Removal of higher order magnetic interference in magnetic field based current sensors

Abstract

A system for measuring current includes a conductive trace comprising N substantially parallel straight sections having a substantially constant cross-section, N4. Adjacent substantially straight sections are spaced apart by a given distance and each pair of adjacent straight sections is connected by a respective loop of the current trace such that current in odd-numbered straight sections flows in a first direction and current in even-numbered straight sections flows in an opposite direction. The N magnetic field based current sensors are each positioned on a respective straight section of the conductive trace. The current is calculated based on $\frac{\begin{array}{c}(S\left(1\right)-\left(\begin{array}{c}N-1\\ 1\end{array}\right)S\left(2\right)+\left(\begin{array}{c}N-1\\ 2\end{array}\right)S\left(3\right)-\mathrm{.Math.}-\\ \left(\begin{array}{c}N-1\\ N-3\end{array}\right)S\left(N-2\right)+\left(\begin{array}{c}N-1\\ N-2\end{array}\right)S\left(N-1\right)-S\left(N\right))\end{array}}{2^{\left(N-1\right)}};$$\left(\begin{array}{c}M\\ k\end{array}\right)=\frac{M!}{\left(M-k\right)!k!};$
where M=N1, and S(i) is the measured signal read at magnetic field based current sensor i.

Claims

1. A system for measuring current comprising: a conductive trace comprising N substantially parallel straight sections having a substantially constant cross-section, wherein adjacent substantially straight sections are spaced apart by a given distance and each pair of adjacent substantially straight sections is connected by a respective loop of the current trace such that current in the odd numbered substantially straight sections flow in a first direction and current in the even numbered substantially straight sections flow in an opposite direction; and N magnetic field based current sensors, each current sensor being positioned on a respective substantially straight section of the conductive trace, wherein N4, wherein the N magnetic field based current sensors collectively sense a magnetic field value that corresponds to a magnetic field generated by the current while canceling out only the N2 highest order terms of an interference magnetic field, and wherein the current in the conductive trace is determined based on: $\frac{\begin{array}{c}(S\left(1\right)-\left(\begin{array}{c}N-1\\ 1\end{array}\right)S\left(2\right)+\left(\begin{array}{c}N-1\\ 2\end{array}\right)S\left(3\right)-\mathrm{.Math.}-\\ \left(\begin{array}{c}N-1\\ N-3\end{array}\right)S\left(N-2\right)+\left(\begin{array}{c}N-1\\ N-2\end{array}\right)S\left(N-1\right)-S\left(N\right))\end{array}}{2^{\left(N-1\right)}},$ where S(i) is the measured magnetic field signal read at magnetic field based current sensor i and $\left(\begin{array}{c}M\\ k\end{array}\right)=\frac{M!}{\left(M-k\right)!k!},$ where M=N1.

2. The system as recited in claim 1, wherein the magnetic field based current sensors are fluxgate sensors.

3. The system as recited in claim 1, wherein the magnetic field based current sensors are magneto-resistive (XMR) sensor elements.

4. The system as recited in claim 3, wherein the XMR sensor elements are anisotropic magneto-resistive (AMR).

5. The system as recited in claim 3, wherein the XMR sensor elements are giant magneto-resistive (GMR).

6. The system as recited in claim 3, wherein the XMR sensor elements are tunneling magneto-resistive (TMR).

7. The system as recited in claim 3, wherein the XMR sensor elements are colossal magneto-resistive (CMR).

8. The system as recited in claim 1, wherein the each respective loop of the conductive trace has a curvilinear shape.

9. A method of measuring current comprising: providing a conductive trace that comprises N substantially parallel straight sections having a substantially constant cross-section, wherein adjacent substantially straight sections are spaced apart by a given distance and each pair of adjacent straight sections is connected by a respective loop of the current trace such that current in the odd-numbered straight sections flows in a first direction and current in the even-numbered straight sections flows in an opposite direction; positioning N magnetic field based current sensors on a respective straight section of the conductive trace; and determining the current in the conductive trace based on $\frac{\left(S\left(1\right)-\left(\begin{array}{c}N-1\\ 1\end{array}\right)S\left(2\right)+\left(\begin{array}{c}N-1\\ 2\end{array}\right)S\left(3\right)-\mathrm{.Math.}-\left(\begin{array}{c}N-1\\ N-3\end{array}\right)S\left(N-2\right)+\left(\begin{array}{c}N-1\\ N-2\end{array}\right)S\left(N-1\right)-S\left(N\right)\right)}{2^{\left(N-1\right)}},$ where S(i) is the measured magnetic field signal read at magnetic field based current sensor i and $\left(\begin{array}{c}M\\ k\end{array}\right)=\frac{M!}{\left(M-k\right)!k!},$ where M=N1, wherein N4.

