FDFD-TL calculation method for single-conductor electromagnetic coupling

Abstract

The invention requests to protect an FDFD-TL calculation method for single-conductor electromagnetic coupling under the action of a long-time interference source, and the method comprises the steps: firstly constructing an electromagnetic coupling model of a plane wave irradiation single conductor according to a transmission line equation in combination with an analytical solution of a single-conductor excitation field; then, a transmission line equation is solved by applying an FDFD method, and an FDFD-TL matrix equation suitable for single-wire electromagnetic coupling calculation is deduced; and finally, solving the FDFD-TL matrix equation by adopting a complex conjugate gradient method, and obtaining the current response of each point along the single conductor and the terminating load. The algorithm has the advantages that the problems of later time instability, much time consumption and the like caused by long-time interference source time domain simulation are avoided, and the current response along the single conductor is quickly obtained under the condition that direct modeling of the single conductor is not needed. The correctness and the high efficiency of the FDFD-TL algorithm are verified through numerical simulation of related calculation examples and comparison with a full-wave simulation result of a moment method.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic coupling calculation of a single conductor, and in particular belongs to a FDFD-TL calculation method for electromagnetic coupling of a single conductor. Background Art

[0002] There is a type of electromagnetic pulse source in space with high energy, narrow frequency band and long duration, such as lightning electromagnetic pulse, mid- and late-stages of high-altitude nuclear electromagnetic pulse, etc. These strong electromagnetic pulses are extremely destructive to various sensitive electronic and electrical equipment because the strong electromagnetic pulse energy generates strong interference signals through the equipment cable coupling, which flows into the cable termination circuit to cause interference or damage and affect the working performance of the equipment. Therefore, conducting electromagnetic coupling research on transmission lines under the radiation effect of long-term interference sources can provide important technical support for the analysis and suppression of electromagnetic interference of electronic and electrical equipment.

[0003] For the radiation coupling problem of long-term interference sources, time domain simulation will consume a lot of computing time, and the post-time is unstable and easy to diverge. At this time, frequency domain simulation is more appropriate. Finite Element Method (FEM), Method of Moments (MoM) and Finite Difference Frequency Domain (FDFD) are the most widely used frequency domain full-wave algorithms. However, the full-wave algorithm requires direct modeling of fine transmission lines, large meshing volume and low computational efficiency. Therefore, domestic and foreign scholars have proposed a variety of efficient field line coupling algorithms based on the transmission line equation theory, among which the BLT equation is the most widely used field line coupling frequency domain algorithm. Although the BLT equation does not require direct modeling of the fine structure of the transmission line, it can only solve the interference response of the transmission line terminal load, and cannot obtain the voltage or current along the transmission line, making it difficult to carry out subsequent transmission line secondary radiation simulation.

[0004] Therefore, this paper combines the frequency domain finite difference method and the transmission line equation and proposes a new field line coupling frequency domain algorithm to realize the rapid calculation of the electromagnetic coupling of a single conductor under the action of a long-term interference source, and at the same time obtain the current response of each point along the single conductor.

[0005] The closest prior art is the inventor's prior application CN112507647B, a method for time-domain modeling and analysis of electromagnetic coupling of bifurcation lines of spatial electromagnetic fields.

[0006] This patent protects a time-domain hybrid algorithm for calculating electromagnetic coupling of bifurcation lines, which requires the iterative solution of the excitation field of the bifurcation line through the FDTD method. When the spatial incident wave is a long-term interference source, the number of iterations required for the FDTD calculation is very large, resulting in a long execution time, which causes numerical divergence and makes it difficult to complete the calculation. The FDFD-TL method invented by this patent is a frequency domain method that samples the long-term interference source into multiple frequency points for field line coupling calculations, effectively avoiding the problem of divergence caused by long-term calculations of the time domain algorithm. Summary of the invention

