Self-calibration method of tunneling magnetoresistive (TMR) sensor and TMR sensor array for current measurement

Abstract

The invention provides a self-calibration method of a TMR (Tunnel Magnetoresistive) sensor and a TMR sensor array for current measurement, and relates to the technical field of quantum current sensors. According to the method, a double Wheatstone bridge structure is adopted, a to-be-measured bridge is used for measuring a to-be-measured magnetic field, and a reference bridge is used for measuring a known reference magnetic field; the self-calibration of the TMR sensor is realized by calculating the ratio of the output voltages of the two bridges, so that measurement errors caused by environmental factors such as temperature, humidity and mechanical vibration are eliminated; moreover, the invention provides a TMR sensor array for current measurement, the application of the TMR sensor array further enhances the adaptive capacity of the TMR sensor array in a complex environment, and the array is formed by a plurality of TMR sensor units, so that not only can the spatial resolution of measurement be improved, but also the fault-tolerant capability of the system can be improved through redundancy configuration, and the system reliability is improved. The array structure enables the TMR sensor to perform accurate measurement at a plurality of measurement points at the same time to obtain accurate measurement current.

Description

Technical Field

[0001] The present application relates to the technical field of quantum current sensors, and in particular to a self-calibration method for a tunnel magnetoresistive (TMR) sensor and a TMR sensor array for current measurement. Background Art

[0002] With the increasing demand for precise measurement in modern power systems, communication networks, and microelectronic devices, traditional current sensing technology faces many challenges, especially in applications with high sensitivity, low power consumption, and high-precision measurements. In the scenarios of ultra-high frequency, high voltage, and small current measurements, traditional sensors are often unable to meet the strict accuracy requirements due to limitations in materials and measurement technology. Therefore, sensor technology based on quantum effects has gradually become a research focus. Among them, tunnel magnetoresistance (TMR) sensors, as a new type of quantum sensing technology, have extremely high sensitivity and accuracy, becoming an important tool for solving the above problems.

[0003] The TMR effect is a quantum mechanical phenomenon that describes the resistance change caused by electron tunneling between two magnetic layers. When the magnetization directions of the magnetic layers are parallel, the resistance is low; when the magnetization directions are opposite, the resistance increases significantly. The TMR effect allows this resistance change to be used to detect very weak currents and magnetic fields, making it widely used in high-precision current sensors. Compared with traditional current measurement technologies, TMR sensors offer higher accuracy, lower power consumption, and greater immunity to interference.

[0004] However, the application of TMR sensors still faces several technical challenges, particularly in terms of long-term stability and self-calibration. TMR sensor measurements can be affected by factors such as ambient temperature fluctuations, external magnetic field fluctuations, and material aging, which can lead to measurement errors. Therefore, developing a TMR sensor that can automatically correct for its own deviations is crucial for improving its measurement accuracy and stability, and this technical challenge urgently needs to be addressed. Summary of the Invention

[0005] In view of the above problems, the present application is proposed to provide a self-calibration method for a tunnel magnetoresistive (TMR) sensor and a TMR sensor array for current measurement that overcomes or at least partially resolves the above problems. The technical solution is as follows:

[0006] In a first aspect, a self-calibration method for a tunnel magnetoresistive (TMR) sensor is provided, comprising:

[0007] Constructing a double Wheatstone bridge comprising a bridge to be measured and a reference bridge, wherein the bridge to be measured is used to detect a magnetic field to be measured, and the reference bridge is used to detect a reference magnetic field;

[0008] The bridge to be measured is used to measure the magnetic field to be measured. test Under the condition of , the resistance of the magnetic tunnel junction changes, and the output voltage of the bridge to be measured is U out,test The output voltage of the bridge to be measured is proportional to the magnetic field to be measured, and is expressed as follows:

[0009]

[0010] Where ΔR is the resistance change of the magnetic tunnel junction caused by the magnetic field, R is the original resistance of the magnetic tunnel junction, and U in is the input voltage of the bridge to be measured, f c1 is the drift error function of the influence of environmental interference on the output voltage of the bridge to be measured, and k is the magnetoresistance sensitivity of the magnetic tunnel junction;

