A method for simulating and calculating the magnetic field of a transmission line, a computer device, and a storage medium

Abstract

The present invention provides a transmission line magnetic field simulation calculation method, computer equipment, and storage medium for finite element magnetic field simulation of quasi-three-dimensional transmission lines. The method includes the following steps: calculating a full-wave equation based on the magnetic field of the transmission line to be simulated according to Maxwell's equations; calculating the impedance boundary conditions satisfied by the magnetic field of the transmission line to be simulated according to Ohm's law; performing variational processing on the full-wave equation of the magnetic field and obtaining a variational equation of the magnetic field based on the impedance boundary conditions; discretizing the variational equation of the magnetic field using a finite element algorithm to obtain a finite element discrete variational equation of the magnetic field; and solving the finite element discrete variational equation of the magnetic field to obtain the magnetic field of the transmission line to be simulated. This solution can directly and accurately calculate the magnetic field during transmission line simulation, thereby improving the simulation accuracy and efficiency of the transmission line and providing more efficient and accurate technical support for electronic design and electromagnetic field analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of transmission line simulation, and in particular to a transmission line magnetic field simulation calculation method, computer equipment and storage medium. Background Art

[0002] Transmission lines are widely used in various electronic circuits in electronic circuit design. Therefore, transmission line simulation has long been an important research topic in the field of electronic design automation (EDA). Currently, in high-frequency transmission line simulations, they primarily rely on full-wave algorithms based on the electric field, which infer the magnetic field from the electric field. This approach can lead to large errors in the magnetic field calculations. However, in some calculations, particularly transmission line impedance calculations and energy-based error estimation, accurate magnetic field information is crucial. Therefore, a full-wave algorithm that can directly calculate the magnetic field during transmission line simulation is urgently needed to improve the accuracy of magnetic field calculations and, therefore, enhance the accuracy and efficiency of transmission line simulations. Summary of the Invention

[0003] The purpose of the present invention is to provide a transmission line magnetic field simulation calculation method, computer equipment and storage medium, which can directly and accurately calculate the magnetic field during transmission line simulation, thereby improving the simulation accuracy and efficiency of the transmission line, and providing more efficient and accurate technical support for electronic design and electromagnetic field analysis.

[0004] The technical solutions provided by the present invention are as follows:

[0005] The present invention provides a transmission line magnetic field simulation calculation method for finite element magnetic field simulation of a quasi-three-dimensional transmission line, comprising the steps of:

[0006] The full-wave equation of the transmission line to be simulated based on the magnetic field is obtained by calculation according to Maxwell's equations;

[0007] Obtaining impedance boundary conditions satisfied by the magnetic field of the transmission line to be simulated by calculation according to Ohm's law;

[0008] performing variational processing on the full-wave equation of the magnetic field, and obtaining the variational equation of the magnetic field according to the impedance boundary condition;

[0009] Discretizing the variational equation of the magnetic field using a finite element algorithm to obtain a finite element discrete variational equation of the magnetic field;

[0010] The finite element discrete variational equation of the magnetic field is solved to obtain the magnetic field of the transmission line to be simulated.

[0011] In some embodiments, the calculation of the full-wave equation of the transmission line to be simulated based on the magnetic field according to Maxwell's equations specifically includes:

[0012] Obtain Maxwell's equations in the presence of dielectrics;

[0013] Obtain the corresponding relationship between electric field intensity and electric displacement vector, as well as the corresponding relationship between magnetic field intensity and magnetic flux density in homogeneous dielectric materials;

[0014] Obtaining the corresponding relationship between the electric field intensity and the input signal under the time harmonic signal, as well as the corresponding relationship between the magnetic flux density and the input signal;

[0015] The full-wave equation of the transmission line to be simulated based on the magnetic field is obtained by calculation according to the Maxwell equations, the correspondence between the electric field intensity and the electric displacement vector, the correspondence between the magnetic field intensity and the magnetic flux density, the correspondence between the electric field intensity and the input signal, and the correspondence between the magnetic flux density and the input signal.

