Patent Publication Number: US-10309992-B2

Title: Stray magnetic field rejection for in-hole current-measurement systems

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to as the National Stage of International Application No. PCT/US2014/031807 filed on Mar. 26, 2014 and entitled STRAY MAGNETIC FIELD REJECTION FOR IN-HOLE CURRENT-MEASUREMENT SYSTEMS, which claims priority to: 1) U.S. Provisional Patent Application Ser. No. 61/872,351 entitled ACCURACY IMPROVEMENT FOR CURRENT SENSOR IMBEDDED IN THE CONDUCTOR, and filed Aug. 30, 2013, and 2) U.S. Provisional Patent Application Ser. No. 61/876,104 entitled CURRENT SENSOR IMBEDDED IN METAL CONDUCTOR, and filed Sep. 10, 2013, all three of which are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     Various embodiments relate generally to current measurement using sensors embedded within a conductor carrying current to be measured. 
     BACKGROUND 
     Current sensors are widely used to determine the consumption of electricity and controlling devices operated with electrical current. Current sensors are also used for scientific analyses and experiments. Measuring large currents can be done by measuring the magnetic field surrounding a conductor. But these high-current sensors can be large. Often these large current sensing devices surround the conductor with a magnetic core. A step-down transformer may be used to attenuate the large signal that high-currents produce. These step-down transformers may also be used to generate an opposing magnetic field to permit the use of low-field sensors. These step-down transformers can be expensive large and heavy. Adjacent electrical conductors sometimes carry large currents as well. These adjacent current carrying conductors also generate magnetic fields which can interfere with the measurement. The magnetic cores and step-down transformers increase the size, weight, and cost of current measurement systems. 
     SUMMARY 
     Apparatus and associated methods relate to a measurement system that calculates a current in a conductor based on an odd-order spatial derivative function of signals representing magnetic-field strengths within a hole in the conductor. In an illustrative embodiment, the odd-order spatial derivative function may generate an output signal representing a spatial derivative of the in-hole magnetic field greater than the first-order. The three or more magnetic-field sensors may be configured to align on the hole&#39;s axis when inserted into the hole. When inserted into the hole, the sensors may be aligned on an axis perpendicular to a direction of current flow and be responsive to a magnetic-field directed perpendicular to both the direction of current flow and the aligned axis. Some embodiments may advantageously provide a precise measurement indicative an electrical current in the electrical conductor while substantially rejecting a stray magnetic field originating from an adjacent electrical conductor. 
     Some embodiments may have three or more magnetic-field sensors and a transient-disturbance selection module configured to form an output signal from a selected subset of sensor signals while decoupling the output signals from a non-selected subset of sensor signals during a predetermined time window when a disturbance signal is expected at the non-selected set of sensor signals. In an illustrative example, a disturbance producing operation may be performed on alternating subsets of sensors while the undisturbed subset of sensors measures an electrical current in the electrical conductor. For example, each selected subset of sensors may be aligned on an axis configured to be mounted perpendicular to current flow within a hole in the electrical conductor. Some embodiments may advantageously provide continuous electrical current measurement while being uninterrupted by the predetermined transient disturbances. 
     Some embodiments may have two or more magnetic field sensing devices located approximately in the center of a hole located in a conductor. Each of the magnetic field sensing devices may measure the magnetic field along a specific direction at a location within the hole. Near the center of the hole, the magnetic field resulting from current carried by the conductor may be relatively small in the measured direction. The small magnetic fields at the sensor locations may permit the use of high-precision sensors. In some embodiments, the measurement differences between pairs of the two or more sensing devices may be used to determine a current carried by the conductor. The measurement differences may be substantially insensitive to stray magnetic fields. 
     Various embodiments may achieve one or more advantages. For example, some embodiments may permit the use of very sensitive current sensors. Some embodiments may include an array of Anisotropic Magnetoresistive sensors, for example. Such sensing devices may be manufactured on a single silicon die. This small die may be relatively inexpensive. A small device may permit adjacent bus bars to be located in close proximity one to another. A small device may facilitate installation and maintenance. Small measurement devices may permit the measurement of many different sizes and types of conductors. Measurement accuracy may be improved by permitting high-precision devices to be used. Measurement accuracy may be improved by the rejection of stray magnetic fields. A single unipolar supply voltage may be used in some embodiments. Various embodiments may be realized using low power. Low-cost solutions using various embodiments may be realized. The precision requirement for locating the sensor may be substantially relieved because of the relative position insensitivity of the sensor array. If more sensors are in the array than are needed, such redundancy may permit accurate measurements even after an individual sensor fails. 
     The details of various embodiments are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts a schematic drawing of a current carrying bus bar with an in-hole current sensor. 
         FIG. 2  depicts block diagram of an exemplary four sensor device for use in a position-insensitive stray-rejecting in-hole current sensor. 
         FIG. 3  depicts a perspective drawing of a bus bar with a hole for an in-hole sensor. 
         FIG. 4  depicts a graph of simulated magnetic field as a function of position within a hole. 
         FIG. 5  depicts a block diagram of an exemplary embodiment of an in-hole current sensing system. 
         FIG. 6  depicts three-dimensional finite-element simulation results of an experimental in-hole current measurement system. 
         FIG. 7  depicts experimental measurement results of the magnetic field as a function of current and position within an in-hole bus bar. 
         FIG. 8  depicts the residual error between measurement and a cubic curve-fit. 
         FIG. 9  depicts experimental results of an exemplary difference solution of an in-hole current measurement system. 
         FIG. 10  depicts photos of the experimental setup for collecting experimental data of an in-hole current measurement system. 
         FIG. 11  depicts an exemplary system for measuring current using an array of sensors located in a hole in a conductor. 
         FIG. 12  depicts a schematic of an exemplary signal processing circuit for an exemplary in-hole current measurement system. 
         FIG. 13  depicts a block diagram of an exemplary transient-disturbance-tolerant in-hole current-measurement system. 
         FIG. 14  depicts an exemplary set/reset circuit for aligning magnetic domains in an AMR sensor. 
         FIG. 15  depicts a block diagram of an exemplary AMR sensor system having set/reset and offset-nulling capabilities. 
         FIG. 16  depicts an exemplary timing diagram showing Set/Reset selection and ADC sampling timing. 
         FIG. 17  depicts an exemplary silicon substrate with four gradiometers patterned along an axis. 
         FIG. 18  depicts an exemplary AMR sensor with set/reset and offset straps. 
         FIG. 19  depicts and exemplary block diagram of both common-mode and differential mode offset nulling. 
         FIG. 20  depicts a flow chart of an exemplary method of calibrating an in-hole current-measurement system. 
         FIG. 21  depicts a flow chart of an exemplary method of measuring current in a conductor using an in-hole current-measurement device. 
