Electromagnetic network coupling analysis method and system based on discontinuous Galerkin technology

Abstract

The invention discloses an electromagnetic network coupling analysis method and system based on a discontinuous Galerkin technology, and the method employs the network parameter-S parameter of an external circuit to represent a complex circuit network, and achieves the coupling between an electric field and a circuit. A numerical flux suitable for frequency domain field-circuit coupling is derived, and a frequency domain field-circuit joint simulation model is established. According to the method, co-simulation of an electromagnetic field and a circuit system is supported, a field equation and a circuit equation can be directly coupled by enabling a circuit to be equivalent to an S parameter of the circuit, errors caused by traditional step-by-step solving are avoided, and the calculation efficiency is improved while the calculation precision is guaranteed.

Description

Technical Field

[0001] This invention relates to frequency domain methods in computational electromagnetics, and in particular to a method and system for electromagnetic network coupling analysis based on discontinuous Galerkin technique. Background Technology

[0002] With the rapid development of modern electronic devices and communication systems, electromagnetic field simulation has become increasingly important in engineering design and scientific research. Traditional electromagnetic simulation methods, such as the finite element method (FEM), finite difference method (FDM), and method of moments (MoM), face many challenges in complex multiphysics problems and high-precision calculations, especially when dealing with non-uniform media, complex geometries, and field-circuit coupling problems, where the computational efficiency and accuracy of traditional methods often fail to meet the requirements.

[0003] The Discontinuous Galerkin Method (DGM), as an efficient numerical computation method, has demonstrated significant advantages in solving partial differential equations since its introduction in the 1980s. In 1973, Reed and Hill first applied DGM to solving hyperbolic neutron transport equations, and since then, this method has been widely used in fluid dynamics, multiphysics coupling, and electromagnetics. The core advantage of DGM lies in its flexible mesh generation capability, allowing the use of different basis functions in different medium regions, thus handling complex computational objectives more efficiently. Furthermore, while ensuring the continuity of field quantities, DGM allows for discontinuities in basis functions at element boundaries, making it more adaptable to handling non-uniform media and complex geometries.

[0004] Currently, the combination of Direct Motion Governing (DGM) and the Time-Domain Finite Element Method (FEM) has yielded significant research results, particularly in solving Maxwell's equations, where the Riemann Solver ensures numerical stability and computational accuracy across different subdomains. However, in frequency-domain electromagnetic simulations, the frequency-domain FEM based on the vector wave equation only involves solving for a single electric or magnetic field quantity, rendering traditional Riemann boundary conditions inapplicable. Therefore, effectively combining DGM with the frequency-domain FEM while ensuring numerical stability during the computation process has become a crucial issue that urgently needs to be addressed.

[0005] Furthermore, in practical engineering applications, electromagnetic systems often involve field-circuit coupling problems, such as in the simulation and analysis of integrated circuits, antenna design, and power electronic equipment. Traditional methods typically employ step-by-step solutions or simplified models when dealing with field-circuit coupling, leading to reduced computational accuracy or a significant increase in computational load. Therefore, there is an urgent need for an efficient and high-precision electromagnetic simulation method for field-circuit coupling that can leverage the advantages of DGM in the frequency domain to flexibly handle complex electromagnetic structures while ensuring computational efficiency and stability. Summary of the Invention

[0006] The purpose of this invention is to provide an electromagnetic network coupling analysis method and system based on discontinuous Galerkin technique. This method can effectively utilize the advantages of DGM in handling non-uniform media and complex geometric models, and can also achieve efficient calculation in field-circuit co-simulation. This provides a more accurate numerical solution scheme for high-frequency electromagnetic analysis, microwave circuit design and multi-field coupling simulation.

[0007] The technical solution for achieving the objective of this invention is as follows:

[0008] An electromagnetic network coupling analysis method based on discontinuous Galerkin technique includes the following steps:

[0009] Step 1: Construct an electromagnetic model of the field-circuit coupling to be solved. Cut the model into three sub-regions according to the coordinate position of the discontinuity. Then, perform tetrahedral meshing on the entire computational domain of the electromagnetic model to obtain information on all elements, edges and nodes. Simultaneously, complete the global numbering of all nodes and edges, and identify the physical properties of the edges.

