Patent Publication Number: US-10310028-B2

Title: Coil actuated pressure sensor

Description:
FIELD 
     This application relates to pressure sensing and, more particularly, to sensing pressure by detecting a reflected magnetic field. 
     BACKGROUND 
     Magnetic field sensors are often used to detect a ferromagnetic target. They often act as sensors to detect motion or position of the target. Such sensors are ubiquitous in many areas of technology including robotics, automotive, manufacturing, etc. For example, a magnetic field sensor may be used to detect when a vehicle&#39;s wheel locks up, triggering the vehicle&#39;s control processor to engage the anti-lock braking system. In this example, the magnetic field sensor may detect rotation of the wheel. Magnetic field sensor may also detect distance to an object. For example, a magnetic field sensor may be used to detect the position of a hydraulic piston. 
     SUMMARY 
     In an embodiment, a pressure sensor includes a chamber comprising a conductive portion and a deformable portion coupled to the conductive portion and susceptible to deformation in response to a pressure differential between an interior of the chamber and an exterior of the chamber; at least one coil responsive to an AC coil drive signal; at least one magnetic field sensing element disposed proximate to the at least one coil and to the conductive portion of the chamber and configured to generate a magnetic field signal in response to a reflected magnetic field generated by the at least one coil and reflected by the conductive portion; and a circuit coupled to the at least one magnetic field sensing element to generate an output signal of the pressure sensor indicative of the pressure differential between the interior of the chamber and the exterior of the chamber in response to the magnetic field signal. 
     One or more of the following features may be included. 
     The chamber may comprise an elongated tube. 
     The conductive portion and the deformable portion may comprise a membrane disposed at a first end of the tube proximate to the at least one magnetic field sensing element. 
     The membrane may be comprised of one or more of stainless steel, copper beryllium, titanium alloys and sapphire. 
     The at least one magnetic field sensing element may comprise at least two spaced apart magnetic field sensing elements, wherein the circuit is configured to detect a difference between a first distance between the conductive portion and a first one of the magnetic field sensing elements and a second distance between the conductive portion and a second one of the magnetic field sensing elements in order to generate the output signal of the pressure sensor. 
     The first one of the magnetic field sensing elements may be substantially aligned with an edge of the membrane and the second one of the magnetic field sensing elements is substantially aligned with a central region of the membrane. 
     The at least one magnetic field sensing element may comprise a first magnetic field sensing element supported by a first substrate and a second magnetic field sensing element supported by a second substrate. 
     The deformable portion may comprise a sidewall portion of the elongated tube configured to elongate in response to the pressure differential. 
     The conductive portion may comprise an end of the elongated tube proximate to the at least one magnetic field sensing element. 
     The elongated tube may comprise a first elongated tube and the pressure sensor further comprises a second elongated tube in which the first elongated tube is disposed. 
     A substrate may be included, wherein the substrate comprises a first substrate, and the pressure sensor further comprises a second substrate having a first surface in which a recess is formed and a second, opposing surface. A conductive material may be disposed in the recess of the second substrate, wherein the first substrate and the second substrate are attached, with the first surface of the second substrate adjacent to the first substrate such that the chamber comprises the recess of the second substrate and the conductive portion comprises the conductive material. 
     The chamber may be maintained at a predetermined reference pressure. 
     The recess may be an etched recess. 
     The conductive material may comprise copper or aluminum. 
     The at least one magnetic field sensing element may comprise one or more of a Hall effect element, a giant magnetoresistance (MR) element, an anisotropic magnetoresistance element (AMR), a tunneling magnetoresistance (TMR) element, or a magnetic tunnel junction (MTJ). 
     The at least one magnetic field sensing element and/or the coil may be supported by a substrate. 
     The substrate may comprise a first substrate and the pressure sensor may comprise a second substrate, wherein the at least one magnetic field sensing element is supported by the second substrate. 
     The chamber may be divided into smaller parts, each of them experiencing a possible different pressure to produce a mapping of the pressure. 
     In another embodiment, a pressure sensor comprises a chamber comprising a conductive portion and a deformable portion coupled to the conductive portion and susceptible to deformation in response to a pressure differential between an interior of the chamber and an exterior of the chamber; means for generating a reflected magnetic field from the chamber; means for generating a magnetic field signal in response to the reflected magnetic field; and means for generating an output signal of the pressure sensor indicative of the pressure differential between the interior of the chamber and the exterior of the chamber in response to the magnetic field signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing features may be more fully understood from the following description of the drawings. The drawings aid in explaining and understanding the disclosed technology. Since it is often impractical or impossible to illustrate and describe every possible embodiment, the provided figures depict one or more examples of embodiments. Accordingly, the figures are not intended to limit the scope of the invention. Like numbers in the figures denote like elements. 
         FIG. 1  is a block diagram of a system for sensing a target. 
         FIG. 2  is an isometric diagram of a system for sensing a target. 
         FIG. 2A  shows cross-sectional views of the system of  FIG. 2 . 
         FIG. 3  is a schematic diagram of a coil and magnetoresistance (MR) elements for sensing a target. 
         FIG. 3A  is a schematic diagram of an embodiment of a coil and MR elements for sensing a target, including bond pads. 
         FIG. 3B  is schematic diagram of an embodiment of coil and MR elements for sensing a target. 
         FIG. 4  is a cross-sectional view of a system for sensing a target. 
         FIG. 5  is a schematic diagram of a coil and MR elements for sensing a target. 
         FIG. 5A  is schematic diagram of an embodiment of a coil and MR elements for sensing a target. 
         FIG. 5B  is schematic diagram of an embodiment of a coil and MR elements for sensing a target, including a lead frame. 
         FIG. 5C  is schematic diagram of an embodiment of a coil and MR elements for sensing a target. 
         FIG. 6  is schematic diagram of an embodiment of a coil and MR elements for sensing a target. 
         FIG. 7  is a cross-sectional view of coils and MR elements for sensing a target. 
         FIG. 8  is an isometric view of a pressure sensor. 
         FIG. 8A  is an isometric view of embodiments of the pressure sensor of  FIG. 8 . 
         FIG. 9  is a cross-sectional view of an embodiment of a pressure sensor including substrates. 
         FIG. 10  is a block diagram of a circuit for sensing a magnetic target. 
         FIG. 10A  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 11  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 11A  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 11B  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 11C  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 11D  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 11E  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 11F  is a block diagram of an embodiment of a circuit for sensing a magnetic target. 
         FIG. 12  is a diagram representing an output signal for a system with sensitivity detection. 
         FIG. 12A  is a block diagram of a magnetic field detection circuit with sensitivity detection. 
         FIG. 12B  is a block diagram of an embodiment of a magnetic field detection circuit with sensitivity detection. 
         FIG. 12C  is a block diagram of an embodiment of a magnetic field detection circuit with sensitivity detection. 
         FIG. 13  is a schematic diagram of an embodiment of a magnetic field detection circuit with sensitivity detection including a coil and MR elements. 
         FIG. 13A  is a schematic diagram of an embodiment of a coil having countercoils and gaps between traces. 
         FIG. 13B  is a block diagram of an embodiment of a magnetic field detection circuit with sensitivity detection. 
         FIG. 14  is a side view of a magnetic field sensor and a magnetic target having material of varying thickness. 
         FIG. 14A  is a side view of a magnetic field sensor and a magnetic target having material of varying thickness. 
         FIG. 14B  is a side view of a magnetic field sensor and a magnetic target having material of varying thickness. 
         FIG. 15  is a side view of a magnetic field sensor and a magnetic target having material with multiple thicknesses. 
         FIG. 15A  is a side view of a magnetic field sensor and a magnetic target having material with multiple thicknesses. 
         FIG. 15B  is a side view of a magnetic field sensor and a magnetic target having material with multiple thicknesses. 
         FIG. 15C  is a side view of a magnetic field sensor and a magnetic target having material with multiple thicknesses. 
         FIG. 16  is a side view of a magnetic field sensor and a magnetic target having an inclined plane. 
         FIG. 16A  is a side view of a magnetic field sensor and a magnetic target having an inclined plane. 
         FIG. 17  is a side view of a substrate and lead frame connected by lead wires. 
         FIG. 17A  is a side view of a substrate and lead frame connected by solder bumps. 
         FIG. 18  is a schematic diagram of a dual-die package including one or more coils. 
         FIG. 18A  is a schematic diagram of a dual-die package including one or more coils. 
         FIG. 19  is a schematic diagram of a multi-die package including one or more coils. 
     
    
    
