Field line coupling calculation method for shielding cable in any path based on transmission line theory

Abstract

The invention relates to the field of shielding cable field line coupling calculation, in particular to an arbitrary path shielding cable field line coupling calculation method based on a transmission line theory. According to the scheme, the method comprises the following steps: discretizing a shielding cable path, and confirming basic geometric parameters, shielding layer types and terminating conditions of a to-be-analyzed cable; sampling an external electric field to obtain an electric field vector at each node of the path; calculating to obtain an equivalent coupling source distributed along an outer loop and an equivalent coupling source at a terminal based on the vector electric field data, obtaining current distribution of the outer loop of the cable based on a unit length parameter of the outer loop, obtaining an equivalent distribution voltage source of an inner loop of the cable based on the current distribution of the outer loop, and obtaining an equivalent distribution voltage source of the inner loop of the cable based on a unit length parameter of the inner loop; and obtaining the terminal current of the loop in the cable. The method is suitable for shielding cable field line coupling calculation.

Description

Technical Field

[0001] This invention relates to the field of field-line coupling calculation for shielded cables, and specifically to a method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory. Background Technology

[0002] Field-line coupling analysis is a core foundation for studying EMC problems caused by external electromagnetic fields coupling to cables. In practical engineering applications, shielded cables are widely used in various electronic systems and can effectively resist electromagnetic interference in complex electromagnetic environments. However, due to limitations in spatial layout and installation conditions, shielded cables often employ complex or non-uniform wiring paths, which significantly alters their electromagnetic coupling characteristics. Therefore, extending field-line coupling analysis to shielded cables with arbitrary paths, establishing accurate calculation methods for field-line coupling, and accurately predicting coupling responses are of crucial guiding significance for electromagnetic compatibility design and system-level sensitivity assessment in practical engineering. Currently, there are two main types of methods used to analyze field-line coupling problems in cables:

[0003] Full-wave numerical simulation methods include the finite element method, the finite difference time-domain method, and the method of moments. These methods can handle complex machine structures and arbitrary field distributions, but they have drawbacks such as large computational load (high-frequency simulation of meter-level cables is difficult to evaluate quickly), complex modeling (the braided structure of the shielding layer, metal contact, etc. are difficult to accurately represent in the three-dimensional model), and unsuitability for repeated calculations (each time the cable path, load, or field direction is changed, the mesh needs to be re-established and solved).

[0004] Traditional transmission line field-line coupling models, represented by Agrawal, Taylor, and Rachidi models, can quickly solve the coupling problem of straight cables under plane wave excitation. However, these methods still have significant limitations: on the one hand, they are mainly applicable to straight-line deployment scenarios and are difficult to adapt to arbitrary three-dimensional paths; on the other hand, most of them focus on unshielded cables and lack targeted modeling of the "outer loop - inner loop" layered structure of the shielding layer.

[0005] Therefore, existing technologies face many technical problems that urgently need to be solved: there is currently no unified modeling method that can handle arbitrary three-dimensional paths and adapt to shielded cables, and there is a lack of fast algorithms based on the transmission line theory framework; in addition, for shielded cables with sheaths, there is still a gap in the analytical characterization of their electromagnetic properties (such as unit length parameters), and a mature theoretical modeling method has not yet been formed. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the field-line coupling of shielded cables with arbitrary paths based on transmission line theory, so as to realize the unified modeling of the outer and inner loops of shielded cables with arbitrary three-dimensional paths on the ground plane.

[0007] The present invention achieves the above objectives by adopting the following technical solution: The present invention provides a method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory, comprising:

[0008] S1, Calculate the path discretization and geometric parameters;

[0009] S2. External electric field sampling to obtain the electric field vector at each node along the path;

[0010] S3. Construct an equivalent source for the external loop;

[0011] S4. Calculation of unit length parameters for the external loop of shielded cable;

[0012] S5. Solve the current distribution of the shielded cable's external circuit based on the external circuit unit length parameter;

[0013] S6. Construct an equivalent source for the internal loop;

[0014] S7. Calculation of unit length parameters for internal loops of shielded cables;

[0015] S8. Solve for the terminal current of the inner loop based on the unit length parameter of the inner loop, and finally obtain the voltage and current vectors at both ends of the inner loop of the shielded cable.

[0016] Furthermore, step S1 specifically includes:

[0017] Discretize the shielded cable path to characterize the cable geometry:

[0018] Divide the shielded cable path into N electrical segments, and calculate the length of each electrical segment and the unit direction vector of each segment. and the endpoint coordinate matrix of the electrical small segment ;

[0019] Store path geometry information for subsequent field sampling and chain parameter calculation.

