CN111290029A - Towed electromagnetic device with non-coplanar Bucking compensation and manufacturing method - Google Patents

Abstract

A non-coplanar locking compensated dragging type electromagnetic device and a manufacturing method relate to the field of geophysical exploration electromagnetic method detection, and the device comprises a transient electromagnetic system host, a transmitting coil, a locking compensation coil, a receiving coil and a movable loading platform, wherein the transmitting coil, the receiving coil and the locking compensation coil are not coplanar with the central axis; the Bucking compensation coil is connected with the transmitting coil in series, the winding direction of the Bucking compensation coil is opposite to that of the transmitting coil, and the Bucking compensation coil is positioned above the receiving coil; the invention solves the technical problems of detection blind area, primary field coupling interference and low detection efficiency of the current transient electromagnetic small-size central loop detection device.

Description

Towed electromagnetic device with non-coplanar Bucking compensation and manufacturing method

technical field

The invention relates to the field of electromagnetic detection in geophysical exploration, in particular to a towed electromagnetic device with non-coplanar Bucking compensation applied to urban underground geological exploration and a manufacturing method.

Background technique

With the gathering of urban population, the utilization rate of urban land resources has become more and more tense. The development and utilization of underground space and the safe operation of underground space have become important issues that need to be solved urgently in large and medium-sized cities in my country. To achieve safe and efficient use of underground space, we must first detect the geological structure of underground space. As an important geophysical exploration method, ground transient electromagnetic method has the advantages of large detection depth and convenient working method in urban underground space detection compared with shallow seismic and ground penetrating radar methods. The transient electromagnetic center loop device is the preferred loop device for urban underground space due to its advantages of large sensitivity to underground anomalies and high lateral resolution. However, due to the limitation of urban road measurement environment, transient electromagnetic small-scale detection is required coil. At this time, the receiving coil and the transmitting coil are relatively close, and the primary field interference is more serious, and measures must be taken to compensate.

In the traditional aviation transient electromagnetic method, a Bucking compensation coil is introduced for the center loop device, that is, a reverse transmitting coil is added between the receiving coil and the surface where the transmitting coil is located, so that the primary field coupling effect at the receiving coil is weakened and the receiving amplifier is prevented. saturation, and due to the high altitude, the near-zone effect caused by the Bucking compensation coil is negligible. However, when this method is applied to the small-sized detection coil on the ground, it will inevitably bring about the near-area effect, that is, due to the introduction of the Bucking compensation coil, there is almost no secondary field response in the formation near the receiving coil, which brings the theoretical Detection of blind spots. For the urban road environment, the shallow geology often contains abnormal bodies such as pipelines and cables, which requires high shallow detection resolution, and the detection efficiency of traditional transient electromagnetic manual mobile detection is low. Therefore, it is of great significance to study transient electromagnetic detection technology with shallow non-blind zone, low primary field coupling and high detection efficiency.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a non-coplanar Bucking-compensated towed electromagnetic device and a manufacturing method in view of the above-mentioned deficiencies of the prior art. By introducing a movable loading platform, the relative position of the detection coil is optimized, and the current transient electromagnetic device is solved. The small size center loop detection coil has the technical problems of detection blind area, primary field coupling interference and low detection efficiency.

The purpose of this invention is to realize through the following technical solutions:

The invention proposes a non-coplanar Bucking compensation towed electromagnetic device, which is characterized by comprising: a transient electromagnetic system host, a transmitting coil, a Bucking compensation coil, a receiving coil and a movable loading platform. The transient electromagnetic system The host is set on the movable loading platform. The host of the transient electromagnetic system is connected with the transmitting coil and the receiving coil respectively. The host of the transient electromagnetic system is used to pass the pulse current signal to the transmitting coil, and at the same time receive the primary field induction fed back by the receiving coil to it. Voltage information; the transmitting coil is fixed on the table top of the movable loading platform, the transmitting coil is located under the receiving coil and the Bucking compensation coil, and the transmitting coil, the receiving coil and the Bucking compensation coil are not coplanar with the central axis; the Bucking compensation coil and The transmitting coil is connected in series, and the winding direction of the Bucking compensation coil is opposite to that of the transmitting coil. The Bucking compensation coil is located above the receiving coil, and the Bucking compensation coil is fixed on the movable loading platform through an insulating bracket; the receiving coil is set between the transmitting coil and the Bucking coil. Between the compensation coils, the receiving coil is fixed on a movable loading platform through an insulating bracket; the movable loading platform is an insulating platform.