     DETAILED DESCRIPTION 
     As used herein, the term “magnetic field sensing element” is used to describe a variety of electronic elements that can sense a magnetic field. The magnetic field sensing element can be, but is not limited to, a Hall Effect element, a magnetoresistance (MR) element, or a magnetotransistor. As is known, there are different types of Hall Effect elements, for example, a planar Hall element, a vertical Hall element, and a Circular Vertical Hall (CVH) element. As is also known, there are different types of magnetoresistance elements, for example, a semiconductor magnetoresistance element such as Indium Antimonide (InSb), a giant magnetoresistance (MR) element, an anisotropic magnetoresistance element (AMR), a tunneling magnetoresistance (TMR) element, and a magnetic tunnel junction (MTJ). The magnetic field sensing element may be a single element or, alternatively, may include two or more magnetic field sensing elements arranged in various configurations, e.g., a half bridge or full (Wheatstone) bridge. Depending on the device type and other application requirements, the magnetic field sensing element may be a device made of a type IV semiconductor material such as Silicon (Si) or Germanium (Ge), or a type III-V semiconductor material like Gallium-Arsenide (GaAs) or an Indium compound, e.g., Indium-Antimonide (InSb). 
     As is known, some of the above-described magnetic field sensing elements tend to have an axis of maximum sensitivity parallel to a substrate that supports the magnetic field sensing element, and others of the above-described magnetic field sensing elements tend to have an axis of maximum sensitivity perpendicular to a substrate that supports the magnetic field sensing element. In particular, planar Hall elements tend to have axes of sensitivity perpendicular to a substrate, while metal based or metallic magnetoresistance elements (e.g., MR, TMR, AMR) and vertical Hall elements tend to have axes of sensitivity parallel to a substrate. 
     As used herein, the term “magnetic field sensor” is used to describe a circuit that uses a magnetic field sensing element, generally in combination with other circuits. Magnetic field sensors are used in a variety of applications, including, but not limited to, an angle sensor that senses an angle of a direction of a magnetic field, a current sensor that senses a magnetic field generated by a current carried by a current-carrying conductor, a magnetic switch that senses the proximity of a ferromagnetic object, a rotation detector that senses passing ferromagnetic articles, for example, magnetic domains of a ring magnet or a ferromagnetic target (e.g., gear teeth) where the magnetic field sensor is used in combination with a back-biased or other magnet, and a magnetic field sensor that senses a magnetic field density of a magnetic field. 
     As used herein, the terms “target” and “magnetic target” are used to describe an object to be sensed or detected by a magnetic field sensor or magnetic field sensing element. The target may comprise a conductive material that allows for eddy currents to flow within the target, for example a metallic target that conducts electricity. 
       FIG. 1  is a block diagram of a system  100  for detecting a conductive target  102 . Target  102  may be magnetic or non-magnetic in various embodiments. System  100  includes one or more magnetoresistance (MR) elements  104  and an MR driver circuit  106 . MR driver circuit may include a power supply or other circuit that provides power to MR elements  104 . In embodiments, MR elements  104  may be replaced with other types of magnetic field sensing elements such as Hall effect elements, etc. MR elements  104  may comprise a single MR element or multiple MR elements. The MR elements may be arranged in a bridge configuration, in certain embodiments. 
     System  100  may also include one or more coils  108  and a coil driver circuit  110 . Coils  108  may be electrical coils, windings, wires, traces, etc. configured to generate a magnetic field when current flows through the coils  108 . In embodiments, coils  108  comprise two or more coils, each a conductive trace supported by substrate, such as a semiconductor substrate, a glass substrate, a ceramic substrate, or the like. In other embodiments, coils  108  may not be supported by a substrate. For example, coils  108  may be supported by a chip package, a frame, a PCB, or any other type of structure that can support traces of a coil. In other embodiments, coils  108  may be free standing wire, i.e. not supported by a separate supporting structure. 
     Coil driver  110  is a power circuit that supplies current to coils  108  to generate the magnetic field. In an embodiment, coil driver  110  may produce an alternating current so that coils  108  produce alternating magnetic fields (i.e. magnetic fields with magnetic moments that change over time). Coil driver  110  may be a circuit implemented, in whole or in part, on the semiconductor die. 
     System  100  may also include processor  112  coupled to receive signal  104   a  from MR elements  104 , which may represent the magnetic field as detected by MR elements  104 . Processor  100  may receive signal  104   a  and use it to determine a position, speed, direction, or other property of target  102 . 
     MR elements  104  and coils  108  may be positioned on substrate  114 . Substrate  114  may comprise semiconductor substrates, such as silicon substrates, a chip package, PCB or other type of board-level substrates, or any type of platform that can support MR elements  104  and coils  108 . Substrate  114  may include a single substrate or multiple substrates, as well as a single type of substrate or multiple types of substrates. 
     In operation, MR driver  106  provides power to MR elements  104  and coil driver  110  provides current to coils  108 . In response, coils  108  produce a magnetic field that can be detected by MR elements  104 , which produce signal  104   a  representing the detected magnetic field. 
     As target  102  moves in relation to the magnetic field, its position and movement through the field changes the field. In response, signal  104   a  produced by MR elements  104  changes. Processor  112  receives signal  104   a  and processes the changes in (and/or the state of) the signal to determine position, movement, or other characteristics of target  102 . In an embodiment, system  100  can detect movement or position of target  102  along axis  116 . In other words, system  100  may detect the position of target  102  in proximity to MR elements  104  as target  102  moves toward or away from MR elements  104  and coils  108 . System  102  may also be able to detect other types of position or movement of target  102 . 
     Referring now to  FIG. 2 , system  200  may be the same as or similar to system  100 . Substrate  202  may be the same as or similar to substrate  114 , and may support coil  204 , coil  206 , and MR element  208 . Although one MR element is shown, MR element  208  may comprise two or more MR elements depending on the embodiment of system  200 . Target  203  may be the same as or similar to target  102 . 
     Although not shown, an MR driver circuit  106  may provide current to MR element  208  and coil driver circuit  110  may provide current to coils  204  and  206 . 
     Coil  204  and  206  may be arranged so that the current flows through coils  204  and  206  in opposite directions, as shown by arrow  208  (indicating a clockwise current in coil  204 ) and arrow  210  (indicating a counterclockwise current in coil  206 ). As a result, coil  204  may produce a magnetic field having a magnetic moment in the negative Z direction (i.e. down, in  FIG. 2 ), as indicated by arrow  212 . Similarly, coil  206  may produce a magnetic field having a magnetic moment in the opposite direction, the positive Z direction, as indicated by arrow  214 . An aggregate magnetic field  211  produced by both coils may have a shape similar to that shown by magnetic field lines  211 . It will be appreciated that coils  204 ,  206  may be formed by a single coil structure respectively wound so that the current through the coils flows in opposite directions. Alternatively, coils  204 ,  206  may be formed by separate coil structures. 
     In an embodiment, MR element  208  may be placed between coils  204  and  206 . In this arrangement, absent any other magnetic fields aside from those produced by coils  204  and  206 , the net magnetic field at MR element  208  may be zero. For example, the negative Z component of the magnetic field produced by coil  204  may be canceled out by the positive Z component of the magnetic field produced by coil  206 , and the negative X component of the magnetic field shown above substrate  202  may be canceled out by the positive X component of the magnetic field shown below substrate  202 . In other embodiments, additional coils may be added to substrate  202  and arranged so that the net magnetic field at MR element  208  is substantially nil. 
     To achieve a substantially zero magnetic field at the location of MR element  208 , coil  204  and coil  206  may be placed so that current through the coils flows in circular patterns substantially in the same plane. For example, the current through coil  204  and  206  is flowing in circular patterns through the coils. As shown, those circular patterns are substantially coplanar with each other, and with the top surface  216  of substrate  202 . 
     As noted above, coil driver  110  may produce an alternating field. In this arrangement, the magnetic field shown by magnetic field lines  211  may change direction and magnitude over time. However, during these changes, the magnetic field at the location of MR element  208  may remain substantially nil. 
     In operation, as target  203  moves toward and away from MR element  208  (i.e. in the positive and negative Z direction), magnetic field  211  will cause eddy currents to flow within target  203 . These eddy currents will create their own magnetic fields, which will produce a non-zero magnetic field in the plane of the MR element  208 , which non-zero magnetic field can be sensed to detect the motion or position of target  203 . 
     Referring to  FIG. 2A , a cross-sectional view  250  of system  200 , as viewed at line  218  in the Y direction, illustrates the eddy currents within target  203 . The ‘x’ symbol represents a current flowing into the page and the symbol represents a current flowing out of the page. As noted above, the current through coils  204  and  206  may be an alternating current, which may result in an alternating strength of magnetic field  211 . In embodiments, the phase of the alternating current through coil  204  matches the phase of the alternating current through coil  206  so that magnetic field  211  is an alternating or periodic field. 
     Alternating magnetic field  211  may produce reflected eddy currents  240  and  242  within magnetic target  203 . Eddy currents  240  and  242  may be opposite in direction to the current flowing through coils  204  and  206 , respectively. As shown, eddy current  246  flows out of the page and eddy current  248  flows into the page, while coil current  251  flows into the page and current  252  flows out of the page. Also, as shown, the direction of eddy current  242  is opposite the direction of the current through coil  206 . 
     Eddy currents  240  and  242  form a reflected magnetic field  254  that has a direction opposite to magnetic field  211 . As noted above, MR element  208  detects a net magnetic field of zero due to magnetic field  211 . However, MR element  208  will detect a non-zero magnetic field in the presence of reflected magnetic field  254 . As illustrated by magnetic field line  256 , the value of reflected magnetic field  254  is non-zero at MR element  208 . 
     As target  203  moves closer to coils  204  and  206 , magnetic field  211  may produce stronger eddy currents in target  203 . As a result, the strength of magnetic field  254  may change. In  FIG. 2A , magnetic field  211 ′ (in the right-hand panel of  FIG. 2A ) may represent a stronger magnetic field than magnetic field  211  due, for example, to the closer proximity of target  203  to coils  204  and  206 . Thus, eddy currents  240 ′ and  242 ′ may be stronger currents than eddy currents  240  and  242 , and magnetic field  254 ′ may be stronger than magnetic field  254 . This phenomenon may result in MR element  208  detecting a stronger magnetic field (i.e. magnetic field  254 ′) when target  203  is closer to coils  204  and  206 , and a weaker magnetic field (i.e. magnetic field  254 ) when target  203  is further away from coils  204  and  206 . 
     Also, eddy currents  240 ′ and  242 ′ generally occur on or near the surface of target  203 . Therefore, as target  203  moves closer to co MR element  208 , MR element  208  may experience a stronger magnetic field from the eddy currents because the source of the magnetic field is closer to MR element  208 . 
       FIG. 3  is a schematic diagram of a circuit  300  including coils  302  and  304 , and MR elements  306  and  308 . Coils  302  and  304  may be the same as or similar to coils  204  and  206 , and MR elements  306  and  308  may each be the same as or similar to MR element  208 . 
     In an embodiment, coils  302  and  304 , and MR elements  306  and  308  may be supported by a substrate. For example, coils  302  and  304  may comprise conductive traces supported by a substrate and MR elements  306  and  308  may be formed on a surface of or in the substrate. 
     In an embodiment, coils  302  and  304  may comprise a single conductive trace that carries current. The portion of the trace forming coil  302  may loop or spiral in a direction opposite to the portion of the trace forming coil  304 , so that the current through each coil is equal and flows in opposite directions. In other embodiments, multiple traces may be used. 
     Coils  302  and  304  are symmetrically positioned on opposite sides of MR elements  306  and  308 , with MR elements  308  and  304  in the middle. This may result in MR elements  306  and  308  being in the center of the magnetic field produced by coils  302  and  304 , so that, absent any other stimulus, the magnetic field detected by MR elements  306  and  308  as a result of magnetic fields produced by coils  302  and  304  (referred to herein as the directly coupled magnetic field) is substantially nil. 
       FIG. 3A  is a schematic diagram of an embodiment of a magnetic field detection circuit  300 ′, which may be the same as or similar to system  100  in  FIG. 1 . Coils  302  and  304  may be supported by a substrate as described above. Circuit  300 ′ may include four MR elements  310 ,  312 ,  314 , and  316 , which may be coupled in a bridge configuration  318 . In embodiments, bridge  318  may produce a differential output consisting of signals  318   a  and  318   b.    
     Arranging the MR elements in a bridge may, in certain embodiments, increase the sensitivity of the magnetic field sensor. In an embodiment, a target is movable with respect to the circuit  300 ′ such that as the target approaches the circuit it mainly moves towards MR elements  310 ,  312 , but not towards MR elements  314 ,  316 . With this configuration, the resistance of MR elements  310  and  312  may change and the resistance of MR elements  314  and  316  may remain relatively constant as the target approaches and recedes from the MR elements. If, for example, MR elements are aligned so that the MR resistance of  310 ,  312  decreases and the resistance of MR elements  314 ,  316  increases as the target approaches, then signal  318   a  will decrease and signal  318   b  will increase in voltage as the target approaches. The opposite reaction of the MR elements (and the differential signals  318   a  and  318   b ) may increase sensitivity of the magnetic field detection circuit while also allowing the processor that receives the differential signal to ignore any common mode noise. 
     In embodiments, arranging MR elements  310 - 316  in a bridge may allow for detection of the difference in the position of the target over the set of resistors and/or detection of a phase difference between the bridge outputs. This may be utilized, for example, to detect tilt or deformation of a target. 
