阅读说明：本技术 空间电磁场作用分叉线的电磁耦合时域建模分析方法 (Electromagnetic coupling time domain modeling analysis method for space electromagnetic field action bifurcation line ) 是由 叶志红 吴小林 汝梦祖 石艳超 鲁唱唱 张玉 于 2020-12-15 设计创作，主要内容包括：本发明提供了一种空间电磁场作用分叉线的电磁耦合时域建模分析方法,首先,将分叉线按照分叉节点分解成多段独立的多导体传输线和分叉节点的级联网络结构。然后,采用传输线方程结合插值技术,构建各段多导线对应的电磁耦合模型,并采用时域有限差分(FDTD)方法的中心差分格式对传输线方程进行离散,迭代求解得到各段多导线上的电压和电流响应。最后,提取各段多导线对分叉节点作用的诺顿等效电路,结合电路分析方法,获得分叉节点各端口电压,并作为激励源反馈给各段多导线作为边界条件,实现各段多导线之间的干扰信号传输。本发明在避免对分叉线结构直接建模的前提下,从时域的角度实现了空间电磁场作用分叉线的场线耦合快速协同仿真。(The invention provides an electromagnetic coupling time domain modeling analysis method of a space electromagnetic field acting bifurcation, which comprises the following steps of decomposing the bifurcation into a plurality of sections of independent multi-conductor transmission lines and a cascade network structure of the bifurcation according to the bifurcation. And then, constructing an electromagnetic coupling model corresponding to each section of the multi-conductor by combining a transmission line equation with an interpolation technology, dispersing the transmission line equation by adopting a central difference format of a Finite Difference Time Domain (FDTD) method, and iteratively solving to obtain voltage and current responses on each section of the multi-conductor. And finally, extracting a Norton equivalent circuit acted by each section of multi-conductor on the bifurcation node, combining a circuit analysis method to obtain the voltage of each port of the bifurcation node, and feeding the voltage as an excitation source back to each section of multi-conductor to be used as a boundary condition to realize the transmission of interference signals among each section of multi-conductor. On the premise of avoiding direct modeling of a bifurcate structure, the method realizes the field line coupling rapid collaborative simulation of the bifurcate under the action of the space electromagnetic field from the angle of the time domain.)

1. The electromagnetic coupling time domain modeling analysis method of the space electromagnetic field action bifurcation is characterized by comprising the following steps of:

according to the branch node, the branch line is decomposed into a plurality of sections of independent multi-conductor transmission lines;

constructing an electromagnetic coupling model of each section of multi-conductor transmission line under the action of a space electromagnetic field by adopting a transmission line equation;

calculating unit length distribution parameters of each section of multi-conductor according to an empirical formula, calculating an excitation field of each section of multi-conductor by combining an FDTD (finite Difference time division) method and a corresponding interpolation technology, and introducing a transmission line equation as an equivalent distribution source term;

carrying out backward difference discretization on a transmission line equation by adopting an FDTD method, and iteratively solving to obtain voltage and current transient response on each section of multi-conductor;

according to the Noton theorem, a Noton equivalent circuit of each section of multi-conductor acting on the branched node is extracted, the voltage response of each port of the branched node is obtained by solving in combination with a circuit analysis method, and the voltage response is fed back to each section of multi-conductor as an excitation source to realize the transmission of interference signals.

2. The method for electromagnetic coupling time domain modeling analysis of a spatial electromagnetic field effect bifurcation of claim 1, wherein: the electromagnetic coupling model of the space electromagnetic field acting on each section of the multi-conductor transmission line is as follows:

wherein L represents the position of each point on the multi-conductor, t represents different time, V (L, t) and I (L, t) respectively represent the voltage and current vectors on the multi-conductor, L and C are the unit length inductance and capacitance distribution parameter matrixes of the multi-conductor, respectively, V_F(l, t) and I_FAnd (l, t) are an equivalent distributed voltage source and a distributed current source of the transmission line equation respectively.