[0016] In some embodiments, the calculation of the impedance boundary condition satisfied by the magnetic field of the transmission line to be simulated according to Ohm's law specifically includes:

[0017] The corresponding conditions of electric field intensity and magnetic field intensity satisfied by the electromagnetic field on the surface of the conductor are calculated according to Ohm's law;

[0018] The impedance boundary conditions satisfied by the magnetic field of the transmission line to be simulated are calculated based on the corresponding conditions of the electric field strength and the magnetic field strength, the Maxwell equations, the corresponding relationship between the electric field strength and the electric displacement vector, the corresponding relationship between the electric field strength and the input signal, and the corresponding relationship between the magnetic flux density and the input signal.

[0019] In some embodiments, it also includes: using common parameters to replace the different variables of the full-wave equation of the magnetic field, the impedance boundary conditions satisfied by the magnetic field, and the full-wave equation of the electric field, and the impedance boundary conditions satisfied by the electric field, so as to unify the calculation equations for the magnetic field and the calculation equations for the electric field.

[0020] In some embodiments, performing variational processing on the full-wave equation of the magnetic field and obtaining the variational equation of the magnetic field according to the impedance boundary condition specifically includes:

[0021] A variational method is used in a two-dimensional cross section, and the impedance boundary condition is substituted into the full-wave equation of the magnetic field to obtain the variational equation of the magnetic field.

[0022] In some embodiments, the method further includes simplifying the variational equation of the magnetic field by replacing variables.

[0023] In some embodiments, solving the finite element discrete variational equation of the magnetic field specifically includes:

[0024] Obtaining a finite element matrix of generalized eigenvalues satisfied by the electromagnetic field of the transmission line to be simulated according to the finite element discrete variational equation of the magnetic field;

[0025] The finite element matrix of the generalized eigenvalues is solved to obtain the electric field, magnetic field and propagation constant of the transmission line to be simulated.

[0026] In some embodiments, after obtaining the magnetic field of the transmission line to be simulated, the method further includes:

[0027] The port impedance of the transmission line to be simulated is obtained by calculation according to the magnetic field.

[0028] In a second aspect, the present application provides a computer device comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of a transmission line magnetic field simulation calculation method described in the first aspect.

[0029] In a third aspect, the present application provides a computer storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implements the steps of a transmission line magnetic field simulation calculation method described in the first aspect.

[0030] The present invention provides a transmission line magnetic field simulation calculation method, computer device, and storage medium. By deriving the full-wave equation for the magnetic field, impedance boundary conditions, and computable finite element equations from Maxwell's equations, this method achieves high-precision quasi-3D full-wave finite element simulation of the magnetic field. This method significantly improves the accuracy of magnetic field calculations, thereby enhancing the accuracy of transmission line impedance calculations and energy-based error estimation. Simultaneously, it enhances simulation efficiency and accuracy, enabling high-precision simulation even under limited hardware conditions. This significantly shortens R&D cycles, reduces R&D costs, and enhances product market competitiveness, with significant social and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The preferred implementation scheme will be described below in a clear and understandable manner with reference to the accompanying drawings to further illustrate the above-mentioned characteristics, technical features, advantages and implementation methods of this solution.

[0032] Figure 1 It is a schematic diagram of the overall process of an embodiment of the present invention. DETAILED DESCRIPTION

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the specific embodiments of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings and other embodiments can be obtained based on these drawings without inventive work.

[0034] To simplify the drawings, only the parts relevant to the present invention are schematically shown in each figure. They do not represent the actual structure of the product. Furthermore, to simplify the drawings and facilitate understanding, in some figures, only one of the components with the same structure or function is schematically depicted or labeled. As used herein, "one" not only means "only one" but also "more than one."