     Circuit  300 ′ may also include a bond pads  320  having multiple leads  322  that can be accessed and form connections external to a chip package (not shown). Lead wires or conductive traces  324  may connect MR elements  310 ,  312 ,  314 , and  316  to external leads or pads  322  so they can be coupled to other circuits like, for example, MR driver  106 . 
     Referring to  FIG. 3B , a circuit  323  includes four coils  324 - 330  and three rows  332 ,  334 , and  336  of MR elements. Circuit  323  may be used to detect location or motion of a target. 
     The coils may produce magnetic fields in alternating patterns. For example, coil  324  may produce a field going into the page, coil  326  may produce a field coming out of the page, coil  328  may produce a field going into the page, and coil  330  may produce a field coming out of the page. As a result, the magnetic field detected by the MR elements in rows  332 ,  334 , and  336  as a result of magnetic fields produced by coils  324 ,  326 ,  328 ,  330  may be substantially nil. 
     Circuit  323  may also be extended by adding additional coils and additional MR elements. In embodiments, the additional coils may be configured to create magnetic fields with alternating directions, as described above, and the MR elements between the coils may be placed so that they detect a magnetic field that is substantially nil. 
     The MR elements in rows  332 ,  334 , and  336  may form a grid. As a target moves above the grid and approaches the MR elements, the MR elements will be exposed to and detect the reflected magnetic field produced by the eddy currents flowing in the target as a result of the magnetic fields produced by the coils  324 - 330 . For example, if a target moves over MR elements  338  and  340 , those MR elements may detect the reflected magnetic field and produce an output signal indicating as much. A processor receiving the output signals from the MR elements can then identify the location of the target as above or near MR elements  338  and  340 . If the target then moves close to MR element  342 , MR element  342  will detect the reflected magnetic field from the target and produce an output signal indicating the target was detected. The processor receiving the output signals can then identify the location of the target as above or near MR element  342 . 
     A single large target may be placed in front of the grid  332 ,  334  and  336 . Then the difference of reflected fields experienced by each MR element is a mapping of the parallelism of the target and the plane of the grid. It can be also used to map the deformations of the target as function of an external constraint. 
     Referring to  FIG. 4 , a system  400  for detecting a target  402  may use a single coil and MR element to detect target  402 . MR element  404  may be placed proximate to coil  406 . In an embodiment, MR element  404  may be placed between coil  406  and target  402 . In other embodiments, the traces of coil  406  may be placed between MR element  404  and target  402  (not shown). 
     In the single coil configuration, MR element  404  may be subject to a magnetic field even in the absence of magnetic target  402 . If magnetic target  402  is absent, there will be no eddy current and no reflected magnetic field. However, because MR element  404  is placed proximate to a single coil  406 , and not placed between two opposing coils, it may be subject to a directly coupled magnetic field  405  produced by the coil  406 . 
     The presence of target  402  may result in a reflected magnetic field and this additional field can be detected by MR element  404  to indicate the presence of target  402 . For example, current through coil  406  may produce eddy currents (shown by currents  408  and  410 ) in target  402 , which may produce reflected magnetic field  412 . Reflected magnetic field  412  may increase the strength of the magnetic field experienced by MR element  404 . Thus, when target  402  is present, MR element  404  may detect a stronger magnetic field than when target  402  is absent. 
     The proximity of target  402  may also increase or decrease the strength of the reflected magnetic field detected by MR element  404 . As target  402  moves closer to coil  406  (or vice versa), the eddy currents (shown by currents  408 ′ and  410 ′) will increase in strength, which will produce a reflected magnetic field  412 ′ with greater strength. Thus, MR element  404  will detect stronger magnetic field as target  402  moves closer to coil  406 . 
     In the embodiment shown in  FIG. 4 , MR element  404  is positioned adjacent to loops of coil  406 . This may result in greater sensitivity of MR element  404  to detect reflected field  412 . However, because the field produced by coil  406  is not zero at the position of MR element  404 , MR element  404  may also detect not only the reflected field, but also the magnetic field directly produced by the coil  406 , i.e. a “directly coupled” magnetic field. Various techniques may be used to reduce MR element  404 &#39;s sensitivity to the directly coupled magnetic field. 
     Referring to  FIG. 5 , circuit  500  includes a coil  502  and four MR elements 1-4 placed above or below traces of coil  502 . The MR elements may be connected in a bridge configuration  504 . The bridge configuration may provide a differential output consisting of signals  504   a  and  504   b.    
     In embodiments, circuit  500  may be used as a single-coil circuit for detecting a target. For example, as a target approaches MR elements 1 and 2, output signal  504   a  may change, and as the target approaches MR elements 3 and 4, output signal  504   b  may change. MR elements 1-4 may be aligned so that, as the target approaches elements 1-4, output signal  504   a  increase in value and output signal  504   b  decreases in value, or vice versa. For example, in such embodiments, the field created by the coil near the elements 1 and 2 is opposite is sign compared to the field created by the coil near the elements 3 and 4. Hence the reflected fields are in opposite direction enhancing the sensitivity of the bridge differential output to the reflected field while suppressing the variation due to external common fields. 
     Referring to  FIG. 5A , circuit  500 ′ includes a coil  506  arranged so that, if current flows through coil  506  in the direction shown by arrow  508 , the current will flow through coil portion  510  in a clockwise direction and through a counter-loop coil portion  512  in a counterclockwise direction. Thus, coil portions  510  and  512  may produce local magnetic fields having opposite direction, as described above. MR elements 1-4 may be arranged as shown to form a bridge that provides a differential signal as the target approaches. The counter-loop may reduce the directly-coupled magnetic field produced by the coil and detected by the MR elements. For example, a magnetic field produced by coil  506  may be directly detected by (e.g. directly coupled to) MR elements 1-4. Coil portions  510  and  512  may each create a local magnetic field in the opposite direction of the magnetic field produced by coil  506 . Thus, the local magnetic fields may (at least partially) cancel out the directly coupled field produced by coil  506  at least in the local area around MR elements 1-4. This may reduce or eliminate the directly-coupled field as detected by MR elements 1-4 so that the magnetic field detected by MR elements 1-4 is the reflected field from the target. 
     In embodiments, the counter-loop is used to measure reflected field and the direct field of the coil to provide sensitivity detection. Also, in this configuration, MR elements 1-4 can be placed so they do not see the field created by the main coil. 
     In embodiments, the target may be positioned adjacent to MR elements 1 and 3, but not 2 and 4 (or vice versa). If MR elements 1-4 are arranged in a bridge formation, a differential output of the bridge may change as the target moves toward or away from MR elements 1 and 3, for example. 
     In embodiments, the target may be positioned so that MR elements 1 and 2 experience the reflected magnetic field in one direction (e.g. experience one side of the reflected magnetic field) and MR elements 3 and 4 experience the reflected magnetic field in the opposite direction (e.g. experience the other side of the reflected magnetic field). In this embodiment, as the target moves closer to the MR elements, signal  504   a  may increase and signal  504   b  may decrease (or vice versa) to produce a differential signal. 
     Referring to  FIG. 5B , circuit  500 ″ includes two MR bridges. MR bridge  514  includes MR elements 1-4 and produces a differential output signal consisting of signals  514   a  and  514   b , whereas MR bridge  516  includes MR elements  508  and produces a differential output signal consisting of signals  516   a  and  516   b . As a target approaches the MR elements 1-8, the output signals of MR bridges  514  and  516  may change to indicate the presence and proximity of the target. Circuit  500 ″ is also shown with bond pads  518 . 
     In an embodiment, the target may be positioned adjacent to bridge  514  (MR elements 1-4) so that the differential output of bridge  514  is affected as the target moves closer to or further from bridge  514 . In this embodiment, the output of bridge  516  may remain relatively stable as the target moves. Thus, the output of bridge  516  may be used as a reference. In particular, this arrangement may work in situations where the target to be detected is relatively close to bridge  514 , so that movement of the target has a greater effect on bridge  514  and a smaller or zero effect on bridge  516 . 
     Additionally or alternatively, the same configuration can be used to measure a difference of distance, the first distance being between a large target and the lock of MR elements 1, 2, 3, and 4 and the second distance being between the corresponding target and MR elements 5, 6, 7, and 8. 
     Additionally or alternatively, the same configuration of  FIG. 5B  can be used to determine accurately the centering of a target along a plane perpendicular to the plane of the coil and crossing the plane of the coil along the line  530  situated at equal distance between the bridges  514  and  516 . 
     Referring to  FIG. 5C , circuit  501  includes a coil  520  and multiple MR elements  522  arranged at intervals around coil  520 . MR elements  522  may form a grid, similar to the grid described above and shown in  FIG. 3B . In embodiments, MR elements  522  may be connected in bridge configurations. In other embodiments, MR elements  522  may act (or be part of) individual circuits that are not shared with other MR elements. In either case, MR elements  522  may produce a signal when a target (and its reflected magnetic field) are detected. A processor may receive these signals and calculate the location, position, speed, parallelism, angle or other properties of the target. 
     In an embodiment, circuit  501  may be used to detect the position of the target in three dimensions with respect to the coil. Because the MR elements are positioned in a plane along coil  520 , they may act as a grid. As the target approaches one (or more) of the MR elements, they will produce an output signal that can be used to determine the location of the target along the two dimensions of the grid. Also, as described above, coil  520  and the MR elements may be used to detect distance from the MR elements in a direction orthogonal to the two dimensions of the coil and grid (i.e. a direction into and out of the page). 
     Referring now to  FIG. 6 , a circuit  600  for detecting a target may include a coil  602  and one or more MR elements  604  and  606 . Coil  602  may have two coiled portions  608  and  610 , separated by a gap  612 . In embodiments, the current through portions  608  and  610  flows in the same direction. For example, if the current through portion  608  flows in a clockwise direction around the coil, the current through portion  610  may also flow in a clockwise direction. 
     MR elements  604  and  606  may be placed within the gap so that they are not directly above (or below) traces of coil  602 . Placing MR elements within gap  612  may reduce capacitive or inductive coupling between coil  602  and MR elements  604  and  606 . Also, gap  612  may have a width W that is smaller than the distance between the MR elements and the target. As a result of gap  612  being relatively small, the eddy currents induced in the target and the resulting reflected magnetic field may appear (i.e. may be detected by the MR elements) as if a single coil without any gap between portions were producing the magnetic field. 
     In embodiments, positioning MR elements within gap  612  may reduce sensitivity of the MR elements to the directly coupled magnetic field produced by gap  612 , thus allowing the MR elements to maintain sensitivity to the reflected field. 
     In other embodiments, coil  602  may include a jog in one or more of the traces. MR elements  604  and  606  may be aligned with the jog. 
       FIG. 7  is a cross-sectional view of a circuit having MR elements  604  and  606  sandwiched between traces of coil  700 . In an embodiment, coil  700  may be the same as or similar to coil  602 . Coil traces  602   a  and  602   b  may be positioned on the surface of a substrate (not shown). MR elements  604  and  606  may be placed atop traces  602   a  and  602   b  so that traces  602   a  and  602   b  are positioned between MR elements  604  and  606  and the substrate. An additional layer of traces  614   a  and  614   b  may be positioned atop MR elements  604  and  606 . Traces  602   a ,  602   b ,  614   a , and  614   b  may be part of the same coil so that current flowing through the traces flows in a circular or spiral pattern to induce a magnetic field. Placing MR elements  604  and  606  between traces of the coil may reduce directly coupled magnetic field produced by the coil. 
     Referring to  FIG. 8 , a pressure sensor  800  includes a magnetic field sensor  802 , having a substrate  803  that supports a coil  804  and MR elements  806  and  808 . In embodiments, magnetic field sensor  802  may be the same as or similar to circuit  500  in  FIG. 5 , circuit  300  in  FIG. 3 , or any of the magnetic field detection circuits described above that can detect proximity of a target. 
     In embodiments, coil  804  and MR elements  806 ,  808  may be supported by the same substrate  803 . In other embodiments, MR element  806 , MR element  808 , and coil  804  may be supported on different substrates (not shown). For example, coil  804  may be supported by one substrate while MR elements  806  and  808  may be supported by a different substrate. In another example, MR element  806 , MR element  808 , and coil  804  may each be supported by a separate substrate. Any other combinations of substrates supporting circuit elements are also possible. 
     Pressure sensor  800  includes a chamber  810  having a conductive portion  811  and a deformable portion  812 . In an embodiment, chamber  810  is formed by an elongate tube. In the embodiment of  FIG. 8 , the conductive portion and the deformable portion  812  may comprise a membrane disposed at one end of the tube that can act a diaphragm, and can be deformed to move toward or away from magnetic field detection circuit  802 . 
     Deformable portion  812  may be formed of stainless steel, copper beryllium, titanium alloys, super alloys, and/or sapphire. When the pressure inside chamber  810  is greater than the pressure outside chamber  810 , deformable portion  812  may extend toward magnetic field detection circuit  802 . If the pressure outside chamber  810  is greater, deformable portion  812  may retract away from magnetic field detection circuit  812 , and if the pressure inside and outside chamber  810  is in equilibrium, deformable portion may adopt a neutral position between the extended and retracted positions. 
     In case of a circular deformable portion, the deformation of the membrane is given by the formula: 
     