         FIG. 22  depicts a flow chart of an exemplary method of performing set/reset operation while providing continuous current-measurement signals. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     To aid understanding, this document is organized as follows. First, the technique for using in-hole magnetic-field sensors to measure electrical current in an electrical conductor will be described, with reference to  FIGS. 1-6 . Then the rejection of stray magnetic fields by use of in-hole magnetic-field sensors will be described with reference to  FIGS. 7-10 . Then exemplary embodiments of in-hole current-measurement systems will be described with reference to  FIGS. 11-12 . The ability to make continuous current measurements while performing transient-disturbance operations on a subset of the magnetic field sensors will be described with reference to  FIGS. 13-16 . Finally, precise current measurements are facilitated by precisely locating the magnetic-field sensors on a single semiconductor substrate. Exemplary embodiments of a single IC implementation will be described with reference to  FIGS. 17-19 . 
       FIG. 1  depicts a schematic drawing of a current carrying bus bar with an in-hole current sensor. In  FIG. 1 , a bus bar  100  has a current sensing system  105  within a hole  110 . The bus bar  100  may carry high-current. The bus bar may be made of copper. In some embodiments, the bus bar may be made of aluminum. The bus bar  100  has a length  115  in the direction of current flow. At the ends of the length  115  are shown holes  120  for mounting the bus bar to current carrying conductors. The bus bar  100  has a width  125  and a depth  130 . The hole  110  traverses the entire depth  130 . The current sensing system  105  may have a circuit board  135  and a sensor projection  140 . On the sensor projection may be a sensor array  145 . In the depicted embodiment two sensor outputs  150 ,  155  are shown. The sensor array  145  is located substantially half way between a top surface  160  and a bottom surface  165  of the bus bar. The hole  110  is fashioned substantially in the middle of the width of the bus bar, and the sensor array  145  is located substantially in the middle of the hole  110 . The sensor array may be located in such a fashion so that a magnetic field is very modest, the magnetic field resulting from a longitudinal current flow in the bus bar. The magnetic field at the center of such a hole may be small enough to permit the use of very sensitive magnetic-field sensors even for measuring large bus bar currents. 
       FIG. 2  depicts block diagram of an exemplary four sensor device for use in a position-insensitive stray-rejecting in-hole current sensor. In  FIG. 2 , an array  200  of Anisotropic MagnetorResistive (AMR) sensors  205  is depicted. The array  200  may be fabricated upon a single silicon substrate, for example. In some embodiments separate sensors may be positioned adjacent to one another on a circuit board. Each AMR sensor  205  may be precisely separated one from another. The separation may result in each sensor measuring a magnetic field at a slightly different position within the hole  110 . The AMR sensors  205 , being fabricated on the same substrate, may respond similarly to a magnetic field. Good uniformity of sensor response may simplify sensor calibration. Sensor spacing may be very precise, which may minimize errors resulting from sensor spacing variations. The sensors may be located within a small distance one from another. Such close separation may permit the sensors  205  to all be located in a low magnetic field region of the hole  110 . Because the sensors may be located at a low-field position, a current in an offset strap may be sized to correspond to the expected maximum field of the array. In some embodiments, the magnetic field incident upon the sensor may be further decreased by providing an additional current-carrying conductor in close proximity to the sensor. The current carried by the conductor can be predetermined and established in an open-loop fashion. In some embodiments, the current can be determined in a close-loop fashion. In an exemplary embodiment, the field sensor measurement may be driven to zero by this feedback mechanism. In some embodiments, each current sensor may have an offset strap integrated on the same die as the sensor. The offset strap may carry current for the purpose of reducing or nulling the magnetic field incident upon the sensor. 
       FIG. 3  depicts a perspective drawing of a bus bar with a hole for an in-hole sensor. In  FIG. 3 , an exemplary bus bar  300  includes a circular hole  305  for use in an exemplary in-hole current-measurement system. An x-axis  310  defines an diameter of the hole  305  aligned with a width  315  of the bus bar  300 . A y-axis would be directed along a length of the bus bar  300 . The field sensors  205  may be positioned along the x-axis  310  and aligned to detect a magnetic field directed in a z-direction. The z-direction would be aligned with a thickness of the bus bar  300 . The magnetic field sensors  205  may be positioned along the x-axis  310  which is depicted to be located midway within the depth of the hole  305 . 
       FIG. 4  depicts a graph of simulated magnetic field as a function of position within a hole. In  FIG. 4 , a graph  400  has an x-axis  405  which represents the locations along the x-axis  310  at which a magnetic field sensor  205  is located. The graph  400  has a y-axis  410  indicating the magnetic field strength measured by the magnetic field sensor  205 . A function  415  indicates a functional relationship between sensor location and measured field strength. The function  415  indicates a cubic relationship between the x-location of the sensor and the measure magnetic field strength. This relationship may result from the hole geometry. Various hole geometries may produce different functional relationships, for example. In some embodiments, the sensors may be aligned to measure the magnetic field in a direction different than the z-direction. For example a y-direction magnetic field may be measured. 
       FIG. 5  depicts a block diagram of an exemplary embodiment of an in-hole current sensing system.  FIG. 5  depicts a system  500  of using multiple magnetic field sensors to accurately measure current flow. The magnetic field sensors may be distributed along a line transverse to the direction of current flow and within a hole in the conductor carrying the current. The depicted system  500  includes four magnetic field sensors  505 ,  510 ,  515 ,  520 . Three differential amplifiers  525 ,  530 ,  535  compute the difference between the signals of adjacent pairs of sensors. The difference signals are then digitized by ADCs  540 ,  545 ,  550  and sent to a signal processing unit  555 . A high-speed amplifier  565  bypasses the ADCs  540 ,  545 ,  550  to provide a fast response to rapid electrical current changes. Such a fast response may be used to report a short circuit event, for example. In some embodiments, the high-speed amplifier  565  may respond to current changes in as little as one micro-second. The signal processing unit  555  computes a coefficient for a desired modeling term of the modeled functional relationship of the measured magnetic field strength to the sensor position. In some embodiments, the computed coefficient is the highest-order term of a polynomial model, for example. The coefficient for the highest-order term may be substantially invariant to the actual sensor array position within the hole. In some embodiments more than one term coefficient may be computed. The computed term coefficients may be combined for use as a current indicator. The computed term coefficients may be combined so as to minimize the combined response to a stray field, for example. 
     Sensor alignment variations within the hole may result in a coordinate transformation of the functional model. Coordinate transformations may result in a change to some of the modeling term coefficients. Some of the modeling term coefficients may be invariant to coordinate transformations. Using invariant terms to measure the current may reduce the sensitivity to alignment. Some of the coefficients may be less sensitive to stray fields, for example. Using substantially stray-invariant coefficients may reduce the sensitivity to nearby conductors, for example. There are many different ways to compute a modeling term coefficient. In the depicted embodiment, signal differences between adjacent sensors are used to reduce the order of the polynomial by one degree. Other embodiments may use the sensor signals themselves and not the differences between adjacent sensors. One may use a four term polynomial model:
 