[0035] In electronic circuit design, transmission lines are widely used in various circuits. Therefore, in the field of electronic design automation (EDA), the simulation of transmission lines has always been an important research direction. At present, in the high-frequency field, transmission line simulation mainly relies on a full-wave algorithm based on the electric field, and then the magnetic field is inferred from the electric field. This method will lead to large errors in the calculation of the magnetic field. However, in some calculations, especially in the calculation of transmission line impedance and energy-type error estimation, accurate magnetic field information is crucial. Therefore, there is an urgent need for a full-wave algorithm that can directly calculate the magnetic field during transmission line simulation to improve the calculation accuracy of the magnetic field, thereby improving the simulation accuracy and efficiency of the transmission line. This application realizes high-precision quasi-3D magnetic field full-wave finite element simulation by deriving the full-wave equation of the magnetic field, the impedance boundary conditions and the computable finite element equations from Maxwell's equations. This method can significantly improve the accuracy of the magnetic field calculation, thereby improving the accuracy of the transmission line impedance calculation and the accuracy of the energy-type error estimation. The following is a detailed description of this scheme with reference to the accompanying drawings:

[0036] In one embodiment, the reference Figure 1 The present invention provides a transmission line magnetic field simulation calculation method for simulating a quasi-three-dimensional transmission line, comprising the steps of:

[0037] S100, calculating and obtaining a full-wave equation of the transmission line to be simulated based on the magnetic field according to Maxwell's equations;

[0038] S200, calculating and obtaining the impedance boundary condition satisfied by the magnetic field of the transmission line to be simulated according to Ohm's law;

[0039] S300, performing variational processing on the full-wave equation of the magnetic field, and obtaining the variational equation of the magnetic field according to the impedance boundary condition;

[0040] S400, discretizing the variational equation of the magnetic field using a finite element algorithm to obtain a finite element discrete variational equation of the magnetic field;

[0041] S500 , solving the finite element discrete variational equation of the magnetic field to obtain the magnetic field of the transmission line to be simulated.

[0042] This solution derives the full-wave equation of the magnetic field from Maxwell's equations and obtains the impedance boundary conditions satisfied by the magnetic field. It can perform variational processing on the full-wave equation of the magnetic field to obtain the variational equation of the magnetic field. Finite element discretization is performed on the variational equation of the magnetic field, and the magnetic field of the transmission line can be directly solved. The magnetic field is used to calculate the transmission line impedance and estimate the energy-type error. Compared with the calculation method of first calculating the electric field, then calculating the magnetic field based on the electric field, and then calculating the transmission line impedance and estimating the energy-type error, this solution can reduce the error caused by deducing the magnetic field from the electric field, making the calculation more accurate and efficient.

[0043] Maxwell's equations are the core equations of classical electromagnetism. They describe the relationship between the electric field (E), magnetic field (B), charge (ρ), and current (J). They are the cornerstone of electromagnetism, optics, and modern physics. They include Gauss's law, Gauss's law of magnetism, Faraday's law of electromagnetic induction, and Ampere-Maxwell's law. Since transmission lines contain both conductive and non-conductive dielectrics, the Maxwell equations for transmission lines with dielectrics can be expressed as:

[0044]

[0045] in, is the electric field strength, is the magnetic field strength, is the electric displacement vector, is the magnetic flux density, is the excitation current density, is the excitation charge density.

[0046] In a specific implementation, the full-wave equation of the transmission line to be simulated based on the magnetic field is obtained by calculation according to Maxwell's equations, which specifically includes:

[0047] S110. Obtain Maxwell's equations in the presence of dielectrics;

[0048] S120, obtaining a corresponding relationship between electric field intensity and electric displacement vector, and a corresponding relationship between magnetic field intensity and magnetic flux density in a uniform isotropic dielectric material;

[0049] S130, obtaining a corresponding relationship between the electric field intensity and the input signal under the time harmonic signal, and a corresponding relationship between the magnetic flux density and the input signal;

[0050] S140. According to Maxwell's equations, the correspondence between the electric field intensity and the electric displacement vector, the correspondence between the magnetic field intensity and the magnetic flux density, the correspondence between the electric field intensity and the input signal, and the correspondence between the magnetic flux density and the input signal, a full-wave equation of the transmission line to be simulated based on the magnetic field is calculated.