3. The method for electromagnetic coupling time domain modeling analysis of a spatial electromagnetic field effect bifurcation of claim 1, wherein: the unit length distribution parameter of each section of the multi-conductor comprises the following calculation steps: the value of each element of the inductance parameter matrix L in unit length can be calculated by a formula L_ii＝μ₀ln(2h_i/r_i) A sum of/2 piCalculated, where i and j represent the ith and jth transmission lines, μ₀Denotes the permeability of free space, h_i,h_jAnd d_ijRespectively representing the height of the ith and jth transmission lines and the distance between two wires; the capacitance parameter matrix C per unit length can be represented by the formula C ═ μ₀ε₀L^-1Is obtained as₀The representation represents the dielectric constant of free space.

4. An electromagnetic coupling time domain modeling analysis method of a spatial electromagnetic field effect bifurcation of any one of claims 1-3, characterized in that: and the step of calculating the excitation field of each section of the multi-wire comprises calculating the incident electric field component along the multi-wire and the vertical incident electric field component between the multi-wire and the grounding plate.

5. The method for electromagnetic coupling time domain modeling analysis of a spatial electromagnetic field effect bifurcation of claim 4, wherein: the calculation of the excitation field of each section of the multi-conductor specifically comprises the following steps:

dividing the transmission line into a plurality of sections of independent cable units according to the FDTD grid, wherein the starting point and the end point of each section of cable unit are positioned on the FDTD grid, the central point is positioned on the central plane of the FDTD grid, and then the electric field along the cable unit at the central point is expressed as E.e by vector product_l＝E_x·a_xe_x+E_y·a_ye_yWherein E and E_lRespectively representing the electric field at the center point of the cable unit and the direction vector of the cable unit. e.g. of the type_xAnd e_yUnit direction vectors, a, representing the x and y directions, respectively_xAnd a_yRespectively the ratio of the components of the electric field along the line in the x and y directions, E_xAnd E_yThe electric field components representing the x and y directions at the central point of the cable unit need to be obtained by interpolating the electric field components of four adjacent FDTD grids, E_yIs expressed as:

E_y＝(1-η)[ξE_y1+(1-ξ)E_y3]+η[ξE_y2+(1-ξ)E_y4]

wherein E is_y1,E_y2,E_y3And E_y4The electric field component on the y-direction edge of the FDTD grid is represented by eta and xi respectively representing the proportion factors of the central point in the z direction and the x direction of the FDTD grid; e_xThe interpolation formula of (2) is the same;

for the vertical incident electric field component between any one of the conductive lines and the ground plateBy two adjacent FDTD grid electric field components E_zThe interpolation yields, expressed as:

transmission line vertical electric field component adjacent theretoBy 4 adjacent FDTD grid electric field components E_zThe interpolation yields, expressed as:

where α and β represent the scale factors of the starting or ending point of the cable unit in the x-and z-direction of the FDTD grid, respectively, E_z1，E_z2，E_z3，E_z4，E_z5，E_z6Respectively representing the electric field components of the z-direction edges of the grids adjacent to the starting point or the ending point of the cable unit.

6. The method for electromagnetic coupling time domain modeling analysis of a spatial electromagnetic field effect bifurcation of claim 1, wherein: the backward difference discretization specifically comprises: v_NTerminal voltage of any section of transmission line, I_LFor the current flowing into the port, after applying backward difference processing, it is expressed as:

deltax and Deltat respectively represent the space step and the time step required by differential dispersion, C represents the capacitance distribution parameter of the unit length of the transmission line,representing the current in the transmission line in the vicinity of the terminal,andrespectively representing the current and voltage at a moment on the norton circuit port,andrespectively representing the current and voltage at the new moment of the norton circuit port.

7. The method for electromagnetic coupling time domain modeling analysis of a spatial electromagnetic field effect bifurcation of claim 6, wherein: the Norton equivalent circuit is as follows:

wherein, I_LHAnd G_eqRespectively representing the current source term and the equivalent admittance of the norton equivalent circuit.

8. The method for analyzing electromagnetic coupling time domain modeling of the spatial electromagnetic field acting bifurcation according to claim 1, 6 or 7, wherein: the action of the transmission line on the branch node is equivalent through the norton circuit, specifically: the action of each segment of the inclined multi-conductor on the branching node is equivalent through a controlled current source and a parallel circuit of equivalent admittance, and the action of each segment of the inclined multi-conductor on the branching node is replaced through a controlled voltage source.

9. The method of claim 8, wherein the method comprises the following steps:

the circuit analysis method solves the voltage response of each port of the bifurcation node, and constructs a relation matrix between the voltage and the current of each port of the bifurcation node, which is expressed as follows:

GU＝I

wherein, U and I respectively represent the voltage vector and the current vector of the branch node port, and G is a network admittance matrix.