[0007] The present invention aims to solve the above problems of the prior art. A FDFD-TL calculation method for single-conductor electromagnetic coupling is proposed. The technical solution of the present invention is as follows:

[0008] A FDFD-TL calculation method for single-conductor electromagnetic coupling includes the following steps:

[0009] Step 1: Based on the transmission line equation and the analytical solution of the excitation field of a single conductor, an electromagnetic coupling model of a plane wave irradiating a single conductor is constructed;

[0010] Step 2, using the finite difference method in the frequency domain (FDFD) to solve the transmission line equation, and derive the FDFD-TL matrix equation suitable for single conductor electromagnetic coupling calculation;

[0011] Step 3: Use the complex conjugate gradient method to solve the FDFD-TL matrix equation and obtain the current response of each point along the single conductor and the terminal load.

[0012] The advantages and beneficial effects of the present invention are as follows:

[0013] Based on the finite difference frequency domain (FDFD) method and the transmission line equation, the present invention proposes a new field-line coupled frequency domain algorithm (FDFD-TL), which solves the electromagnetic coupling calculation problem of a single conductor under the action of a long-term interference source.

[0014] The present invention organically combines the frequency domain finite difference method and the transmission line equation, and proposes a new frequency domain algorithm for field line coupling, which effectively solves the problem of rapid calculation of electromagnetic coupling of multi-conductor transmission lines under the action of long-term interference sources. First, the FDFD matrix equation associated with the spatial electromagnetic field and the current response of multi-conductor transmission lines is derived. Then, the complex conjugate gradient method is used in combination with the OpenMP parallel technology to achieve rapid iterative solution of the current at each point along the multi-conductor line. Through the numerical simulation of the corresponding calculation example, the calculation results of the FDFD-TL algorithm and the full-wave algorithm are compared in terms of accuracy and time consumption, which fully verifies the correctness and efficiency of the algorithm.

[0015] The innovation of this invention is that the FDFD method is applied to the calculation of transmission line equations for the first time, and the FDFD-TL matrix equation is derived and established. This method does not have the problem of numerical divergence when calculating the electromagnetic coupling of a single conductor under the action of a long-term interference source, and can obtain the current response of each point along the single conductor. Moreover, the simulation results have the same calculation accuracy as the full-wave algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A flow chart showing the present invention;

[0017] Figure 2 A schematic diagram showing the calculation of the spatial electric field when a plane wave at any angle is incident on the ground;

[0018] Figure 3 Schematic diagram showing the FDFD differential dispersion of a single conductor;

[0019] Figure 4 A schematic diagram showing the differential discrete format of the load current at the beginning and end of a single conductor;

[0020] Figure 5 Represents the electromagnetic coupling model of an ideal single conductor on the ground;

[0021] Figure 6 represents the current response on load R1;

[0022] Figure 7 Indicates load R 2 The current response on . DETAILED DESCRIPTION

[0023] The following will describe the technical solutions in the embodiments of the present invention in detail in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention.

[0024] The technical solution of the present invention to solve the above technical problems is:

[0025] 1. FDFD-TL Algorithm Theory

[0026] The electromagnetic coupling of a single conductor is modeled by the transmission line equation, expressed as:

[0027]

[0028] Where I(x,ω) and V(x,ω) represent the current and voltage on a single conductor respectively. L and C are the distributed parameters of the inductance and capacitance per unit length of multiple conductors respectively. F (x,ω) and I F (x, ω) are the equivalent distributed voltage source and current source terms of the transmission line equation, respectively, expressed as:

[0029]

[0030] I F (x,ω)=-jωCE T (x,ω) (4)

[0031] in,

[0032]

[0033] Among them, E T (x,ω) is the vertical incident electric field component between the ground and the transmission line position The integral along the line, E L (x,ω) is the tangential incident electric field component at the location of the transmission line The difference between the electric field component tangential to the ground.