       
         
           
             d 
             = 
             
               
                 3 
                 16 
               
               ⁢ 
               
                 p 
                 
                   Eh 
                   3 
                 
               
               ⁢ 
               
                 ( 
                 
                   1 
                   - 
                   
                     v 
                     2 
                   
                 
                 ) 
               
               ⁢ 
               
                 
                   ( 
                   
                     
                       a 
                       2 
                     
                     - 
                     
                       r 
                       2 
                     
                   
                   ) 
                 
                 2 
               
             
           
         
       
     
     Where h is the thickness of the deformable portion, v is the Poisson module, E is the young module, a is the radius of the deformable portion, r is the point where the deformation is measured. 
     In embodiments, the maximal deformation may be low enough that the deformable portion is always in the elastic domain of the material even at temperature above 180° C. For that reason, super alloys like maraging alloys or titanium alloys may be suitable materials. 
     Magnetic field detection circuit  802  may include at least one magnetic field sensing element  806  and/or  808  disposed proximate to coil  804 , as described above. Coil  804  may produce a magnetic field that induces eddy current and a reflected magnetic field in the conductive portion  812 , similar to the eddy currents and reflected fields described above. Magnetic field detection circuit  802  may also include a circuit to generate an output signal indicative of the pressure differential between the interior and exterior of chamber  810 . 
     In embodiments, magnetic field detection circuit  802  comprises two spaced apart MR elements  806  and  808  and detects a distance between the conductive portion  812  and one of the MR elements  806  and  808  as deformable portion extends toward and/or retracts away from the MR elements. In embodiments, magnetic field detection circuit  802  may be configured to detect a difference between a) the distance between the conductive portion  812  and magnetic field sensor  808 , and b) the distance between conductive portion  812  and magnetic field sensor  806 . The difference between these distances may be used to produce an output signal of magnetic field detection circuit  802 . 
     The output signal produced by magnetic field detection circuit  802  may represent the distance, which can then be received by a processor to calculate an associated pressure within chamber  810 . MR elements  806  and  808  may comprise multiple MR elements and may be arranged in a bridge configuration, as described above, to produce a differential output. 
     In an embodiment, MR element  806  is aligned with an edge of conductive, deformable portion  812  and MR element  808  is aligned with the center or a central region of conducive, deformable portion  812 . In this arrangement, MR element  808  will react as deformable portion  812  moves toward and away from MR element  808 , and MR element  806  will not be affected or will be affected to a significantly lesser degree than element  808 , and thus may have a relatively constant resistance value. Positioning the MR elements in this way may be used to remove errors due to stray field. It may also help compensate for air gap tolerance between MR elements. For example, the difference in distance detected by the two sensors may be used to compensate for small changes in air gap over time, temperature, etc. 
     Referring to  FIG. 8A , another embodiment of a pressure sensor  818  includes a first elongated tube  820  having a deformable sidewall  821  and an opening  823  that allows a fluid to enter a chamber within elongated tube  820 . As the fluid creates pressure within tube  820 , the sidewall  821  may expand like a balloon or extend. An end  828  of tube  820  may be conductive. 
     Pressure sensor  818  also includes a second elongated tube  822  having an opening  824 . Elongated tube  822  may have a rigid wall  826 , and an opening  824 . Opening  824  may have a diameter or size large enough for tube  820  to be inserted into opening  824 . 
     Pressure sensor  818  may include a magnetic field sensor  830 , which may be the same as or similar to magnetic field sensor  802 , and/or any of the magnetic field sensors described above. 
     In embodiments, when the tubes  820 ,  822  are assembled, conductive end  828  of tube  820  may be positioned proximate to MR element  808 . As the pressure within tube  820  increases and decreases, the rigid wall of tube  822 &#39;s may keep deformable sidewall  821  from expanding laterally. However, end  828  may expand and extend toward MR element  808  and retract away from MR element  808  as pressure within tube chamber  823  changes. Magnetic field sensor  830  may detect the change in distance and produce an output signal representing the distance between end  828  and MR element  808 . In embodiments, magnetic field detection circuit  802  may be configured to detect a difference between a) the distance between conductive end  828  and magnetic field sensor  808 , and b) the distance between conductive  808  and magnetic field sensor  806 . The difference between these distances may be used to produce an output signal of magnetic field detection circuit  830 . A processor circuit may receive the signal and calculate a pressure within tube  820  based on the distance. 
     Referring also to  FIG. 9 , pressure sensor  900  includes a first substrate  902 , that may be the same or similar to substrate  803  of  FIG. 8 , and a second substrate  904  attached to the first substrate  902 . Second substrate  904  may include a surface  908  and recess  906  formed in the surface. Recess  906  may be etched into the substrate. In embodiments, wafer  904  may be etched so that it is thin enough to deflect under pressure, as shown by dotted lines  910 . MR elements supported by substrate  902  may detect (via a reflected magnetic field as describe above) the deflection of wafer  904 . The detected deflection may be subsequently correlated to a pressure. 
     In embodiments, the MR elements on substrate  902  may be positioned so that one or more MR elements are adjacent to an edge (e.g. a non-deflecting portion) of recess  906  and one or more MR elements are adjacent to the center (e.g. a deflecting portion) of recess  906 , similar to the arrangement described above and illustrated in  FIG. 8A . 
     In embodiments, substrate  904  may be formed from a conductive material, for example copper. Therefore, motion of a conductive deformable portion of substrate  904  caused by pressure on substrate  904  (and/or pressure within recess  906 ) can be detected by a magnetic field sensors on substrate  902 . 
     Alternatively the substrate  904  may be formed by a crystalline material like sapphire coated by a thick enough conductive material like copper for example. 
     In embodiments, recess  906  is evacuated during the manufacturing process to determine a reference pressure. In embodiments, the reference pressure is a vacuum or a pressure that is less than standard pressure (e.g. less than 100 kPa). In certain configurations, one or more of the output signals of an MR bridge (e.g. bridge  318  in  FIG. 3A ) may be used to generate to represent the value of the reference pressure. 
     Referring to  FIG. 10 , a block diagram of a magnetic field sensor  1000  is shown. Magnetic field sensor includes a coil  1002  to produce a magnetic field, coil driver  1004  to provide power to the coil, MR element  1006 , and MR driver circuit  1008  to provide power to MR element  1006 . MR element  1006  may be a single MR element or may comprise multiple MR elements, which may be arranged in a bridge configuration. As described above, coil  1002  and MR element  1006  may be configured to detect the distance of a conductive target. In embodiments, coil driver  1004  and/or MR driver  1008  may produce an AC output to drive coil  1002  and MR element  1008 , as described above and as indicated by AC source  1010 . AC source  1010  may be a common source used to drive both coil  1002  and MR element  1006 . In embodiments, signal  1012  may be an AC signal. 
     Magnetic field sensor  1000  also includes an amplifier to amplify the output signal  1012  of MR element  1006 . Output signal  1012  may be a differential signal and amplifier  1014  may be a differential amplifier. Output signal  1012  and amplified signal  1016  may a DC signal. 
     Magnetic field sensor  1000  may also include a low pass filter  1018  to filter noise and other artifacts from signal  1016 , and an offset module  1024  which may scale the output signal according to temperature (e.g. a temperature measure by temperature sensor  1020 ) and a type of material according to material type module  1022 . A segmented linearization circuit  1026  may also be included, which may perform a linear regression on compensated signal  1028  and produce output signal  1030 . 
     In embodiments, the reflected magnetic field from the target will have a frequency f (the same frequency as the coil driver  1004 ). Because the magnetic field produced by coil  1002  and the reflected field have the same frequency, the output of MR element  1006  may include a 0 Hz (or DC) component, a component at frequency f, and harmonic components at multiples of frequency f. One skilled in the art will recognize that the lowest frequency harmonic component may occur at frequency 2*f. However, any difference in the equilibrium of the MR bridge may generate a frequency component that may be present in the signal. Thus, low pass filter  1018  may be configured to remove the frequency f and higher (i.e. low pass filter  1018  may include a cut-off frequency f cutoff , where f cutoff &lt;f. In embodiments, the filter may be designed to remove possible f signals. Accordingly, the frequency f may be chosen as a frequency greater than the frequency range of motion of the target. 
     In embodiments, the sensitivity of MR element  1008  changes with temperature. The strength of the reflected field may also change with temperature depending of target material type and frequency. To compensate, module  1022  may contain parameters to compensate for the effects of the temperature and/or material used. The parameters may include linear and/or second order compensation values. 
     In embodiments, processing circuit  1032  may process the signal representing the magnetic field. Because a common source  1010  is used to drive MR element  1006  and coil  1002 , the frequency of coil  1002  and MR element  1006  is substantially the same. In this case, post processing of the signal may include filtering, linear regression, gain and amplification, or other signal shaping techniques. 
     MR element  1006  may detect the magnetic field directly produced by coil  1002  and also the reflected magnetic field produced by eddy currents in a conductive target, induced by the magnetic field generated by current through coil  1002 . 
     Referring to  FIG. 10A , magnetic field sensor  1000 ′ may include coil  1002 , coil driver  1004 , common AC source  1010 , MR driver  1008 , MR element  1006 , amplifier  1014 , and low pass filter  1018  as described above. 
     Magnetic field sensor  1000 ′ may differ from sensor  1000  of  FIG. 10  in that it is a closed loop sensor and so may also include a second coil  1035 , which may operate at a different AC frequency than coil  1002 . In this example, coil  1035  may be 180 degrees out of phase with coil  1002  as indicated by the “−f” symbol. Coil  1035  may also produce a first magnetic field that can be used to detect a target. In embodiments, coil  1035  may be relatively smaller than coil  1002 . Coil  1035  may be placed adjacent to MR element  1006  to produce a magnetic field that can be detected by MR element  1006 , but which does not produce eddy currents in the target. 
     In embodiments, coil  1035  may be used to offset errors due to the magnetoresistance of the MR element. For example, the magnitude of current driven through coil  1035  may be changed until the output of MR element  1006  is zero volts. At this point, the current through coil  1035  may be measured (for example, by measuring voltage across a shunt resistor in series with coil  1035 ). The measured current may be processed similarly to the output of MR element  1006  to remove a magnetoresistance error associated with MR  1006 . 
     Magnetic field sensor  1000 ′ may also include an amplifier  1036  to receive signal  1038 . Magnetic field sensor  1000 ′ may also include low pass filter  1019 , material type module  1022 , temperature sensor  1020 , offset module  1024 , and segmented linearization module  1026  as described above. 
       FIGS. 11-11F  include various examples of magnetic field sensors having signal processing to reduce inductive coupling or other noise from affecting signal accuracy. The example magnetic field sensors in  FIGS. 11-11F  may also employ various features related to detecting a reflected field from a target, such as frequency hopping, etc. Such magnetic field sensors may also include circuitry to compute a sensitivity value. 
     Referring now to  FIG. 11 , a magnetic field sensor  1100  may include coil  1002 , coil driver  1004 , AC driver  1010 , MR driver  1008 , MR element  1006 , amplifier  1014 , low pass filter  1018 , temperature sensor  1020 , material type module  1022 , offset module  1024 , and segmented linearization module  1026 . 
     MR element  1006  may be responsive to a sensing element drive signal and configured to detect a directly-coupled magnetic field generated by coil  1002 , to produce signal  1012  in response. Processing circuitry may compute a sensitivity value associated with detection, by MR element  1006 , of the directly-coupled magnetic field produced by coil  1002 . The sensitivity value may be substantially independent of a reflected field produced by eddy currents in the target. 
     As shown, AC driver  1010  is coupled to coil driver  1004 , but is not coupled to MR driver  1008  in sensor  1100 . In this embodiment, MR driver  1008  may produce a DC signal (e.g. a signal with a frequency of about zero) to drive MR element  1006 . 
     Coil  1002  may produce a DC (or substantially low frequency AC) magnetic field that can be detected by MR element  1006 , but which does not produce eddy currents in the target. The signal produced by detection of the DC (or substantially low frequency AC) magnetic field may be used to adjust sensitivity of the magnetic field sensor. 
     Coil  1002  may also produce an AC magnetic field at higher frequencies that induces eddy currents in the target, which produce a reflected magnetic field at those higher frequencies that can be detected by MR element  1006 . 
     MR element  1006  may produce signal  1012 , which may include frequency components at the DC or substantially low AC frequency (e.g. a “directly coupled” signal or signal component) representing the lower frequency magnetic field that does not cause eddy currents in the target, and/or frequency components at the higher AC frequency (e.g. a “reflected” signal or signal component) that represent the detected reflected field. The directly coupled signals may be used to adjust sensitivity of the sensor while the reflected signals may be used to detect the target. Coil driver  1004  and/or MR driver  1008  may use the directly coupled signals as a sensitivity signal adjust their respective output drive signals in response to the sensitivity signal. 
     In embodiments, the directly coupled signal and the reflected signal may be included as frequency components of the same signal. In this case, coil  1002  may be driven to produce both frequency components at the same time. In other embodiments, generation of the directly coupled signal and the reflected signals may be generated at different times, for example using a time-division multiplexing scheme. 
     Sensor  1100  may also include a demodulator circuit  1050  that can modulate signal  1016  to remove the AC component from the signal or shift the AC component within the signal to a different frequency. For example, demodulator circuit  1050  may modulate signal  1016  at frequency f. As known in the art, because signal  1016  includes signal components at frequency f representing the detected magnetic field, modulating signal  1016  at frequency f may shift the signal elements representing the detected magnetic field to 0 Hz or DC. Other frequency components within signal  1016  may be shifted to higher frequencies so they can be removed by low-pass filter  1018 . In embodiments, the DC or low frequency component of signal  1016 , which may represent a sensitivity value, can be fed back to coil driver  1004  to adjust the output of coil  1002  in response to the signal, and/or to MR driver  1008  to adjust drive signal  1009  in response to the sensitivity value. DC output signal  1052  may represent proximity of the target to MR element  1006 . 
     In other embodiments, a time-division multiplexing scheme may be used. For example, coil driver  1004  may drive coil  1002  at a first frequency during a first time period, at a second frequency during a second time period, etc. In some instances, the first and second (and subsequent) time periods do not overlap. In other instances, the first and second time periods may overlap. In these instances, coil driver  1004  may drive coil  1002  at two or more frequencies simultaneously. When the first and second time periods do not overlap, demodulator  1050  may operate at the same frequency as the coil driver  1004 . When the time periods overlap, multiple modulators can be used, the first running at the first frequency, and the second running at the second frequency in order to separate out the signals at each frequency. 
     While it can be advantageous to reduce the directly coupled magnetic field that the MR element  1006  detects in order to achieve an accurate read of the reflected field (and thus the detected target), it may also be advantageous to have some amount of direct coupling (i.e., to directly detect the magnetic field produced by coil  1002 ) to permit a sensitivity value to be computed. The simultaneous measure of both the field reflected and the field created by the coil allows to determine accurately the distance of the object independent of the sensitivity of the MR elements, coil drive current, etc. . . . The sensitivity of MR elements may vary with temperature and/or with the presence of unwanted DC or AC stray fields in the plane of the MR array. The ratio between the reflected field and the coil field is just dependent on geometrical design and is hence a good parameter to accurately determine a distance. 
     Referring to  FIG. 11 , a frequency hopping scheme may be used. For example, coil driver  1004  may drive coil  1002  at different frequencies (e.g. alternate between frequencies over time, or produce a signal containing multiple frequencies). In such embodiments, sensor  1100  may include multiple demodulator circuits and/or filters to detect a signal at each frequency. 
     Referring to  FIG. 11A , a magnetic field sensor  1100 ′ includes coil  1002 , coil driver  1004 , AC driver  1010 , MR driver  1008 , MR element  1006 , amplifier  1014 , low pass filter  1018 , temperature sensor  1020 , material type module  1022  and offset module  1024 . 
     As shown, AC driver  1010  is coupled to coil driver  1004  to drive coil  1002  at a frequency f1. MR driver  1008  is coupled to AC driver  1102  to drive MR element  1006  at a frequency f2. Frequencies f1 and f2 may be different frequencies and may be non-harmonic frequencies (in other words, f1 may not be a harmonic frequency of f2 and vice versa). In embodiments, frequency f1 is lower than frequency f2. In other embodiments, frequency f1 and f2 may be relatively close to each other so that the difference between the two frequencies falls well below f1 and f2. Frequency f2 may be a zero value or non-zero-value frequency but alternatively, we may choose f1 larger than f2. Then the demodulation is done at f2-f1. 
     In an embodiment, frequency f1 may be selected to avoid generating an eddy current greater than a predetermined level in the target and/or selected to provide full reflection in the target. The reflected field may be related to the skin depth in the target according to the following formula: 
     