[0010] Step 2: Using the generated global number and edge attribute labels, perform electromagnetic field frequency domain analysis to complete the numerical modeling of the electromagnetic field;

[0011] Step 3: Integrate the microwave circuit module into the numerical model solution framework of the electromagnetic field and perform field-circuit coupling analysis: convert the S-parameters of the microwave circuit into the admittance matrix, add the admittance matrix to the discontinuity in the form of an equivalent source to form a lumped port on the discontinuity, and convert the admittance matrix into the voltage and current equations at the lumped port to establish the coupling relationship between the electromagnetic field and the circuit network.

[0012] Step 4: Based on the coupling relationship between the electromagnetic field and the circuit network, the current excitation effect introduced by the microwave circuit is addressed: For the lumped ports on the discontinuity, the Robin boundary conditions containing the current excitation term are derived by combining the upwind flux theory and Maxwell's equations; the admittance matrix of the microwave circuit is equivalent to the current source at the discontinuity, and it is embedded into the interface between adjacent units through numerical flux to realize the energy interaction between the electromagnetic field and the circuit, thus obtaining a linear global sparse matrix system;

[0013] Step 5: Solve the linear global sparse matrix system to obtain the electric field distribution and circuit port response on each discrete unit;

[0014] Step 6: Extract the electric field values ​​of each cell in the electromagnetic model, calculate the port current and scattering parameters based on the coupling relationship between the electromagnetic field and the circuit network, and complete the field-circuit cooperative performance analysis.

[0015] Furthermore, using the generated global identifiers and edge attribute labels, electromagnetic field frequency domain analysis is performed to complete the numerical modeling of the electromagnetic field. Specifically, this includes: using vector edge basis functions to perform Galerkin discretization on the wave equation; triggering the Robin boundary condition loading mechanism for edges marked as discontinuities; calculating the electric field continuity constraint through coupling terms; and assembling the discretization results into a sparse global matrix based on the global identifiers to achieve the mapping from local attributes to the global system, thus completing the numerical modeling of the electromagnetic field.

[0016] Furthermore, the admittance matrix is ​​transformed into equations for voltage and current at the lumped port, establishing the coupling relationship between the electromagnetic field and the circuit network, specifically including:

[0017] For any two-port circuit network, its admittance matrix can be expressed as:

[0018]

[0019] Among them, U i I represents the voltage supplied to the circuit by the electromagnetic field at the i-th port. i Y represents the current supplied to the circuit by the electromagnetic field at the i-th port; 11 Y 12 Y 21 Y 22 These are the parameters of the admittance matrix;

[0020] The electromagnetic field at the i-th port provides the voltage U to the circuit. i Obtained by integrating the electric field at the port surface:

[0021]

[0022] In the formula, Let E represent the basis functions of the physical domain expansion, where n represents the number of basis functions. j The electric field value at the port is represented by l, and the port width is represented by e. l The direction of the line integral;

[0023] Voltage U i Set as the input source of the circuit, obtain the current value, and convert the current equivalently to the port surface current density as follows:

[0024]

[0025] Where J1 represents the current density of the first lumped port, J2 represents the current density of the second lumped port, and W D This indicates the width of the port face.

[0026] Furthermore, the Robin boundary conditions containing the current excitation term are:

[0027]

[0028] Where, μ r1 μ represents the relative permeability of the first sub-region. r2 Represents the relative permeability of the second sub-region. Represents the electric field intensity of the first sub-region. Represents the electric field intensity of the second sub-region. Represents wave number, ε r2 The relative permittivity of the second sub-region is represented by m, where m is the transport coefficient. and Let be the normal vectors on the discontinuities of the first and second sub-regions. ε0 represents the current density at the port surface, ε0 represents the permittivity in vacuum, and μ0 represents the permeability in vacuum. It is a Hamiltonian operator.

[0029] Furthermore, the global sparse matrix system includes volume integral matrices [S] and [T], electric field and current coupling matrices belonging to different regions on the discontinuity, and electromagnetic field and circuit coupling matrices that introduce current as an unknown quantity, in the form of Ax = b.

[0030] Furthermore, the S matrix is:

[0031]

[0032] in, This represents the test basis function for the first subregion.

[0033] Furthermore, the T matrix is:

[0034]

[0035] Where, ε r1 This represents the relative permittivity of the first subregion.