[0034] Since the equivalent distributed source term of a single conductor is obtained only from the spatial incident electric field and has nothing to do with the single conductor scattering field, the physical structure of the single conductor can be removed when calculating the single conductor excitation field. Assume that the incident wave hits the ground at an arbitrary angle, and the azimuth, elevation and polarization angles of the incident wave are θ, ψ and α respectively, as shown in Figure 2 As shown, the electric field at any position on the ground is obtained by superimposing the incident wave and the reflected wave.

[0035] First, the incident wave of arbitrary polarization is decomposed into two parts: vertical polarization component and horizontal polarization component. Then, the vertical polarization electric field component and the horizontal polarization electric field component are multiplied by the corresponding ground reflection coefficient to obtain the vertical polarization and horizontal polarization components of the reflected wave. Finally, the incident wave and the reflected wave are superimposed to obtain the electric field at any position in space, which is expressed as:

[0036]

[0037] Where k is the phase propagation constant, E 0 (ω) is the incident wave amplitude. R v and R h are the ground reflection coefficients for vertical polarization and horizontal polarization respectively, and the calculation formula is:

[0038]

[0039] Among them, σ g and ε r are the earth's electrical conductivity and relative permittivity, ε 0 is the dielectric constant of vacuum.

[0040] The key to the new FDFD-TL algorithm proposed in this paper lies in the construction and solution of the FDFD-TL matrix equation. These two parts will be introduced in detail below.

[0041] 1.1 Derivation of the matrix equation of FDFD-TL

[0042] First, divide the single conductor into N segments according to the FDFD grid Δx, as Figure 3 As shown, the voltage and current on a single conductor are sampled alternately, and the current is located at the full grid node and the voltage is located at the half grid node.

[0043] The transmission line equations (Equation (1) and Equation (2)) are discretized using the central difference format of FDFD to obtain:

[0044]

[0045] In order to eliminate the voltage term in equation (12), we can rearrange equation (13) to obtain:

[0046]

[0047] Replacing k in formula (14) with k-1, we can obtain:

[0048]

[0049] Then, by substituting equations (14) and (15) into equation (12), we can obtain the FDFD equation only for current, which is expressed as:

[0050]

[0051] Simplifying formula (16), we can get:

[0052] -I(k+1)-I(k-1)+[(jωC)(jωL)Δx 2 +2]I(k)=jωCΔx 2 E L (k) (17)

[0053] like Figure 4 As shown, the current at the beginning and the terminal load of a single conductor does not satisfy the central differential format of FDFD and needs to be discretized using forward differential and backward differential respectively.

[0054] For the starting current, the forward difference format is used to discretize equation (1), and the obtained value is:

[0055]

[0056] Among them, V s Represents the voltage vector of the starting port. According to Ohm’s law, V s =-I(0)R s , where R S is the initial load impedance matrix, and I(0) is the initial load current vector.

[0057] According to formula (13), and ignoring the influence of the vertical electric field near the load, we can get

[0058]

[0059] Arranging equation (19) yields the calculation formula for V(1 / 2), which is substituted into equation (18) to obtain the FDFD equation for the initial load current, which is:

[0060]

[0061] Similarly, the terminal load is discretized using backward differentiation, expressed as:

[0062]

[0063] Among them, V L Represents the terminal port voltage vector, and according to Ohm's law, V L =I(N)R L , where R L is the terminal load impedance matrix, and I(N) is the terminal load current vector.

[0064] Similarly, from formula (13), we can get

[0065]

[0066] According to formula (22), the calculation formula of V(N-1 / 2) is obtained and substituted into formula (21), and the FDFD equation of the terminal load current is obtained, which is:

[0067]

[0068] 1.3 Fast solution of FDFD-TL matrix equation

[0069] Combining equations (17), (20) and (23), we construct the complete FDFD-TL matrix equation, which is expressed as:

[0070]

[0071] Define the coefficient matrix of the matrix equation as A, where A 0,0 , A 0,1 and A N,N-1 , A N,N They represent the FDFD equation coefficients of the current nodes at the beginning and end of a single conductor, respectively. k,k-1 , A k,k and A k,k+1 They represent the FDFD equation coefficients of each current node in the middle of a single conductor. The calculation formula corresponding to each element of matrix A is:

[0072]

[0073] Define the current vector to be determined as I, expressed as I = [I(0), I(1), ..., I(N)] T , each vector element represents the current at different node positions along the single conductor.