[0020] Furthermore, step S2 specifically includes:

[0021] By combining the plane wave direction, polarization angle, and frequency, calculate the electric field vector at each node along the path. ;

[0022]

[0023] In the formula, θ and φ represent the plane wave directions, η represents the polarization angle, and x, y, and z represent the three-dimensional coordinates of the path nodes, respectively. Let f represent the propagation constant of the plane wave, c0 represent the speed of light in free space, f represent the frequency, E0 represent the electric field strength of the plane wave, and j represent the imaginary unit.

[0024] Furthermore, step S3 specifically includes:

[0025] Calculate the equivalent coupling sources along the line:

[0026] Based on the unit direction vector, length, and three-dimensional electric field vector at discrete nodes of the electric segment, the real and imaginary parts of the three-dimensional electric field vector are respectively... The equivalent coupling source along the line is calculated according to the following formula. ;

[0027]

[0028] Calculate the coupling sources at the terminal along the line:

[0029] Based on the three-dimensional electric field vectors at both ends of the shielded cable's outer loop and its height above the ground, the equivalent coupling sources at the left and right ends of the outer loop are calculated using the following formula. ;

[0030] .

[0031] Furthermore, step S4 specifically includes:

[0032]

[0033] In the formula, , The relative permittivity and relative permeability of the outer loop of a shielded cable, r e r m The equivalent electromagnetic dimension is represented by z, where z represents the z-coordinate of the left node of the small electric segment. These represent the capacitance and inductance per unit length of the electrical segment, respectively.

[0034] Furthermore, step S5 specifically includes:

[0035] Based on the unit length parameter of the shielded cable outer loop, calculate the transmission link parameter matrix for each electrical segment of the shielded cable outer loop. ;

[0036] Based on transmission line theory and the external loop termination of cables, the following system of linear equations is obtained:

[0037]

[0038] Based on the linear equations, the voltage and current at both ends of the cable's external circuit are obtained. Then, the current distribution of any cable segment is obtained by recursively calculating the reverse chain parameters:

[0039] .

[0040] Furthermore, step S6 specifically includes:

[0041] Based on the shielding characteristics of the cable to be analyzed, the analytical model of transfer impedance is applied, which is expressed as a transfer impedance matrix. Then, based on the external loop current distribution, calculate the internal loop equivalent source matrix for any cable segment. ;

[0042] .

[0043] Furthermore, step S7 specifically includes:

[0044]

[0045] In the formula, , Let r represent the relative permittivity and relative permeability of the inner loop of the shielded cable, respectively. e, u With r m, v Let each represent the equivalent electromagnetic dimensions of the u-th inner conductor. These represent the capacitance coefficient and inductance matrix per unit length of any cable segment within the inner circuit of the shielded inner conductor cable, respectively.

[0046] Furthermore, step S8 specifically includes:

[0047] Based on the unit length parameter of the inner loop of the shielded cable, the transmission link parameter matrix of each cable segment in the inner loop is calculated. Based on transmission line theory and the internal loop termination conditions of the cable, the following system of linear equations for solving the internal loop termination current is obtained:

[0048]

[0049] Solving the linear equations based on the terminal current of the inner loop yields the voltage and current vectors at both ends of the cable's inner loop. .

[0050] The beneficial effects of this invention are as follows:

[0051] This invention supports arbitrary three-dimensional path field-coupled transmission line modeling for shielded cables: by discretizing the actual cable layout path and using a chain parameter recursion method, unified transmission line modeling of the outer and inner loops can be achieved for shielded cables with straight, broken, curved, spiral, and other arbitrary three-dimensional curved paths on the ground plane.

[0052] This invention is compatible with both plane waves and numerical fields: it can be applied not only to electromagnetic compatibility standard plane wave irradiation experiments, but also to field coupling analysis in aircraft fuselages, cavity interiors, and complex structures.

[0053] This invention combines transfer impedance to achieve shielding effectiveness modeling: various shielding models (tubular shielding layer, braided shielding layer, multi-layer shielding) can be inserted.