[0036] Furthermore, the electric field and current coupling matrices belonging to different regions on the discontinuous surface are as follows:

[0037]

[0038] Where [D1] represents the effect of the electric field of the first sub-region on its own current. This indicates the self-coupling of the electric field in the first sub-region; [D] 12 Describe the contribution of the electric field in the first sub-region to the current in the second sub-region. Reflecting the mutual coupling of the electric fields between the first and second sub-regions, the matrix [D] T The matrix represents the effect of the current in the first sub-region on its own electric field. Describes the self-coupling of the current in the first sub-region; matrix The matrix reflects the influence of the current in the first sub-region on the electric field in the second sub-region. Characterized by the mutual coupling of the currents in the first and second sub-regions, ω represents the angular frequency. This represents the test basis function for the first sub-region. Γ represents the basis function expansion of the second subregion. 12 The integration region is located at the interface between the first and second sub-regions.

[0039] Furthermore, the electromagnetic field coupling matrix with the circuit, which introduces current as an unknown quantity, is:

[0040]

[0041] This represents the effect of the electric field of the first sub-region on the equivalent current density at port 1. This represents the effect of the magnetic field of the first sub-region on the equivalent current density at port 1.

[0042] An electromagnetic network coupling analysis system based on discontinuous Galerkin technique, comprising:

[0043] The electromagnetic model is divided into units to construct the electromagnetic model of the field-circuit coupling to be solved. The model is cut into three sub-regions according to the coordinate position of the discontinuity. Then, the entire computational domain of the electromagnetic model is divided into tetrahedral meshes to obtain the information of all units, edges and nodes. At the same time, the global numbering of all nodes and edges is completed, and the physical properties of the edges are identified.

[0044] The electromagnetic field frequency domain analysis unit uses the generated global number and edge attribute labels to perform electromagnetic field frequency domain analysis and complete the numerical modeling of the electromagnetic field.

[0045] The field-circuit coupling analysis unit converts the S-parameters of the microwave circuit into the admittance matrix, adds the admittance matrix to the discontinuity in the form of an equivalent source to form a lumped port on the discontinuity, and transforms the admittance matrix into the voltage and current equations at the lumped port to establish the coupling relationship between the electromagnetic field and the circuit network.

[0046] A linear global sparse matrix construction unit is used to derive Robin boundary conditions containing current excitation terms for lumped ports on discontinuities, combining wind flux theory and Maxwell's equations. The microwave circuit admittance matrix is ​​equivalent to a current source at the discontinuity, and it is embedded into the interface of adjacent units through numerical flux to realize the energy interaction between the electromagnetic field and the circuit, thus obtaining a linear global sparse matrix system.

[0047] The solution element solves the linear global sparse matrix system to obtain the electric field distribution and circuit port response on each discrete element.

[0048] The performance analysis unit extracts the electric field values ​​of cells in each region of the electromagnetic model, calculates port current and scattering parameters based on the coupling relationship between the electromagnetic field and the circuit network, and completes the field-circuit cooperative performance analysis.

[0049] Compared with the prior art, the significant advantages of this invention are:

[0050] (1) The method of the present invention pre-designs the S-parameters of the external circuit and converts them into the admittance matrix and inserts them into the global system equation. It eliminates the need to repeatedly derive the coupling equation for different circuit components, and can significantly improve the computational efficiency while ensuring accuracy.

[0051] (2) The method of the present invention introduces a current term on the basis of the traditional Robin boundary condition by deriving the Robin boundary condition that considers field-circuit coupling, which ensures the regional continuity of the electric field at the discontinuity and can accurately describe the relationship of field-circuit coupling.

[0052] (3) The method of the present invention uses tetrahedral discretization technology and vector edge basis functions, which significantly reduces the modeling error of non-uniform media and complex geometric structures compared with traditional rectangular mesh. Attached Figure Description

[0053] Figure 1 This is a structural dimension diagram of a microstrip transmission line.

[0054] Figure 2 This is a complete electromagnetic simulation diagram of a microstrip transmission line.

[0055] Figure 3 The equivalent circuit diagram for Gap-Cap chip capacitor G15BU200K5PX05.

[0056] Figure 4 The diagram shows a comparison of the S21 values ​​of the transmission line coupling Gap-Cap chip capacitor and HFSS and ADS calculated using the method of this patent.

[0057] Figure 5 This is the equivalent circuit model diagram of an active circuit.

[0058] Figure 6A comparison diagram of S11 for transmission line coupled active circuits and CST and ADS calculated using the method of this patent.