Further, the transmitting coil is wound with copper enameled wire to form a multi-turn square loop, and the side length of the transmitting coil is smaller than the width of the urban road.

Further, the Bucking compensation coil is wound with a copper enameled wire to form a single-turn square loop, and the side length of the Bucking compensation coil is between 0.2 and 0.3 times the side length of the transmitting coil.

Further, the receiving coil is wound with copper enameled wire to form a multi-turn square loop, and the side length of the receiving coil is less than or equal to 0.3 times the side length of the transmitting coil.

The towed electromagnetic device for non-coplanar Bucking compensation is characterized in that: when winding the transmitting coil, a section is reserved for reversely winding the Bucking compensation coil, and the transmitting coil and the Bucking compensation coil (3) are connected to the section Winding in twisted pair form.

The present invention also proposes a method for manufacturing the above-mentioned non-coplanar Bucking-compensated towed electromagnetic device, which is characterized by comprising the following steps:

S1. Wind the copper enameled wire clockwise to form a square coil with side length a and number of turns N _a , and leave a certain amount of copper wire allowance to obtain a transmitting coil, and place the transmitting coil in the center of the movable loading platform, which can be moved The height of the loading platform from the ground is h ₀ ;

S2. Wind the remaining copper enameled wire of the transmitting coil at a distance h directly above the transmitting coil, and coaxially reversely wind it into a square coil with side length b and number of turns N _b to obtain a Bucking compensation coil;

S3. Wind the receiving coil into a square coil with side length c and number of turns N _c , and fix it coaxially between the transmitting coil and the Bucking compensation coil, the distance between the receiving coil and the transmitting coil is h _ac meters, and the receiving coil The distance from the Bucking compensation coil is h _bc meters, h=h _ac +h _bc ;

Wherein, the distance h between the Bucking compensation coil and the transmitting coil is obtained as follows:

It is determined according to the ratio of the vertical magnetic field strength of the coaxial position point on the ground together with the transmitting coil after the Bucking compensation coil is introduced to the vertical magnetic field strength of the point when only the transmitting coil is greater than 0.9, and the following formula is satisfied:

B _a (h ₀ )-B _b (h ₀ +h)≥0.9B _a (h ₀ )

where B _a (h ₀ ) is the vertical magnetic field strength at the point where the transmitter coil is located along the central axis of the ground, h ₀ is the vertical distance between the transmitter coil and the ground, which is a known quantity; B _b (h ₀ +h) is The magnetic field strength in the vertical direction of the point where the Bucking compensation coil is located along the central axis of the ground;

式中I为方形线圈电流大小，d为沿中心轴线上点距离方形线圈平面中心点的距离，μ₀为真空磁导率；将发射线圈与Bucking补偿线圈的尺寸距离参数代入该公式，即可确定Bucking补偿线圈与发射线圈的距离h；According to Bio-Savart's law, the magnetic field strength B _z (d) at d on the central axis of the square current-carrying coil with side length 2r satisfies:

In the formula, I is the current of the square coil, d is the distance from the point on the central axis to the center point of the square coil plane, and μ ₀ is the vacuum permeability; the parameter of the size distance between the transmitting coil and the Bucking compensation coil is substituted into this formula, you can Determine the distance h between the Bucking compensation coil and the transmitting coil;

Wherein, the method for determining the distance h _ac between the receiving coil and the transmitting coil and the distance h _bc between the receiving coil and the Bucking compensation coil includes the following steps:

①Using the Neumann formula to calculate the side length dimension of a, the number of turns is _{Na, the length of the opposite side of the transmitting coil is c, and the number of turns is N c The mutual inductance coefficient M ac of the} receiving coil

In the formula, x _a , y _a correspond to the abscissa and ordinate of the integration point on the transmitting coil; x _c , y _c correspond to the abscissa and ordinate of the integration point on the receiving coil; f(x _a , x _c ) and f(y _a , y _{c )} ) is the line element integral coefficient, which satisfies the following formula:

②In the same way, calculate the mutual inductance M _bc of the Bucking compensation coil whose side length is b and the number of turns is N _b to the receiving coil as

where x _b and y _b correspond to the abscissa and ordinate of the integration point on the transmitting coil; x _c and y _c correspond to the abscissa and ordinate of the integration point on the receiving coil;

③Using the known conditions of h=h _ac +h _bc , the above integral formula can be used to obtain the distance h _ac between the receiving coil and the transmitting coil and the distance h between the receiving coil and the Bucking compensation coil when M _ac =M _{bc bc} , the parameters obtained at this time can make the receiving coil in a state of primary field zero coupling.