10. The method as recited in claim 9, wherein N=4 and the current is determined based upon the measured magnetic field as (S(1)3*S(2)+3*S(3)S(4))/8.

11. The method as recited in claim 9, wherein N=6 and the current is determined based upon the measured magnetic field as (S(1)5*S(2)+10*S(3)10*S(4)+5*S(5)S(6))/32.

12. The method as recited in claim 9, wherein N=8 and the current is determined based upon the measured magnetic field as (S(1)7*S(2)+21*S(3)35*S(4)+35*S(5)21*S(6)+7*S(7)S(8))/128.

13. The method as recited in claim 9, wherein the each respective loop of the conductive trace comprises a curved portion having first and second ends, the first and second ends connected to respective ones of a pair of adjacent straight sections.

14. The method as recited in claim 9, wherein the N magnetic field based current sensors collectively sense a magnetic field value that corresponds to a magnetic field generated by the current while canceling out the N2 highest order terms of an interference magnetic field.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the present disclosure are illustrated by way of example, and not by way of limitation, in the Figures of the accompanying drawings in which like references indicate similar elements. It should be noted that different references to an or one embodiment in this disclosure are not necessarily to the same embodiment, and such references may mean at least one. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

(2) The accompanying drawings are incorporated into and form a part of the specification to illustrate one or more exemplary embodiments of the present disclosure. Various advantages and features of the disclosure will be understood from the following Detailed Description taken in connection with the appended claims and with reference to the attached drawing Figures in which:

(3) FIG. 1 depicts an example of a system for sensing current using magnetic field based non-contact current sensors according to an embodiment of the disclosure;

(4) FIG. 1A depicts an example of a system for sensing current using magnetic field based non-contact current sensors according to an embodiment of the disclosure;

(5) FIG. 2A depicts an example of a system for sensing current that has an interfering current trace according to an embodiment of the disclosure;

(6) FIG. 2B depicts a graph that illustrates the current interference versus lateral distance of the interfering current trace from the sensor according to the embodiment of FIG. 2A;

(7) FIG. 2C depicts a graph that illustrates the magnetic field interference versus lateral distance of an interfering magnetic source from the sensor according to the embodiment of FIG. 2A;

(8) FIG. 3A depicts an example of a system for sensing current and an interfering magnet according to an embodiment of the disclosure;

(9) FIG. 3B depicts a graph of the strength of the interference field versus angle of the interfering magnet from the sensor according to the embodiment of FIG. 3A;

(10) FIG. 3C depicts the graph of FIG. 3B greatly magnified;

(11) FIG. 4 illustrates a method of measuring current; and

(12) FIG. 5 depicts an example of a system for current sensing as known in the art.

DETAILED DESCRIPTION OF THE DRAWINGS

(13) Specific embodiments of the invention will now be described in detail with reference to the accompanying Figures. In the following detailed description of embodiments of the invention, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to one of ordinary skill in the art that the invention may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description.

(14) Referring now to the drawings and more particularly to FIG. 1, current-measuring system 100 is disclosed according to an embodiment of the disclosure. In this embodiment, current trace 102 is a conductive material having a substantially constant cross-sectional profile, which may be round, square or rectangular. The conductive material can be aluminum, copper, or any other conductive material currently known or unknown. In this figure, trace 102 has already been narrowed to concentrate the magnetic field. Trace 102 includes four substantially parallel sections 102A, 102B, 102C, 102D. Adjacent parallel sections are joined by loop sections 102E, 102F, 102G. That is, parallel sections 102A and 102B are joined by loop section 102E; parallel sections 102B and 102C are joined by loop section 102F; and parallel sections 102C and 102D are joined by loop section 102G. Magnetic field based current sensors 104A, 104B, 104C, 104D are placed above a respective parallel section of trace 102 to measure the current therein. For purposes of discussion the XY coordinates are defined as shown in the figure, although in order to calculate the X component of an interference field, the X-axis is defined to run through current sensors 104. Each adjacent pair of parallel sections of trace 102 is separated by a distance EX. It can be noted that magnetic field based current sensors 104A, 104B, 104C, 104D are arranged in a linear fashion in the embodiment shown. In some embodiments, magnetic field based current sensors 104 are not totally linear, e.g., through process variation. In such instances, the results are still an improvement over the previous solutions, although the accuracy may be somewhat affected. In at least one embodiment the magnetic field based current sensors are fluxgate sensors. In an alternate embodiment, magnetic field based current sensors 104 can be magneto-resistive (XMR) sensor elements, such as anisotropic magneto-resistive (AMR), giant magneto-resistive (GMR), tunneling magneto-resistive (TMR) and colossal magneto-resistive (CMR).