[0059] Figure 7 A comparison diagram of S21 for transmission line coupled active circuits calculated using the method of this patent and CST and ADS. Detailed Implementation

[0060] This invention proposes an electromagnetic network coupling analysis method based on discontinuous Galerkin technology. According to... Figure 1 Taking a microstrip line transmission model as an example, the specific steps of this method are described.

[0061] The first step is to construct an electromagnetic model of the field-circuit coupling to be solved, and to perform tetrahedral meshing on the entire computational domain to obtain information on all elements, edges and nodes.

[0062] The second step is to simultaneously assign global numbers to all nodes and edges based on the mesh generation results; at the same time, identify the physical properties of the edges (such as conductors and discontinuities) to provide a classification basis for subsequent boundary condition loading and field-path coupling.

[0063] The third step is the analysis of the spatial electromagnetic field. Using the generated global identifiers and edge attribute labels, frequency domain analysis of the electromagnetic field is performed. The wave equation is Galerkin discretized using vector edge basis functions. For edges marked as "discontinuities," the Robin boundary condition loading mechanism is automatically triggered, and the electric field continuity constraint is forced to be satisfied through coupling term calculation. Based on the global identifiers, the discretized results are assembled into a sparse global matrix, realizing the mapping from local attributes to the global system, thus completing the numerical modeling of the electromagnetic field.

[0064] The fourth step is the analysis of field-circuit coupling. The microwave circuit module is integrated into the electromagnetic field solution framework. Specifically, the S-parameters of the microwave circuit are converted into admittance matrices (Y-parameters), and the admittance matrices are added to the discontinuity in the form of equivalent sources to form lumped ports on the discontinuity, thereby establishing the coupling relationship between the electromagnetic field and the circuit network.

[0065] The fifth step, based on the field-circuit coupling framework established in step four, further addresses the current excitation effect introduced by the microwave circuit: for the lumped ports on the discontinuity, combining the upwind flux theory and Maxwell's equations, an improved Robin boundary condition containing current excitation terms is derived to ensure the physical consistency of the field-circuit coupling; the microwave circuit admittance matrix (Y parameter) is equivalent to a current source at the discontinuity, and it is embedded into the interface of adjacent units through numerical flux to realize the energy interaction between the electromagnetic field and the circuit, resulting in a global sparse matrix system;

[0066] Step 6: Solving the system of equations. The resulting global sparse matrix system is solved quickly using the direct solver PARDISO to obtain the electric field distribution and circuit port response on each discrete element.

[0067] Step 7, post-processing. Extract the electric field values ​​of each region's cells, calculate key indicators such as port current and scattering parameters based on the electromagnetic-circuit coupling relationship, and complete the field-circuit cooperative performance analysis.

[0068] In the first step, an electromagnetic model of the problem to be analyzed is constructed, and the entire computational domain is tetrahedral discretized to obtain information on all elements, edges, and nodes. Specifically, in ANSYS, a model is constructed according to the dimensions of the model to be analyzed, and the positions of the observation points need to be segmented to accurately calculate the electric field values ​​at the observation points. Tetrahedral discretization is used to discretize the entire computational domain to obtain information on all elements, edges, and nodes.

[0069] In the second step, based on the mesh generation results, the four nodes and six edges of each element are locally numbered, and then all nodes and edges are globally numbered. Simultaneously, the physical properties of the edges (such as conductors and discontinuities) are identified. Specifically, the entire computational domain is divided into multiple regions based on the physical properties of the discontinuities. Then, all edges within each region are numbered, resulting in a sort of all unknowns within that region, defined as the region's local number. For the edges on the discontinuous surfaces of each region, they are sorted according to the triangle numbers to obtain the sorting of edges on the DG surface (discontinuous surface electric field unknowns), which in turn yields the sorting of surface current unknowns. Finally, the unknowns in each region are arranged sequentially according to their region numbers to obtain the global unknown numbering.

[0070] In the third step, the spatial electromagnetic field is analyzed. Using the generated global identifiers and edge attribute labels, frequency domain analysis of the electromagnetic field is performed, and the wave equation is discretized using vector edge basis functions. Specifically, the entire computational domain is divided into different regions based on the discontinuity attributes, and each region must independently satisfy the vector wave equation and boundary conditions. For edges marked as "discontinuities," the Robin boundary condition loading mechanism is automatically triggered, forcibly satisfying the electric field continuity constraint through coupling term calculation. The discretized results are assembled into a sparse global matrix based on the global identifiers, realizing the mapping from local attributes to the global system, completing the numerical modeling of the electromagnetic field.