Technical Field

The invention relates to an electromagnetic coupling time domain modeling analysis method of a bifurcation wire under the action of a space electromagnetic field, provides a high-efficiency field wire coupling time domain algorithm, and is suitable for electromagnetic interference analysis of a bifurcation wire end connection circuit under a complex electromagnetic environment.

Background

In complex objects such as airplanes, trains, etc., it is often necessary to use multiple types of cables to enable data communication between different devices. In order to save space for cable laying, cables are bundled and routed in a local area and then separated and conveyed to different equipment, and the cable type is called a branch line. Because of the numerous devices contained in the airplanes and the trains, some devices can not spontaneously generate electromagnetic leakage when in work, then the electromagnetic leakage is radiated to act on the branch line to generate a strong interference signal, and then the strong interference signal flows into a branch line end connection circuit to cause interference or damage. Therefore, in order to ensure the safety and reliability of the running of the targets such as airplanes and trains, the electromagnetic coupling time domain modeling analysis method for the space electromagnetic field action bifurcation is developed, and the method has very important research significance and engineering application value.

To avoid direct modeling of fine cable structures, foreign and domestic scholars propose hybrid algorithms combining full-wave algorithms with transmission line theory, such as BLT equation, FDTD-SPICE method, etc. However, the conventional BLT equation is a frequency domain algorithm, and only a single-frequency cable interference response can be obtained through one calculation, and when the spatial electromagnetic field is a broadband signal, the calculation efficiency is low. The FDTD-SPICE method is a time domain algorithm, which solves a cable excitation field through a Finite Difference Time Domain (FDTD) method, then uses SPICE software to construct an electromagnetic coupling model of a cable, and simulates to obtain transient response on the cable and a terminating load thereof. However, this method requires a complicated theoretical derivation when establishing a cable SPICE equivalent circuit model, and the spatial electromagnetic field and the cable transient response need to be calculated separately, which leads to a sharp drop of the algorithm efficiency with the increase of the calculation time. Therefore, an efficient field line coupling algorithm is urgently needed to be researched, under the condition that the calculation accuracy is the same as that of a full-wave algorithm, the transient response of the branch line and the terminal load of the branch line is obtained through quick calculation, and the collaborative simulation of the space electromagnetic field radiation and the transient response of the branch line can be realized.

Disclosure of Invention

The invention aims to solve the technical problem that time domain modeling cannot be realized and a field circuit cannot be coordinated when the electromagnetic coupling of a bifurcated line is processed in the prior art, and provides a high-efficiency field line coupling time domain algorithm which can quickly simulate and analyze the electromagnetic interference problem of a space electromagnetic field acting on the bifurcated line.

The invention solves the technical problem, adopts the technical scheme that the electromagnetic coupling time domain modeling analysis method of the space electromagnetic field action bifurcation comprises the following steps:

the split line is split into multiple independent multi-conductor transmission lines according to the split node.

And constructing an electromagnetic coupling model of the space electromagnetic field acting on each section of the multi-conductor transmission line by adopting a transmission line equation.

According to an empirical formula, calculating unit length distribution parameters of each section of multi-conductor, combining an FDTD method and a corresponding interpolation technology, calculating an excitation field of each section of multi-conductor, and introducing a transmission line equation as an equivalent distribution source term.

And carrying out backward difference discretization on the transmission line equation by adopting an FDTD method, and iteratively solving to obtain the transient response of the voltage and the current on each section of the multi-conductor.

According to the Noton theorem, a Noton equivalent circuit of each section of multi-conductor acting on the branched node is extracted, the voltage response of each port of the branched node is obtained by solving in combination with a circuit analysis method, and the voltage response is fed back to each section of multi-conductor as an excitation source to realize the transmission of interference signals.