[0054] Compared with full-wave simulation, this invention has higher computational efficiency and is suitable for engineering scanning and optimization. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the equivalent transmission line circuit model provided by the present invention;

[0056] Figure 2 This is a flowchart of the field-line coupling calculation method for shielded cables with arbitrary paths based on transmission line theory provided by the present invention;

[0057] Figure 3 This is a schematic diagram of the physical scene construction and cable discretization under plane wave incidence provided by the present invention;

[0058] Figure 4 This is a schematic diagram of physical scene construction and cable discretization under complex electromagnetic environment provided by the present invention;

[0059] Figure 5 This is a schematic diagram of the equivalent calculation model for the unit length parameter of the external loop provided by the present invention;

[0060] Figure 6 This is a schematic diagram of the equivalent calculation model of the unit length parameter of the inner loop provided by the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0062] like Figure 1 As shown, this invention abstracts the shielded cable into two mutually coupled transmission line networks, that is, the field-line coupling equivalent circuit model based on transmission line theory.

[0063] External circuit: Composed of a shielding layer and a ground plane;

[0064] Inner circuit: It consists of an inner conductor and a shielding layer, and can be a single conductor or multiple conductors.

[0065] The external field acts directly only on the external loop, equivalent to a voltage source along the line and at the cable terminal. The external loop current then passes through the transfer impedance matrix Z. T The driving inner loop is equivalent to a voltage source along the inner loop line. The entire cable path is discretized into N electrical segments in three-dimensional space.

[0066] Based on this, the present invention provides a method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory, such as... Figure 2 As shown, it includes:

[0067] S1, Calculate the path discretization and geometric parameters;

[0068] Discretize the shielded cable path to characterize its geometric path. Identify the basic geometric parameters, shielding layer type, and termination details of the shielded cable to be analyzed.

[0069] Specifically, the shielded cable path is divided into N electrical segments, and the length of each electrical segment (taking the i-th segment as an example) is calculated. Unit direction vector of small electrical segment and endpoint coordinate matrix (The left and right endpoints of the i-th segment);

[0070] Store path geometry information for subsequent field sampling and chain parameter calculation.

[0071] S2. External electric field sampling to obtain the electric field vector at each node along the path;

[0072] Determine whether the incident field can be analytically modeled (whether it is a plane wave). If so, apply the plane wave formula for analytical modeling to obtain vector electric field data at discrete points along the cable path. Specifically:

[0073] like Figure 3 As shown, for a plane wave incident, the electric field vector at each node along the path is calculated by combining the plane wave direction (θ, φ), polarization angle (η), and frequency. ;

[0074]

[0075] Where x, y, and z are the three-dimensional coordinates of the path nodes, respectively. is the propagation constant of the plane wave, c0 is the speed of light in free space; f is the frequency; E0 is the electric field strength of the plane wave; j is the imaginary unit.

[0076] If it is not a plane wave, then it is a complex electromagnetic environment. In the full-wave simulation software, set the incident field parameters, establish the scene model to be analyzed, set vector electric field data monitoring points at the discrete path points of the cable to be analyzed, start the full-wave simulation, and obtain the vector electric field data at the discrete path points of the cable.

[0077] like Figure 4 As shown, for complex electromagnetic environments, in scenarios where the shielded cable to be analyzed does not exist, by establishing a geometric model of the scenario and the field excitation source, the electric field vectors at discrete nodes of the cable path are obtained through numerical simulation / experiment (or three-dimensional interpolation). .

[0078] S3. Construct an equivalent source for the external loop;

[0079] Equivalent coupling source along the line: Taking the i-th segment as an example, based on the unit direction vector, length, and the three-dimensional electric field vector (real and imaginary parts) at the discrete node (left end) of the cable segment, the coupling source is... The equivalent coupling source along the line can be obtained from the following formula. .

[0080]

[0081] The previous step calculated the vector electric field data at each node along the cable path. .first It is a function of spatial location. For any cable node, a vector field data can be obtained. For example, the electric field vector at the left node of the i-th cable segment. Then, the position coordinates of that node in the first step are represented as Q(S). i，L The second step is to express the three-dimensional electric field vector E at that location. k (Q(S) i，L (), where k is x, y, or z, representing the rectangular coordinate components. Secondly, the electric field vector E k (Q(S) i，L According to the mathematical definition, an integer having both a real part and an imaginary part can be expressed as E. k (Q(S) i，L ))= E k，RE (Q(S) i，L ))+j E k，IM (Q(S) i，L The electric field vector expression (calculation) at other cable nodes is similar.

[0082] Coupled sources at the cable terminals: Based on the three-dimensional electric field vectors at both ends of the cable's external loop, the height above the ground, and the following formula, the equivalent coupling sources at the left and right ends of the external loop can be obtained. .

[0083]

[0084] S4. Calculation of unit length parameters for the external loop of shielded cable;

[0085] like Figure 5 As shown, based on the electromagnetic parameters of the cable's external circuit (relative permittivity) Relative permeability ), equivalent electromagnetic dimensions (r) e r m The capacitance and inductance per unit length of any cable segment (e.g., the k-th segment) in the outer loop of the shielded cable can be obtained from the ground clearance (height above ground, z-coordinate of the left node of the cable segment) and the following formula. .