[0071] In the fourth step, the microwave circuit module is integrated into the electromagnetic field solution framework. The microwave circuit is represented by its S-parameters, which are then converted into an admittance matrix (Y-parameters) using network theory. The microwave circuit is then incorporated into the field-circuit coupling solution based on the discontinuous Galerkin frequency domain finite element algorithm in the form of the admittance matrix. Therefore, the admittance matrix is ​​transformed into equations for the voltage and current at the lumped ports, which are added to the electromagnetic field solution framework. For any two-port circuit network, its admittance matrix can be expressed as:

[0072]

[0073] U i The voltage supplied to the circuit by the electromagnetic field at the i-th port can be obtained by integrating the electric field across the port surface:

[0074]

[0075] In the formula, E represents the basis functions of the physical domain expansion. j The electric field value at the port is represented by l, and the port width is represented by e. l The direction of the line integral is represented. The voltage generated by the electromagnetic field in the circuit is derived from equation (1.2). This voltage is set as the input source of the circuit, and the value of the current I can be obtained. Finally, this current is equivalently converted to the port surface current density, expressed as:

[0076]

[0077] J1 represents the current density of the first lumped port, J2 represents the current density of the second lumped port, W D This indicates the width of the port face.

[0078] In the fifth step, based on the field-circuit coupling framework established in step four, the current excitation effect introduced by the microwave circuit is further processed: for the lumped port on the discontinuity, combined with the wind flux theory and Maxwell's equations, the improved Robin boundary conditions containing the current excitation term are derived.

[0079] Windward flux:

[0080]

[0081] Maxwell's equations:

[0082]

[0083] in This represents the magnetic field strength of the first sub-region. Represents the electric field intensity of the first sub-region. This represents the magnetic field strength of the second sub-region. Represents the electric field intensity of the second sub-region. Represents the current density at the port surface. This represents the intrinsic impedance of the first sub-region. This represents the intrinsic impedance of the second sub-region. Taking the first sub-region as an example, the Robin boundary conditions for field-path coupling are derived according to (1.4) and (1.5):

[0084]

[0085] Where, μ r1 μ represents the relative permeability of the first sub-region. r2 Represents the relative permeability of the second sub-region. Represents wave number, ε r2 The relative permittivity of the second sub-region is represented by m, which is defined as the transport coefficient. and Defined as the normal vector on the discontinuous surface.

[0086] To maintain the generality of the discussion, we will take the case of three discontinuous regions as an example. A brief derivation of the formula is given below.

[0087] In a lossless medium, the conductivity is 0, then the wave equation in the lossless medium is:

[0088]

[0089] The boundary conditions are ideal electric walls and ideal magnetic walls:

[0090]

[0091]

[0092] Where, ε r μ r , respectively, are the relative permittivity and relative permeability, and k0 is the wave number.

[0093] To ensure the rationality of the solution in the computational domain, the field at the interface of discontinuous regions must remain continuous. Therefore, Robin boundary conditions are introduced to transform the volume continuity problem into a surface continuity problem. Equation (1.6) is used as the boundary condition at the lumped port.

[0094] make

[0095]

[0096] The traditional Galerkin method is used to discretize each different region, and for each region, we can obtain (the subscript i indicates the i-th region):

[0097]

[0098] Taking the first sub-region as an example:

[0099]

[0100] in, To test the basis functions, To expand the basis functions, Let V be the volume and S be the area, and let V be the basis function for testing the first sub-region. Substituting the Robin boundary condition (1.6) considering the field path into equation (1.15), we can obtain the area integral part of the discretized wave equation:

[0101]

[0102] We define:

[0103]

[0104] These represent the current and electric field at the interface, respectively.