 z=dx   3   +cx   2   +bx+a  
 
     The coefficients of this model may be determined if one knows the positions of the sensors within the hole relative to an assigned coordinate system. The zero of the coordinate system may be chosen such that the center of the hole in the bus bar is the zero location. If one uses four sensors, the highest order coefficient can be obtained by solving the series of equations: 
     
       
         
           
             
               
                 [ 
                 
                   
                     
                       1 
                     
                     
                       
                         
                           - 
                           1.5 
                         
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         2.25 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         
                           - 
                           3.375 
                         
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       1 
                     
                     
                       
                         
                           - 
                           0.5 
                         
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         0.25 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         
                           - 
                           0.125 
                         
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       1 
                     
                     
                       
                         0.5 
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         0.25 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         0.125 
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       1 
                     
                     
                       
                         1.5 
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         2.25 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         3.375 
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                 
                 ] 
               
               ⁡ 
               
                 [ 
                 
                   
                     
                       a 
                     
                   
                   
                     
                       b 
                     
                   
                   
                     
                       c 
                     
                   
                   
                     
                       d 
                     
                   
                 
                 ] 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       z 
                       1 
                     
                   
                 
                 
                   
                     
                       z 
                       2 
                     
                   
                 
                 
                   
                     
                       z 
                       3 
                     
                   
                 
                 
                   
                     
                       z 
                       4 
                     
                   
                 
               
               ] 
             
           
         
       
     
     The solution to the above system of equations can be simply solved by inverting the matrix and multiplying the inverted matrix by the four magnetic field measurements (z 1 , z 2 , z 3 , z 4 ). The d coefficient here represents the cubic coefficient. If one assumes the Δ scaling terms into the coefficients (a, b, c, and d), one finds:
 
 d=− 0.167 z   1 +0.5 z   2 −0.5 z   3 +0.167 z   4  
 
     If one were to use more than four magnetic field sensors, one could still obtain a cubic coefficient by simply regressing the measured data to obtain the coefficients for a cubic function. The following system of equations would represent a five-sensor system: 
     
       
         
           
             
               
                 [ 
                 
                   
                     
                       1 
                     
                     
                       
                         
                           - 
                           2 
                         
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         4 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         
                           - 
                           8 
                         
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       1 
                     
                     
                       
                         
                           - 
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                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         1 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         
                           - 
                           1 
                         
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       1 
                     
                     
                       0 
                     
                     
                       0 
                     
                     
                       0 
                     
                   
                   
                     
                       1 
                     
                     
                       
                         1 
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         1 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         1 
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       1 
                     
                     
                       
                         2 
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         4 
                         ⁢ 
                         
                           Δ 
                           2 
                         
                       
                     
                     
                       
                         8 
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                 
                 ] 
               
               ⁡ 
               
                 [ 
                 
                   
                     
                       a 
                     
                   
                   
                     
                       b 
                     
                   
                   
                     
                       c 
                     
                   
                   
                     
                       d 
                     
                   
                 
                 ] 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       z 
                       1 
                     
                   
                 
                 
                   
                     
                       z 
                       2 
                     
                   
                 
                 
                   
                     
                       z 
                       3 
                     
                   
                 
                 
                   
                     
                       z 
                       4 
                     
                   
                 
                 
                   
                     
                       z 
                       5 
                     
                   
                 
               
               ] 
             
           
         
       
     
     The solution to the above system of equations can be simply solved by multiplying the measurement results (z 1 , z 2 , z 3 , z 4 , z 5 ) by the regression matrix. The regression matrix can be simply obtained using the A matrix, which multiplies the coefficient array (a, b, c, d). The regression is performed as follows: 
     
       
         
           
             
               [ 
               
                 
                   
                     a 
                   
                 
                 
                   
                     b 
                   
                 
                 
                   
                     c 
                   
                 
                 
                   
                     d 
                   
                 
               
               ] 
             
             = 
             
               
                 
                   ( 
                   
                     
                       A 
                       T 
                     
                     ⁢ 
                     A 
                   
                   ) 
                 
                 
                   - 
                   1 
                 
               
               ⁢ 
               
                 
                   A 
                   T 
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         
                           z 
                           1 
                         
                       
                     
                     
                       
                         
                           z 
                           2 
                         
                       
                     
                     
                       
                         
                           z 
                           3 
                         
                       
                     
                     
                       
                         
                           z 
                           4 
                         
                       
                     
                     
                       
                         
                           z 
                           5 
                         
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
     The d coefficient here again represents the cubic coefficient. Here A T  represents the transpose of the A matrix. When performing the above operation, only the d coefficient is needed. For the above example, the following d coefficient is found using the following equation:
 
 d=− 0.083 z   1 +0.167 z   2 −0.167 z   4 +0.083 z   5  
 
     Interestingly, the third (middle) sensor (z 3 ) is not used in the regression result. And using six uniformly spaced sensors results in:
 
 d=− 0.046 z   1 +0.065 z   2 +0.037 z   3 −0.037 z   4 −0.065 z   5 +0.046 z   6  
 
       FIG. 6  depicts three-dimensional finite-element simulation results of an experimental in-hole current measurement system. In  FIG. 6  a graph  600  shows that a quadratic coefficient for the system shows good (linear) correlation to the current in the bus bar. This quadratic coefficient may represent the system of  FIG. 5  in which the differences between adjacent sensors are used as inputs. In such a system, as will be shown, the quadratic coefficient is related to the cubic coefficient of the solution obtained using the sensor outputs themselves as inputs as described above. Also shown in  FIG. 6  is a graph  605  depicting the difference between the quadratic fit to that actual current. This may represent the error in using the quadratic coefficient as a measure of current. 
       FIG. 7  depicts experimental measurement results of the magnetic field as a function of current and position within an in-hole bus bar. In  FIG. 7  a graph  700  has an x-axis  705  indicating the x-location of a magnetic field sensor. The graph  700  also has a y-axis  710  indicating the measurement of the magnetic field. Each line  715  corresponds to a different value of current flowing in a conductor. As the current increases, the slope of the field measurement increases. The graph  720  has an x-axis  725  indicating the x-location of a magnetic field sensor. The graph  720  also has a y-axis  730  indicating the measure magnetic field. Again each line  735  corresponds to a value of current flowing in a conductor. The graph  720  differs from the graph  700  because in graph  720 , a stray conductor is carrying a large current (e.g. 20 Amps). The stray conductor is located immediately adjacent to the conductor whose current is being measured. The graph  720  is substantially translated in the y-axis direction as a result of the 20 Amps of current flowing in the adjacent conductor. The functional dependencies of the magnetic field measurements to x-location are otherwise substantially invariant to the stray current. This graph indicates that using the high-order functional coefficient to measure the current may provide a measure of stray rejection. 
       FIG. 8  depicts the residual error between measurement and a cubic curve-fit. In  FIG. 8  a graph  800  indicates the residual difference between the cubic curve fit for each of the lines  715  and a cubic function fit to the lines  715 . The lines  715  represent measured magnetic field data with no current flowing in an adjacent conductor. In  FIG. 8  a graph  805  indicates the residual difference between the cubic curve fit for each of the lines  735  and a cubic function fit to the lines  735 . The lines  735  represent measured magnetic field data with 20 Amps of current flowing in and adjacent conductor. The residual error appears uncorrelated the next lowest order polynomial terms. Thus, the polynomial model used may be sufficient to well-model the system. 
       FIG. 9  depicts experimental results of an exemplary difference solution of an in-hole current measurement system. In  FIG. 9  a graph  900  depicts the relationship between a quadratic coefficient of the difference between adjacent magnetic field sensors and the current flow. Also in  FIG. 9 , a graph  905  depicts an error between the current predicted by the quadric coefficient fit and the actual current flowing in the conductor.  FIG. 10  depicts photos of the experimental setup for collecting experimental data of an in-hole current measurement system. 
       FIG. 11  depicts an exemplary system for measuring current using an array of sensors located in a hole in a conductor. In this figure, an exemplary system  1100  for measuring current includes a bus bar  1105  with a sensor array  1110  position in a hole  1115 . The system  1100  has a signal processor  1120  configured to receive the signals representing the magnetic field measurements of the sensor array  1110 . Various embodiments may use different types of processors. For example some embodiments may use a microcontroller. In some embodiments an FPGA may be used. Some embodiments may employ PLDs, for example. The signal processor  1120  is connected to non-volatile memory  1125 . The signal processor has a microprocessor  1145  for executing instructions for calculating a signal representative of a current flowing in the bus bar  1105 . The non-volatile memory  1125  contains both program-memory locations  1130  and data-memory locations  1135 . The program-memory locations  1130  may store the instructions that are executed by the microprocessor  1120 . The signal processor  1120  may process the data received from the sensor array  1110  and produce a measurement indicative of the current in the bus bar  1105 . The measurement data may be logged in data memory  1135 . The measurement data may be displayed for view by a user on a computer display  1140 . In some embodiments an alarm may be sounded if the measurement exceeds a predetermined threshold, for example. 
     It has been observed that the magnetic field in the z-direction has a cubic dependence with x-position. A cubic polynomial has four coefficients. A series of four sensors may measure the magnetic field in the z-direction at four adjacent x-locations. One need not know the exact x-locations, but simply the relative x-offset between adjacent x-locations to determine the cubic coefficient. The cubic coefficient is substantially insensitive to the exact x-location of the sensors. One can observe this by simplifying a cubic polynomial with an unknown x-offset:
 
