2.5d full-wave simulation via grid radius compensation method, device, equipment and medium

Abstract

This invention relates to the field of electronic design automation (EDA) technology, and provides a method, apparatus, device, and medium for via mesh radius compensation in 2.5D full-wave simulation, including: S110: obtaining the positive end node index, negative end node index, and current index of the via; S120: establishing the topological equation and filling the global matrix with the contribution coefficients of the unknown current and voltage; S130: extracting the electromagnetic parameters of the dielectric layer, the physical radius of the via, and the equivalent numerical radius of the via; S140: calculating the numerical self-impedance of the via based on the equivalent numerical radius of the via; S150: calculating the physical self-impedance based on the physical radius of the via and symmetrically correcting it to obtain the corrected physical self-impedance; S160: calculating the compensated self-impedance and passively correcting it to obtain the corrected compensated self-impedance; S170: filling the global matrix with the negative of the corrected compensated self-impedance. This invention does not significantly increase the mesh density, makes the input impedance of the via in the parallel plate waveguide fit the analytical solution, maintains matrix symmetry, and balances the accuracy and efficiency of electromagnetic simulation.

Description

Technical Field

[0001] This invention relates to the field of electronic design automation technology, particularly to 2.5D full-wave electromagnetic simulation technology for power distribution networks in circuit boards and packaging structures, specifically to a via mesh radius compensation method, device, equipment, and medium in 2.5D full-wave simulation. Background Technology

[0002] As high-speed digital systems operate at frequencies in the microwave and millimeter-wave bands, vias in multilayer printed circuit boards (PCBs) and advanced packages, as key structures connecting traces across different layers and power / ground planes, have a significant impact on signal integrity and power integrity due to their electromagnetic characteristics. Accurately and efficiently extracting the impedance parameters of vias has become a challenging task in simulation design.

[0003] Currently, the mainstream via modeling methods can be divided into the following categories: 1. Three-dimensional full-wave electromagnetic simulation, such as the finite element method, has high accuracy but consumes huge computational resources, making it difficult to apply to the simulation of a whole board containing hundreds or thousands of vias.

[0004] 2. The lumped equivalent circuit method simplifies vias into a series and parallel network of resistors, inductors, and capacitors. This method can meet the requirements at low frequencies, but its accuracy is poor at high frequencies.

[0005] 3. The quasi-static parasitic extraction method only solves for the electrostatic field and the static magnetic field, ignoring the time harmonic wave effect, and extracts the RLGC parasitic matrix. However, it also cannot meet the high-frequency accuracy requirements.

[0006] 4.2.5D layered planar electromagnetic modeling method treats the power / ground plane pair as a two-dimensional parallel plate waveguide, performs full-wave discretization in the planar direction, and uses analytical mode expansion in the vertical direction. Vias serve as lumped current sources connecting the upper and lower waveguides or microstrip lines, and are coupled to the two-dimensional full-wave field through the superposition principle. This method achieves a good balance between efficiency and accuracy and has become the mainstream solution in the industry.

[0007] In 2.5D full-wave hybrid simulations, vias are typically modeled as axial current wires. When the field between parallel metal plates is discretized using a finite element mesh, the mesh's geometry and basis function form will produce an equivalent excitation aperture, which is usually not equal to the via's true physical radius. This difference leads to a non-negligible deviation between the simulated input impedance and the true solution. Although refining the mesh around the via can reduce the error in the equivalent radius and accurately calculate the voltage distribution near the via, this approach drastically increases the number of unknowns in the system and computation time, reducing computational efficiency.

[0008] Therefore, it is necessary to propose a method, device, equipment, and medium for compensating the via mesh radius in 2.5D full-wave simulation to solve the above problems. Summary of the Invention

[0009] The purpose of this invention is to provide a via mesh radius compensation method, device, equipment, and medium in 2.5D full-wave simulation, so as to make the input impedance of the via in the parallel plate waveguide highly consistent with the analytical solution without significantly increasing the mesh density, while maintaining the symmetry of the system matrix, thereby improving the accuracy and efficiency of the electromagnetic simulation system.