[0011] Control the reference bridge in a known reference magnetic field H ref Working under , the component parameters of the reference bridge and the bridge to be measured are consistent, and the reference bridge output voltage U out,ref As shown in the following formula (2):

[0012] U out,ref =k·H ref ·U in ·f c2 (2);

[0013] Among them, f c2 is the drift error function of the influence of environmental interference on the output voltage of the reference bridge; since the factors causing the drift error in the environment of the reference bridge are the same as those in the environment of the bridge to be tested, f c1 =f c2 ;

[0014] Perform self-calibration of the TMR sensor and calculate the ratio of the output voltage of the bridge to be tested to the output voltage of the reference bridge According to this ratio, combined with the known reference magnetic field H ref , use the following formula (3) to calculate the magnetic field H to be measured test :

[0015]

[0016] In a second aspect, a TMR sensor array for current measurement is provided, wherein each TMR sensor in the TMR sensor array is self-calibrated using the above-mentioned TMR sensor self-calibration method, the TMR sensor array is divided into a first number of groups, each group of TMR sensor arrays includes a second number of TMR sensors, and the second number of TMR sensors are used to measure components of the magnetic field of a test point on different axes, respectively. The first number of TMR sensor arrays are arranged on a circle with a radius of r, and the conductive wire is within the circle formed by the first number of TMR sensor arrays.

[0017] In a possible implementation, the first number of groups is four groups, and the second number of TMR sensors is three TMR sensors.

[0018] In one possible implementation, three TMR sensors are used to measure the components of the magnetic field at the test point on the X-axis, Y-axis, and Z-axis, respectively. Four groups of sensor arrays are arranged on a circle with a radius of r, and their positions are (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0), respectively.

[0019] In one possible implementation, assume that the angle between the wire and the Z axis is θ, the angle between the wire and the X axis is γ, the intersection point of the wire and the circular surface is (x0, y0, 0), the direction of the wire is (l, m, n), and the current of the wire is I;

[0020] According to Biot-Savart's law, for any point (x r ,y r ,0), the magnetic field strength at this point is H r (H rx ,H ry ,H rz ) is calculated by the following formula (4):

[0021]

[0022] The magnetic field strengths of the four test points (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0) are H1(H 1x ,H 1y ,H 1z ),H2(H 2x ,H 2y ,H 2z ),H3(H 3x ,H 3y ,H 3z ),H4(H 4x ,H 4y ,H 4z), the intersection points of the four test points and the circular surface are (x1, y1, 0), (x2, y2, 0), (x3, y3, 0), (x4, y4, 0); According to the above formula (4), the following formula (5) is obtained:

[0023]

[0024] Solve equation (5) and calculate the intersection point (x0, y0, 0) between the wire and the circular surface, as shown in equation (6):

[0025]

[0026] According to the above formula (4), we can know that:

[0027]

[0028] Solve equation (7) and calculate the direction of the wire (l, m, n), as shown in equation (8):

[0029]

[0030] Then we can find any point (x r ,y r ,0), the distance between the conductor and r , as shown in the following formula (9):

[0031]

[0032] The current I of the wire is obtained as:

[0033] I=2πl r H r (10)

[0034] Based on the above analysis, the current I of the wire is calculated using the following steps:

[0035] The magnetic field strengths of the four test points (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0) are measured by four sets of TMR sensor arrays, and the values are H1 (H 1x ,H 1y ,H 1z ),H2(H 2x ,H 2y ,H 2z ),H3(H 3x ,H 3y ,H 3z ),H4(H 4x ,H 4y ,H 4z), the intersection points of the four test points and the circular surface are (x1,y1,0),(x2,y2,0),(x3,y3,0),(x4,y4,0);

[0036] Calculate the proportional coefficients k1 to k8 according to equations (5) and (7);

[0037] According to formula (6), the intersection position (x0, y0, 0) of the wire and the plane of the four TMR sensor arrays is calculated;

[0038] Calculate the conductor current direction angle (l, m, n) according to formula (8);

[0039] Calculate the current I according to equations (9) and (10).