The method is based on the Noton theorem and the replacement theorem, combines the advantages of a transmission line equation for efficiently constructing a field line coupling model and the characteristics of FDTD method time domain full wave simulation, introduces a corresponding interpolation technology, forms an efficient field-path mixed time domain algorithm, and realizes the rapid collaborative simulation of the field paths of the space electromagnetic field action branch line. The algorithm firstly decomposes a bifurcation line into a plurality of sections of independent multi-conductors according to the Norton theorem and the displacement theorem, the action of each section of multi-conductor on the bifurcation node is equivalent through a Norton circuit, and the action of each section of multi-conductor on the bifurcation node is displaced through a controlled voltage source. Then, aiming at each section of the multi-conductor, an electromagnetic coupling model is constructed by adopting a transmission line equation, an FDTD method is combined with an interpolation technology to calculate an excitation field of the multi-conductor, the transmission line equation is introduced on each time step to serve as an equivalent distribution source item, on the basis, the transmission line equation is subjected to differential dispersion by using a central differential format of the FDTD method, voltage and current responses on each section of the multi-conductor are obtained through iterative solution on the time step of the FDTD, and the cooperative calculation of space electromagnetic field radiation and multi-conductor transient response is realized. Then, according to the voltage and current response on each section of the multiple conductors, the current source item and the equivalent admittance size of each Noton circuit are obtained, a circuit analysis method is applied to solve and obtain the voltage response of the equivalent circuit port of the forked node, the voltage response is fed back to each section of the multiple conductors to obtain the size of the controlled voltage source, and the transmission of interference signals among each section of the multiple conductors can be completed in the next time step, so that the collaborative simulation of the field path is realized.

The method has the advantages that firstly, the electromagnetic coupling model of each section of the multi-conductor transmission line is constructed by adopting a transmission line equation, so that the direct modeling of the fine structure of the multi-conductor is avoided; then, calculating a multi-wire excitation field by combining an FDTD method with an interpolation technology, and introducing a transmission line equation into each time step, so that time domain collaborative simulation of space electromagnetic field radiation and transmission line transient response can be realized; and finally, according to the Noton theorem and the replacement theorem, the bifurcation line is decomposed into a cascade network of a plurality of independent multi-conductor and bifurcation node Noton equivalent circuit models, and a circuit analysis method is applied to realize the effective transmission of interference signals among the multi-conductor sections. The method realizes the collaborative simulation of the radiation of the space electromagnetic field and the transient response of the bifurcation line from the angle of the time domain, and solves the electromagnetic coupling modeling problem of the bifurcation line under the action of the space electromagnetic field.

Drawings

In order to more clearly illustrate the embodiments of the present invention, drawings and tables to be used in the embodiments will be briefly described below.

FIG. 1 is a flow chart of the present invention;

fig. 2 is a schematic structural view of a bifurcation line on a ground plate;

FIG. 3 is a schematic diagram of the calculation of the distribution parameters per unit length of a multi-conductor transmission line;

FIG. 4 is a schematic diagram of electric field interpolation calculation at a central point of a cable unit;

FIG. 5 is a schematic diagram of interpolation calculation of vertical electric fields at the starting point and the ending point of a cable unit;

FIG. 6 is a schematic diagram of backward differential processing of transmission line port voltage;

FIG. 7 is a Nonton equivalent circuit diagram of a bifurcated node;

FIG. 8 is an equivalent circuit model diagram of the overall structure of a branch line;

FIG. 9 is a schematic diagram of the calculation of the voltage at the node port of the bifurcation;

FIG. 10 is a graph of the voltage response across the load 14 from a field line coupled time domain algorithm versus CST simulation.

Detailed Description

The technical solution of the present invention is described in detail below with reference to the accompanying drawings and examples.

This embodiment will be described by taking a branched line electromagnetic coupling formed by five transmission lines acting on a space electromagnetic field as an example.

The electromagnetic coupling model of the spatial electromagnetic field acting bifurcation is shown in fig. 2 and comprises a ground plate 1, a first transmission line 2, a second transmission line 3, a third transmission line 4, a bifurcation node 5, loads 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and an incident wave 16. The size of the ground plate 1 is L_c×W_c. The first transmission line 2 has a length l₁. The second transmission line 3 and the third transmission line 4 have a projection length l in the direction of the first transmission line 2₂The angles between the wiring direction and the direction of the first transmission line 2 are respectively theta₂And theta₁. The first, second and third transmission lines 2, 3 and 4 have a height h, a wire spacing d and a wire radius r. The load 6, the load 7, the load 8, the load 9, the load 10, the load 11, the load 12, the load 13, the load 14 and the load 15 are all resistors, and the resistance values of the resistors can be defined by themselves. The incident wave 16 is a source of disturbance. L is_c、W_c、l₁、l₂、h、d、r、θ₁And theta₂The specific parameter value can be set by self.