[0086]

[0087] In the formula, and These are respectively expressed as vacuum permittivity and vacuum permeability. Indicates the height of the cable segment above the ground, such as Figure 5 As shown, an infinitely large ideal ground plane is placed at z=0, so the height of each node of the cable above the ground is naturally the z-axis coordinate of that cable node.

[0088] S5. Solve the current distribution of the shielded cable's external circuit based on the external circuit unit length parameter;

[0089] Based on the unit length parameter of the outer loop, the transmission line link parameter matrix of each cable segment (e.g., the m-th segment) in the outer loop can be calculated. Based on transmission line theory and the external loop termination of cables, the following system of linear equations can be obtained:

[0090]

[0091] In the formula, Z G,L Z G,R Indicates the external circuit load impedance;

[0092] This represents the right product of the external loop cable segment chain parameter matrix from segment 1 to segment k (the subscript indicates the product symbol). This matrix is ​​then a 2×2 matrix. The elements in the first row and first column, the first row and second column, the second row and first column, and the second row and second column are expressed as follows:

[0093] ;

[0094] , These represent the contributions of the equivalent coupling sources on the first to (k-1)th segments of the external loop cable to the voltage and current at the kth segment, respectively.

[0095] Based on the equations, the voltage and current at both ends of the cable's external circuit can be obtained. Furthermore, based on the following formula, the current of any cable segment (e.g., the current of the k-th segment) can be obtained through recursion using the reverse chain parameters. The current distribution of ).

[0096]

[0097] S6. Construct an equivalent source for the internal loop;

[0098] Based on the shielding characteristics (e.g., braided shielding, tubular shielding, etc.) of the cable to be analyzed (assuming it is a shielded cable with an M conductor), the analytical model of transfer impedance is applied, which is expressed as a transfer impedance matrix (vector). Based on the external loop current distribution, the equivalent source matrix of the internal loop for any cable segment (e.g., the k-th segment) can be obtained. , .

[0099] S7. Calculation of unit length parameters for internal loops of shielded cables;

[0100] like Figure 6 As shown, based on the electromagnetic parameters (relative permittivity) of the cable's internal loop. Relative permeability ), equivalent electromagnetic dimensions (the u-th inner conductor r) e, u r m, u The geometric parameters and the following formula can be used to obtain the capacitance coefficient and inductance matrix per unit length of any cable segment in the inner loop of a shielded multi-conductor cable, i.e. .

[0101]

[0102] In the formula, θ uv This represents the angle between the u-th and v-th conductors. , , These represent the distances from the center of the u-th conductor in the inner loop to the center of the cross-section of the inner loop cable bundle, the distances from the center of the v-th conductor to the center of the cross-section of the inner loop cable bundle, and the distance from the center of the cross-section of the inner loop cable bundle to the shielding layer (i.e., the cable radius excluding the outer shielding layer).

[0103] S8. Solve for the terminal current of the inner loop based on the unit length parameter of the inner loop, and finally obtain the voltage and current vectors at both ends of the inner loop of the shielded cable.

[0104] Based on the unit length parameter of the inner loop, the transmission line link parameter matrix of each cable segment (e.g., the m-th segment) in the inner loop can be calculated. Based on transmission line theory and the internal loop termination of cables, the following system of linear equations can be obtained:

[0105]

[0106] This represents the right multiplication of the inner loop cable segment chain parameter matrix from segment 1 to segment k (the subscript indicates the multiplication symbol). This matrix is ​​then a 2×2 block matrix. The matrix blocks in the first row and first column, the first row and second column, the second row and first column, and the second row and second column are expressed as follows:

[0107] ;

[0108] , These represent the contributions of the equivalent coupling sources on the inner loop cable segments from segment 1 to segment (k-1) to the voltage and current at segment k.

[0109] Based on the system of equations, the voltage and current vectors at both ends of the cable loop can be obtained. This is the final output parameter of the present invention.

[0110] In summary, compared with the prior art, this invention can achieve unified modeling of the outer and inner loops of shielded cables with arbitrary three-dimensional paths on the ground plane; this invention supports plane wave analytical modeling and numerical modeling of complex electromagnetic environments; this invention achieves rapid solution of current, voltage, and power of the entire line based on chain parameter recursion; and realizes analytical modeling of unit length parameters of the inner and outer loops of sheathed shielded cables.