[0074] Define the excitation source vector as S, expressed as S = [s(0), s(1), ..., s(N)] T , each element represents the equivalent distributed source item at different node positions along the single conductor, expressed as:

[0075]

[0076] Among them, E L (k) is the tangential component of the incident electric field at the node k of a single conductor.

[0077] Since the coefficient matrix A is a super-large-scale sparse matrix, the iterative method is preferred to solve the FDFD-TL matrix equation. Since the complex conjugate gradient method has no special requirements for the matrix element structure, this paper will use this iterative method to achieve fast calculation of the FDFD-TL matrix equation. The specific iterative solution process is as follows:

[0078] Step 1: Set the initial value I (0) and tolerance ε, calculate r (0) =S-AI (0) , d (0) =r (0) , (r (0) conjugation of ),

[0079] Step 2: Perform iterative calculations in the order of k = 0, 1, 2, ...:

[0080]

[0081] Step 3: After executing one iteration in step 2, determine the convergence condition || r (k+1) Whether || / ||b||<ε is reached, if it is reached, output x (k+1) , end the calculation, otherwise return to step 2 to continue the iterative calculation.

[0082] In the above iterative solution process, ||·|| represents the Euclidean norm, A H represents the conjugate transposed matrix of the complex matrix A, represents the conjugate of corresponding elements and (*,*) represents the inner product.

[0083] 3 Numerical simulation

[0084] Aiming at the electromagnetic coupling problem of an ideal single-ground conductor, the FDFD-TL algorithm and MOM are used to simulate the problem, and the calculation results and time are compared to verify the correctness of the algorithm.

[0085] Figure 5 The electromagnetic coupling model of a single conductor on the ideal ground irradiated by a space electromagnetic field. The length, height and radius of the single conductor are 3m, 1cm and 1mm respectively, and the terminal loads are R 1 =50Ω and R 2 =100Ω. The incident wave waveform is a nuclear electromagnetic pulse, and the waveform expression is E(t)=E 0 [exp(-αt)-exp(-βt)], where E 0 =65000V / m,α=4×10 7 s -1 , β=6×10 8 s -1 , according to the azimuth angle θ = 90°, the pitch angle The single conductor is illuminated in the direction of polarization angle α = 0°. The spatial step size selected for the differential discrete transmission line equation of the FDFD-TL algorithm is 0.01m, the frequency scanning interval is 1MHz, and the total number of frequency points is 300.

[0086] Figure 6 and Figure 7 The current responses on the terminated loads R1 and R2 obtained by FDFD-TL and MOM simulation are given respectively. It can be seen that the simulation results of the two methods have a very high degree of consistency, which verifies the correctness of the algorithm proposed in this paper.

[0087] 4 Conclusion

[0088] This paper organically combines the frequency domain finite difference method and the transmission line equation, and proposes a new frequency domain algorithm for field line coupling, which effectively solves the problem of fast calculation of electromagnetic coupling of multi-conductor transmission lines under the action of long-term interference sources. First, the FDFD matrix equation associated with the spatial electromagnetic field and the current response of multi-conductor transmission lines is derived. Then, the complex conjugate gradient method is used in combination with OpenMP parallel technology to achieve fast iterative solution of the current at each point along the multi-conductor line. Through numerical simulation of the corresponding calculation examples, the calculation results of the FDFD-TL algorithm and the full-wave algorithm are compared in terms of accuracy and time consumption, which fully verifies the correctness and efficiency of the algorithm.