 z=d ( x−x   0 ) 3   +c ( x−x   0 ) 2   +b ( x−x   0 )+ a  
 
     Simplifying:
 
 z=dx   3 +( c− 3 dx   0 ) x   2 +( b− 2 bc+ 3 dx   0   2 ) x +( a−bx   0 +2 cx   0   2   −dx   0   3 )
 
     As can be seen from the above equation, the cubic coefficient has no dependency on the offset term (x 0 ). Thus, if one can obtain the cubic coefficient from the measurement of the four sensors, one may obtain a measure of the current. One way to obtain a measure of the cubic coefficient is to simplify the equation by using the derivative of the equation: 
     
       
         
           
             
               
                 ∂ 
                 z 
               
               
                 ∂ 
                 x 
               
             
             = 
             
               
                 3 
                 ⁢ 
                 
                   dx 
                   2 
                 
               
               + 
               
                 2 
                 ⁢ 
                 
                   ( 
                   
                     c 
                     - 
                     
                       3 
                       ⁢ 
                       
                         dx 
                         0 
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 x 
               
               + 
               
                 ( 
                 
                   b 
                   - 
                   
                     2 
                     ⁢ 
                     
                       cx 
                       0 
                     
                   
                   + 
                   
                     3 
                     ⁢ 
                     
                       dx 
                       0 
                       2 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Taking the difference between measurements of two adjacent sensors approximates taking the derivative of the measurements: 
     
       
         
           
             
               
                 ( 
                 
                   
                     z 
                     2 
                   
                   - 
                   
                     z 
                     1 
                   
                 
                 ) 
               
               Δ 
             
             ≈ 
             
               
                 3 
                 ⁢ 
                 
                   dx 
                   2 
                 
               
               + 
               
                 2 
                 ⁢ 
                 
                   ( 
                   
                     c 
                     - 
                     
                       3 
                       ⁢ 
                       
                         dx 
                         0 
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 x 
               
               + 
               
                 ( 
                 
                   b 
                   - 
                   
                     2 
                     ⁢ 
                     bc 
                   
                   + 
                   
                     3 
                     ⁢ 
                     
                       dx 
                       0 
                       2 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Here Δ is simply the x-distance between adjacent sensors. Thus, one simply needs to obtain the quadratic coefficient of the above difference equation to obtain a measure of the original cubic coefficient. Note that the two adjacent difference equations are: 
     
       
         
           
             
               
                 ( 
                 
                   
                     z 
                     3 
                   
                   - 
                   
                     z 
                     2 
                   
                 
                 ) 
               
               Δ 
             
             ≈ 
             
               
                 3 
                 ⁢ 
                 
                   
                     d 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         + 
                         Δ 
                       
                       ) 
                     
                   
                   2 
                 
               
               + 
               
                 2 
                 ⁢ 
                 
                   ( 
                   
                     c 
                     - 
                     
                       3 
                       ⁢ 
                       
                         dx 
                         0 
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     x 
                     + 
                     Δ 
                   
                   ) 
                 
               
               + 
               
                 ( 
                 
                   b 
                   - 
                   
                     2 
                     ⁢ 
                     
                       cx 
                       0 
                     
                   
                   + 
                   
                     3 
                     ⁢ 
                     
                       dx 
                       0 
                       2 
                     
                   
                 
                 ) 
               
             
           
         
       
       
         
           
             
               
                 ( 
                 
                   
                     z 
                     4 
                   
                   - 
                   
                     z 
                     3 
                   
                 
                 ) 
               
               Δ 
             
             ≈ 
             
               
                 3 
                 ⁢ 
                 
                   
                     d 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         + 
                         
                           2 
                           ⁢ 
                           Δ 
                         
                       
                       ) 
                     
                   
                   2 
                 
               
               + 
               
                 2 
                 ⁢ 
                 
                   ( 
                   
                     c 
                     - 
                     
                       3 
                       ⁢ 
                       
                         dx 
                         0 
                       
                     
                   
                   ) 
                 
                 ⁢ 
                 
                   ( 
                   
                     x 
                     + 
                     
                       2 
                       ⁢ 
                       Δ 
                     
                   
                   ) 
                 
               
               + 
               
                 ( 
                 
                   b 
                   - 
                   
                     2 
                     ⁢ 
                     
                       cx 
                       0 
                     
                   
                   + 
                   
                     3 
                     ⁢ 
                     
                       dx 
                       0 
                       2 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Combining the above three difference equations yields: 
     
       
         
           
             
               3 
               ⁢ 
               d 
             
             = 
             
               
                 
                   ( 
                   
                     
                       z 
                       2 
                     
                     - 
                     
                       z 
                       1 
                     
                   
                   ) 
                 
                 - 
                 
                   2 
                   ⁢ 
                   
                     ( 
                     
                       
                         z 
                         3 
                       
                       - 
                       
                         z 
                         2 
                       
                     
                     ) 
                   
                 
                 + 
                 
                   ( 
                   
                     
                       z 
                       4 
                     
                     - 
                     
                       z 
                       3 
                     
                   
                   ) 
                 
               
               
                 2 
                 ⁢ 
                 
                   Δ 
                   2 
                 
               
             
           
         
       
     