[0051] Since the conductor medium in the transmission line is generally a homogeneous isotropic dielectric material, the corresponding relationship between the electric field intensity and the electric displacement vector, as well as the corresponding relationship between the magnetic field intensity and the magnetic flux density can be expressed as follows:

[0052]

[0053] in, is the relative electrical constant of the medium, is the vacuum electrical constant of the medium, is the relative magnetic constant of the medium, is the vacuum magnetic constant of the medium.

[0054] Under the time-harmonic signal, the corresponding relationship between the electric field intensity and the input signal, as well as the corresponding relationship between the magnetic flux density and the input signal can be expressed as:

[0055]

[0056] in, is the angular frequency, is the signal frequency.

[0057] When calculating the full-wave equation of the transmission line to be simulated based on the magnetic field, the curl is calculated on both sides of formula (1) and substituted into formulas (4), (5), (6), (7) and (8) to obtain the full-wave equation of the magnetic field:

[0058]

[0059] in, is the vacuum wave number, , is a unit imaginary number.

[0060] In a specific implementation, calculating the impedance boundary condition satisfied by the magnetic field of the transmission line to be simulated according to Ohm's law specifically includes:

[0061] The corresponding conditions of electric field intensity and magnetic field intensity satisfied by the electromagnetic field on the surface of the conductor are calculated according to Ohm's law;

[0062] The impedance boundary conditions satisfied by the magnetic field of the transmission line to be simulated are calculated based on the corresponding conditions of electric field intensity and magnetic field intensity, Maxwell's equations, the corresponding relationship between electric field intensity and electric displacement vector, the corresponding relationship between electric field intensity and input signal, and the corresponding relationship between magnetic flux density and input signal.

[0063] The corresponding conditions of electric field intensity and magnetic field intensity satisfied by the electromagnetic field on the conductor surface of the transmission line can be expressed as:

[0064]

[0065] in is the normal vector to the conductor surface, is the surface impedance of the conductor, and

[0066]

[0067] in, is the electrical conductivity of the conductor, which is inversely proportional to the surface impedance of the conductor; is the skin depth, which is the distance the electromagnetic field penetrates into the transmission line.

[0068] When calculating the impedance boundary conditions satisfied by the magnetic field, combining formula (11) with formulas (3) and (8) yields:

[0069]

[0070] in, is the vacuum impedance,

[0071] At the same time, cross-producting both sides of formula (11) yields,

[0072]

[0073] Combining formula (14) with formulas (4), (5) and (7), we can obtain the impedance boundary condition satisfied by the magnetic field,

[0074] .

[0075] Since the full-wave equations of the magnetic field and electric field and the impedance boundary conditions are highly symmetrical, common parameters can be used to replace the different variables of the full-wave equation of the magnetic field and the impedance boundary conditions satisfied by the magnetic field, respectively, and the full-wave equation of the electric field and the impedance boundary conditions satisfied by the electric field, so as to unify the calculation equations for the magnetic field and the calculation equations for the electric field. For example, the common parameter F can be used to replace the magnetic field H and the electric field E. The calculation equations for the full-wave equation of the magnetic field and the boundary conditions of the magnetic field can be rewritten as:

[0076] .

[0077] In a specific implementation, a variational process is performed on the full-wave equation of the magnetic field, and the variational equation of the magnetic field is obtained according to the impedance boundary condition, specifically including:

[0078] The variational method is used in the two-dimensional cross section, and the impedance boundary condition is substituted into the full-wave equation of the magnetic field to obtain the variational equation of the magnetic field. The variational equation of the magnetic field can be expressed as formula (20):

[0079]

[0080] in, , is the field propagation direction, is the propagation constant.