[0111] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory, characterized in that, include: S1, Calculate the path discretization and geometric parameters; S2. External electric field sampling to obtain the electric field vector at each node along the path; S3, Construct an equivalent source for the external loop; S4. Calculation of unit length parameters for the external loop of shielded cable; S5. Solve the current distribution of the shielded cable's external circuit based on the external circuit unit length parameter; S6. Construct an equivalent source for the internal loop; S7. Calculation of unit length parameters for internal loops of shielded cables; S8. Solve for the terminal current of the inner loop based on the unit length parameter of the inner loop, and finally obtain the voltage and current vectors at both ends of the inner loop of the shielded cable.

2. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 1, characterized in that, Step S1 specifically includes: Discretize the shielded cable path to characterize the cable geometry: Divide the shielded cable path into N electrical segments, and calculate the length of each electrical segment and the unit direction vector of each segment. and the endpoint coordinate matrix of the electrical small segment ; Store path geometry information for subsequent field sampling and chain parameter calculation.

3. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 1, characterized in that, Step S2 specifically includes: By combining the plane wave direction, polarization angle, and frequency, calculate the electric field vector at each node along the path. ; ； In the formula, θ and φ represent the plane wave directions, η represents the polarization angle, and x, y, and z represent the three-dimensional coordinates of the path nodes, respectively. Let f represent the propagation constant of the plane wave, c0 represent the speed of light in free space, f represent the frequency, E0 represent the electric field strength of the plane wave, and j represent the imaginary unit.

4. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 2, characterized in that, Step S3 specifically includes: Calculate the equivalent coupling sources along the line: Based on the unit direction vector, length, and three-dimensional electric field vector at discrete nodes of the electric segment, the real and imaginary parts of the three-dimensional electric field vector are respectively... The equivalent coupling source along the line is calculated according to the following formula. ; ； Calculate the coupling sources at the terminal along the line: Based on the three-dimensional electric field vectors at both ends of the shielded cable's outer loop and its height above the ground, the equivalent coupling sources at the left and right ends of the outer loop are calculated using the following formula. ; 。 5. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 1, characterized in that, Step S4 specifically includes: ； In the formula, , The relative permittivity and relative permeability of the outer loop of a shielded cable, r e r m The equivalent electromagnetic dimension is represented by z, where z represents the z-coordinate of the left node of the small electric segment. Let represent the capacitance and inductance per unit length of the electrical segment, respectively. and These are respectively expressed as vacuum permittivity and vacuum permeability. This indicates the height of the cable segment above the ground.

6. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 5, characterized in that, Step S5 specifically includes: Based on the unit length parameter of the shielded cable outer loop, calculate the transmission link parameter matrix for each electrical segment of the shielded cable outer loop. ; Based on transmission line theory and the external loop termination of cables, the following system of linear equations is obtained: ； Based on the linear equations, the voltage and current at both ends of the cable's external circuit are obtained. Then, the current distribution of any cable segment is obtained by recursively calculating the reverse chain parameters: 。 7. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 1, characterized in that, Step S6 specifically includes: Based on the shielding characteristics of the cable to be analyzed, the analytical model of transfer impedance is applied, which is expressed as a transfer impedance matrix. Then, based on the external loop current distribution, calculate the internal loop equivalent source matrix for any cable segment. ; 。 8. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 1, characterized in that, Step S7 specifically includes: ； In the formula, , Let r represent the relative permittivity and relative permeability of the inner loop of the shielded cable, respectively. e, u With r m, u Let each represent the equivalent electromagnetic dimensions of the u-th inner conductor. Let θ represent the capacitance and inductance matrix per unit length of any cable segment within the inner circuit of the shielded inner conductor cable, respectively. uv This represents the angle between the u-th and v-th conductors. , , These represent the distances from the center of the u-th conductor in the inner loop to the center of the cross-section of the inner loop cable bundle, the distance from the center of the v-th conductor to the center of the cross-section of the inner loop cable bundle, and the distance from the center of the cross-section of the inner loop cable bundle to the shielding layer, respectively.

9. The method for calculating field-line coupling of shielded cables with arbitrary paths based on transmission line theory according to claim 8, characterized in that, Step S8 specifically includes: Based on the unit length parameter of the inner loop of the shielded cable, the transmission link parameter matrix of each cable segment in the inner loop is calculated. Based on transmission line theory and the internal loop termination conditions of the cable, the following system of linear equations for solving the internal loop termination current is obtained: ； Solving the linear equations based on the terminal current of the inner loop yields the voltage and current vectors at both ends of the cable's inner loop. .

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