[0010] In a first aspect, the present invention provides a method for compensating the radius of via meshes in 2.5D full-wave simulation, the method comprising: S110: In the 2.5D field-circuit coupled frequency domain simulation, each via is treated as an independent circuit branch, the unknown quantity of the via current is assigned, and the index of the positive terminal node of the via, the index of the negative terminal node of the via, and the index of the via current are obtained. S120: Based on Kirchhoff's current law and voltage law, establish the topological equation for the connection between the via and the external circuit, and fill the contribution coefficients of the unknown current and voltage in the global matrix. S130: Extract the electromagnetic parameters of the dielectric layer at the location of the via, and obtain the physical radius and equivalent numerical radius of the via; S140: Based on the equivalent numerical radius of the via, calculate the numerical self-impedance of the via corresponding to the mesh using the via impedance analytical formula. S150: Based on the physical radius of the via, calculate the physical self-impedance of the via using the via impedance analytical formula, and perform symmetry correction on the physical self-impedance to obtain the corrected physical self-impedance. S160: Calculate the difference between the corrected physical self-impedance and the numerical self-impedance, multiply the difference by the field-circuit coupling coefficient to obtain the compensated self-impedance, perform passive correction on the compensated self-impedance, and obtain the corrected compensated self-impedance. S170: Fill the global matrix with the negative of the corrected and compensated self-impedance.

[0011] In one possible embodiment, the via impedance analytical formula is: ; Where j is the imaginary unit; h is the via height; η is the dielectric impedance; and k is the wave number. It is a zero-order Hankel function of the second kind; It is a first-order Hankel function of the second kind; is the self-impedance; r is the via radius.

[0012] In one possible embodiment, the physical self-impedance is symmetrically corrected to obtain the corrected physical self-impedance, including: The physical self-impedance is reciprocally corrected using the numerical self-impedance to obtain the corrected physical self-impedance, such that the corrected physical self-impedance and the numerical self-impedance satisfy reciprocal symmetry.

[0013] In one possible embodiment, the field-path coupling coefficient comprises the product of the voltage gain coefficient and the current gain coefficient.

[0014] In one possible embodiment, step S170 specifically includes: The negative of the corrected and compensated self-impedance is filled into the intersection of the row containing the via current equation and the column containing the target via current segment in the global matrix; when the target via current segment is the current via, the diagonal elements of the global matrix are corrected; if the target via current segment is an adjacent via, the off-diagonal elements of the global matrix are corrected.

[0015] In one possible embodiment, when performing passive correction on the compensated self-impedance, if the real part of the compensated self-impedance is negative, the real part is forcibly set to zero.

[0016] In one possible embodiment, during the 2.5D field-circuit coupled frequency domain simulation, the electromagnetic field part is solved using the finite element method, while the circuit part uses an improved node analysis method to construct a global matrix.

[0017] Secondly, this invention also provides a via mesh radius compensation device for 2.5D full-wave simulation. This device includes modules / units that execute any of the possible design methods described in the first aspect. These modules / units can be implemented in hardware or by hardware executing corresponding software.

[0018] Thirdly, embodiments of the present invention also provide an electronic device, including a processor and a memory. The memory stores one or more computer programs; when the one or more computer programs stored in the memory are executed by the processor, the electronic device is able to implement any of the possible design methods described in the first aspect.

[0019] Fourthly, this invention also provides a computer-readable storage medium comprising a computer program that, when run on an electronic device, causes the electronic device to perform any of the possible designs described in the first aspect.

[0020] Fifthly, embodiments of the present invention also provide a method comprising a computer program product, which, when the computer program product is run on an electronic device, causes the electronic device to perform any possible design of any of the above aspects.