Through the above-mentioned design scheme, the present invention can bring the following beneficial effects: the present invention proposes a non-coplanar Bucking compensation towed electromagnetic device and a manufacturing method. First, according to the design requirements, determine the size of the transmitting coil, the Bucking compensation coil and the receiving coil, According to Bio-Savart's law, the position of the Bucking compensation coil, which can ignore the near-zone effect, is obtained. The mutual inductance coefficient between the coils is used to calculate the optimal position of the receiving coil. In actual operation, the position of the receiving coil can be adjusted up and down to make up for the size. The error caused by the inaccuracy of the design makes the receiving coil easier to be in the zero coupling position of the primary field. The invention can reduce the primary field coupling interference of the receiving coil, make the near-area effect brought by the compensation coil negligible, the overall downward emission magnetic moment loss of the detection coil is small, and due to the non-coplanar design, the receiving coil has zero coupling The state is relatively better adjusted. In addition, the design of the towable movable loading platform makes the on-site detection efficiency higher and has greater practical application value.

Description of drawings

1 is a schematic structural diagram of a towed electromagnetic device for non-coplanar Bucking compensation in an embodiment of the present invention;

2 is a flow chart of the fabrication of a towed electromagnetic device with non-coplanar Bucking compensation in an embodiment of the present invention;

FIG. 3 is a test flow chart of the towed electromagnetic device with non-coplanar Bucking compensation according to an embodiment of the present invention.

In the picture: 1-transient electromagnetic system host; 2-transmitting coil; 3-bucking compensation coil; 4-receiving coil; 5-movable loading platform; 6-plastic column; 7-twisted pair.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

1 shows a schematic structural diagram of the non-coplanar Bucking-compensated towed electromagnetic device of the present invention, which includes a transient electromagnetic system host 1 , a transmitter coil 2 , a Bucking compensation coil 3 , a receiver coil 4 and a movable loading platform 5 .

The transient electromagnetic system host 1 integrates a transient electromagnetic transmitting system and a receiving system, and has a human-computer interaction interface, which can set the transmitting current, transmitting frequency, transmitting waveform and receiving sampling rate. At the same time, the transient electromagnetic system host 1 has a large The capacity storage space is used to store the collected data; the transient electromagnetic system host 1 is respectively connected with the transmitting coil 2 and the receiving coil 4, and the transient electromagnetic system host 1 is used to pass the pulse current signal to the transmitting coil 2, and simultaneously receive the receiving coil 4. The primary field induced voltage information fed back to it.

The transmitting coil 2 is wound into a multi-turn square loop with copper enameled wire. The transmitting coil 2 is fixed on the table top of the movable loading platform 5, and is located below the receiving coil 4 and the Bucking compensation coil 3. At the same time, it is connected with the receiving coil 4 and the Bucking compensation coil 3 is not coplanar with the central axis, and the side length dimension of transmitting coil 2 is smaller than the width of urban road (less than 2.3m). In this embodiment, the side length dimension of transmitting coil 2 is selected to be 2m.

The Bucking compensation coil 3 is wound into a single-turn square loop by using copper enameled wire. The Bucking compensation coil 3 is connected in series with the transmitting coil 2. The winding direction of the Bucking compensation coil 3 is opposite to that of the transmitting coil 2. The Bucking compensation coil 3 is located at Above the receiving coil 4, the Bucking compensation coil 3 is fixed on the movable loading platform 5 through the plastic column 6; The length of the three sides of the compensation coil is 0.56m.

The receiving coil 4 is made of copper enameled wire to make a multi-turn square loop, placed between the transmitting coil 2 and the Bucking compensation coil 3, and fixed by the plastic column 6, so that the receiving coil 4 is in a relatively uniform area, and the receiving coil is in a relatively uniform area. The side length dimension of 4 is generally not more than 0.3 times of the side length dimension of the transmitting coil 2. In this embodiment, the side length dimension of the receiving coil 4 is selected to be 0.3m.

The movable loading platform 5 is a movable insulating plastic loading platform, which is used for loading the entire transient electromagnetic system. The platform surface of the movable loading platform 5 is used to fix the transient electromagnetic system host 1 and the transmitting coil 2. The plastic column 6 on the movable loading platform 5 fixes the Bucking compensation coil 3 and the receiving coil 4 .