       
         
           
             δ 
             = 
             
               1 
               
                 
                   σμπ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   f 
                 
               
             
           
         
       
     
     In the formula above, σ is the conductivity of the target material, μ is the magnetic permittivity of the target material, and f is the working frequency. If the thickness of the target material is larger than about 5 times the skin depth δ, the field may be totally reflected. In the case where the thickness of the target is equal to the skin depth, only about the half of the field may be reflected. Hence a frequency f chosen to be low enough so the skin depth becomes larger than the thickness of the target may induce low eddy currents and a reflected field with reduced strength. The formula given above may be valid for high conductive and low magnetic materials. For material with low conductivity or for ferromagnetic material, losses of the eddy currents, which may be translated at a complex skin depth, may result in reduction of reflected field strength. 
     Circuit  1100 ′ may also include a band pass filter  1104  and a demodulator circuit  1106 . Band pass filter  1104  may have a pass band that excludes frequencies f1 and f2 but conserves frequency |f1−f2|. In this way, inductive noise from the coil and/or GMR driver into the magnetic sensors may be filtered out. Circuit  1100 ′ may also include a demodulator circuit  1106  that demodulates at frequency |f1−f2| and a low pass filter to recover a signal centered around DC, which may represent the magnetic field seen by the magnetic sensors at f1. In embodiments, the signal at frequency |f1−f2| may include information about the target and/or the directly coupled magnetic field, but may have reduced noise from inductive coupling or other noise sources. 
     Referring now to  FIG. 11B , a magnetic field sensor  1100 ″ includes coil  1002 , coil driver  1004 , AC driver  1010 , MR driver  1008 , MR element  1006 , amplifier  1014 , low pass filter  1018 , temperature sensor  1020 , material type module  1022 , offset module  1024 , and segmented linearization module  1026 . 
     As shown, AC driver  1010  is coupled to coil driver  1004 , but is not coupled to MR driver  1008  in sensor  1100 . In this embodiment, MR driver  1008  may produce a DC signal (e.g. a signal with a frequency of about zero) to drive MR element  1006 . 
     Coil  1002  may produce an AC magnetic field that induces eddy currents and a reflected magnetic field in a target. 
     Sensor  1100 ″ may also include a demodulation circuit  1060  that can demodulate signal  1016 . Demodulation circuit  1060  may multiply signal  1016  by a signal at frequency f, which may shift information about the target in signal  1016  to DC, and may shift noise or other information in the signal to higher frequencies. Low pass filter  1018  may the remove the noise at higher frequencies from the signal. In embodiments, demodulation circuit  1060  may be a digital circuit that demodulates signal  1016  in the digital domain or an analog signal the demodulates signal  1016  in the analog domain. 
     Sensor  1100 ″ may also include a phase detection and compensation circuit  1062  that detects the phase and/or frequency of the current in coil  1002  and the magnetic field it produces. Circuit  1062  may detect and compensate for discrepancies in phase in coil  1002  and f and produce a corrected signal  1063  that can be used to modulate signal  1016 . 
     In embodiments, the frequency f, the type of material of the target, the shape of the target, wiring and electronics, and/or other factors may cause a phase shift between the drive signal  1010  to coil  1002  and the reflected magnetic field detected by MR element  1008 . The phase between the signals can be measured and used to adjust the phase of signal  1063  from phase detection and compensation circuit  1062  to match the phase of signal  1016 . 
     A frequency hopping scheme may also be used. For example, coil driver  1004  and/or MR driver  1008  may drive signals at multiple frequencies. At each frequency, phase detection and compensation module  1062  may adjust the phase of signal  1063  to match the phase of signal  1016 . 
     Referring now to  FIG. 11C , a magnetic field sensor  1100 ′″ includes coil  1002 , coil driver  1004 , AC driver  1010 , MR driver  1008 , MR element  1006 , amplifier  1014 , temperature sensor  1020 , material type module  1022 , offset module  1024 , and segmented linearization module  1026 . 
     As shown, AC driver  1010  is coupled to coil driver  1004 , but is not coupled to MR driver  1008  in sensor  1100 . In this embodiment, MR driver  1008  may produce a DC signal (e.g. a signal with a frequency of about zero) to drive MR element  1006 . 
     Coil  1002  may produce an AC magnetic field that induces eddy currents and a reflected magnetic field in a target. The reflected magnetic field can be detected by MR element  1006 , which produces signal  1012  representing the detected magnetic field. 
     Sensor  1100 ′″ may also include a fast Fourier transform (FFT) circuit  1070  that can perform an FFT on signal  1016 . Performing the FFT may identify one or more frequency components in signal  1016 . In an embodiment, FFT circuit  1070  may identify the frequency component with the greatest amplitude in signal  1016 , which may represent the detected magnetic field at frequency f. FFT circuit  1070  may produce an output signal  1072  including the detected signal at frequency f, as well as any other frequency components of signal  1016 . 
     Alternatively, the driver can generate simultaneously different frequencies fa, fb, fc, and the FFT module may calculate the amplitudes at fa, fb, fc, which may be used to determine different parameters of the target including position, material, thickness, etc. In addition, if a disturbance (e.g. from a deformation of the target, a stray magnetic field, a noise source, etc.) occurs at a particular frequency, the system can detect the disturbance and ignore data at that frequency. The amplitudes calculated by the FFT module may also be used to determine if there is a disturbance at any particular frequency, which can be ignored by subsequent processing. In embodiments, the FFT temperature gain compensation and linearization may be calculated in the analog and/or digital domain. 
     Referring now to  FIG. 11D , a magnetic field sensor  1100 D includes coil  1002 , coil driver  1004 , MR driver  1008 , and MR element  1006 . The output signal  1007  of MR sensor  1006  may represent a detected magnetic field. Although not shown, sensor  1100 D may also include amplifier  1014 , low pass filter  1018 , temperature sensor  1020 , material type module  1022 , offset module  1024 , and segmented linearization module  1026 . An oscillator  1182  may be used to operate coil driver  1004  at a frequency f. 
     As shown, oscillator  1182  is coupled to coil driver  1004 , but is not coupled to MR driver  1008  in sensor  1100 D. In this embodiment, MR driver  1008  may produce a DC signal (e.g. a signal with a frequency of about zero) to drive MR element  1006 . 
     Sensor  1100 D also includes a quadrature demodulation circuit  1180 . Quadrature demodulation circuit  1180  includes shift circuit  1188  to produce a 90° shift of the driving frequency f. Oscillator  1182  may produce a cosine signal at frequency f. Thus, the output of  1188  may be a sine signal at frequency f. Hence by a multiplication in the demodulators  1190  and  1192  (and subsequent low pass filtering), the detected signal of the MR sensor  1006  may be separated into in-phase and out-of-phase components (e.g. signals  1184   a  and  1186   a ). The resulting phase and magnitude can be used to determine information about the reflected field and the target. For example, phase information may be used to determine if there is a defect or abnormality in the target, to determine magnetic properties of the material of the target, whether the target is aligned properly, etc. Oscillator  1182  may also produce a square wave with period 1/f, and shift circuit  1188  may shift the square wave in time by 1/(4f). 
     Referring to  FIG. 11E , in another embodiment, magnetic field sensor  1100 E may produce a quadrature modulated signal via two signal paths as an alternative to providing both the in-phase and out-of-phase information. In circuit  1100 E, half of the MR elements may be driven by a signal at frequency f and half of the MR elements may be driven with a frequency 90° out of phase. The demodulation chain (e.g. the circuits that comprise a demodulation function of the system) may be the same as or similar to the demodulation circuits in  FIG. 10  including a low pass filter at DC and compensation and linearization. 
     In embodiments, quadrature modulation may be used to determine the absolute magnitude and phase of the returned signal. This may allow for automatic correction of unwanted dephasing of the signal, which may provide a more accurate determination of target properties and retrieval of information related to magnetic or loss properties of the material. 
     Referring to  FIG. 11F , a magnetic field sensor  1100 F includes coil driver  1004  that drives coil  1002  at a frequency of f 1 . MR driver  1008  may drive MR element at the same frequency f 1 , but 90 degrees out of phase with respect to coil drive  1004 . As a result, the signal  1016  produced by MR element  1006  may have a frequency that is two times f 1  (i.e. 2*f 1 ), which may be a result of multiplying a sine and a cosine. Sensor  1100 F may include a demodulator circuit  1195  that may demodulate the signal to convert the reflected field information to a frequency around DC. 
     Referring to  FIG. 12 , signal  1270  may represent a signal used by coil driver  1004  to drive coil  1002 . When the signal is high, coil driver  1004  may drive coil  1002  with current flowing in one direction, and when the signal is low, coil driver may drive coil  1002  with current flowing in the opposite direction. In embodiments, coil driver  1004  may drive coil  1002  with direct current (i.e. at DC) or at a frequency sufficiently low so that the magnetic field produced by coil  1002  does not create eddy currents in the target. 
     As an example, referring to the skin depth formula above, the skin depth of copper at r 50 Hz may be about 10 mm and at 10 kHz it may be about 600 μm. Hence, given a 0.5 mm thick copper target, a frequency below 5 kHz may create reflected magnetic fields with relatively low strength. 
     Coil driver  1004  may drive coil  1002  at a relatively low or DC frequency, as shown by signal portions  1272  and  1274 . The frequency may be sufficiently low, and thus the duration of portions  1272  and  1274  may be sufficiently long, so that any eddy currents generated in the target by switching of signal  1270  (for example, switching from a high value during portion  1272  to a low value during portion  1274 ) have time to settle and dissipate. The directly-coupled signal shown during portions  1272  and  1274  may switch from high to low (representing a change in the detected magnetic field) in order to remove any offset due to the directly-coupled magnetic field of coil  1002 . 