[0040] By means of the above technical solution, the self-calibration method of the tunnel magnetoresistance TMR sensor provided in the embodiment of the present application ensures the stability of the TMR sensor in different working environments through real-time feedback and automatic correction. The self-calibration module can adjust and compensate for deviations caused by environmental factors such as temperature fluctuations, external magnetic field interference, humidity changes and mechanical vibrations in real time according to changes in the output voltages of the measured bridge and the reference bridge. Ultimately, the sensor can provide accurate magnetic field measurement results.

[0041] In addition, the TMR sensor array for current measurement provided in the embodiment of the present application further enhances its adaptability in complex environments. By forming an array of multiple TMR sensor units, not only can the spatial resolution of the measurement be improved, but the fault tolerance of the system can also be improved through redundant configuration. The array structure enables the TMR sensor to perform accurate measurements at multiple measurement points simultaneously to obtain accurate measured current, thereby improving the data processing speed and the overall responsiveness of the system. Moreover, this embodiment also combines self-calibration technology to ensure that the sensor always maintains high precision in different working environments by real-time monitoring and correction of the sensor's working status. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for describing the embodiments of the present application.

[0043] Figure 1 The structure of the magnetic tunnel junction element and its measurement principle diagram provided by the embodiment of the present application are shown;

[0044] Figure 2 The figure shows a double Wheatstone bridge structure for TMR sensor self-calibration provided in an embodiment of the present application;

[0045] Figure 3 A flow chart of a self-calibration method for a TMR sensor provided in an embodiment of the present application is shown;

[0046] Figure 4 FIG2 shows a layout diagram of a TMR sensor array for current measurement provided by an embodiment of the present application;

[0047] Figure 5 A flow chart of measuring conductor current using a TMR sensor array provided in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0048] The following describes exemplary embodiments of the present application in more detail with reference to the accompanying drawings. Although exemplary embodiments of the present application are shown in the accompanying drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present application and to fully convey the scope of the present application to those skilled in the art.

[0049] It should be noted that the terms "first," "second," and the like in the specification and claims of this application and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or precedence. It should be understood that such usage is interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein. In addition, the term "including" and its variations are to be interpreted as open-ended terms meaning "including but not limited to."

[0050] To solve the above technical problems, this embodiment uses a TMR sensor to measure the spatial magnetic field, and then indirectly measures the current based on the spatial magnetic field. The core structure of the TMR sensor is a magnetic tunnel junction, which consists of three layers: a soft magnetic layer, a thin insulating layer, and a hard magnetic layer. The structure and principle diagram of the magnetic tunnel junction element for measuring the magnetic field are shown in the figure below. Figure 1 As shown in Figure 1, when current passes through the TMR sensor, electrons pass through the insulating layer between the two layers of magnetic material, and the efficiency of their passage depends on the magnetization direction of the two layers of magnetic material. If the magnetization directions of the two magnetic layers are parallel, the probability of the tunneling effect is high and the resistance is small; if the magnetization directions are opposite, the probability of the tunneling effect is greatly reduced and the resistance increases. The TMR sensor uses the change in resistance caused by the change in magnetization direction to sense current. When current flows through the TMR structure, the current causes the magnetization direction of the magnetic layer to change, which in turn affects the strength of the tunneling effect and changes the resistance. By measuring the change in resistance, the change in external magnetic field or current can be inferred. The magnetic tunnel junction can measure the magnitude of the external magnetic field H, and the rate of change of the resistance of the magnetic tunnel junction element is proportional to the external magnetic field, as shown in formula (11):

[0051]

[0052] Wherein, ΔR is the resistance change of the magnetic tunnel junction caused by the magnetic field, R is the original resistance of the magnetic tunnel junction, and k is the magnetoresistance sensitivity of the magnetic tunnel junction.

[0053] Theoretically, the external magnetic field can be measured based on the rate of change of the resistance of the magnetic tunnel junction element. However, in reality, the measurement results of the external magnetic field will be affected by environmental factors and produce measurement errors. In particular, factors such as temperature changes, external magnetic field fluctuations, humidity changes and mechanical vibrations will interfere with the component measurement results.