The implementation process of the invention comprises the following steps:

step 1, decomposing the branch line into 3 sections of independent multi-conductor transmission lines according to the branch nodes, and cascading each section of multi-conductor transmission line through the branch nodes.

Step 2, the electromagnetic coupling of each section of the multi-conductor transmission line under the action of the space electromagnetic field can be expressed as follows through a transmission line equation:

where l represents the position of each point on the multi-lead, which is determined by the coordinates of each point in the rectangular coordinate system. t represents different moments in time. V (L, t) and I (L, t) represent voltage and current vectors on the multiple wires, respectively, and L and C are unit-length inductance and capacitance distribution parameter matrices of the multiple wires, respectively. V_F(l, t) and I_F(l, t) are the equivalent distributed voltage source and distributed current source, respectively, of the transmission line equation, which can be expressed as

E_T(l, t) and E_L(l, t) is calculated by a space electromagnetic field, and the calculation formula is as follows:

where i denotes the ith transmission line, h_iDenotes the distance between the ith transmission line and the ground plate, [ E ]_T(l,t)]_iRepresenting the incident electric field component perpendicular to the ith transmission lineIntegral along the line of [ E ]_L(l,t)]_iIncident electric field tangential component representing the ith transmission line positionThe difference of the tangential electric field component with the surface of the ground plane. x, y and z respectively represent three coordinate points of the position of the space electromagnetic field. Since the equivalent distributed source term is independent of the fringe field of the multiple wires, the multiple wires can be removed when calculating the spatial incident electromagnetic field.

And 3, according to the formula (1) and the formula (2), the modeling precision of the transmission line equation depends on the unit length distribution parameters of the multiple wires and the accurate calculation of the equivalent distribution source term.

For each section of the multi-conductor transmission line, the unit length distribution parameter can be calculated by an empirical formula and is expressed as: the value of each element of the inductance parameter matrix L in unit length can be calculated by a formula L_ii＝μ₀ln(2h_i/r_i) A sum of/2 piCalculated, where i and j represent the ith and jth transmission lines, μ₀Which represents the permeability of free space. h is_i,h_jAnd d_ijRespectively, the height of the ith and jth transmission lines and the distance between the two wires, as shown in fig. 3. The capacitance parameter matrix C per unit length can be represented by the formula C ═ μ₀ε₀L^-1And (4) obtaining. Epsilon₀Representing the dielectric constant of free space.

Because the multiple wires of each section are placed in different directions and have random heights, the multiple wires are free ofThe method is completely positioned on the edge of the FDTD grid, and incident electric field components along the multiple wires and in the vertical direction cannot be directly obtained from the electric field components on the FDTD grid, and a corresponding interpolation technology is required for processing. First, the incident electric field component along the multi-conductor line is calculated to obtain E_LParameter values of (l, t). For clarity of description of the solution process, we use any one of the multiple wires as an example for illustration. As shown in fig. 4, the transmission line is divided into a plurality of independent cable units according to the FDTD grid, and the start point and the end point of each cable unit are located on the FDTD grid, and the central point of each cable unit is located on the central plane of the FDTD grid. Then, the electric field along the wire unit at the center point is represented by a vector product as E.e_l＝E_x·a_xe_x+E_y·a_ye_yWherein E and E_lRespectively representing the electric field at the center point of the cable unit and the direction vector of the cable unit. e.g. of the type_xAnd e_yRepresenting unit direction vectors in the x and y directions, respectively. a is_xAnd a_yThe ratio of the electric field components along the line in the x and y directions, respectively, is denoted as a_xSin θ and a_yCos θ, where θ denotes the angle between the transmission line along the line direction and the horizontal direction. E_xAnd E_yThe electric field components representing the x and y directions at the center point of the cable unit need to be interpolated from the electric field components of the four adjacent FDTD grids. With E_yFor example, the interpolation formula is expressed as:

wherein E is_y1,E_y2,E_y3And E_y4Is the electric field component at the y-direction edge of the FDTD grid. Eta and xi respectively represent the scale factors of the central point in the z direction and the x direction of the FDTD grid.