[0021] The beneficial effects of the via mesh radius compensation method, device, equipment, and medium in 2.5D full-wave simulation of this invention are as follows: In 2.5D full-wave simulation, an analytical compensation method for via mesh radius is employed. By accurately compensating for the impedance difference between the equivalent and true mesh radii, the impedance characteristics of the vias in the parallel plate waveguide are significantly enhanced, resulting in a marked improvement in simulation accuracy. Furthermore, this method eliminates the need for extreme local refinement of the vias, maintaining the 2.5D mesh size and nearly identical matrix solution time to the uncompensated case, thus preserving the high efficiency advantage of the 2.5D field-path hybrid method. During the compensation process, by simultaneously filling voltage-current and current-voltage contributions at diagonal and off-diagonal positions, the system matrix remains symmetrical (or structurally symmetrical), allowing for efficient solution using a sparse symmetric matrix solver, accelerating the 2.5D full-wave simulation. Additionally, during matrix filling, pruning of the negative real parts avoids potential energy growth near resonant points, ensuring the stability of the 2.5D full-wave simulation. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the via mesh radius compensation method in the 2.5D full-wave simulation of this invention.

[0023] Figure 2 This is a schematic diagram illustrating how the via mesh radius compensation method in the 2.5D full-wave simulation of this invention integrates the via model into a field-path hybrid global sparse matrix system during the extraction of S-parameters of a signal network in a PCB structure using the modified node analysis method.

[0024] Figure 3 This is a schematic diagram illustrating the via mesh radius compensation method used in the 2.5D full-wave simulation of this invention to identify the connection position of vias in the circuit network.

[0025] Figure 4 This is a schematic diagram illustrating how the via mesh radius compensation method in the 2.5D full-wave simulation of this invention reads the equivalent numerical radius of the via under the current mesh distribution from the unknown data structure of the field.

[0026] Figure 5 This is a graph comparing the via mesh radius compensation method in 2.5D full-wave simulation of this invention with and without the via mesh radius compensation method in 2.5D full-wave simulation of this invention, and the S-parameter curves of commercial software.

[0027] Figure 6This is an alternative curve comparing the via mesh radius compensation method in 2.5D full-wave simulation using the present invention and the via mesh radius compensation method without the present invention with the S-parameter curves of commercial software.

[0028] Figure 7 This is a schematic diagram of the via mesh radius compensation device in the 2.5D full-wave simulation of the present invention.

[0029] Figure 8 This is a schematic diagram of the structure of the electronic device of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] In the following embodiments, for ease of understanding, the key terms involved are first defined and explained.

[0032] Vias: Conductive structures in multilayer printed circuit boards or packages that connect traces on different layers and power / ground planes. In 2.5D full-wave simulation, vias are modeled as axial current wires.

[0033] Modified Nodal Analysis (MNA): A matrix construction method commonly used in circuit simulation, which treats node voltages and branch currents as unknowns and constructs the circuit equation matrix based on Kirchhoff's current law and voltage law.

[0034] Via physical radius: The actual geometric radius of the via, derived from the via model data structure.

[0035] Equivalent numerical radius of a via: After the finite element mesh is discretized, due to the interpolation characteristics of the mesh geometry and basis function forms, the radius of the equivalent excitation aperture generated by the axial current wire of the via on the mesh. This radius reflects the geometric characteristics after mesh discretization and is usually not equal to the physical radius of the via.

[0036] Dielectric wave impedance: The ratio of electric field to magnetic field when an electromagnetic wave propagates in a medium, determined by the permeability and permittivity of the medium.

[0037] Wave number: The phase constant of an electromagnetic wave propagating in a medium, determined by the simulation frequency, the permeability of the medium, and the dielectric constant.

[0038] The second-order Hankel function is a special function describing outwardly propagating cylindrical waves. The zeroth-order and first-order second-order Hankel functions are used to characterize the field distribution of radially propagating cylindrical waves excited by an axial current source in a parallel-plate waveguide.

[0039] Global matrix: In 2.5D field-circuit hybrid simulation, it is a unified sparse matrix composed of the electromagnetic field and circuit components. The circuit component is constructed using an improved nodal analysis method, while the electromagnetic field component is solved discretized using the finite element method.

[0040] Via current segments: If a complete physical via spans multiple different dielectric layers, it will be divided into multiple independent via current segments according to the dielectric layer. Each via current segment corresponds to one dielectric layer thickness, and each via current segment is assigned an independent set of node indices and current unknowns. When a single isolated via passes through only one dielectric layer, it corresponds to only one via current segment.