[0054] Therefore, this embodiment adopts Figure 2 The double Wheatstone bridge structure shown in the circuit, one of the bridges (i.e. the bridge to be measured) is used to detect the magnetic field H to be measured. test , the other bridge (i.e. reference bridge) is used to detect the reference magnetic field H ref ;U in is the input voltage of the bridge to be measured, U out,test is the output voltage of the bridge to be measured, U out,ref is the reference bridge output voltage. By monitoring and comparing the output voltages of the two bridges in real time, the system can eliminate errors caused by environmental factors such as temperature changes, magnetic field interference, humidity changes, and mechanical vibration, thus achieving self-calibration of the TMR sensor. This method not only eliminates temperature drift but also compensates for the effects of other environmental factors on the sensor output.

[0055] The self-calibration method of the TMR sensor proposed in this embodiment is as follows: Figure 3 As shown, the following steps S301 to S303 are included:

[0056] Step S301, constructing a double Wheatstone bridge including a bridge to be measured and a reference bridge, wherein the bridge to be measured is used to detect a magnetic field to be measured, and the reference bridge is used to detect a reference magnetic field;

[0057] The bridge to be measured is used to measure the magnetic field to be measured. test Under this condition, the resistance of the magnetic tunnel junction changes, and the output voltage of the bridge to be measured is U out,test The output voltage of the bridge to be measured is proportional to the magnetic field to be measured, and is shown in the following formula (1):

[0058]

[0059] Where ΔR is the resistance change of the magnetic tunnel junction caused by the magnetic field, R is the original resistance of the magnetic tunnel junction, and U in is the input voltage of the bridge to be measured, f c1 is the drift error function of the environmental interference on the output voltage of the bridge to be measured, k is the magnetoresistance sensitivity of the magnetic tunnel junction;

[0060] Step S302: Control the reference bridge to a known reference magnetic field H.ref Working under the same conditions, the reference bridge and the bridge to be tested have the same component parameters, and the reference bridge output voltage U out,ref As shown in the following formula (2):

[0061] U out,ref =k·H ref ·U in ·f c2 (2);

[0062] Among them, f c2 is the drift error function of the influence of environmental interference on the output voltage of the reference bridge; since the factors causing the drift error in the environment of the reference bridge are the same as those in the environment of the bridge to be measured, f c1 =f c2 ;

[0063] Step S303: perform self-calibration of the TMR sensor and calculate the ratio of the output voltage of the bridge to be tested to the output voltage of the reference bridge. According to this ratio, combined with the known reference magnetic field H ref , use the following formula (3) to calculate the magnetic field H to be measured test :

[0064]

[0065] The self-calibration method for the tunnel magnetoresistive (TMR) sensor provided in this embodiment ensures the stability of the TMR sensor in different operating environments through real-time feedback and automatic correction. The self-calibration module can adjust and compensate for deviations caused by environmental factors such as temperature fluctuations, external magnetic field interference, humidity changes, and mechanical vibration in real time based on changes in the output voltages of the test bridge and the reference bridge. Ultimately, the sensor can provide accurate magnetic field measurement results.

[0066] This embodiment also proposes a TMR sensor array for current measurement, wherein each TMR sensor in the TMR sensor array adopts the above Figure 3 The method shown is used for self-calibration, wherein the TMR sensor array is divided into a first number of groups, each group of TMR sensor arrays includes a second number of TMR sensors, and the second number of TMR sensors are respectively used to measure components of the magnetic field of the test point on different axes. The first number of TMR sensor arrays are arranged on a circle with a radius of r, and the conductive wire is within the circle formed by the first number of TMR sensor arrays.

[0067] In an embodiment of the present application, a possible implementation is provided, where the first number of groups is four groups, and the second number of TMR sensors is three TMR sensors.

[0068] In an embodiment of the present application, a possible implementation method is provided, in which three TMR sensors are used to measure the components of the magnetic field of the measured point on the X-axis, Y-axis, and Z-axis, respectively. Four groups of sensor arrays are arranged on a circle with a radius of r, and their positions are respectively (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0).