[0089] The systems, devices, modules or units described in the above embodiments may be implemented by computer chips or entities, or by products with certain functions.

[0090] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0091] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0092] The above embodiments should be understood to be only used to illustrate the present invention and not to limit the protection scope of the present invention. After reading the contents of the present invention, technicians can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A FDFD-TL calculation method for single-conductor electromagnetic coupling, characterized in that: The following steps are involved: Step 1: Based on the transmission line equation and the analytical solution of the excitation field of a single conductor, an electromagnetic coupling model of a plane wave irradiating a single conductor is constructed; Step 2, using the frequency domain finite difference (FDFD) method to solve the transmission line equation, deriving the FDFD-TL matrix equation suitable for single conductor electromagnetic coupling calculation; Step 3: Use the complex conjugate gradient method to solve the FDFD-TL matrix equation and obtain the current response of each point along the single conductor and the terminal load.

2. The FDFD-TL calculation method for single-conductor electromagnetic coupling according to claim 1, characterized in that: The step 1 constructs an electromagnetic coupling model of a plane wave irradiating a single conductor based on the transmission line equation and the analytical solution of the excitation field of the single conductor, which specifically includes: The electromagnetic coupling of a single conductor is modeled by the transmission line equation, expressed as: Where I(x,ω) and V(x,ω) represent the current and voltage on a single conductor, respectively. L and C represent the distributed parameters of the inductance and capacitance per unit length of multiple conductors, respectively. V F (x,ω) and I F (x, ω) are the equivalent distributed voltage source and current source terms of the transmission line equation, respectively, expressed as: I F (x,ω)=-jωCE T (x,ω) (4) in, in, represents the vertical incident electric field component of the transmission line, and They represent the tangential electric field component along the transmission line and the tangential electric field component on the ground surface, E T (x,ω) is the vertical incident electric field component between the ground and the transmission line position The integral along the line, E L (x,ω) is the tangential incident electric field component at the location of the transmission line The difference between the tangential electric field component and the ground; Assuming that the incident wave hits the ground at an arbitrary angle, the azimuth, elevation and polarization angles of the incident wave are θ, ψ and α respectively, and the electric field at any position on the ground is obtained by superposing the incident wave and the reflected wave; First, the incident wave of arbitrary polarization is decomposed into two parts: vertical polarization component and horizontal polarization component. Then, the vertical polarization electric field component and the horizontal polarization electric field component are multiplied by the corresponding ground reflection coefficient to obtain the vertical polarization and horizontal polarization components of the reflected wave. Finally, the incident wave and the reflected wave are superimposed to obtain the electric field at any position in space, which is expressed as: in, denote the x, y, and z components of the total electric field at any position above the ground, denote the x, y and z components of the incident electric field at any position above the ground, They represent the x, y and z components of the incident electric field at any position above the ground. k0 is the phase propagation constant, E0(ω) is the incident wave amplitude; R v and R h are the ground reflection coefficients for vertical polarization and horizontal polarization respectively, and the calculation formula is: Among them, σ g and ε r are the earth's electrical conductivity and relative dielectric constant respectively, and ε0 is the vacuum dielectric constant.