     Now that the cubic coefficient has been obtained in this manner, it may be used as a metric of the current within the conductor. Note also that if one simplifies the above solution one can see that it is equal to the solution obtained by inverse matrix methods:
 
 dΔ   2 =−0.167 z   1 +0.5 z   2 −0.5 z   3 +0.167 z   4  
 
       FIG. 12  depicts a schematic of an exemplary signal processing circuit for an exemplary in-hole current measurement system. In  FIG. 12 , an exemplary signal processing circuit  1200  may perform the receive inputs from four adjacent magnetic field sensors. Each magnetic field sensor may provide a voltage to an input node  1205 ,  1210 ,  1215 ,  1220 . An op-amp  1225  may be used in the signal processing circuit  1200 . The transfer function for this signal processing circuit may be:
 
 V   out =−0.333 z   1   +z   2   −z   3 +0.333 z   4  
 
       FIG. 13  depicts a block diagram of an exemplary transient-disturbance-tolerant in-hole current-measurement system. In the  FIG. 13  embodiment, an exemplary in-hole current-measurement system  1300  includes four distinct AMR sensors  1302 ,  1304 ,  1306 ,  1308 . The four AMR sensors  1302 ,  1304 ,  1306 , and  1308  are grouped into two pairs; a first pair includes sensors  1302  and  1304 . The second pair includes sensors  1306 ,  1308 . Three difference amplifiers  1310 ,  1312 ,  1314  have their input nodes connected to two of the output nodes of two of the AMR sensors. The outputs of the first and second AMR sensors  1302 ,  1304  connect to the first difference amplifier  1310 . The outputs of the second and third AMR sensors  1304 ,  1306  connect to the second difference amplifier  1312 . And the outputs of the third and fourth AMR sensors  1306 ,  1308  connect to the third difference amplifier  1314 . In this way, the first and third difference amplifiers are connected to mutually exclusive pairs of AMR sensors. 
     The in-hole current-measurement system  1300  generates a periodic high-accuracy output  1320  and a fast output  1322 . A high speed analog switch  1330  connects either the output of the first difference amplifier  1310  or the third difference amplifier  1314  to the fast output node  1322 . This selection between the first and third difference amplifiers permits the fast output node  1322  to be always driven by one of these difference amplifiers. If, for example, the first AMR sensor  1302  is experiencing a transient disturbance, the high speed analog switch  1330  can select the output of the third difference amplifier  1314 , which in turn is connected to the outputs of the undisturbed third and fourth AMR sensors. If, on the other hand, the third AMR sensor is experiencing a transient disturbance, the high speed analog switch  1330  can select the output of the first difference amplifier  1310 , which in turn is connected to the outputs of the undisturbed first and second AMR sensors. 
     The fast output  1322  can provide a signal representative of the current in the electrical conductor throughout a transient disturbance that affects only one of the first and third difference amplifiers. The fast output may be connected to threshold detection circuit. The threshold detection circuit may report a short circuit event if the fast output signal exceeds a predetermined threshold, for example. In some embodiments, a circuit breaker may be tripped (opened) if such a predetermined threshold is exceeded. The difference between adjacent AMR sensors may be approximately proportional to the electrical current flowing in the electrical conductor. And the difference between the third and fourth AMR sensors may be approximately equal in response to an electrical current as the difference between the first and the second AMR sensors, for example. Although the difference between pairs of adjacent AMR sensors may be approximately equal, small differences may arise. But these differences may be not significant for the system purposes of the fast output signal. 
     The output of all three of the difference amplifiers are shown connected to an Analog-to-Digital Converter (ADC)  1340 . The ADC  1340  may have three input channels for converting all three signals, for example. The ADC  1340  may convert all three of the input channels in parallel. In some embodiments, the ADC  1340  may serially convert each of the three difference amplifier outputs. An analog multiplexer may sequence through each of the three channels to obtain three digital representations of the three difference amplifier outputs. The ADC  1340  may have three sample-and-hold circuits that simultaneously sample the three input channels. Simultaneous sampling may ensure that the sampled signals are all representative of the same sampling time. The output of the ADC  1340  is connected to a microprocessor  1350 . The microprocessor  1350  may perform calculations to convert the digital representations of the output signals of the difference amplifiers to a signal representative of the electrical current in the electrical conductor. For example, the microprocessor  1350  may perform some of the calculations described in the description above. 
     The microprocessor  1350  may also schedule the setting and resetting of the alignment of magnetic domains in the AMR sensors. The setting and resetting of the magnetic domains of the AMR sensors may permit the determination of an offset of a Wheatstone bridge arrangement, for example. The setting and resetting of the magnetic domains in the AMR sensors may align the magnetic domains parallel to an easy axis. In some embodiments, periodically aligning the magnetic domains of the ARM sensors may facilitate precise sensor measurements of magnetic fields. The AMR sensors may have a set/reset conductor that passes directly over and/or under the AMR sensors in a substantially perpendicular direction to the easy axis of the AMR sensors. If the set/reset strap runs both over and under the AMR sensor, the current flow within the conductor running over the AMR sensor must be anti-parallel to the current flow in within the conductor running under the AMR strap for proper set/reset operation. The current flow may be in one direction for the set operation and in the opposite direction in the reset operation. The magnetic field directions will be governed by the right-hand rule used in magnetic fields originating by a flow of charged particles. 
       FIG. 14  depicts an exemplary set/reset circuit for aligning magnetic domains in an AMR sensor. In the  FIG. 14  depiction, an exemplary set/reset circuit  1400  includes a capacitor  1405  connected between a set/reset strap  1410  and the output of an inverter  1415 . When a control signal  1420  is high, a transistor  1425  connects an inverter side of the capacitor to a negative supply  1430 . The set/reset side of the capacitor is connected to ground through the conductive set/reset strap  1415 . In this way, the capacitor  1405  will be charged with a 5 volt difference across its terminals (for a −5 volt negative supply as indicated in the figure). When the control signal  1420  goes low, a transistor  1435  connects the inverter side of the capacitor  1405  to a positive supply  1440  (in this case +5 volts). The set/reset side of the capacity will instantaneously be at 10 volts, thereby providing a 10 volt difference across the set/reset strap  1415 . The set/reset strap  1415  is typically of low-resistance metal and thus the capacitor  1405  will be soon discharged through the set/reset strap  1415 . But this discharge event itself may create a large current in the set/reset strap  1415 . The large current may generate a large field—one that is sufficient to align the magnetic domains of the AMR sensors parallel with the easy axis. When the discharge is complete, the capacitor  1405  will have a −5 volt difference across its terminals. This prepares the capacitor  1405  for an oppositely directed discharge which may result in the magnetic field domains aligned antiparallel to that which resulted from the first discharge event.  FIG. 13  depicts two distinct set/reset modules  1360 ,  1362 . The first set/reset module  1360  performs the set/reset operation to the third and fourth AMR sensors  1306 ,  1308 . The second set/reset module  1362  performs the set/reset operation to the first and second AMR sensors  1302 ,  1304 . Thus, while the first set/reset module  1360  is operating on the third and fourth AMR sensors  1306 ,  1308 , the first difference amplifier  1310  may be receiving outputs form the undisturbed first and second AMR sensors  1302 ,  1304 . Then, when the second set/reset module  1362  is operating on the first and second AMR sensors  1302 ,  1304 , the third difference amplifier  1314  may be receiving outputs from the undisturbed third and fourth AMR sensors  1306 ,  1308 . The microprocessor  1350  may send the appropriate selection signal to the high speed analog switch  1330  to connect the appropriate undisturbed signal to the fast output  1322 . 
     During such set/reset events. The AMR sensors to which the set/reset operation is applied may be temporarily disturbed by the set/reset event. The output signals of such disturbed AMR sensors may not accurately reflect the magnetic field incident upon the AMR sensor during the set/reset operation. The microprocessor  135  may select AMR signals that are not undergoing a set/reset event for connection to the fast output during such an operation. In this way, a set/reset operation may be performed on a subset of AMR sensors while permitting other sensors to measure the magnetic field induced by electrical current flow in the conductor. 