Then, the vertical incident electric field of the multiple wires is calculated and integrated along the line to obtain E_TParameter values of (l, t). As shown in fig. 5, for a vertically incident electric field componentCan be composed of two adjacent FDTD grid electric field components E_zThe interpolation yields, expressed as:

electric field component adjacent to transmission lineIt is necessary to have 4 adjacent FDTD grid electric field components E_zThe interpolation yields, expressed as:

where α and β represent the scale factors of the cable unit starting or ending point in the x-direction and z-direction of the FDTD grid, respectively. E_z1，E_z2，E_z3，E_z4，E_z5，E_z6Respectively representing the electric field components of the z-direction edges of the grids adjacent to the starting point or the ending point of the cable unit.

After a transmission line equation is established, the center difference format of the FDTD method is adopted for discretization, and an FDTD iterative solution formula of voltage and current on the cable is obtained, so that voltage and current responses on the multi-conductor and the terminating load of the multi-conductor are obtained through solution.

And 4, the voltage of the port connected with each section of the multi-conductor and the bifurcation node cannot be dispersed by using the central differential format of FDTD, and backward differential processing is required. As shown in fig. 6, the terminal voltage V of any one of the transmission lines_NFor example, assume that the current flowing into the port is I_LAfter applying backward difference processing, it is expressed as:

Δ x and Δ t denote a space step and a time step required for differential dispersion, respectively, and C denotes a unit of a transmission lineThe length-capacitance distribution parameter is,representing the current in the transmission line in the vicinity of the terminal,andrespectively representing the current and voltage at a moment on the norton circuit port,andrespectively representing the current and voltage at the new moment of the norton circuit port.

Thus, the arrangement yields a current I_LThe calculation formula of (2) is as follows:

wherein the content of the first and second substances,

equation (11) shows that the effect of the transmission line on the branch node can be equivalent to a current source I_LHAnd equivalent admittance G_eqParallel norton circuits, as shown in fig. 7.

According to the above processing method, the action of the transmission line on the branch node is equalized by the norton circuit, and an electromagnetic coupling model of the electromagnetic wave action branch line can be obtained, as shown in fig. 8. The specific setting mode is as follows: the action of each segment of the inclined multi-conductor on the branching node is equivalent through a controlled current source and a parallel circuit of equivalent admittance, and the action of each segment of the inclined multi-conductor on the branching node can be replaced through a controlled voltage source.

Step 5, mutual inductance and mutual capacitance exist among the multiple wires, so that a crosstalk problem is inevitably generated, and the norton circuits in the equivalent circuit of the branched node are inevitably influenced mutually. Therefore, as shown in fig. 9, the bifurcated node equivalent circuit is regarded as a multi-port network, and the relation between the voltage and the current of each port is described by constructing an admittance matrix of the network, and the formula is expressed as follows:

GU＝I (14)

where U is a port voltage vector, denoted as U ═ U₁,...,U_i,...,U_N]^TWhere N represents the port number, in an embodiment of the present invention, N is 5. I is a port current vector, denoted I ═ I₁,...,I_i,...,I_N]^TIn which I_i＝-(I_SHi+I′_SHi) I denotes the ith port, I_SHiAnd l'_SHiRespectively representing the current source items of the two side ports of the network. G is a network admittance matrix, whereinG_ij＝-(G_eqij+G′_eqij),i≠j。G_eqijAnd G'_eqijRespectively representing the equivalent admittance between the ith and jth transmission lines on both sides of the network.

The voltage of each port of the network can be obtained by solving the inverse of equation (14), which can be expressed as:

U＝G^-1I (15)

and feeding the port voltage value obtained by calculation back to each section of inclined multi-conductor as a boundary condition, so as to realize the transmission of interference signals among the plurality of sections of transmission lines.

Step 6, shown in FIG. 10, is given at L_c＝1.2m、W_c＝1.0m、h＝1cm、d＝1cm、r＝1mm、l₁＝0.5m、l₂＝0.2m，θ₁＝45°、θ₂Under the conditions that the resistance of the load 6-10 is 50 ohms, the resistance of the load 11-15 is 100 ohms, and the incident wave 16 is a Gaussian pulse with the amplitude of 1000V/m and the pulse width of 2ns, the voltage response on the load 14 is calculated by the field line coupling time domain algorithm and the electromagnetic field simulation software CST, and therefore the calculation results of the two methods have good matching degree, and the correctness of the method is verified.