The Bucking compensation coil 3 is generally set aside when the transmitting coil 2 is wound, and is used for reversely winding the non-coplanar Bucking compensation coil 3. The connecting section between the transmitting coil 2 and the Bucking compensation coil 3 adopts a twisted pair 7 . Form winding.

Referring to FIG. 2, a flow chart of device fabrication is shown, including the following steps:

S1. Place the transmitting coil 2 in the center of the movable loading platform 5, the height of the movable loading platform 5 from the ground is h ₀ =0.3m, and the copper enameled wire is wound clockwise to make the side length a = 2m, and the number of turns is A square coil with Na = 4, and leave _a certain amount of copper wire allowance;

S2. The remaining copper wire of the transmitting coil 2 is placed at a distance h directly above the transmitting coil 2, and a single-turn Bucking compensation coil 3 with a side length of b=0.56m is coaxially reversely wound;

S3. Similarly, wind the receiving coil 4 into a square coil with a side length of c=0.56m and a number of turns of _Nc =128, and fix it coaxially between the transmitting coil 2 and the Bucking compensation coil 3, and the receiving coil The distance between 4 and the transmitting coil 2 is h _ac meters, and the distance between the receiving coil 4 and the Bucking compensation coil 3 is h _bc meters, h=h _ac +h _bc ;

Wherein, the distance h between the Bucking compensation coil 3 and the transmitting coil 2 is obtained as follows:

It is determined according to the ratio of the vertical magnetic field strength of the coaxial position point on the ground together with the transmitting coil 2 after the Bucking compensation coil 3 is introduced to the vertical magnetic field strength of the point when only the transmitting coil 2 is greater than 0.9, and the following formula is satisfied:

B _a (h ₀ )-B _b (h ₀ +h)≥0.9B _a (h ₀ )

Among them, B _a (h ₀ ) is the vertical magnetic field strength of the point where the transmitter coil 2 is located along the central axis of the ground, and h ₀ is the vertical distance between the transmitter coil 2 and the ground, which is a known quantity; B _b (h ₀ +h ) is the vertical magnetic field strength at the point where the ground position of the Bucking compensation coil 3 is located along the central axis;

式中I为方形线圈电流大小，d为沿中心轴线上点距离方形线圈平面中心点的距离，μ₀为真空磁导率；将发射线圈2与Bucking补偿线圈3的尺寸距离参数代入该公式，即可确定Bucking补偿线圈3与发射线圈2的距离，本实施例中求得Bucking补偿线圈3与发射线圈2的距离h＝0.3m；According to Bio-Savart's law, the magnetic field strength B _z (d) at d on the central axis of the square current-carrying coil with side length 2r satisfies:

In the formula, I is the current of the square coil, d is the distance from the point on the central axis to the center point of the square coil plane, and μ ₀ is the vacuum permeability; the size distance parameter of the transmitting coil 2 and the Bucking compensation coil 3 is substituted into this formula, The distance between the Bucking compensation coil 3 and the transmitting coil 2 can be determined. In this embodiment, the distance h=0.3m between the Bucking compensation coil 3 and the transmitting coil 2 is obtained;

The method for determining the value of the distance h _ac between the receiving coil 4 and the transmitting coil 2 and the distance h _bc between the receiving coil 4 and the Bucking compensation coil 3 includes the following steps:

①Using the Neumann formula to calculate the mutual inductance coefficient M _ac of the transmitting coil 2 with side length a, the number of turns is N _a , and the side length of the transmitting coil 2 is c, and the number of turns is N _c The receiving coil 4

In the formula, x _a , y _a correspond to the abscissa and ordinate of the integration point on the transmitting coil 2; x _c , y _c correspond to the abscissa and ordinate of the integration point on the receiving coil 4; f(x _a , x _c ) and f(y _a , y _c ) is the line element integral coefficient, which satisfies the following formula:

②In the same way, calculate the mutual inductance coefficient M _bc of Bucking compensation coil 3 with side length b and number of turns N _b to receiving coil 4 as

where x _b and y _b correspond to the abscissa and ordinate of the integration point on the transmitting coil 2 ; x _c and y _c correspond to the abscissa and ordinate of the integration point on the receiving coil 4 ;

③Using the known conditions of h=h _ac +h _bc , the above integral formula can be used to obtain the distance h _ac between the receiving coil 4 and the transmitting coil 2 and the receiving coil 4 and the Bucking compensation coil when M _ac =M _bc The distance h _bc of 3, in this embodiment, h _ac =0.24m, h _bc =0.06m;

S4. When the mutual inductance is equal, since the transmitting coil 2 and the Bucking compensation coil 3 are in series structure, the current is the same in magnitude and opposite in direction. At this time, the total magnetic flux on the surface where the receiving coil 2 is located is zero.