[0041] To address the problems existing in the above-mentioned technologies, embodiments of the present invention provide a via mesh radius compensation method in 2.5D full-wave simulation, applicable to 2.5D field-circuit hybrid frequency domain simulation under a parallel plate waveguide model. The via is abstracted as an axial current wire model. See [link to relevant documentation]. Figure 1 The method includes: S110: In the 2.5D field-circuit coupled frequency domain simulation, each via is treated as an independent circuit branch, the unknown quantity of the via current is assigned, and the index of the positive terminal node of the via, the index of the negative terminal node of the via, and the index of the via current are obtained.

[0042] Specifically, in the sparse matrix construction process of the 2.5D field-circuit hybrid simulation system, node identification and variable definition are performed for the electrical connection relationships of vias. The via model objects are traversed to identify the connection positions of vias in the circuit network, and the globally unique index numbers of the positive and negative nodes of the vias are obtained in the solver. Branch currents are introduced as additional unknowns to improve the node analysis method system, and the globally unique identifiers of the via branch currents in the solver are obtained. Electromagnetic field unknowns that overlap with or are adjacent to the physical locations of the vias are identified, and these electromagnetic field unknowns participate as controlled source variables in subsequent matrix construction.

[0043] S120: Based on Kirchhoff's current law and voltage law, establish the topological equation for the connection between the via and the external circuit, and fill the contribution coefficients of the unknown current and voltage in the global matrix.

[0044] Based on the improved node analysis method, the basic circuit constraint equations of vias are filled into a global sparse matrix to form an initial matrix structure. In the row corresponding to the positive terminal node of the via, the column positions corresponding to the unknown via current are filled with positive unit coefficients; in the row corresponding to the negative terminal node of the via, the column positions corresponding to the unknown via current are filled with negative unit coefficients. In the row corresponding to the via branch current variables, the column positions corresponding to the positive terminal node of the via are filled with positive unit coefficients, and the column positions corresponding to the negative terminal node of the via are filled with negative unit coefficients. This row of equations expresses the relationship between the difference between the voltage at the positive terminal node and the voltage at the negative terminal node of the via and other impedance terms, but does not yet include the impedance characteristics of the via.

[0045] S130: Extract the electromagnetic parameters of the dielectric layer at the location of the via, and obtain the physical radius and equivalent numerical radius of the via.

[0046] For each via segment, the associated unknowns in the numerical simulation mesh are located using the via data structure. The corresponding medium parameter objects for that region are then extracted. A pre-defined electromagnetic parameter mapping table is then retrieved, using the medium parameter objects as indexes to match the corresponding physical parameter set. The electromagnetic parameters include permittivity, permeability, and thickness. The physical radius of the via is read from the via model data structure, and the equivalent numerical radius of the via under the current mesh distribution is read from the field unknown data structure. This equivalent numerical radius reflects the geometric characteristics after mesh discretization.

[0047] S140: Based on the equivalent numerical radius of the via, the numerical self-impedance of the via corresponding to the mesh is calculated using the via impedance analytical formula.

[0048] Based on the geometric characteristics of the discretized mesh, the numerical impedance of the via is calculated under the current mesh as a reference. Using the analytical impedance calculation formula, the dielectric parameters (dielectric constant, permeability, thickness), simulation frequency, and equivalent numerical radius of the via are input to calculate the numerical self-impedance of the via under mesh discretization. This numerical self-impedance of the via includes the influence of mesh size on the impedance calculation, and typically deviates from the actual physical impedance.

[0049] S150: Based on the physical radius of the via, the physical self-impedance of the via is calculated using the via impedance analytical formula, and the physical self-impedance is corrected by symmetry to obtain the corrected physical self-impedance.

[0050] Based on realistic physical geometric characteristics, and using analytical impedance calculation formulas, the theoretical physical self-impedance of the via is calculated by inputting dielectric parameters, simulation frequency, and via physical radius. This physical self-impedance represents the input impedance of an ideal cylindrical via in an infinitely large parallel plate or a specific medium. When multiple via segments or adjacent via coupling exist, the physical self-impedance is symmetrically corrected to ensure electromagnetic reciprocity, resulting in the corrected physical self-impedance. This ensures the symmetry of the impedance terms in the matrix and avoids non-physical energy transfer directions.