[0081] Assume that the field propagation direction is , on the spot ,in is the propagation constant, and is a complex number. Its real part describes the loss of the electromagnetic field during propagation, and its imaginary part describes the fluctuation of the electromagnetic field during propagation. represents the complex conjugate. The first term in formula (20) is a global equation, which can be simplified to formula (21):

[0082] .

[0083] Preferably, the variational equation of the magnetic field can be simplified by replacing variables. Specifically, according to and ,as well as , replace the variables in formula (21) to get formula (22):

[0084] .

[0085] In a specific implementation, the variational equation of the magnetic field is discretized using a finite element algorithm to obtain the finite element discrete variational equation of the magnetic field, specifically including:

[0086] The finite element algorithm is used to discretize the variational equation of the magnetic field to obtain the finite element equation of the magnetic field, including:

[0087] Finite element discretization ,according to , ,in is the vector basis function, is a scalar basis function, formula (22) can be simplified as:

[0088]

[0089] in,

[0090]

[0091] The second term of formula (20) is the variational equation at the boundary, which can be simplified to,

[0092]

[0093] The finite element equation is,

[0094]

[0095] in,

[0096] .

[0097] In a specific implementation, solving the finite element discrete variational equation of the magnetic field specifically includes:

[0098] Obtaining a finite element matrix of generalized eigenvalues satisfied by the electromagnetic field of the transmission line to be simulated according to the finite element discrete variational equation of the magnetic field;

[0099] The finite element matrix of the generalized eigenvalues is solved to obtain the electric field, magnetic field and propagation constant of the transmission line to be simulated.

[0100] Specifically, the formula for solving the finite element equation of the magnetic field is:

[0101] .

[0102] Using the Ritz process, the finite element matrix of the generalized eigenvalues satisfied by the electromagnetic field can be derived. By solving this matrix, the propagation constant and the electromagnetic field can be obtained.

[0103] In a specific implementation, after obtaining the magnetic field of the transmission line to be simulated, the method further includes: obtaining the port impedance of the transmission line to be simulated by calculation according to the magnetic field.

[0104] This approach achieves high-precision quasi-3D full-wave finite element simulation of the magnetic field by deriving the full-wave equation for the magnetic field, impedance boundary conditions, and computable finite element equations from Maxwell's equations. This allows for direct and accurate calculation of the magnetic field during transmission line simulation. This method significantly improves the accuracy of magnetic field calculations, thereby enhancing the accuracy of transmission line impedance calculations and energy-based error estimation. Simultaneously, it enhances simulation efficiency and accuracy, enabling high-precision simulation even under limited hardware conditions. This will significantly shorten R&D cycles, reduce R&D costs, and enhance product market competitiveness, with significant social and economic benefits.

[0105] In one embodiment, the present application provides a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of a transmission line magnetic field simulation calculation method of the aforementioned embodiment.

[0106] In one embodiment, the present application provides a computer storage medium having a computer program or instructions stored thereon. When the computer program or instructions are executed by a processor, the steps of a transmission line magnetic field simulation calculation method of the aforementioned embodiment are implemented.

[0107] It should be noted that the above embodiments can be freely combined as needed. The above description is only a preferred embodiment of the present invention. It should be pointed out that those skilled in the art can make several improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A transmission line magnetic field simulation calculation method for finite element magnetic field simulation of quasi-three-dimensional transmission lines, characterized in that: Including steps: The full-wave equation of the transmission line to be simulated based on the magnetic field is obtained by calculation according to Maxwell's equations; The impedance boundary condition satisfied by the magnetic field of the transmission line to be simulated is calculated according to Ohm's law: ,in, is the relative dielectric constant of the medium, is the magnetic field strength, is the vacuum wave number, , is a unit imaginary number, is the normal vector to the conductor surface, is the surface impedance of the conductor, is the vacuum impedance, is the vacuum magnetic constant of the medium; The full-wave equation of the magnetic field is subjected to variational processing, and the variational equation of the magnetic field is obtained according to the impedance boundary condition, specifically comprising: using a variational method on a two-dimensional cross section, substituting the impedance boundary condition into the full-wave equation of the magnetic field to obtain the variational equation of the magnetic field, and simplifying the variational equation of the magnetic field by variable substitution to obtain the simplified variational equation of the magnetic field: ； in, , , is the relative magnetic constant of the medium, is the field propagation direction, is the propagation constant, represents the complex conjugate, , ; The variational equation of the magnetic field is discretized by the finite element algorithm to obtain the finite element discrete variational equation of the magnetic field. Specifically, the finite element discrete field is used ,according to , The variational equation of the magnetic field is discretized, where is the vector basis function, is a scalar basis function, we get: ,in, , ， ， ； The variational equation at the boundary represented by the second term of the variational equation of the magnetic field is simplified to: , and its finite element equation is ,in, ， ； The finite element discrete variational equation of the magnetic field is solved to obtain the magnetic field of the transmission line to be simulated. The solution formula is: .