After the theoretical position of the receiving coil 4 is actually obtained, since there will inevitably be errors caused by factors such as manual winding of the coil, the receiving coil 4 is slightly moved and adjusted near the theoretical position value, and the receiving coil 4 is observed through an oscilloscope. The received signal state of the secondary eddy current field is adjusted to the optimal position, and finally fixed.

Referring to Figure 3, it shows the test flow chart of testing the non-coplanar Bucking-compensated towed electromagnetic device after fabrication, including the following steps:

S1. After the transmitting coil 2, the Bucking compensation coil 3, the receiving coil 4 and the transient electromagnetic system host 1 are assembled and fixed on the movable loading platform 5, the transmitting coil 2, the Bucking compensation coil 3 and the receiving coil 4 are input and output ports It is connected with the interface of the host 1 of the transient electromagnetic system through the lead wire, and the transmitting coil 2, the Bucking compensation coil 3 and the receiving coil 4 constitute the detection coil;

S2. According to the on-site situation, arrange the towed electromagnetic device with non-coplanar Bucking compensation, select the measuring point and measuring line, set the transient electromagnetic emission parameters and data acquisition parameters through the transient electromagnetic system host 1, and carry out the whole process data acquisition;

S3. Drag the movable loading platform 5 to measure the measurement points along the measurement line in turn, and record the measurement data until the end of the measurement;

S4. After data preprocessing is performed on the measurement data, an apparent resistivity algorithm is used for imaging.

Using the above parameters, the non-coplanar Bucking-compensated transient electromagnetic device structure was modeled and simulated in the commercial finite element software ANSYS Electronics. The transmit current was set to 10A, the turn-off time was set to 3 microseconds, and the receiving coil was explored in a uniform half space. 4, the simulation results show that in the traditional coplanar Bucking compensation design, the primary field induced voltage is 3V. Under the non-coplanar Bucking compensation structure design of this embodiment, the primary field induced voltage is only 30mV, which is more effective The primary field coupling interference is suppressed.

Claims (6)

1. A non-coplanar Bucking compensated towed electromagnetic device, comprising: the transient electromagnetic system comprises a transient electromagnetic system host (1), a transmitting coil (2), a packing compensating coil (3), a receiving coil (4) and a movable loading platform (5), wherein the transient electromagnetic system host (1) is arranged on the movable loading platform (5), the transient electromagnetic system host (1) is respectively connected with the transmitting coil (2) and the receiving coil (4), and the transient electromagnetic system host (1) is used for supplying a pulse current signal to the transmitting coil (2) and simultaneously receiving primary field induced voltage information fed back by the receiving coil (4) to the transmitting coil (2); the transmitting coil (2) is fixed on the table top of the movable loading platform (5), the transmitting coil (2) is positioned below the receiving coil (4) and the packing compensating coil (3), and the transmitting coil (2), the receiving coil (4) and the packing compensating coil (3) are different in center axis and are coplanar; the Bucking compensation coil (3) is connected with the transmitting coil (2) in series, the winding direction of the Bucking compensation coil (3) is opposite to that of the transmitting coil (2), the Bucking compensation coil (3) is positioned above the receiving coil (4), and the Bucking compensation coil (3) is fixed on the movable loading platform (5) through an insulating support; the receiving coil (4) is arranged between the transmitting coil (2) and the Bucking compensation coil (3), and the receiving coil (4) is fixed on the movable loading platform (5) through an insulating support; the movable loading platform (5) is an insulating platform.

2. The non-coplanar Bucking compensated towed electromagnetic device of claim 1, wherein: the transmitting coil (2) is formed by winding a copper enameled wire into a multi-turn square loop, and the side length of the transmitting coil (2) is smaller than the width of an urban road.

3. The non-coplanar Bucking compensated towed electromagnetic device of claim 2, wherein: the Bucking compensation coil (3) is wound by a copper enameled wire to form a single-turn square return wire, and the side length of the Bucking compensation coil (3) is 0.2-0.3 times of that of the transmitting coil (2).