[0105] Substituting (1.17) into (1.16), we get:

[0106]

[0107] Substituting (1.18) into (1.15), we obtain the final equation to be solved:

[0108]

[0109] in:

[0110] S-matrix: T matrix:

[0111] The area fraction introduced by the discontinuous Galerkin method (1.18) has the following relationship: the first term on the right-hand side reflects the self-coupling and mutual coupling of the electric field and current at the interface, and the second term is the electromagnetic field-circuit coupling matrix with the current as an unknown quantity. It can be expressed as the following coupling matrix:

[0112]

[0113] [D1] indicates the effect of the electric field of the first sub-region on its own current. This indicates the self-coupling of the electric field in the first sub-region; [D] 12 Describe the contribution of the electric field in the first sub-region to the current in the second sub-region. This reflects the mutual coupling of the electric fields between the first and second sub-regions. This represents the effect of the electric field of the first sub-region on the equivalent current density at port 1.

[0114] To ensure the continuity of the electric field on the discontinuous surface, current is introduced as an unknown quantity, and additional equations are added to guarantee the solvability of the equation system. Substituting equation (1.17) into equation (1.6), and then according to Faraday's law of electromagnetic induction, we can obtain:

[0115]

[0116] Similarly, Galerkin transform is performed on (1.25).

[0117]

[0118] Similarly, equation (1.26) also forms a coupling matrix:

[0119]

[0120] Matrix [D] T The matrix represents the effect of the current in the first sub-region on its own electric field. Describes the self-coupling of the current in the first sub-region; matrix The matrix reflects the influence of the current in the first sub-region on the electric field in the second sub-region. Characterizes the mutual coupling of currents between the first and second sub-regions. This represents the effect of the magnetic field of the first sub-region on the equivalent current density at port 1.

[0121] Finally, by solving the simultaneous equations (1.20), (1.21), (1.22), (1.23), (1.24), (1.27), (1.28), and (1.29), a linear system of the form Ax = b can be obtained.

[0122] In the sixth step, the global sparse matrix system formed in steps three to five is solved quickly using the direct solver PARDISO to obtain the electric field distribution and circuit port response on each discrete unit.

[0123] In the seventh step, post-processing is performed. The electric field values ​​of each regional cell are extracted, and key indicators such as port current and scattering parameters are calculated based on the electromagnetic-circuit coupling relationship to complete the field-circuit cooperative performance analysis.

[0124] This invention also provides an electromagnetic network coupling analysis system based on discontinuous Galerkin technology, comprising:

[0125] The electromagnetic model is divided into units to construct the electromagnetic model of the field-circuit coupling to be solved. The model is cut into three sub-regions according to the coordinate position of the discontinuity. Then, the entire computational domain of the electromagnetic model is divided into tetrahedral meshes to obtain the information of all units, edges and nodes. At the same time, the global numbering of all nodes and edges is completed, and the physical properties of the edges are identified.

[0126] The electromagnetic field frequency domain analysis unit uses the generated global number and edge attribute labels to perform electromagnetic field frequency domain analysis and complete the numerical modeling of the electromagnetic field.

[0127] The field-circuit coupling analysis unit converts the S-parameters of the microwave circuit into the admittance matrix, adds the admittance matrix to the discontinuity in the form of an equivalent source to form a lumped port on the discontinuity, and transforms the admittance matrix into the voltage and current equations at the lumped port to establish the coupling relationship between the electromagnetic field and the circuit network.

[0128] A linear global sparse matrix construction unit is used to derive Robin boundary conditions containing current excitation terms for lumped ports on discontinuities, combining wind flux theory and Maxwell's equations. The microwave circuit admittance matrix is ​​equivalent to a current source at the discontinuity, and it is embedded into the interface of adjacent units through numerical flux to realize the energy interaction between the electromagnetic field and the circuit, thus obtaining a linear global sparse matrix system.

[0129] The solution element solves the linear global sparse matrix system to obtain the electric field distribution and circuit port response on each discrete element.

[0130] The performance analysis unit extracts the electric field values ​​of cells in each region of the electromagnetic model, calculates port current and scattering parameters based on the coupling relationship between the electromagnetic field and the circuit network, and completes the field-circuit cooperative performance analysis.