[0051] S160: Calculate the difference between the corrected physical self-impedance and the numerical self-impedance, multiply the difference by the field-circuit coupling coefficient to obtain the compensated self-impedance, perform passive correction on the compensated self-impedance, and obtain the corrected compensated self-impedance.

[0052] The difference between the corrected physical self-impedance and the numerical self-impedance is calculated, and this difference is multiplied by the field-circuit coupling coefficient to obtain the compensated self-impedance. The field-circuit coupling coefficient is used to correctly map the impedance difference calculated in the field domain to the voltage / current ratio of the circuit matrix. The real part of the compensated self-impedance is checked. If the real part is less than zero, it indicates that grid compensation may cause non-physical energy gain in the system, i.e., negative resistance. In this case, a passivity correction is performed, forcing the real part to zero or adjusting it to a non-negative value to obtain the corrected self-impedance. This step ensures that the corrected system matrix satisfies the passivity condition, guaranteeing the convergence and physical rationality of the simulation solution.

[0053] S170: Fill the global matrix with the negative of the self-impedance after correction and compensation.

[0054] Determine the row containing the via branch current variable, and the column containing the coupled field current variable or via segment variable. Call the sparse matrix solver element addition interface, and subtract the corrected self-impedance at the corresponding row and column. After the above filling, the behavioral equation corresponding to the via in the global sparse matrix accurately expresses the via voltage-current relationship after considering mesh compensation.

[0055] In one embodiment, the topological equation is formulated as follows: ;in, For the first The via current segment corresponds to the via branch current, which is a newly added unknown quantity of branch current in the improved node analysis method. The voltage at the positive terminal node p of the via; The voltage at the negative terminal node n of the via; For the first The via branch voltage of a via current segment characterizes the voltage drop generated across the via impedance.

[0056] This set of topological equations is obtained by the combined constraints of Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). The first two lines of the equations correspond to KCL current constraints: the coefficients +1 and -1 represent the current relationship of the via branch current flowing out of the positive node and flowing into the negative node, respectively. This constraint is used to fill the coefficients corresponding to the node rows in the global sparse matrix, respectively constraining the current conservation of the via branch current flowing out of the positive node and flowing into the negative node. The third line is a KVL voltage constraint, representing that the voltage difference between the two nodes of the via is equal to the voltage drop on the via branch. In this stage of matrix construction, only the coefficients corresponding to the above topological relationships are filled in; the impedance matrix elements are not filled in yet. The correlation coefficients of the via's self-impedance, mutual impedance, and compensation impedance will be added to the matrix in subsequent impedance calculation and matrix filling steps.

[0057] Furthermore, The formula is as follows: ;in, For the first The via branch voltage corresponding to each via current segment; For the first Branch current of each via current segment; These are the matrix elements of the via impedance submatrix, including the via's self-impedance, mutual impedance, and compensation impedance.

[0058] When summing index When it equals i, Corresponding to the self-impedance of the diagonal element, it represents the voltage drop across the via caused by the branch current of the via itself; when the summation index j is not equal to i, The corresponding off-diagonal mutual impedance represents the additional voltage induced on the current i-th via current segment by the electromagnetic field coupling effect of currents from other via current segments. Impedance matrix elements It consists of two superimposed parts: one part is the original numerical impedance obtained from mesh discretization simulation, and the other part is the compensated impedance calculated by this invention. The compensated impedance is used to compensate for the impedance calculation deviation introduced by the inconsistency between the equivalent numerical radius and the physical radius of the mesh. Substituting this voltage expression into the aforementioned KVL topological constraints, the complete via matrix row equations can be obtained: This complete equation describes the mathematical relationship between the voltage at the via node, the current in each via branch, and all impedance terms under the field-circuit hybrid simulation framework. It is also the mathematical basis for embedding the compensation impedance terms into the global sparse matrix in the future.

[0059] In one embodiment, the via impedance analytical formula is as follows: Where j is the imaginary unit; h is the via height; η is the dielectric impedance; and k is the wave number. It is a zero-order Hankel function of the second kind; It is a first-order Hankel function of the second kind; is the self-impedance; r is the via radius.