     Portion  1276  of signal  1270  may represent the magnetic field detected by MR element  1006  while coil driver  1004  drives coil  1002  at a frequency sufficiently high to induce eddy currents in the target. While portion  1276  is active, MR element  1006  may detect the directly-coupled magnetic field produced directly by coil  1002 , and also the magnetic field produced by eddy currents in the target. The detected signal may be subsequently processed to separate the directly-coupled field from the field produced by the eddy currents. Although not shown, portion  1276  may have a larger or smaller magnitude than portion  1272  because the portions may contain different information. For example, portion  1276  may include the reflected signal as well as the directly-coupled signal. 
     As shown in signal  1270 , low frequency portions  1272  and  1274  of different polarities may be adjacent to each other within signal  1270 . In other embodiments, as shown in signal  1270 ′, low frequency portions  1272 ′ and  1274 ′ of different polarities may not be adjacent to each other within the signal. For example, they may be separated by high frequency signal portion  1276 . 
     In other embodiments, the coil may be driven at both the low frequency (of low frequency portions  1272  and  1274 ) and at the high frequency (of high frequency portion  1276 ) simultaneously. The frequencies may then be separated using signal processing techniques to measure a MR element&#39;s response. 
     In certain instances, the ration of the low frequency portions  1272  and  1274  to the high frequency portion  1276  can be used to determine or indicate the magnitude of the reflected signal. Measuring the ratio in this way may reduce sensitivity of the magnitude measurement to external, unwanted variations such as variations due to temperate, stray magnetic fields, etc. 
     Referring now to  FIG. 12A , magnetic field sensor  1200  may be configured to adjust the output signal of the magnetic field sensor in response to the sensitivity value. Sensor  1200  may include a coil  1202  and coil driver  1204 . MR element  1206  may detect a magnetic field produced by coil  1202 , and as reflected by a target, as described above. In embodiments, the output signal  1208  of MR element  1206  may comprise a first frequency and a second frequency. For example, the first frequency may be the frequency of the coil driver, and the second frequency may be 0 Hz, or DC. In this case, MR element  1206  may be driven by a DC bias circuit  1210 . In other examples, the second frequency may be a non-zero frequency. 
     In another embodiment, coil driver  1204  may drive coil  1202  at one frequency during a first time period, and by another frequency during a second time period. The time periods may alternate and not overlap. 
     Sensor  1200  may also include a separator circuit, which may include one or more low pass filters  1214  and  1216 , as well as demodulators  1224  and  1226 . Sensor  1200  may also include mixer circuit  1212 . Oscillators  1218  and  1220  may provide oscillating signals used to drive coil  1202  and process signal  1208 . In embodiments, oscillator  1220  may provide a signal with a higher frequency (f high ) than that of oscillator  1218  (f low ). In embodiments, f low  is a sufficiently low frequency so that any reflected field produced by the target as a result of frequency flow is zero, sufficiently small that it is not detected, or sufficiently small so that its effect on the output is negligible or within system tolerances. 
     Mixer  1212  may mix (e.g. add) the signals from oscillator  1218  and  1220  to produce signal  1222 , which it feeds to coil driver  1204 . Coil driver  1204  may then drive coil  1202  according to the mixed signal  1202 . 
     Because coil  1202  is driven by the mixed signal, output signal  1208  may include oscillations at f high  and f low  as detected by MR sensor  1206 . Demodulator  1226  may demodulate signal  1208  at frequency f high  in order to separate the portion of signal  1208  at frequency f high  from other frequencies in the signal. One skilled in the art may recognized that the demodulation process may result in the other frequencies being shifted to higher frequencies in the signal. Low pass filter  1214  may then remove these frequencies from the signal and produce a filtered signal  1228  comprising primarily information at frequency f high  or at DC. 
     Similarly, demodulator  1224  may demodulate signal  1208  at frequency f low  in order to separate the portion of signal  1208  at frequency f low  from other frequencies in the signal. One skilled in the art may recognized that the modulation process may result in the other frequencies being shifted to higher frequencies in the signal. Low pass filter  1216  may then remove these frequencies from the signal and produce a filtered signal  1230  comprising primarily information at frequency f low  or at DC. Processing circuit  1232  may process signals  1228  and  1230  to produce output signal  1232  representing the detected target. 
     Processing circuit  1232  may process signals  1228  and  1230  in various ways including, taking the ratio of the signals to provide an output that is substantially insensitive to undesirable variations caused by stray magnetic field interference, temperature shifts, package stresses, or other external stimuli. Taking the ratio of the signals can also provide an output that is substantially insensitive to variations in the coil driver (e.g. variations in current or voltage provided by the coil driver) due to temperature, changes in supply voltage, external stimuli, etc. 
     Signal  1230  may also be used as a sensitivity signal fed into DC bias circuit  1220 , as shown by arrow  1234 . DC Bias circuit  1210  may adjust the voltage level used to drive MR element  1206  based on the value of signal  1230 , to compensate for changes in system sensitivity due to temperature, stray magnetic fields, package stress, etc. 
     Referring to  FIG. 12B , magnetic field sensor  1200 ′ may be similar to sensor  1200 , and may also include an additional in-plane field coil  1236 . DC bias circuit  1236  may drive coil  1232  with a DC current to create a constant magnetic field. The constant magnetic field may be detected directly by MR element  1206  and may be a biasing magnetic field. In other embodiments, the magnetic field produced by in-plane field coil  1232  may be used to generate a signal proportional to the MR sensitivity, which can be detected by MR element  1206  and subsequently fed back and used to adjust the sensitivity of circuit  1200 ′. In embodiments, the magnetic field produced by in-plane field coil  1232  may be perpendicular to the magnetic field produced by coil  1202  and used to increase/decrease the sensitivity of the MR element. DC bias circuit  1236  may drive coil  1232  in such a way to compensate for changes in sensitivity seen by the closed loop system. In other words, DC bias circuit may change the magnitude of the driving current supplied to coil  1232  in response to feedback signal  1234  to compensate for sensitivity errors up to the bandwidth of the feedback loop system. The bandwidth may be determined (or at least heavily influenced) by the cutoff frequency of filter  1216 . 
     As shown, DC bias circuit  1236  may receive signal  1230  and adjust the amount of current provided to in-plane field coil  1232 , which may subsequently adjust thus the strength the magnetic field produced by in-plane field coil  1232 . Although not shown in  FIG. 12B , DC bias circuit  1210 ′ may also receive signal  1230  and use it to adjust the current that drives MR element  1206 . In embodiments, DC bias circuit  1210 ′, DC bias circuit  1236 , or both may adjust their outputs based on signal  1230 . 
     Referring to  FIG. 12C , a magnetic field sensor  1240  includes oscillator  1220 , oscillator  1218 , and mixer  1212 . Coil driver  1204  receives the signal produced by mixer  1212  and drives coil  1202  with a signal comprising frequencies f high  and f low . 
     Sensor  1240  may include two (or more) MR elements  1254  and  1256 . MR driver  1250  may be coupled to oscillator  1220  and may drive MR sensor  1254  at frequency f high , and MR driver  1252  may be coupled to oscillator  1218  and my driver MR sensor  1256  at frequency f low . Low pass filter  1216  may filter output signal  1258  from MR sensor  1254  and low pass filter  1264  may filter output signal  1260  from MR sensor  1256 . Due to the frequencies at which MR sensors  1254  and  1256  are driven, output signal  1258  may include a frequency component at f high  and output signal  1260  may include a frequency component at f low . Filtered signal  1230  may be a sensitivity signal that can be used to adjust the sensitivity of sensor  1240 . Thus, signal  1230  may be fed back to MR driver  1252 , MR driver  1250 , and/or coil driver  1204 , which may each adjust their output based on the value of signal  1230 . In embodiments, signal  1230  may be a DC or oscillating signal. 
     Referring to  FIG. 13 , a circuit  1300  includes a coil  1302  and MR elements 1-8 arranged in bridge configurations. Coil  1302  may include so called countercoil portions  1304 A, B and  1306 A, B. First countercoil portion  1304 A may produce a field to the left for MR elements below it. Subsequently, portion  1304 B may produce a field to the right, portion  1306 A may produce a field to the right, and portion  1306 B may produce a field to the left. MR elements 1 and 3 are positioned near countercoil portion  1304 A and MR elements 2 and 4 are positioned near countercoil portion  1304 B. MR elements 5, 6 are positioned near countercoil portion  1306 A, and MR elements 7, 8 are positioned near countercoil portion  1306 B. Also, the MR bridges are split so that some of the elements in each bridge are located near countercoil portion  1304  and some of the elements are located near countercoil portion  1306 . For example, MR bridge  1308  comprises MR elements 1 and 3 (positioned near countercoil portion  1304 ) and MR elements 5 and 6 (positioned near countercoil portion  1306 ). Providing countercoil portions  1304  and  1306  may influence the magnitude and polarity of the directly coupled field on the MR elements. 
     MR elements 1, 3 may have a first coupling factor with relation to coil  1302 , MR elements 2, 4 may have a second coupling factor, MR elements 5 and 6 may have a third coupling factor, and MR elements 7, 8 may have a fourth coupling factor with relation to coil  1302 . In an embodiment, the coupling factor of MR elements 1, 3, 7, and 8 may be equal and opposite to the coupling factor of MR elements 2, 4, 5, and 6. This may be due, for example, to coil portions  1304 A, B and  1306 A, B carrying equal current in opposite coil directions, as well as the positioning of the MR elements in relation to them. 
     In an embodiment, bridges  1308  and  1310  will respond to a reflected field equally. However, they may respond oppositely to the directly coupled field. The addition of the outputs of the two bridges may contain information about the reflected field and the subtraction of the two bridges may contain information about the directly coupled field. The directly coupled field information can then be used as a measure of system sensitivity and be used to normalize the reflected field information. In another embodiment, bridges  1308  and  1310  respond to a reflected field equally. However, they may respond differently (not necessarily exactly oppositely) to the directly coupled field. The subtraction of the two bridges still results in a signal only containing information about the directly coupled field, which can be used as a measure of system sensitivity. The addition of the two bridges may include some directly coupled field information along with information about the reflected field. However, this can be compensated for with the linearization block, as it shows up as a constant offset. 
     For example, during operation, the following formulas may apply:
 