4. The non-coplanar Bucking compensated towed electromagnetic device of claim 3, wherein: the receiving coil (4) is made into a multi-turn square loop by winding a copper enameled wire, and the side length of the receiving coil (4) is less than or equal to 0.3 time of that of the transmitting coil (2).

5. The non-coplanar Bucking compensated towed electromagnetic device of claim 4, wherein: and when the transmitting coil (2) is wound, a section is reserved for reversely winding the packing compensation coil (3), and the connecting section of the transmitting coil (2) and the packing compensation coil (3) is wound in a twisted-pair manner.

6. A method of making the non-coplanar Bucking compensated towed electromagnetic device of claim 5, comprising the steps of:

s1, clockwise winding a copper enameled wire into side length a, wherein the number of turns is N_aThe method comprises the steps of (1) obtaining a transmitting coil (2) by reserving a certain copper wire allowance, placing the transmitting coil (2) in the center of a movable loading platform (5), wherein the height of the movable loading platform (5) from the ground is h₀；

S2, coaxially and reversely winding the residual copper enameled wire of the transmitting coil (2) at a position h right above the transmitting coil (2) to form a side length b, wherein the number of turns is N_bThe Bucking compensation coil (3) is obtained by the square coil;

s3, winding the receiving coil (4) to a side length of c and a turn number of N_cThe square coil is coaxially fixed between the transmitting coil (2) and the Bucking compensation coil (3), and the distance between the receiving coil (4) and the transmitting coil (2) is h_acThe distance between the receiving coil (4) and the Bucking compensation coil (3) is h_bcRice, h ═ h_ac+h_bc；

Wherein, the distance h between the Bucking compensation coil (3) and the transmitting coil (2) is obtained by the following method:

the magnetic field strength of the point which is coaxial with the ground and is provided with the Bucking compensation coil (3) and the transmitting coil (2) together is determined when the ratio of the magnetic field strength of the point in the vertical direction to the magnetic field strength of the point in the vertical direction when only the transmitting coil (2) is larger than 0.9, and the following formula is satisfied:

B_a(h₀)-B_b(h₀+h)≥0.9B_a(h₀)

wherein B is_a(h₀) A magnetic field strength h in a direction perpendicular to a point where a ground position of the transmitting coil 2 is located in a direction of the central axis₀The vertical distance between the transmitting coil (2) and the ground is a known quantity; b is_b(h₀+ h) is the magnetic field intensity of the Bucking compensation coil (3) in the vertical direction at the point where the ground position is located along the central axis direction;

according to the Bio savart law, the magnetic field intensity B at the position d on the central axis of the square current-carrying coil with the side length of 2r_z(d) Satisfies the following conditions:

wherein I is the current of the square coil, d is the distance from the central point of the plane of the square coil along the central axis of the square coil, and mu₀Is a vacuum magnetic conductivity; substituting the size distance parameters of the transmitting coil (2) and the Bucking compensation coil (3) into the formula to determine the distance h between the Bucking compensation coil (3) and the transmitting coil (2);

wherein the distance h between the receiving coil (4) and the transmitting coil (2)_acAnd the distance h between the receiving coil (4) and the Bucking compensation coil (3)_bcThe method for determining the value comprises the following steps:

① calculating the side length a and the number of turns N by using the Noemann formula_aThe length of the opposite side of the transmitting coil (2) is c, the number of turns is N_cMutual inductance M of the receiving coil (4)_ac

In the formula x_a、y_aCorresponding to the horizontal and vertical coordinates of the integral point on the transmitting coil (2); x is the number of_c、y_cCorresponding to the horizontal and vertical coordinates of the integral point on the receiving coil (4); f (x)_a,x_c) And f (y)_a,y_c) For the line element integral coefficient, the following equation is satisfied:

② calculating side length with b and N turns_bThe mutual inductance coefficient M of the Bucking compensation coil (3) to the receiving coil (4)_bcIs composed of

In the formula x_b、y_bCorresponding to the horizontal and vertical coordinates of the integral point on the transmitting coil (2); x is the number of_c、y_cCorresponding to the horizontal and vertical coordinates of the integral point on the receiving coil (4);

③ using h-h_ac+h_bcUnder known conditions, the proper M can be obtained through the integral formula_ac＝M_bcWhile the distance h between the receiving coil (4) and the transmitting coil (2)_acAnd the distance h between the receiving coil (4) and the Bucking compensation coil (3)_bcThe parameters obtained in this case enable the receiving coil (4) to be in a primary field zero coupling state.

Images