       FIG. 15  depicts a block diagram of an exemplary AMR sensor system having set/reset and offset-nulling capabilities. In the  FIG. 15  depiction, an exemplary AMR sensor system  1500  includes an AMR magnetic-field sensor  1505 . A controller  1510  may control the timing of set/reset operations of the AMR magnetic-field sensor  1505 . The magnetic field sensor  1505  may have a nulling strap. The nulling strap may be the same as the set/reset strap or it may be a different strap. The nulling strap may be used to correct for an offset of the Wheatstone bridge due to mismatched bridge elements, for example. The offset may be used in a closed-loop sensor operation that keeps the sensor nominally at a zero condition. If a magnetic field is incident upon the sensor, a closed-loop operation may generate a current in the offset strap that generates a magnetic field equal in magnitude to the external field but opposite in polarity to the external magnetic field. This current in the offset strap corresponds to the magnitude and direction of the external field. In this way, the current in the offset strap becomes a measure of the external magnetic field incident upon the AMR sensor. 
     While an AMR sensor is undergoing a set/reset operation to align the magnetic domains of the thin file (e.g. Permalloy), the offset nulling operation may be disabled. An analog switch  1510  may permit the controller to disable measurement and closed loop offset nulling during a set/reset operation. During a set/reset operation, disconnecting the output of an AMR sensor from the circuitry that is responsive to the output prevents these responsive circuits from wildly behaving during the set/reset operation. Such prevention may minimize the transient disturbance to the common connections (e.g. power supply lines, etc.) to other circuitry. In the depicted embodiment, an integrator  1520  and a low-pass filter  1525  may be in the closed loop nulling path. 
       FIG. 16  depicts an exemplary timing diagram showing Set/Reset selection and ADC sampling timing. In the  FIG. 16  depiction, an exemplary timing diagram  1600  shows the switch timing  1605  of the analog switch  1515  operation with respect to the set timing  1610  of a set operation and a reset timing  1615  of a reset operation. The switch timing  1605  represents the time when the analog switch disconnects the output of the AMR sensor from circuitry responsive to the output. Also depicted in  FIG. 16  is the ADC sampling timing  1620  with respect to the set timing  1610  of the set operation and the reset timing  1615  of the reset operation. The ADC sampling time begins a time period after the completion of the set or reset operation so as to permit the circuitry to settle before performing a sampling of an AMR sensor signal. The ADC sampling completes before any subsequent set or reset operation begins so that the sampling operation is not disturbed by a transient disturbance associated with the set and reset operations. 
       FIG. 17  depicts an exemplary silicon substrate with three gradiometers patterned along an axis. In the depicted embodiment, an exemplary in-hole current-measurement system  1700  is depicted on a single semiconductor substrate  1705 . On the substrate are three distinct gradiometers  1710 ,  1715 ,  1720 . Each gradiometer has two separate AMR sensing bridges. The three gradiometers  1710 ,  1712 , and  1714  are aligned on a common axis  1725 . The leftmost gradiometer  1710  has two separately located AMR bridge sensors  1711 ,  1712 . The center gradiometer  1715  has two separately located AMR bridge sensors  1716 ,  1717 . The rightmost gradiometer  1720  has two separately located AMR bridge sensors  1721 ,  1722 . The semiconductor substrate also has two additional AMR bridge sensors for measuring a common-mode magnetic field of a pair of AMR bridge sensors. The leftmost common-mode bridge sensor  1730  measures the common-mode magnetic field of AMR bridge sensors  1711  and  1715 . The rightmost common-mode bridge sensor  1735  measures the common-mode magnetic field of AMR bridge sensors  1715  and  1722 . The outputs of the AMR bridge sensors corresponding to each gradiometer may be connected to the input nodes of a difference amplifier. In the depicted embodiment, each gradiometers are interdigitated with its nearest neighbor gradiometer. In some embodiments, such interdigitation may advantageously permit a larger difference between the output signals of the AMR bridge sensors associated with a gradiometer. 
       FIG. 18  depicts an exemplary AMR sensor with set/reset and offset straps. In the  FIG. 18  depiction, a single AMR bridge sensor  1800  is depicted as having four AMR bridge elements  1802 ,  1804 ,  1806 ,  1808 . Each AMR bridge element has diagonal runners of high conductivity material. Such diagonal runners may direct the current flow in the lower conductivity AMR thin film in a direction perpendicular to the direction of the runners. In some embodiments, the easy axis is parallel the longitudinal axis of the AMR thin film. In such embodiments, the runners direct the current in the AMR thin film in a direction of approximately 45 degrees with respect to the easy axis. This may permit the AMR thin film to operate in a high sensitivity region of operation. The diagonal alignment of the runners is sometimes referred to as a ‘barber pole’ arrangement. The easy axis of each of the four AMR bridge elements may be aligned in the same direction as the thin film for each bridge element may have been simultaneously deposited. The deposition operation may have been performed in the presence of a strong magnetic field orienting the easy axis of the thin layer of AMR material. 
       FIG. 19  depicts and exemplary block diagram of both common-mode and differential mode offset nulling. The  FIG. 19  depiction shows an exemplary block diagram  1900  including both a common-mode feedback amplifier  1905  and a differential-mode feedback operator  1910 . A common-mode AMR bridge sensor  1915  may detect a common-mode magnetic field for two adjacent AMR bridge sensors. One such bridge sensor  1920  is depicted in the figure. The differential-mode feedback operator  1920  may perform the nulling operation that was described above. In this way, the output of the differential-mode operator may be indicative of the difference between the two AMR bridge sensors of a gradiometer. 
       FIG. 20  depicts a flow chart of an exemplary method of calibrating an in-hole current-measurement system. In the  FIG. 20  embodiment, a method  2000  of calibrating an in-hole measurement system is described. The method  2000  is depicted from the perspective of the microprocessor  1145  in  FIG. 11 . The exemplary method  2000  begins with the processor  1145  initializing the raw current measurement to zero  2005 . Then the processor  1145  initializes the term number, N, on which the processor  1145  will calculate to 1, which represents the first term  2010 . The processor  1145  then retrieves the N th  coefficient which may have been precalculated as described above  2015 . For example, the precalculated coefficients may be calculated based upon the positions of the sensors within a hold in an electrical conductor. The coordinate system selected for calculating the coefficients may be one in which the zero coordinate is located at the center of the hole as measured from a top surface of the electrical conductor to a bottom surface of the electrical conductor. In some embodiments, the zero location may be irrelevant for the precalculation. For example, if the model used is a 3 rd  order Taylor series, and four sensors are used for the in-hole measurement device, the cubic term may be independent of zero coordinate location. After retrieving the N th , the processor  1145  then receives the output signal corresponding to the N th  magnetic-field sensor  2020 . The processor  1145  then calculates the N th  model term by determining the product of the retrieved N th  coefficient and the N th  sensor signal  2025 . The processor  1145  then adds the calculated N th  term to the raw current measurement sum  2030 . The processor  1145  then determines if all terms have been calculated and added to the raw current measurement sum  2035 . If all the terms have been calculated, the processor  1145  receives a true measurement of the electrical current flowing in the electrical conductor in which the in-hole current measurement system resides  2040 . The actual measurement may be determined by precision laboratory equipment used in a calibration station, for example. The processor  1145  then calculates a calibration coefficient, K, relating the raw current measurement sum to the actual electrical current being measured  2045 . The processor  1145  then stores the calibration coefficient in a data store  2050 . The calibration coefficient may later be used during run-time operation of the in-hole current-measurement device. If back at step  2035 , the processor  1145  determines that more model terms are still needed, the processor  1145  will increment the term count, N,  2055 . Then the processor  1145  will return to step  2015 . 
     In some embodiments, if one uses a polynomial model for the magnetic field profile along the axis of the magnetic-field sensors, only even order terms may be needed and/or used. If the electrical conductor has mirror symmetry about a plane through the center of the hole and parallel to both top and bottom surfaces of the electrical conductor, one may expect only odd order behavior of the magnetic field profile along the sensor axis. An odd-term-only model may be one such as given here:
 