 V   bridge1 =( C   r   +C   1 )* i*S   1  
 
 V   bridge2 =( C   r   +C   2 )* i*S   2  
 
     In the formulas above, C r  represents the reflected field, C 1  represents the directly coupled field detected by the first MR bridge, C 2  represents the directly coupled field detected by the second MR bridge, i is the current through the coil, S 1  represents the sensitivity of the first MR bridge, and S 2  represents the sensitivity of the second MR bridge. Assuming that S1=S2 and solving for Cr: 
     
       
         
           
             
               C 
               r 
             
             = 
             
               
                 
                   
                     ( 
                     
                       V 
                       
                         bridge 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       C 
                       1 
                     
                     ) 
                   
                 
                 - 
                 
                   
                     ( 
                     
                       V 
                       
                         bridge 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       C 
                       2 
                     
                     ) 
                   
                 
               
               
                 
                   V 
                   
                     bridge 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 - 
                 
                   V 
                   
                     bridge 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
               
             
           
         
       
     
     The equation above provides a formula for C r  independent of current and sensitivity of the MR elements. In embodiments, the geometry of the coil, MR elements, and target my provide that C 1 =−C 2 . In other embodiments, the geometry of the system may provide other ratios of C 1  and C 2 . With a known ratio, C r  can be computed to provide a value for the reflected field. 
     Referring to  FIG. 13A , a coil  1302 ′ may include countercoil portions  1304 ′A, B and  1306 ′A, B and gap between coil elements. In  FIG. 13A , only the middle portion of coil  1302 ′ and MR elements 1-8 are shown. 
     The countercoil portions  1304 ′ and  1306 ′ may each be placed in a respective gap  1350  and  1352  between traces of the main coil. MR elements 1-8 may be placed within the gaps of the main coil. As with the gap in  FIG. 6 , placing the MR elements within gaps  1350  and  1350  may reduce sensitivity of the MR elements to the directly coupled magnetic field. Thus, a coil design for coil  1302 ′ may adjust sensitivity of the MR elements to the directly coupled field by including gaps  1350  and  1352  to reduce the sensitivity and countercoil portions  1304 ′ and  1306 ′ to increase the sensitivity in order to achieve the desired direct coupling on each element. In an embodiment, the direct coupling field is similar in magnitude to the reflected field. 
     Referring to  FIG. 13B , magnetic field sensor  1320  may include coil  1302 , MR bridge  1308 , and MR bridge  1310  as arranged in  FIG. 13 . Coil driver  1322  may drive coil  1302  at frequency f. MR driver  1324  may drive one or both MR bridges  1308  and  1310  at 0 Hz (i.e. DC) or at another frequency. 
     Demodulator  1324  and demodulator  1326  may demodulate the output signals from MR bridges  1308  and  1310 , respectively, at frequency f. This may shift the frequency components of the signals at frequency f to 0 Hz or DC, and may shift other frequency components in the signal to higher frequency bands. Low pass filters  1328  and  1330  may the remove the higher frequency components from the signals and provide a DC signal V1 (corresponding to the magnetic field detected by MR bridge  1308  and a DC signal V2 (corresponding to the magnetic field detected by MR bridge  1310 ) to processing block  1332 . Processing block  1332  may process signals V1 and V2 to produce a signal representing the detected target. In an embodiment, processing block may perform the operation X=(V1+V2)/(V1−V2), where X is the signal representing the detected target. In this embodiment, the position of the MR of the bridges  1308  and  1310  are chosen in a way that the first bridge sees a negative signal from the coil (directly coupled field) and the second an opposite signal from the coil. Both bridges may see the same reflected signal. Hence V1+V2 may substantially comprise the reflective signal and V1−V2 the coil signal. The ratio gives then a quantity X which is independent on the sensitivity change of the MR elements due to the temperature or stray fields for example, as well as variations in coil current. In this embodiment, the position of the MRs (and/or coils) may be chosen so that each MR is seeing (e.g. can detect) a coil signal and a reflected signal of the same range of amplitude i.e. typically a reflected field varying from 0.1% to 100% of the direct detected field. 
     Referring now to  FIG. 14 , system  1400  includes a magnetic field sensor  1402  and target  1404 . Magnetic field sensor  1402  may be the same as or similar to magnetic field sensor  100  and/or any of the magnetic field sensors described above. Accordingly, magnetic field sensor  1402  may include a coil to produce a magnetic field and produce eddy currents within conductive target  1404 , and one or more magnetic field sensing elements to detect a reflected field from the eddy currents. 
     The skin effect of target  1404  may be used to detect linear, speed, and angle (in the case of a rotating target) measurements by controlling the amount of reflected magnetic signal, and using the amount of reflected signal to encode the target position. A target can be created by combining a high conductivity material (shallow skin depth, measured with high frequency signal) and relatively low-conductivity materials (deep skin depth, measured using a medium or low frequency signal). The target can be created by milling or etching a linear slope or digital tooth pattern into the low conductivity material. In a subsequent step a high conductivity material can be deposited over the surface then milled or polished to create a planar surface. Alternatively, the low conductivity material can be omitted. 
     Measurement techniques can also utilize various frequencies (of coil  1002  for example) and the skin effect of the target. A relatively high frequency and shallow skin depth can be used to measure the air gap distance between the sensor and the face of the target. This signal can then be used to calibrate the sensitivity of the system. A medium frequency with a skin depth that exceeds the maximum thickness of the high conductivity material may be used to sense the position of the portion of the target formed by the low conductivity material. A relatively low frequency signal (e.g. low enough that it is not reflected by the target) may be used to measure the overall sensitivity of the MR sensors and provide feedback to compensate for any changes in sensitivity due to stray field, temperature, or package stresses. Referring again to  FIG. 14 , target  1404  may comprise a first material portion  1406  and a second material portion  1408 . First material portion  1406  may be a high-conductivity material, such as a metal; and second material portion  1408  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. In embodiments, the first and second material portions  1406  and  1408  may be a unitary structure as may be integrally formed or may be separate elements physically coupled to each other, as shown in  FIG. 14 . 
     The thickness  1410  of first material portion  1406  may vary along the length of target  1404  so that, at one end  1412 , first material portion  1406  is relatively thick and, at another end  1414 , first material portion  1406  is relatively thin. The eddy currents induced by magnetic field sensor  1402  at the thick end  1412  of first material portion  1406  may differ from those induced at the thin end  1414 . Accordingly, the reflected magnetic field produced at thick end  1406  may also differ from the reflected magnetic field produced at thin end  1414 . Because the thickness of first material portion  1406  varies linearly along the length of target  1404 , the reflected magnetic field may also vary linearly along the length of target  1404 . Thus, the magnetic field sensing elements of magnetic field sensor  1402  may detect the difference in the reflected magnetic field to determine where magnetic field sensor  1402  is positioned along the length of target  1404 . In embodiments, if a relatively high frequency is used to sense the airgap, the thickness at end  1414  may be chosen to be greater than one skin depth and less than five skin depths at the chosen frequency. The thickness at end  1412  may be chosen to be than one skin depth at a relatively lower frequency. 
     In embodiments, target  1404  may move in a linear direction (shown by arrow  1416 ) with respect to magnetic field sensor  1402 . As target  1404  moves, magnetic field sensor  1402  may detect changes in the reflected field to determine the position of target  1404  with respect to magnetic field sensor  1402 . Of course, in other embodiments, target  1416  may be stationary and magnetic field sensor  1402  may move with respect to target  1404 . 
     As another example, multiple frequencies may be used to determine air gap and solve for position of the target  1404 . For example, if the thickness of first material portion  1406  at end  1414  is greater than one skin depth at a frequency f1, then the response at frequency f1 may vary only as a function of air gap between target  1404  and the MR elements. Using a second frequency, if the thickness of first material portion  1406  at end  1414  is less than one skin depth at a frequency f2, the response may vary as a function of both air gap and position of target  1404 . 
     Referring now to  FIG. 14A , system  1400 ′ may include magnetic field sensor  1402  and a rotating target  1418 , which may be in the shape of a cylinder, a gear, etc. Target  1418  may include a first material portion  1420  and a second material portion  1422 . First material portion  1420  may be a high-conductivity material, such as a metal; and second material portion  1422  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. In embodiments, the first and second material portions  1420  and  1422  may be a unitary structure as may be integrally formed or may be separate elements physically coupled to each other, as shown in  FIG. 14 . 
     The thickness  1423  of first material portion  1420  may vary around the circumference of target  1418  as a function of angle around target  1418  so that, at point  1424 , first material portion  1420  is relatively thin and, at point  1426 , first material portion  1420  is relatively thick. The eddy currents induced by magnetic field sensor  1402  in thicker portions of first material  1420  may differ from those induced at thinner portions. Accordingly, the reflected magnetic field produced at point  1424  may also differ from the reflected magnetic field produced at point  1426 . Because the thickness of first material portion  1420  varies around the circumference of target  1418  as a function of an angle around target  1418 , the reflected magnetic field may also vary around the circumference. 
     Magnetic field sensor  1402  may be placed outside the radius of target  1418 , and adjacent to the outside surface of target  1418 . Thus, the magnetic field sensing elements of magnetic field sensor  1402  may detect the difference in the reflected magnetic field to determine the rotational angle of target  1418 . Magnetic field sensor  1402  may also detect rotational speed and/or direction of target  1418 . 
     Referring now to  FIG. 14B , system  1400 ″ may include magnetic field sensor  1402  and a rotating target  1428 . Target  1428  may include a first material portion  1430  and a second material portion  1432 . First material portion  1430  may be a high-conductivity material, such as a metal; and second material portion  1432  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. In embodiments, the first and second material portions  1430  and  1432  may be a unitary structure as may be integrally formed or may be separate elements physically coupled to each other, as shown in  FIG. 14 . 
     In  FIG. 14B , the thickness of first material portion  1430  may extend into the page. The thickness of first material portion  1430  may vary around the circumference of target  1428  as a function of an angle around target  1428  so that, at point  1434 , first material portion  1430  is relatively thick and, at point  1436 , first material portion  1430  is relatively thin. The eddy currents induced by magnetic field sensor  1402  in thicker portions of first material  1430  may differ from those induced at thinner portions. Accordingly, the reflected magnetic field produced at point  1434  may also differ from the reflected magnetic field produced at point  1436 . Because the thickness of first material portion  1430  varies around the circumference of target  1428 , the reflected magnetic field may also vary around the circumference. 
     Magnetic field sensor  1402  may be placed inside the radius of target  1428 , and adjacent to the substantially flat face  1440  of target  1428 . In other words, if target  1428  is placed at the end of a rotating shaft, magnetic field sensor  1402  may be positioned adjacent to the face of one end of the shaft. Thus, the magnetic field sensing elements of magnetic field sensor  1402  may detect the difference in the reflected magnetic field to determine the rotational angle of target  1428 . Magnetic field sensor  1402  may also detect rotational speed and/or direction of target  1418 . 
     Magnetic sensor  1402  can be mounted in a gradiometer mode as illustrated, for example, in  FIG. 3A . Half of the gradiometer may be situated at in a position where the distance between the conductive part  1450  and the target remains substantially constant and half of the gradiometer may be situated in a position where the slope  1404  of the conductive material is present. The difference between the two signals may be used to suppress unwanted fluctuations due to the vibration of the target. 
     Referring to  FIG. 15 , system  1500  may include magnetic field sensing element  1502  and target  1504 . Magnetic field sensor  1502  may be the same as or similar to magnetic field sensor  100  and/or any of the magnetic field sensors described above. Accordingly, magnetic field sensor  1502  may include a coil to produce a magnetic field and produce eddy currents within target  1504 , and one or more magnetic field sensing elements to detect a reflected field from the eddy currents. 
     Target  1504  may comprise a first material portion  1506  and a second material portion  1508 . First material portion  1506  may be a high-conductivity material, such as a metal; and second material portion  1508  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. In embodiments, the first and second material portions  1506  and  1508  may be a unitary structure as may be integrally formed or may be separate elements physically coupled to each other, as shown in  FIG. 14 . 
     First material portion  1506  may comprise a series of alternating wells  1510  and valleys  1512 . Wells  1510  may have a thickness  1514  relatively greater than the thickness of valleys  1512 . Accordingly, the reflected magnetic field produced within wells  1510  may differ from the reflected magnetic field produced at valleys  1512 . Thus, the magnetic field sensing elements of magnetic field sensor  1502  may detect the differing magnetic fields produced by wells  1510  and valleys  1512  as target  1504  moves relative to magnetic field sensor  1502 . The detected magnetic fields may be used to detect speed, position, rotational angle, and/or direction of magnetic target  1500 , for example. 
     System  1500 ′ may include magnetic field sensor  1502  and target  1516 . Target  1516  may comprise one or more first material portions  1518  and a second material portion  1520 . First material portions  1518  may be a high-conductivity material, such as a metal; and second material portion  1522  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. 
     First material portions  1518  may comprise a series of discrete wells positioned in a spaced arrangement along the length of target  1516 . Accordingly, when magnetic field sensor  1502  is adjacent to a tooth  1518 , a reflected magnetic field will be produced and detected. When magnetic field sensing element is adjacent to an insulating area (e.g. area  1522 ), a reflected magnetic field may not be produced by the insulating area  1522 . Thus, the magnetic field sensing elements of magnetic field sensor  1502  may detect the reflected magnetic fields produced by wells  1518  and detect when no reflected magnetic field is produced as target  1516  moves relative to magnetic field sensor  1502 . The detected magnetic fields may be used to detect speed and/or direction of magnetic target  1516 , for example. 