(15) As noted previously, the disclosed arrangement of trace 102 and magnetic field based current sensors 104 is designed in such a way that an appropriate combination of sensor signals will cancel magnetic interference of higher orders while not reducing the signal component of the current measurement. The magnetic field S sensed by each of magnetic field based current sensors 104A, 104B, 104C, 104D can be written as:
S=B.sub.1+B.sub.interference (Equation 1)
where B.sub.1 is the desired magnetic field proportional to current I and B.sub.interference is the magnetic field proportional to the interference.

(16) It is known that the x component of a magnetic field expanded in Taylor series around x=0 is as follows:
B.sub.x(x)=B.sub.x,0+B.sub.x,1x+B.sub.x,2x.sup.2+ (Equation 2)
Therefore, the interference magnetic field can be written as:
B.sub.x,interference(x)=B.sub.0+B.sub.1x+B.sub.2x.sup.2+ (Equation 3)
Using the coordinate system as shown in FIG. 1, the field sensed by each of magnetic field based current sensors 104A, 104B, 104C, 104D can be written as:
S.sub.A=B.sub.1+B.sub.03/2B.sub.1x+9/4B.sub.2x.sup.2+ (Equation 4)
S.sub.B=B.sub.1+B.sub.01/2B.sub.1x+1/4B.sub.2x.sup.2+ (Equation 5)
S.sub.C=B.sub.1+B.sub.0+1/2B.sub.1x+1/4B.sub.2x.sup.2+ (Equation 6)
S.sub.D=B.sub.1+B.sub.0+3/2B.sub.1x+9/4B.sub.2x.sup.2+ (Equation 7)
In order to obtain a cancellation of the interfering magnetic field up to second order interference, we use the equation:

(17) $\begin{array}{cc}\frac{3\left(S_C-S_B\right)-\left(S_D-S_A\right)}{8}=B_I+\mathrm{interference}\mathrm{of}\mathrm{order}3& \left(\mathrm{Equation}8\right)\end{array}$
i.e., we are left with only the original signal and interference of order three or greater.

(18) The system shown in FIG. 1 can be extended further by increasing the number of parallel and loop sections and sensors to an arbitrarily large value. The sensors can be combined to calculate a value for the magnetic field generated by the current (B.sub.1) with rejection of higher order interference terms, such that if N sensors are used, the interference terms up to order N2 are removed. The calculation is performed by multiplying the sensors by the coefficients of a binomial expansion with alternating terms, summing those values, and dividing the final sum by 2.sup.(N-1). In the example system shown in FIG. 1, four sensors are used in calculation such that sensors A/B/C/D are multiplied by the binomial expansion coefficients [+1, 3, +3, 1], and then divided by 2.sup.(4-1)=8. That is, the equation above can be rewritten as:

(19) $\begin{array}{cc}{B}_I+\mathrm{interference}\mathrm{of}\mathrm{order}3=\frac{\left(S_A-3S_B+3S_C-S_D\right)}{8}& \left(\mathrm{Equation}9\right)\end{array}$

(20) A system with six sensors are used in a similar calculation such that sensors A/B/C/D/E/F are multiplied by the binomial expansion coefficients [+1, 5, +10, 10, +5, 1], and then divided by 2.sup.(6-1)=32. That is:

(21) $\begin{array}{cc}{B}_I+\mathrm{interference}\mathrm{of}\mathrm{order}5=\frac{\left(S_A-5S_B+10S_C-10S_D+5S_E-S_F\right)}{32}& \left(\mathrm{Equation}10\right)\end{array}$

(22) FIG. 1A discloses an example system 100A having eight parallel sections and eight sensors 104A, 104B, 104C, 104D, 104E, 104F, 104G, 104H. This system similarly uses the eight sensors in calculation such that they are multiplied by the binomial expansion coefficients [+1, 7, +21, 35, +35, 21, +7, 1] and then divided by 2.sup.(8-1)=128. That is:

(23) $\begin{array}{cc}{B}_I+\mathrm{interference}\mathrm{of}\mathrm{order}7=\frac{\begin{array}{c}(S_A-7S_B+21S_C-35S_D+\\ 35S_E-21S_F+7S_G-S_H)\end{array}}{128}& \left(\mathrm{Equation}11\right)\end{array}$
This equation can thus be generalized for N sensors, where N is even, as:

(24) $\begin{array}{cc}{B}_I+\mathrm{interference}\mathrm{of}\mathrm{order}\left(N-1\right)=\frac{\begin{array}{c}(S\left(1\right)-\left(\begin{array}{c}N-1\\ 1\end{array}\right)S\left(2\right)+\left(\begin{array}{c}N-1\\ 2\end{array}\right)S\left(3\right)-\mathrm{.Math.}-\\ \left(\begin{array}{c}N-1\\ N-3\end{array}\right)S\left(N-2\right)+\left(\begin{array}{c}N-1\\ N-2\end{array}\right)S\left(N-1\right)-S\left(N\right))\end{array}}{2^{\left(N-1\right)}}\mathrm{where}\left(\begin{array}{c}M\\ k\end{array}\right)=\frac{M!}{\left(M-k\right)!k!},& \left(\mathrm{Equation}12\right)\end{array}$
where M=N1.