 z=dx   3   +bx  
 
     Setting up the regression matrix for determining the coefficient relationship to sensor measurement may be given below: 
     
       
         
           
             
               
                 [ 
                 
                   
                     
                       
                         
                           - 
                           1.5 
                         
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         
                           - 
                           3.375 
                         
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       
                         
                           - 
                           0.5 
                         
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         
                           - 
                           0.125 
                         
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       
                         0.5 
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         0.125 
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                   
                     
                       
                         1.5 
                         ⁢ 
                         Δ 
                       
                     
                     
                       
                         3.375 
                         ⁢ 
                         
                           Δ 
                           3 
                         
                       
                     
                   
                 
                 ] 
               
               ⁡ 
               
                 [ 
                 
                   
                     
                       b 
                     
                   
                   
                     
                       d 
                     
                   
                 
                 ] 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       z 
                       1 
                     
                   
                 
                 
                   
                     
                       z 
                       2 
                     
                   
                 
                 
                   
                     
                       z 
                       3 
                     
                   
                 
                 
                   
                     
                       z 
                       4 
                     
                   
                 
               
               ] 
             
           
         
       
     
     Then the regression can again be performed as follows: 
     
       
         
           
             
               [ 
               
                 
                   
                     b 
                   
                 
                 
                   
                     d 
                   
                 
               
               ] 
             
             = 
             
               
                 
                   ( 
                   
                     
                       A 
                       T 
                     
                     ⁢ 
                     A 
                   
                   ) 
                 
                 
                   - 
                   1 
                 
               
               ⁢ 
               
                 
                   A 
                   T 
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         
                           z 
                           1 
                         
                       
                     
                     
                       
                         
                           z 
                           2 
                         
                       
                     
                     
                       
                         
                           z 
                           3 
                         
                       
                     
                     
                       
                         
                           z 
                           4 
                         
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
     The d coefficient here again represents the cubic coefficient. Here A T  again represents the transpose of the A matrix. For the above example, the both the b and the d coefficients are found, the d coefficient obtained is related to the sensor measurements exactly as it was using both even and odd model terms as described above:
 