2. A transmission line magnetic field simulation calculation method according to claim 1, characterized in that: The calculation based on Maxwell's equations to obtain the full-wave equation of the transmission line to be simulated based on the magnetic field specifically includes: Obtain Maxwell's equations in the presence of dielectrics; Obtain the corresponding relationship between electric field intensity and electric displacement vector, as well as the corresponding relationship between magnetic field intensity and magnetic flux density in homogeneous dielectric materials; Obtaining the corresponding relationship between the electric field intensity and the input signal under the time harmonic signal, as well as the corresponding relationship between the magnetic flux density and the input signal; The full-wave equation of the transmission line to be simulated based on the magnetic field is obtained by calculation according to the Maxwell equations, the correspondence between the electric field intensity and the electric displacement vector, the correspondence between the magnetic field intensity and the magnetic flux density, the correspondence between the electric field intensity and the input signal, and the correspondence between the magnetic flux density and the input signal.

3. A transmission line magnetic field simulation calculation method according to claim 2, characterized in that: The impedance boundary condition satisfied by the magnetic field of the transmission line to be simulated is obtained by calculating according to Ohm's law, specifically including: The corresponding conditions of electric field intensity and magnetic field intensity satisfied by the electromagnetic field on the surface of the conductor are calculated according to Ohm's law; The impedance boundary conditions satisfied by the magnetic field of the transmission line to be simulated are calculated based on the corresponding conditions of the electric field strength and the magnetic field strength, the Maxwell equations, the corresponding relationship between the electric field strength and the electric displacement vector, the corresponding relationship between the electric field strength and the input signal, and the corresponding relationship between the magnetic flux density and the input signal.

4. A transmission line magnetic field simulation calculation method according to claim 3, characterized in that: Also includes: Common parameters are used to replace the different variables of the full-wave equation of the magnetic field, the impedance boundary conditions satisfied by the magnetic field, and the full-wave equation of the electric field, the impedance boundary conditions satisfied by the electric field, so as to unify the calculation equations for the magnetic field and the calculation equations for the electric field.

5. The transmission line magnetic field simulation calculation method according to claim 1, characterized in that: The solving of the finite element discrete variational equation of the magnetic field specifically includes: Obtaining a finite element matrix of generalized eigenvalues satisfied by the electromagnetic field of the transmission line to be simulated according to the finite element discrete variational equation of the magnetic field; The finite element matrix of the generalized eigenvalues is solved to obtain the electric field, magnetic field and propagation constant of the transmission line to be simulated.

6. The transmission line magnetic field simulation calculation method according to claim 1, characterized in that: After obtaining the magnetic field of the transmission line to be simulated, the method further includes: The port impedance of the transmission line to be simulated is obtained by calculation according to the magnetic field.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the transmission line magnetic field simulation calculation method according to any one of claims 1 to 6.

8. A computer storage medium having a computer program or instruction stored thereon, characterized in that: When the computer program or instruction is executed by a processor, the steps of the transmission line magnetic field simulation calculation method according to any one of claims 1 to 6 are implemented.

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