[0069] In one possible implementation, Figure 4 The figure shows the arrangement of the sensor array. There are four groups of TMR sensor arrays, namely sensor array 1, sensor array 2, sensor array 3 and sensor array 4. Each group of TMR sensor arrays contains three TMR sensors, which are used to measure the components of the magnetic field of the test point in the X axis, Y axis and Z axis respectively. Figure 4 The X-axis is represented by x, the Y-axis is represented by y, and the Z-axis is represented by z. Four sensor arrays are arranged on a circle with a radius of r, and their positions are (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0). The straight wire is within the circle formed by the four sensor arrays. The angle between the wire and the Z-axis is θ, and the angle between the wire and the X-axis is γ. The intersection of the wire and the circular surface is (x0, y0, z0). Here, z0 can be set to 0, indicating that on the circular surface, the direction of the wire is (l, m, n), and the current of the wire is I;

[0070] According to Biot-Savart's law, for any point (x r ,y r ,0), the magnetic field strength at this point is H r (H rx ,H ry ,H rz ) is calculated by the following formula (4):

[0071]

[0072] The magnetic field strengths of the four test points (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0) are H1(H 1x ,H 1y ,H 1z ),H2(H 2x ,H 2y ,H 2z ),H3(H 3x ,H 3y ,H 3z ),H4(H 4x ,H 4y ,H 4z), the intersection points of the four test points and the circular surface are (x1, y1, 0), (x2, y2, 0), (x3, y3, 0), (x4, y4, 0); According to the above formula (4), the following formula (5) is obtained:

[0073]

[0074] Solve equation (5) and calculate the intersection point (x0, y0, 0) between the wire and the circular surface, as shown in equation (6):

[0075]

[0076] According to the above formula (4), we can know that:

[0077]

[0078] Solve equation (7) and calculate the direction of the wire (l, m, n), as shown in equation (8):

[0079]

[0080] Then we can find any point (x r ,y r ,0), the distance between the conductor and r , as shown in the following formula (9):

[0081]

[0082] The current I of the wire is obtained as:

[0083] I=2πl r H r (10)

[0084] According to the above analysis, the Figure 5 In steps S501 to S505, the current I of the conductor is calculated:

[0085] Step S501: Use four groups of TMR sensor arrays to measure the magnetic field strengths of the four test points (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0). 1x ,H 1y ,H 1z ),H2(H 2x ,H 2y ,H 2z ),H3(H 3x ,H 3y ,H 3z ),H4(H 4x ,H 4y ,H 4z), the intersection points of the four test points and the circular surface are (x1,y1,0),(x2,y2,0),(x3,y3,0),(x4,y4,0);

[0086] Step S502, calculating proportional coefficients k1 to k8 according to equations (5) and (7);

[0087] Step S503, calculating the intersection position (x0, y0, 0) of the wire and the plane of the four TMR sensor arrays according to formula (6);

[0088] Step S504, calculating the conductor current direction angle (l, m, n) according to formula (8);

[0089] Step S505: Calculate the current I according to equations (9) and (10).

[0090] By constructing a dual Wheatstone bridge structure and introducing a self-calibration method, this embodiment effectively eliminates the drift effects of environmental factors such as temperature, humidity, and mechanical vibration on the TMR sensor output, significantly improving the accuracy and stability of magnetic field and current measurements. Compared to traditional sensor systems, this embodiment has the ability to adapt to environmental changes and achieve real-time dynamic compensation without external intervention, enhancing the robustness and long-term reliability of the system. Furthermore, this embodiment combines a three-dimensional TMR sensor array structure with an electromagnetic field inversion model to achieve non-contact and precise inference of the magnitude, direction, and position of current in a spatial conductor. It possesses excellent three-dimensional sensing capabilities and spatial resolution, making it suitable for high-precision current monitoring in complex scenarios. The system has a simple structure, is easy to integrate, and has excellent engineering feasibility and promotional value.

[0091] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that, within the spirit and principles of the present application, they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not deviate from the protection scope of the present application.

