magnetic field that is 
parallel to the bias field adds to the bias field at the first leg 122 and 
the fourth leg 128 to produce a first change in resistance in the first 
leg 122 and the fourth leg 128. Likewise, the component of the incident 
magnetic field that is parallel to the bias field subtracts from the bias 
field at the second leg 124 and the third leg 126 to produce a second 
change in resistance in the second leg 124 and the third leg 126. 
Accordingly, the difference in voltage between the first output net 130 
and the second output net 134 changes, and the amplitude of the voltage 
change is a function of the amplitude of the desired component of the 
incident magnetic field. 
It is contemplated that the bias field may be a DC bias field or an AC bias 
field. When a DC bias field is applied, the direction of the change in 
voltage between the first output net 130 and the second output net 134 
indicates the direction of the desired component of the magnetic field. 
When an AC bias field is applied, the phase of the voltage change between 
the first output net 130 and the second output net 134 indicates the 
direction of the desired component of the magnetic field relative to the 
bias field. 
In accordance with the above, a method for sensing a desired component of 
an incident magnetic field is contemplated. The illustrative method 
comprises the steps of: providing a bias field that is parallel to the 
desired component of the applied magnetic field, wherein the bias field is 
applied in a first direction relative to a first set of the two or more 
magnetoresistive sensor elements and in a second direction relative to a 
second set of the two or more magnetoresistive sensor elements; and 
receiving the incident magnetic field, wherein the desired component of 
the incident magnetic field adds to the bias field incident on the first 
set of magnetoresistive sensor elements, and subtracts from the bias field 
incident on the second set of magnetoresistive sensor elements. The terms 
"add" and "subtract" are used herein are used in the vector sense, 
particularly when an AC bias field is applied. The sensor device then 
senses the desired component of the incident magnetic field by sensing a 
difference in resistance caused by the difference in the magnetic fields 
that are incident on the first set of magnetoresistive sensor elements and 
the second set of magnetoresistive sensor elements. 
Sine wave AC bias field Example 
In this example, the bias field is given by the expression H.sub.b 
(t)=H.sub.0 sin (.omega.t) and .vertline.H.sub.0 
.vertline.&gt;&gt;.vertline.H.vertline., where H is the incident magnetic field 
to be measured. H=H.sub.x i+H.sub.y j, where i and j are unit vectors 
along the x and y axes. Resistance in each leg is then given by the 
equation R=R.sub.0 +R1(H.sub.t), where H.sub.t is the total field, R.sub.0 
is the resistance at zero field, and R1 is the incremental resistance in 
response to the magnetic field. For this illustration, each of the four 
legs 122, 124, 126 and 128 has the same zero field resistance R.sub.0. 
Ignoring hysteresis, a model for the incremental resistance R1(H.sub.t) is 
well approximated by: 
EQU R1(H.sub.t)=(.DELTA.R/R).sub.max .cndot..vertline.H.sub.t 
.vertline./H.sub.sat =C.cndot..vertline.H.sub.t .vertline.(3) 
where H.sub.sat is the maximum field in the linear range, and 
(.DELTA.R/R).sub.max is the magnetoresistance ratio at maximum field. Leg 
122 and leg 128 have the same resistance to each other, and leg 124 and 
leg 126 have the same resistance to each other. H.sub.z is negligible due 
to the large demagnetizing field out of the film plane, as described 
above. Thus, 
EQU R.sub.1,4 =R.sub.0 +C.cndot.sqrt{[H.sub.x +H.sub.0 sin(.omega.t)].sup.2 
+H.sub.y.sup.2 } (4) 
EQU R.sub.2,3 =R.sub.0 +C.cndot.sqrt{[H.sub.x -H.sub.0 sin(.omega.t)].sup.2 
+H.sub.y.sup.2 } (5) 
With a constant voltage excitation, the output of the bridge is given by 
the equation: 
##EQU3## 
After inserting the values for R.sub.1,4 and R.sub.2,3 from equations 4 
and 5 above, this equation yields to linear order in fields: 
##EQU4## 
Thus, to linear order in fields, V.sub.out is a function of H.sub.x, and 
is independent of H.sub.y. This demonstrates the sensitivity to only one 
component of the incident magnetic field. The resulting output voltage of 
V.sub.out is generally represented by the modified square wave shown in 
FIG. 6. The amplitude of the modified square wave is a function of the 
amplitude of the desired component of the incident magnetic field. 
Further, the phase of the modified square wave indicates the direction of 
the desired component of the magnetic field relative to the applied bias 
field. 
With a constant current excitation, the output voltage is much simpler, and 
given by the equation: 
EQU V.sub.out =I.sub.B .cndot.(R.sub.1,4 -R.sub.2,3)=I.sub.B 
.cndot.C.cndot.H.sub.x 
.cndot.2.vertline.sin(.omega.t).vertline./sin(.omega.t) (8) 
As can be seen, the output voltage is a square wave function, as generally 
shown in FIG. 5. As before the amplitude of the square wave is a function 
of the x-component of the incident magnetic field, and is independent of 
the y-component. The phase of the square wave indicates the direction of 
the x-component of the magnetic field relative to the applied bias field. 
Square wave AC bias field Example 
In this example, the bias field is given by the expression H.sub.b 
(t)=H.sub.0 .vertline.sin(.omega.t)/sin(.omega.t), where .vertline.H.sub.0 
.vertline.&gt;&gt;.vertline.H.vertline., where H is the field to be sensed. With 
a constant voltage excitation, the output of the bridge is given by the 
expression: 
##EQU5## 
EQU R.sub.1,4 =R.sub.0 +C.cndot.sqrt{[H.sub.x +H.sub.0 
.vertline.sin(.omega.t).vertline./sin(.omega.t)].sup.2 +H.sub.y.sup.2 
}(10) 
EQU R.sub.2,3 =R.sub.0 +C.cndot.sqrt{[H.sub.x -H.sub.0 
.vertline.sin(.omega.t).vertline./sin(.omega.t)].sup.2 +H.sub.y.sup.2 
}(11) 
After inserting the values for R.sub.1,4 and R.sub.2,3 from equations (10) 
and (11) above, this expression yields to linear order in fields: 
##EQU6## 
Thus, this embodiment produces a square wave output. The amplitude of the 
desired component of the incident magnetic field H.sub.x can be determined 
by examining the amplitude of the square wave, and the polarity of H.sub.x 
can be determined by examining the phase of the square wave. 
With a constant current excitation, the output of the bridge is given by 
the equation: 
EQU V.sub.out =I.sub.B .cndot.(R.sub.1,4 -R.sub.2,3)=I.sub.B 
.cndot.C.cndot.H.sub.x 
.cndot..vertline.sin(.omega.t).vertline./sin(.omega.t) (13) 
This again produces a square wave output. As above, the amplitude and 
polarity of the desired component of the incident magnetic field H.sub.x 
can be determined from the amplitude and phase of the output square wave 
pulse. 
Having thus described the preferred embodiments of the present invention, 
those of skill in the art will readily appreciate that the teachings found 
herein may be applied to yet other embodiments within the scope of the 
claims hereto attached.