Removal of higher order magnetic interference in magnetic field based current sensors
A system for measuring current includes a conductive trace comprising N substantially parallel straight sections having a substantially constant cross-section, N≥4. 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 ( S ( 1 ) - ( N - 1 1 ) S ( 2 ) + ( N - 1 2 ) S ( 3 ) - … - ( N - 1 N - 3 ) S ( N - 2 ) + ( N - 1 N - 2 ) S ( N - 1 ) - S ( N ) ) 2 ( N - 1 ) ; ( M k ) = M ! ( M - k ) ! k ! ; where M=N−1, and S(i) is the measured signal read at magnetic field based current sensor i.
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 N≥4, 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 N−2 highest order terms of an interference magnetic field, and wherein the current in the conductive trace is determined based on:
(
S
(
1
)
-
(
N
-
1
1
)
S
(
2
)
+
(
N
-
1
2
)
S
(
3
)
-
…
-
(
N
-
1
N
-
3
)
S
(
N
-
2
)
+
(
N
-
1
N
-
2
)
S
(
N
-
1
)
-
S
(
N
)
)
2
(
N
-
1
)
,
where S(i) is the measured magnetic field signal read at magnetic field based current sensor i and
(
M
k
)
=
M
!
(
M
-
k
)
!
k
!
,
where M=N−1.
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
(
S
(
1
)
-
(
N
-
1
1
)
S
(
2
)
+
(
N
-
1
2
)
S
(
3
)
-
…
-
(
N
-
1
N
-
3
)
S
(
N
-
2
)
+
(
N
-
1
N
-
2
)
S
(
N
-
1
)
-
S
(
N
)
)
2
(
N
-
1
)
,
where S(i) is the measured magnetic field signal read at magnetic field based current sensor i and
(
M
k
)
=
M
!
(
M
-
k
)
!
k
!
,
where M=N−1, wherein N≥4.
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 N−2 highest order terms of an interference magnetic field.