 b= 0.042 z   1 −1.125 z   2 +1.125 z   3 −0.042 z   4  
 
 d=− 0.083 z   1 +0.167 z   2 −0.167 z   3 +0.083 z   4  
 
       FIG. 21  depicts a flow chart of an exemplary method of measuring current in a conductor using an in-hole current-measurement device. In the  FIG. 21  embodiment, a method  2100  of performing run-time current measurements using an in-hole measurement system is described. The method  2100  is depicted from the perspective of the microprocessor  1145  in  FIG. 11 . The processor  1145  begins the exemplary method by initializing the time of the first measurement  2105 . Then the processor  1145  receives the signals from the outputs of the N magnetic-field sensors  2110 . The processor  1145  then retrieves the coefficients corresponding the N magnetic-field sensors  2115 . These coefficients may have been predetermined as described above, for example. The processor  1145  then calculates the raw current measurement by summing the products of the respective coefficients and sensors output values  2120 . The processor  1145  then retrieves the calibration coefficient from memory  2125 . The calibration coefficient may be temperature dependent. In some embodiments, the calibration coefficient may be temperature independent. For example, the calibration coefficient may be determined by a method as above with reference to  FIG. 20 . The processor  1145  then calculates the measured electrical current by multiplying the retrieved calibration coefficient by the calculated raw current measurement  2130 . Then the processor  1145  sends the calculated measured electrical current to a display driver for display on a display device  2135 . The processor  1145  then stores the measured current along with a time stamp in a data store  2140 . The processor  1145  then determines if more current measurements need to be obtained  2145 . If more current measurements are needed, the processor  1145  updates the time stamp for the upcoming measurement  2150 , and returns to the  2110  operation. If no more current measurements are needed, the method terminates. 
       FIG. 22  depicts a flow chart of an exemplary method of performing set/reset operation while providing continuous current-measurement signals. In the  FIG. 22  embodiment, a method  2200  is described for performing set/reset operations on a pair of AMR sensors while simultaneously using the outputs of another pair of AMR sensors for continuous current measurement. The method  2200  is depicted from the perspective of the microprocessor  1145  in  FIG. 11 . The method begins with the processor  1145  initializing both the time stamp and the pair of AMR sensors to which a set/reset operation will be performed  2205 . The processor  1145  then will retrieve the delta time window length during which the pair of AMR sensors will be disabled  2210 . The processor  1145  then sends a signal to the fast analog multiplexor to select the pair of sensors that will not be disturbed by the set/reset operation  2215 . The selected pair may then provide continuous current measurements during the set/reset operation of the other pair. The processor  1145  then sends a signal to disable the outputs of the sensors to which the set/reset operation will be performed  2220 . By disabling the sensor outputs, the circuitry that normally receives those outputs may not be disturbed by the set/reset operation. The processor  1145  then sends a command for the set/reset module to perform a set or reset operation on the pair of sensors requiring the operation  2225 . The processor  1145  then determines if the time window for disturbance has passed  2230 . If the predetermined time window for disturbance has not completed or passed, the processor remains at this step and waits for the disturbance to settle. If, however, the time window has passed, the processor  1145  then sends a signal to again enable the output of the sensors upon which the set or reset operation has been performed  2235 . The processor  1145  then performs the run-time measurement of current using all four sensors of the two pairs of sensors  2240 . Such an operation may be like the one described in the runtime method  2100  with reference to  FIG. 21 , for example. The processor  1145  then toggles the set/reset parameter so that if the previous operation was a set operation, the upcoming operation will be a reset operation, and vice versa  2245 . The processor  1145  then determines if the sensor has completed both the set operation and the reset operation  2250 . If the sensor has yet to have both the set and the reset operation performed upon it, the processor  1145  returns to step  2220 . If, however, the sensor has had both the set and the reset operations performed, the processor  1145  toggles the pair of sensors that will receive the next set or reset operation  2255 . In this way, alternating pairs of sensors may be selected for performing the continuous current measurement while the other pair is receiving a set/reset operation. 
     In some embodiments, the output signals of the magnetic-field sensors received, for example, by the processor  1145  in the above described exemplary methods  2000 ,  2100 , and  2200 , may be a signal representative of a magnetic field strength and/or polarity. In some embodiments, the output signals of the magnetic-field sensors may represent a gradient of a magnetic field. For example, some exemplary magnetic-field sensors may have a pair of field sensing devices space apart. The output of some such magnetic-field sensors may represent the difference between each of the pair of field sensing devices, for example. 
     Although various embodiments have been described with reference to the Figures, other embodiments are possible. For example, various hole shapes may be used. Each hole shape may result in a different functional relationship between hole position and magnetic field measurement. In some embodiments, a cavity may be used which may be a hole that doesn&#39;t completely go through the conductor. In some embodiments a square hole may be used. In some embodiments, the sensor array may be located intentionally off-center within the hole, either in the hole-direction or the lateral transverse direction or both. In some embodiments, the number of sensors may be more than four. For example in an exemplary embodiment sixteen magnetic field sensors may be used. In some embodiments the sensors may be manufactured all on one silicon die. In some embodiments each sensor may be discrete. The sensors may be mounted on a circuit board. In various embodiments a microcontroller may perform the signal processing. In some embodiments, the signal processing may be performed using analog circuitry. Some embodiments may include a centering fixture which may center the sensor array within a hole. 
     Other embodiments may include a temperature sensor located near the current sensors. The temperature sensor may be used compensate for temperature sensitivities of the current sensors. In some embodiments, variations in feedback current may cause temperature increases. The calculations and equations shown above may be performed fully with an arithmetic unit, for example, or aided with lookup tables. Some embodiments may include a calibration feature. If, for example, the sensor output is dependent on the exact dimensions of the current conductor in the vicinity of the hole, then those dimensions could be measured with caliper by the user and entered in a signal processor interface. A signal processor may calculate the correct output of the sensor based on these entered values, for example. 
     Various exemplary embodiments may include two subsets of sensors for providing substantially continuous current measurement while simultaneously permitting periodic disturbance producing operations on a single subset of sensors. For example, an exemplary current-measurement system may have two subsets, each subset including two magnetic-field sensors. Subsets containing three, four, or any reasonable number of sensors may be possible. In some embodiments, subsets may be mutually exclusive of each other. In some embodiments, subsets may be overlapping. For example, a current-measurement system may include six sensors divided into three overlapping groups of four sensors each. For example, a disturbance producing operation may be performed on two sensors while the complementary group of four sensors provides precise current measurement. In another example, five sensors may be divided into five overlapping groups of four sensors. The above described coefficient determination may then determine the appropriate coefficients for use by each subset of sensors. In an exemplary embodiment, a current-measurement system may include two mutually exclusive subsets of four sensors each. Each group may be interdigitated with the other group, for example. Sensor groups with a large number of sensors (e.g. four or more) may advantageously precisely measure current even during a transient disturbance event affecting a complementary subset of sensors. 
     Some aspects of embodiments may be implemented as a computer system. For example, various implementations may include digital and/or analog circuitry, computer hardware, other sensors (e.g. temperature sensors), firmware, software, or combinations thereof. Apparatus elements can be implemented in a computer program product tangibly embodied in an information carrier, e.g., in a machine-readable storage device, for execution by a programmable processor; and methods can be performed by a programmable processor executing a program of instructions to perform functions of various embodiments by operating on input data and generating an output. Some embodiments can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and/or at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. 
     Suitable processors for the execution of a program of instructions include, by way of example and not limitation, both general and special purpose microprocessors, which may include a single processor or one of multiple processors of any kind of computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memories for storing instructions and data. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including, by way of example, semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and, CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits). In some embodiments, the processor and the member can be supplemented by, or incorporated in hardware programmable devices, such as FPGAs, for example. 
     In some implementations, each system may be programmed with the same or similar information and/or initialized with substantially identical information stored in volatile and/or non-volatile memory. For example, one data interface may be configured to perform auto configuration, auto download, and/or auto update functions when coupled to an appropriate host device, such as a desktop computer or a server. 
     In some implementations, one or more user-interface features may be custom configured to perform specific functions. An exemplary embodiment may be implemented in a computer system that includes a graphical user interface and/or an Internet browser. To provide for interaction with a user, some implementations may be implemented on a computer having a display device, such as an LCD (liquid crystal display) monitor for displaying information to the user, a keyboard, and a pointing device, such as a mouse or a trackball by which the user can provide input to the computer. 
     In various implementations, the system may communicate using suitable communication methods, equipment, and techniques. For example, the system may communicate with compatible devices (e.g., devices capable of transferring data to and/or from the system) using point-to-point communication in which a message is transported directly from the source to the receiver over a dedicated physical link (e.g., fiber optic link, point-to-point wiring, daisy-chain). The components of the system may exchange information by any form or medium of analog or digital data communication, including packet-based messages on a communication network. Examples of communication networks include, e.g., a LAN (local area network), a WAN (wide area network), MAN (metropolitan area network), wireless and/or optical networks, and the computers and networks forming the Internet. Other implementations may transport messages by broadcasting to all or substantially all devices that are coupled together by a communication network, for example, by using omni-directional radio frequency (RF) signals. Still other implementations may transport messages characterized by high directivity, such as RF signals transmitted using directional (i.e., narrow beam) antennas or infrared signals that may optionally be used with focusing optics. Still other implementations are possible using appropriate interfaces and protocols such as, by way of example and not intended to be limiting, USB 2.0, Firewire, ATA/IDE, RS-232, RS-422, RS-485, 802.11 a/b/g/n, Wi-Fi, Ethernet, IrDA, FDDI (fiber distributed data interface), token-ring networks, or multiplexing techniques based on frequency, time, or code division. Some implementations may optionally incorporate features such as error checking and correction (ECC) for data integrity, or security measures, such as encryption (e.g., WEP) and password protection. 
     A number of implementations have been described. Nevertheless, it will be understood that various modification may be made. For example, advantageous results may be achieved if the steps of the disclosed techniques were performed in a different sequence, or if components of the disclosed systems were combined in a different manner, or if the components were supplemented with other components. Accordingly, other implementations are contemplated or within the scope of the following claims.