Claims

1. A self-calibration method for a tunnel magnetoresistive (TMR) sensor, characterized in that: include: Constructing a double Wheatstone bridge comprising a bridge to be measured and a reference bridge, wherein the bridge to be measured is used to detect a magnetic field to be measured, and the reference bridge is used to detect a reference magnetic field; The bridge to be measured is used to measure the magnetic field to be measured. test Under the condition of , the resistance of the magnetic tunnel junction changes, and the output voltage of the bridge to be measured is U out,test The output voltage of the bridge to be measured is proportional to the magnetic field to be measured, and is expressed as follows: Where ΔR is the resistance change of the magnetic tunnel junction caused by the magnetic field, R is the original resistance of the magnetic tunnel junction, and U in is the input voltage of the bridge to be measured, f c1 is the drift error function of the influence of environmental interference on the output voltage of the bridge to be measured, and k is the magnetoresistance sensitivity of the magnetic tunnel junction; Control the reference bridge in a known reference magnetic field H ref Working under , the component parameters of the reference bridge and the bridge to be measured are consistent, and the reference bridge output voltage U out,ref As shown in the following formula (2): U out,ref =k·H ref ·U in ·f c2 (2); Among them, f c2 is the drift error function of the influence of environmental interference on the output voltage of the reference bridge; since the factors causing the drift error in the environment of the reference bridge are the same as those in the environment of the bridge to be tested, f c1 =f c2 ; Perform self-calibration of the TMR sensor and calculate the ratio of the output voltage of the bridge to be tested to the output voltage of the reference bridge According to this ratio, combined with the known reference magnetic field H ref , use the following formula (3) to calculate the magnetic field H to be measured test :

2. A TMR sensor array for current measurement, wherein each TMR sensor in the TMR sensor array is self-calibrated using the method of claim 1, characterized in that: The TMR sensor array is divided into a first number of groups, each group of TMR sensor arrays contains a second number of TMR sensors, and the second number of TMR sensors are used to measure the components of the magnetic field of the test point on different axes. The first number of groups of TMR sensor arrays are arranged on a circle with a radius of r, and the wires are within the circle formed by the first number of groups of TMR sensor arrays.

3. The TMR sensor array for current measurement according to claim 2, wherein: The first number of groups is four, and the second number of TMR sensors is three.

4. The TMR sensor array for current measurement according to claim 3, wherein: The three TMR sensors are used to measure the components of the magnetic field on the X-axis, Y-axis, and Z-axis respectively. The four sensor arrays are arranged on a circle with a radius of r, and their positions are (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0).

5. The TMR sensor array for current measurement according to claim 4, wherein: Assume that the angle between the wire and the Z axis is θ, the angle between the wire and the X axis is γ, the intersection of the wire and the circular surface is (x0, y0, 0), the direction of the wire is (l, m, n), and the current in the wire is I; According to Biot-Savart's law, for any point (x r ,y r ,0), the magnetic field strength at this point is H r (H rx ,H ry ,H rz ) is calculated by the following formula (4): The magnetic field strengths of the four test points (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0) are H1(H 1x ,H 1y ,H 1z ),H2(H 2x ,H 2y ,H 2z ),H3(H 3x ,H 3y ,H 3z ),H4(H 4x ,H 4y ,H 4z ), the intersection points of the four test points and the circular surface are (x1, y1, 0), (x2, y2, 0), (x3, y3, 0), (x4, y4, 0); According to the above formula (4), the following formula (5) is obtained: Solve equation (5) and calculate the intersection point (x0, y0, 0) between the wire and the circular surface, as shown in equation (6): According to the above formula (4), we can know that: Solve equation (7) and calculate the direction of the wire (l, m, n), as shown in equation (8): Then we can find any point (x r ,y r ,0), the distance between the conductor and r , as shown in the following formula (9): The current I of the wire is obtained as: I=2πl r H r (10) Based on the above analysis, the current I of the wire is calculated using the following steps: The magnetic field strengths of the four test points (r, 0, 0), (0, r, 0), (-r, 0, 0), and (0, -r, 0) are measured by four sets of TMR sensor arrays, and the values are H1 (H 1x ,H 1y ,H 1z ),H2(H 2x ,H 2y ,H 2z ),H3(H 3x ,H 3y ,H 3z ),H4(H 4x ,H 4y ,H 4z ), the intersection points of the four test points and the circular surface are (x1,y1,0),(x2,y2,0),(x3,y3,0),(x4,y4,0); Calculate the proportional coefficients k1 to k8 according to equations (5) and (7); According to formula (6), the intersection position (x0, y0, 0) of the wire and the plane of the four TMR sensor arrays is calculated; Calculate the conductor current direction angle (l, m, n) according to formula (8); Calculate the current I according to equations (9) and (10).

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