     Referring to  FIG. 15A , system  1522  may include magnetic field sensor  1502  and rotating target  1524 . Target  1524  may comprise first material portion  1526  and a second material portion  1528 . First material portion  1526  may be a high-conductivity material, such as a metal; and second material portion  1528  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. 
     First material portions  1526  may comprise one or more teeth  1530  positioned in a spaced arrangement around the circumference of target  1524  at various angles around target  1524 . Although two teeth are shown, target  1524  may include one tooth, two teeth, or more teeth in spaced relation around the circumference of target  1524 . The teeth may be spaced evenly or in an uneven pattern. 
     Accordingly, when magnetic field sensor  1502  is adjacent to a tooth  1530 , a reflected magnetic field will be produced and detected. When magnetic field sensing element is not adjacent to tooth, a reflected magnetic field with a different strength may be produced by first material portion  1526 . Thus, the magnetic field sensing elements of magnetic field sensor  1502  may detect the reflected magnetic fields produced by teeth  1530 , and the reflected magnetic field produced by areas of first material  1526  without teeth, as target  1524  rotates relative to magnetic field sensor  1502 . The detected magnetic fields may be used to detect speed and/or direction of magnetic target  1500 , for example. 
     Referring to  FIG. 15B , system  1522 ′ may include magnetic field sensor  1502  and rotational  1532 . Target  1532  may comprise one or more first material portions  1534  and a second material portion  1536 . First material portions  1534  may be a high-conductivity material, such as a metal; and second material portion  1536  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. 
     First material portions  1534  may comprise a series of discrete wells positioned in a spaced arrangement around a radial circumference of target  1532 . First material portions  1530  may be spaced evenly, or according to any type of pattern. Accordingly, when magnetic field sensor  1502  is adjacent to one of the first material portions  1534 , a reflected magnetic field will be produced and detected. When magnetic field sensor  1502  is adjacent to an insulating area (e.g. area  1538 ), a reflected magnetic field may not be produced by the insulating area  1538 . Thus, the magnetic field sensing elements of magnetic field sensor  1502  may detect the reflected magnetic fields produced by first material portions  1534  and detect when no reflected magnetic field is produced by insulating areas  1538  as target  1532  rotates relative to magnetic field sensor  1502 . The detected magnetic fields may be used to detect rotational speed and/or direction of magnetic target  1532 , for example. 
     Magnetic field sensor  1502  may be placed inside the outermost radius of target  1532 , and adjacent to a substantially flat face  1540  of target  1532 . In other words, if target  1532  is placed at the end of a rotating shaft, magnetic field sensor  1502  may be positioned adjacent to the face of one end of the shaft. Thus, as target  1532  rotates, the magnetic field sensing elements of magnetic field sensor  1502  may detect first material portions  1534  as they pass by. 
     Referring to  FIG. 15C , system  1522 ″ may include magnetic field sensor  1502  and rotational target  1532 . Target  1532  may comprise one or more first material portions  1534 ′ and a second material portion  1536 . First material portions  1534  may be a high-conductivity material, such as a metal; and second material portion  1536  may be a relatively low-conductivity material, such as a plastic, ceramic, or other insulating material; or vice versa. 
     First material portions  1534 ′ may comprise several series of discrete wells positioned in a spaced arrangement around different radial circumference of target  1532 . First material portions  1530  may be spaced evenly, or according to any type of pattern. Accordingly, when magnetic field sensor  1502  is adjacent to one of the first material portions  1534 , a reflected magnetic field will be produced and detected. When magnetic field sensor  1502  is adjacent to an insulating area (e.g. area  1538 ), a reflected magnetic field may not be produced by the insulating area  1538 . Thus, the magnetic field sensing elements of magnetic field sensor  1502  may detect the reflected magnetic fields produced by first material portions  1534  and detect when no reflected magnetic field is produced by insulating areas  1538  as target  1532  rotates relative to magnetic field sensor  1502 . The second radial series of wells may be arranged so that each well  1560  in the second radial series is placed adjacent to a gap  1562  between the wells  1534  in the first radial series. As magnetic field sensor  1502  detects each radial series, there may be a 90-degree shift of phase or a different pitch between detection of the first radial series of wells and the second radial series of wells, which may be used to increase the accuracy of angle by a Vernier type of approach. 
     Magnetic field sensor  1502  may be placed inside the outermost radius of target  1532 , and adjacent to a substantially flat face  1540  of target  1532 . In other words, if target  1532  is placed at the end of a rotating shaft, magnetic field sensor  1502  may be positioned adjacent to the face of one end of the shaft. Thus, as target  1532  rotates, the magnetic field sensing elements of magnetic field sensor  1502  may detect first material portions  1534  as they pass by. 
     Referring to  FIG. 16 , system  1600  may include a first magnetic field sensor  1602 , a second magnetic field sensor  1604 , and a rotating target  1606 . Magnetic field sensors  1602  and  1604  may be the same as or similar to magnetic field sensor  100  and/or any of the magnetic field sensors described above. 
     Target  1606  may include a spiral inclined plane  1608  positioned around a central axis  1610 . In embodiments, central axis  1610  may be a rotating shaft. Target  1606  may also include a conductive reference portion  1612 . Reference portion  1612  and inclined plane  1608  may be formed from conductive material. 
     In an embodiment, magnetic field sensor  1602  is positioned adjacent to reference portion  1612 . A coil of magnetic field sensor  1602  produces a magnetic field, which in turn produces eddy currents in reference portion  1612 . Magnetic field sensor  1602  may detect the reflected magnetic field produced by the eddy currents. 
     Similarly, magnetic field sensor  1604  may be positioned relative to inclined plane  1608 . A coil of magnetic field sensor  1608  may produce a magnetic field, which in turn may produce eddy currents in a portion  1614  of inclined plane adjacent to magnetic field sensor  1604 . Magnetic field sensor  1604  may detect the reflected magnetic field produced by the eddy currents in inclined plane  1608 . 
     As target  1606  rotates, the portion  1614  of inclined plane  1608  adjacent to magnetic field sensor  1604  will move toward and/or away from magnetic field sensor  1604 . The proximity D of portion  1614  to magnetic field sensor  1604  can be detected by magnetic field sensor  1604 . Processing circuitry (not shown) can correlate the proximity D to a rotational angle of target  1606  and determine position, speed of rotation, direction of rotation, etc. 
     Referring to  FIG. 16A , system  1600 ′ may include a grid of magnetic field sensors  1616 , and a rotating target  1606 . 
     Target  1606  may include a spiral inclined plane  1608  positioned around a central axis  1610 . In embodiments, central axis  1610  may be a rotating shaft. Target  1606  may also include a conductive reference portion  1612 . Reference portion  1612  and inclined plane  1608  may be formed from conductive material. 
     In an embodiment, magnetic field sensor  1602  of grid  1616  is positioned adjacent to reference portion  1612 . A coil of magnetic field sensor  1602  produces a magnetic field, which in turn produces eddy currents in reference portion  1612 . Magnetic field sensor  1602  may detect the reflected magnetic field produced by the eddy currents. 
     The other magnetic field sensors  1618   a - h  may be positioned in various locations on the grid  1616  relative to inclined plane  1608 . A coil of each of magnetic field sensors  1618   a - h  may produce a magnetic field, which in turn may produce eddy currents in a portion of the inclined plane adjacent to each magnetic field sensor  1618   a - h , which may each detect the local reflected magnetic field produced by the eddy currents in inclined plane  1608 . 
     As target  1606  rotates, the portions of inclined plane  1608  adjacent to magnetic field sensors  1618   a - h  will move toward and/or away from magnetic field sensors  1618   a - h . The proximity D of any portion  1614  to any magnetic field sensor  1618   a - h  can be detected by each magnetic field sensor. Processing circuitry (not shown) can correlate the proximity D to a rotational angle of target  1606  and determine position, speed of rotation, direction of rotation, etc. 
     Referring to  FIG. 16A , a plurality of sensors  1618   a - h  forming a grid may be used to measure the distance of the spiral at different points so it allows to correct vibrations of the spiral on directions perpendicular to the axe of rotation whereas the central sensor of the grid is suppressing the vibrations along the axe of rotation. 
     Referring to  FIG. 17 , a substrate  1700  may support one or more of the magnetic field sensor circuits described above, including coils and magnetic field sensing elements. Substrate  1700  may be positioned (and adhered to) frame  1702 . Substrate  1700  may be a semiconductor substrate, a glass substrate, a ceramic substrate, or the like. Bond wires  1704  may electrically couple connection pads on substrate  1700  to leads of frame  1702 . Frame  1702  may be a lead frame, a pad frame, or any structure that can support substrate  1700 . 
     In embodiments, substrate  1700  may support coil  1701 , which may be the same as or similar to the coils described above. Coil  1701  may produce a magnetic field that may induce eddy current and a reflected magnetic field in a target and/or a magnetic field that may be directly coupled to (e.g. directly detected by) MR elements. As shown, coil  1701  may be positioned adjacent to (or opposite) a gap  1703  in frame  1702 . If frame  1702  is a conductive material (such as metal), the magnetic field produced by coil  1701  could induce eddy currents and a reflected field from frame  1702 . Placing coil  1701  near gap  1703  may reduce or eliminate any unwanted reflected field that might otherwise by generated by frame  1702 . 
     In  FIG. 17A , substrate  1706  may support one or more of the magnetic field sensor circuits described above, including coils and magnetic field sensing elements. Substrate  1706  may be positioned (and adhered to) lead frame  1707 . Substrate  1706  may include one or more vias  1708 , which may be coupled to solder balls (or solder bumps)  1710 . Solder balls  1710  may be coupled to leads of lead frame  1707  to provide an electrical connection between vias  1708  and leads of lead frame  1707 . The electrical connection may couple the sensor circuitry (generally supported by one surface of substrate  1700 ) to external system and components through leads  1707 . 
     In embodiments, substrate  1706  may support coil  1709 , which may be the same as or similar to the coils described above. Coil  1709  may produce a magnetic field that may induce eddy current and a reflected magnetic field in a target and/or a magnetic field that may be directly coupled to (e.g. directly detected by) MR elements. As shown, coil  1709  may be positioned adjacent to (or opposite) a gap  1705  in frame  1707 . If frame  1707  is a conductive material (such as metal), the magnetic field produced by coil  1709  could induce eddy currents and a reflected field from frame  1707 . Placing coil  1709  near gap  1705  may reduce or eliminate any unwanted reflected field that might otherwise by generated by frame  1707 . 
     In embodiments, the grid of sensors  1608   a - h  in  FIG. 16A  may be formed on the surface of substrate  1700  or  1706 . 
     Referring to  FIG. 18 , a magnetic field sensor circuit  1800  may be supported by one or more substrates. As shown in  FIG. 18 , a first substrate  1802  may support one or more coils  1804 ,  1806 , which may produce a magnetic field. A second substrate  1808  may support one or more magnetic field sensing elements  1810 , which may detect the reflected magnetic field as discussed above. The semiconductor dies  1802 ,  1808  may also include additional circuitry discussed above. Circuits supported by substrate  1802  may be electrically coupled to circuits supported by substrate  1808  with lead wires (not shown). The supported circuits may also be coupled to leads of a frame  1811  by lead wires. A semiconductor package (not shown) may enclose the substrates. 
     In an embodiment, second die  1808  may be glued to a top surface of first die  1802 . Alternatively, die  1808  may be reversed and electrically connected to die  1802  with die-to-die electrical connections. 
     The magnetic fields produced by coils  1804  and  1808  may cancel each other out in the area between coils  1804  and  1806 , i.e. the area where MR elements  1810  are positioned. Thus, substrate  1808  may be positioned so that MR elements  1810  fall within the area where the magnetic fields cancel, to minimize any stray or directly coupled field detected by MR elements  1810 . 
     In embodiments, substrates  1802  and  1808  may be different types of substrates. For example, substrate  1802  may be an inexpensive substrate for supporting metal traces such as coils  1804  and  1806 , while substrate  1808  may be a substrate for supporting MR elements and/or other integrated circuits. 
     Referring to  FIG. 18A , a magnetic field sensor circuit  1800 ′ may be supported by multiple semiconductor dies. As shown, a first die  1812  may support two (or more) sets of coils. A first set of coils may include coils  1814  and  1816 . A second set may include coils  1818  and  1820 . A second die  1822  may support a first set of magnetic field sensing elements  1824 , and a third die  1826  may support a second set of magnetic field sensing elements  1828 . 
     In an embodiment, magnetic field sensor circuit  1800 ′ may include two magnetic field sensors. The first sensor may include coils  1814  and  1816 , die  1822 , and magnetic field sensing elements  1824 . The second magnetic field sensor may include coils  1818  and  1820 , die  1826 , and magnetic field sensing elements  1828 . In other embodiments, magnetic field sensor circuit  1800 ′ may include additional magnetic field sensors comprising additional coils, dies, and magnetic field sensing elements. 
     Magnetic field sensor circuit  1800 ′ may be used in any of the systems described above that employ two (or more) magnetic field sensors. Additionally or alternatively, the two magnetic field sensors in circuit  1800 ′ may be driven at different frequencies to avoid cross-talk between the two sensors. 
     Referring to  FIG. 19 , a magnetic field sensor circuit  1900  may be supported by multiple substrates. A first substrate may support coil  1902 . Four smaller substrates  1904 - 1910  may each support one or more magnetic field sensing elements. As shown, substrates  1904 - 1910  may be positioned adjacent to traces of coil  1902 . In some embodiments, substrates  1904 - 1910  may be positioned so the magnetic field sensing elements they support are placed adjacent to gap  1912  between traces of coil  1902 . 
     A fifth substrate  1914  may support circuitry to drive coil  1902  and the magnetic field sensing elements, as well as processing circuitry to process signals received from the magnetic field sensing elements. Circuits on the various die may be coupled together by lead wires  1916 . 
     Although not shown, in another embodiment, the larger substrate  1402  may support the coils and MR elements. The smaller substrate  1904 - 1908  may support circuitry to drive the coils and MR elements and/or circuits to process the magnetic field signals. 
     In an embodiment, the magnetic field sensing elements and coil  1902  may be the same as or similar to the magnetic field sensing elements (e.g. MR elements) and coils described in some or all of the magnetic field detection systems described above. 
     Having described preferred embodiments, which serve to illustrate various concepts, structures and techniques, which are the subject of this patent, it will now become apparent to those of ordinary skill in the art that other embodiments incorporating these concepts, structures and techniques may be used. Accordingly, it is submitted that that scope of the patent should not be limited to the described embodiments but rather should be limited only by the spirit and scope of the following claims. All references cited herein are hereby incorporated herein by reference in their entirety.