(25) In the examples disclosed above, N has been an even number. While having an even number of sensors arranged as disclosed provides a pleasing symmetry in the mathematics used to determine the current, the use of an even number of sensors is not necessary. When these embodiments are extended to an odd number of sensors, appropriate changes to the equation used will be derivable by one skilled in the art. Thus the disclosed embodiments are extendable mutatis mutandis to any number of sensors N where N is greater than or equal to four.

(26) FIGS. 2A-2C provide evidence of the improvement in measured interference using the embodiment of FIG. 1. System 200 in FIG. 2A shows current-measuring system 100 and an interfering current trace 202. Interfering trace 202 has a length of 10 mm, an offset in the Z-axis of 1 mm and a current of 1 A. Data is taken as the offset in the X-axis is varied for this layout. FIG. 2B illustrates the measured current interference when two sensors versus four sensors are used to sense the current interference. With both the two-sensor and the four-sensor versions, the interference is zero when the offset in the X-axis is zero, but immediately goes to a high value, here 10.sup.6 A/A as the offset moves a small distance off of zero. At a distance x=15 mm, the two-sensor measurement has 1 mA/A of interference, while the four-sensor measurement has only 1 mA/10 A, an order of magnitude difference in the interference. Over the entire range of measurements, the four-sensor measurements of current interference are consistently better and drop at a faster rate. FIG. 2C discloses the same measurements for the magnetic field interference; again the four-sensor design consistently exhibits lower magnetic interference and values drop at a faster rate.

(27) FIGS. 3A-3C provide evidence of improvement in measured interference when a magnet is present near the current sensors. System 300 in FIG. 3A shows current-measuring system 100 and an interfering magnet 308. Interfering magnet 308 is located at a distance R from the center of the current-measuring system, with measurements taken as the angle is varied. FIG. 3B illustrates that with a current sensor having two sensors, the interference varies within a range of about nine micro-teslas (i.e., from about 4.5 T to 4.5 T), while the interference from the current sensor having four sensors appears to be a constant value of zero. FIG. 3C provides a view of the same data when the scale of the graph is changed to show the variations in the four-sensor embodiment. From this graph, it can be seen that the interference caused by the magnet varies within a range of about 0.02 micro-teslas (i.e. from about 0.01 T to about 0.01 T).

(28) FIG. 4 illustrates a method of measuring a current according to an embodiment of the disclosure. The method begins by providing (405) a conductive trace that comprises N substantially parallel straight sections having a substantially constant cross-section, where N is an integer greater than or equal to four. Adjacent straight sections are spaced apart by a given distance and each pair of adjacent straight sections is connected by a respective loop of the current trace such that current in the odd-numbered straight sections flows in a first direction and current in the even-numbered straight sections flows in an opposite direction. N magnetic field based current sensors are positioned (410) on a respective straight section of the conductive trace. The current is then determined (415) using the equation below:

(29) $\frac{\begin{array}{c}(S\left(1\right)-\left(\begin{array}{c}N-1\\ 1\end{array}\right)S\left(2\right)+\left(\begin{array}{c}N-1\\ 2\end{array}\right)S\left(3\right)-\mathrm{.Math.}-\\ \left(\begin{array}{c}N-1\\ N-3\end{array}\right)S\left(N-2\right)+\left(\begin{array}{c}N-1\\ N-2\end{array}\right)S\left(N-1\right)-S\left(N\right))\end{array}}{2^{\left(N-1\right)}},$
where S(i) is the measured signal read at magnetic field based current sensor i and

(30) 0$\left(\begin{array}{c}M\\ k\end{array}\right)=\frac{M!}{\left(M-k\right)!k!},$
where M=N1.

(31) Although various embodiments have been shown and described in detail, the claims are not limited to any particular embodiment or example. None of the above Detailed Description should be read as implying that any particular component, element, step, act, or function is essential such that it must be included in the scope of the claims. Reference to an element in the singular is not intended to mean one and only one unless explicitly so stated, but rather one or more. All structural and functional equivalents to the elements of the above-described embodiments that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the present claims. Accordingly, those skilled in the art will recognize that the exemplary embodiments described herein can be practiced with various modifications and alterations within the spirit and scope of the claims appended below.