[0131] According to the method described in this invention, for Figure 1 Simulations were performed using a microstrip transmission line model. For example... Figure 1 As shown, the dielectric substrate dimensions of the microstrip line are 3.6mm × 0.254mm × 17mm, and the relative permittivity ε r =2.17. The dimensions of the metal patch and the port positions are shown in the figure, where ports 1 and 2 are lumped ports. Figure 3 The equivalent circuit of the Gap-Cap chip capacitor G15BU200K5PX05 is shown in the figure, with detailed annotations of the parameters of each component. This circuit is connected to a microstrip line, such as... Figure 1 As shown. (Through) Figure 4 A comparison of the S-parameter results from this patented method with those from HFSS and ADS simulation software shows that the method and the simulation software results exhibit good consistency. Furthermore, we also utilize... Figure 1 The model couples the Y-parameters of the active circuit, and its equivalent circuit is as follows: Figure 5 As shown in the figure, the parameters of each component are also labeled. The connection method between this circuit and the microstrip line is as follows. Figure 1 As shown. Figure 6 and Figure 7 The results show a comparison of the S-parameters of the method described in this patent with those of CST and ADS simulation software, further verifying the consistency between the method of this invention and the simulation software results.

[0132] This invention utilizes the network parameters—S-parameters—of external circuits to represent complex circuit networks, achieving coupling between electric fields and circuits. A numerical flux suitable for frequency-domain field-circuit coupling is derived, and a frequency-domain field-circuit joint simulation model is established. This invention supports co-simulation of electromagnetic fields and circuit systems. By representing the circuit as its equivalent S-parameters, field equations and circuit equations can be directly coupled, avoiding errors caused by traditional step-by-step solutions, ensuring computational accuracy while improving computational efficiency.

[0133] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for electromagnetic network coupling analysis based on discontinuous Galerkin technique, characterized in that, Including the following steps: Step 1: Construct an electromagnetic model of the field-circuit coupling to be solved. Cut the model into three sub-regions according to the coordinate position of the discontinuity. Then, perform tetrahedral meshing on the entire computational domain of the electromagnetic model to obtain information on all elements, edges and nodes. Simultaneously, complete the global numbering of all nodes and edges, and identify the physical properties of the edges. Step 2: Using the generated global number and edge attribute labels, perform electromagnetic field frequency domain analysis to complete the numerical modeling of the electromagnetic field; Step 3: Integrate the microwave circuit module into the numerical model solution framework of the electromagnetic field and perform field-circuit coupling analysis: convert the S-parameters of the microwave circuit into the admittance matrix, add the admittance matrix to the discontinuity in the form of an equivalent source to form a lumped port on the discontinuity, and convert the admittance matrix into the voltage and current equations at the lumped port to establish the coupling relationship between the electromagnetic field and the circuit network. Step 4: Based on the coupling relationship between the electromagnetic field and the circuit network, the current excitation effect introduced by the microwave circuit is addressed: For the lumped ports on the discontinuity, the Robin boundary conditions containing the current excitation term are derived by combining the upwind flux theory and Maxwell's equations; the admittance matrix of the microwave circuit is equivalent to the current source at the discontinuity, and it is embedded into the interface between adjacent units through numerical flux to realize the energy interaction between the electromagnetic field and the circuit, thus obtaining a linear global sparse matrix system; Step 5: Solve the linear global sparse matrix system to obtain the electric field distribution and circuit port response on each discrete unit; Step 6: Extract the electric field values ​​of each cell in the electromagnetic model, calculate the port current and scattering parameters based on the coupling relationship between the electromagnetic field and the circuit network, and complete the field-circuit cooperative performance analysis.

2. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 1, characterized in that, Using the generated global identifiers and edge attribute labels, electromagnetic field frequency domain analysis is performed to complete the numerical modeling of the electromagnetic field. Specifically, this includes: using vector edge basis functions to perform Galerkin discretization on the wave equation; triggering the Robin boundary condition loading mechanism for edges marked as discontinuities; calculating the electric field continuity constraint through coupling terms; and assembling the discretization results into a sparse global matrix based on the global identifiers to achieve the mapping from local attributes to the global system, thus completing the numerical modeling of the electromagnetic field.

3. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 1, characterized in that, The admittance matrix is ​​transformed into equations for voltage and current at the lumped port, establishing the coupling relationship between the electromagnetic field and the circuit network, specifically including: For any two-port circuit network, its admittance matrix is ​​expressed as: Among them, U i I represents the voltage supplied to the circuit by the electromagnetic field at the i-th port. i Y represents the current supplied to the circuit by the electromagnetic field at the i-th port; 11 Y 12 Y 21 Y 22 These are the parameters of the admittance matrix; The electromagnetic field at the i-th port provides the voltage U to the circuit. i Obtained by integrating the electric field at the port surface: In the formula, Let E represent the basis functions of the physical domain expansion, where n represents the number of basis functions. j The electric field value at the port is represented by l, and the port width is represented by e. l The direction of the line integral; Voltage U i Set as the input source of the circuit, obtain the current value, and convert the current equivalently to the port surface current density as follows: Where J1 represents the current density of the first lumped port, J2 represents the current density of the second lumped port, and W D This indicates the width of the port face.

4. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 1, characterized in that, The Robin boundary conditions containing the current excitation term are: Where, μ r1 μ represents the relative permeability of the first sub-region. r2 Represents the relative permeability of the second sub-region. Represents the electric field intensity of the first sub-region. Represents the electric field intensity of the second sub-region. Represents wave number, ε r2 The relative permittivity of the second sub-region is represented by m, where m is the transport coefficient. and Let be the normal vectors on the discontinuities of the first and second sub-regions. ε0 represents the current density at the port surface, ε0 represents the permittivity in vacuum, and μ0 represents the permeability in vacuum. It is a Hamiltonian operator.

5. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 4, characterized in that, The global sparse matrix system includes volume integral matrices [S] and [T], electric field and current coupling matrices belonging to different regions on the discontinuity, and electromagnetic field and circuit coupling matrices that introduce current as an unknown quantity, in the form of Ax = b.

6. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 5, characterized in that, The matrix S is: in, This represents the test basis function for the first subregion.

7. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 5, characterized in that, The matrix T is: Where, ε r1 This represents the relative permittivity of the first subregion.

8. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 5, characterized in that, Electric field and current coupling matrices of different regions on the discontinuous surface: Where [D1] represents the effect of the electric field of the first sub-region on its own current, [T1] e [D] indicates the self-coupling of the electric field in the first sub-region; 12 Describe the contribution of the electric field in the first sub-region to the current in the second sub-region. Reflecting the mutual coupling of the electric fields between the first and second sub-regions, the matrix [D] T [T1] represents the effect of the current in the first sub-region on its own electric field. j Describes the self-coupling of the current in the first sub-region; matrix The matrix reflects the influence of the current in the first sub-region on the electric field in the second sub-region. Characterized by the mutual coupling of the currents in the first and second sub-regions, ω represents the angular frequency. This represents the test basis function for the first sub-region. Γ represents the basis function expansion of the second subregion. 12 The integration region is located at the interface between the first and second sub-regions.

9. The electromagnetic network coupling analysis method based on discontinuous Galerkin technique according to claim 5, characterized in that, The electromagnetic field coupling matrix with the circuit, where current is introduced as an unknown, is: This represents the effect of the electric field of the first sub-region on the equivalent current density at port 1. This represents the effect of the magnetic field of the first sub-region on the equivalent current density at port 1.

10. An electromagnetic network coupling analysis system for implementing the method of any one of claims 1-9, characterized in that, include: The electromagnetic model is divided into units to construct the electromagnetic model of the field-circuit coupling to be solved. The model is cut into three sub-regions according to the coordinate position of the discontinuity. Then, the entire computational domain of the electromagnetic model is divided into tetrahedral meshes to obtain the information of all units, edges and nodes. At the same time, the global numbering of all nodes and edges is completed, and the physical properties of the edges are identified. The electromagnetic field frequency domain analysis unit uses the generated global number and edge attribute labels to perform electromagnetic field frequency domain analysis and complete the numerical modeling of the electromagnetic field. The field-circuit coupling analysis unit converts the S-parameters of the microwave circuit into the admittance matrix, adds the admittance matrix to the discontinuity in the form of an equivalent source to form a lumped port on the discontinuity, and transforms the admittance matrix into the voltage and current equations at the lumped port to establish the coupling relationship between the electromagnetic field and the circuit network. A linear global sparse matrix construction unit is used to derive Robin boundary conditions containing current excitation terms for lumped ports on discontinuities, combining wind flux theory and Maxwell's equations. The microwave circuit admittance matrix is ​​equivalent to a current source at the discontinuity, and it is embedded into the interface of adjacent units through numerical flux to realize the energy interaction between the electromagnetic field and the circuit, thus obtaining a linear global sparse matrix system. The solution element solves the linear global sparse matrix system to obtain the electric field distribution and circuit port response on each discrete element. The performance analysis unit extracts the electric field values ​​of cells in each region of the electromagnetic model, calculates port current and scattering parameters based on the coupling relationship between the electromagnetic field and the circuit network, and completes the field-circuit cooperative performance analysis.

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