3. The FDFD-TL calculation method for single-conductor electromagnetic coupling according to claim 2, characterized in that: The step 2 uses the frequency domain finite difference (FDFD) method to solve the transmission line equation and derive the FDFD-TL matrix equation suitable for single conductor electromagnetic coupling calculation, which specifically includes: First, the single conductor is divided into N segments according to the FDFD grid Δx. The voltage and current on the single conductor are sampled alternately, and the current is located at the full grid node and the voltage is located at the half grid node. The transmission line equations (1) and (2) are discretized using the central difference format of FDFD, and the following is obtained: Where k represents the kth grid node on a single conductor. and They represent the node voltages on the left and right sides of the k-grid node at a distance of half a grid, I(k) and I(k+1) represent the k-grid node current and the k+1-grid node current, respectively; In order to eliminate the voltage term in equation (12), we can rearrange equation (13) to obtain: Replacing k in formula (14) with k-1, we can obtain: Then, by substituting equations (14) and (15) into equation (12), we can obtain the FDFD equation only for current, which is expressed as: Simplifying formula (16), we can get: -I(k+1)-I(k-1)+[(jωC)(jωL)Δx 2 +2]I(k)=jωCΔx 2 E L (k) (17) The current at the beginning and the terminal load of a single conductor does not satisfy the central differential format of FDFD and needs to be discretized using forward differential and backward differential respectively. For the starting current, the forward difference format is used to discretize equation (1), and the obtained value is: Among them, V s Represents the voltage vector of the starting port. According to Ohm’s law, V s =-I(0)R s , where R S is the initial load impedance matrix, I(0) is the initial load current vector; According to formula (13), and ignoring the influence of the vertical electric field near the load, we can get Arranging equation (19) yields the calculation formula for V(1 / 2), which is substituted into equation (18) to obtain the FDFD equation for the initial load current, which is: Similarly, the terminal load is discretized using backward differentiation, expressed as: Among them, V L Represents the terminal port voltage vector, and according to Ohm's law, V L =I(N)R L , where R L is the terminal load impedance matrix, I(N) is the terminal load current vector; Similarly, from formula (13), we can get According to formula (22), the calculation formula of V(N-1 / 2) is obtained and substituted into formula (21), and the FDFD equation of the terminal load current is obtained, which is:

4. The FDFD-TL calculation method for single-conductor electromagnetic coupling according to claim 3, characterized in that: The step 3 adopts the complex conjugate gradient method to solve the FDFD-TL matrix equation to obtain the current response of each point along the single conductor and the terminal load, which specifically includes: Combining equations (17), (20) and (23), we construct the complete FDFD-TL matrix equation, which is expressed as: Define the coefficient matrix of the matrix equation as A, where A 0,0 , A 0,1 and A N,N-1 , A N,N They represent the FDFD equation coefficients of the current nodes at the beginning and end of a single conductor, respectively. k,k-1 , A k,k and A k,k+1 They represent the FDFD equation coefficients of each current node in the middle of a single conductor; the calculation formula corresponding to each element of matrix A is: Define the current vector to be determined as I, expressed as I = [I(0), I(1), ..., I(N)] T , each vector element represents the current at different node positions along the single conductor; Define the excitation source vector as S, expressed as S = [s(0), s(1), ..., s(N)] T , each element represents the equivalent distributed source item at different node positions along the single conductor, expressed as: Among them, E L (k) is the tangential component of the incident electric field at the node k of a single conductor.

5. The FDFD-TL calculation method for single-conductor electromagnetic coupling according to claim 4, characterized in that: The iterative method is used to solve the FDFD-TL matrix equation. The specific iterative solution process is: Step 1: Set the initial value I (0) and tolerance ε, calculate r (0) =S-AI (0) , d (0) =r (0) , (r (0) conjugation of ), r (0) d (0) , represent intermediate variables respectively; Step 2: Perform iterative calculations in the order of k = 0, 1, 2, ...: Among them, α k , β k Calculate the required coefficient terms for the kth iteration, They are α k , β k The conjugation of. Step 3: After executing one iteration in step 2, determine the convergence condition || r (k+1) Whether || / ||S||<ε is reached, if it is reached, output x (k+1) , end the calculation, otherwise return to step 2 to continue the iterative calculation. In the above iterative solution process, ||·|| represents the Euclidean norm, A H represents the conjugate transposed matrix of the complex matrix A, represents the conjugate of corresponding elements and (*,*) represents the inner product.

6. An electronic device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the FDFD-TL calculation method for single-conductor electromagnetic coupling according to any one of claims 1 to 5 is implemented.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the FDFD-TL calculation method for single-wire electromagnetic coupling according to any one of claims 1 to 5 is implemented.

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