[0060] Furthermore, the formula for calculating the dielectric impedance is: ;in, Permeability; is the dielectric constant.

[0061] Furthermore, the formula for calculating the wave number is: ;in, For simulation frequency; Permeability; is the dielectric constant.

[0062] When calculating the numerical self-impedance of a via, the via radius is taken as the equivalent numerical radius of the via, resulting in the numerical self-impedance. When calculating the physical self-impedance, the via radius is taken as the physical radius of the via, resulting in the physical self-impedance. That is, when calculating the numerical self-impedance of a via... When, self-impedance Value self-impedance of via The via radius r is the equivalent numerical radius of the via. In calculating physical self-impedance When, self-impedance Physical self-impedance The via radius r is the physical radius of the via. .

[0063] The analytical formula for via impedance is derived from the radial transmission line model of an axial current source in a parallel-plate waveguide in cylindrical coordinates. The via current excites a radially outward propagating cylindrical wave between the parallel plates, and the self-impedance of the via is determined by the boundary conditions of the radial waveguide. The via radius *r* directly enters the independent variable of the Hankel function and the preceding coefficient factors, making the self-impedance sensitive to the radius.

[0064] In one embodiment, the physical self-impedance is symmetrically corrected to obtain the corrected physical self-impedance, which includes: using the numerical self-impedance to perform reciprocity correction on the physical self-impedance to obtain the corrected physical self-impedance, such that the corrected physical self-impedance and the numerical self-impedance satisfy reciprocity symmetry.

[0065] Furthermore, the physical self-impedance is corrected for symmetry using the following formula: ;in, It is the physical self-impedance; The self-impedance of the via; This is the corrected physical self-impedance. It should be noted that in the above complex geometric mean calculation, the complex square root is selected from the principal branch whose phase is closest to the original physical self-impedance and numerical self-impedance, ensuring that the output corrected physical self-impedance retains the physical characteristics of a passive impedance. Complex geometric mean is a preferred implementation method of this invention, but not the only means of achieving reciprocal symmetry; other impedance symmetry processing methods can also be used.

[0066] In one embodiment, the field-circuit coupling coefficient includes the product of the voltage gain coefficient and the current gain coefficient. It should be noted that the voltage gain coefficient and the current gain coefficient are pre-calculated based on the finite element basis functions and via element geometry information during the mesh preprocessing stage, and are directly read and used during the iterative solution of the simulation frequency points, without needing to be recalculated at each iteration step.

[0067] Specifically, the self-impedance compensation is performed using the following formula: ;in, This is the corrected physical self-impedance; The self-impedance of the via; This is the voltage gain coefficient; This is the current gain coefficient; To compensate for self-impedance.

[0068] The difference between the corrected physical self-impedance and the numerical self-impedance characterizes the deviation between the actual physical via impedance and the numerical impedance caused by mesh discretization. Voltage gain coefficient. Current gain coefficient Together they constitute the field-circuit coupling coefficient. Voltage gain coefficient. subscript Index of corresponding voltage node or via current segment, current gain coefficient subscript This corresponds to the index of the current node or unknown current in the field. The voltage gain coefficient is used to map the impedance difference from impedance dimensions to the contribution ratio of the voltage equation in the MNA matrix. In 2.5D field-circuit hybrid simulation, the solution results of the field part are mapped to the circuit matrix through the field-circuit coupling interface. The mapping process involves the conversion of the voltage scaling factor. The voltage gain coefficient reflects the contribution weight of the voltage expansion coefficient of the field discrete basis function at the via location to the voltage term of the circuit equation. The current gain coefficient is used to map the impedance difference to the contribution ratio of the current equation in the MNA matrix. The current gain coefficient reflects the contribution weight of the current distribution weight of the via axial current on the finite element mesh to the current term of the circuit equation. When equal hour, The product reflects the dimensional conversion ratio of self-impedance compensation; when Not equal to In this case, the product reflects the dimensional transformation ratio of the mutual impedance compensation. Since the field solver and circuit solver use different discretization methods and unknown definitions, directly filling the impedance difference into the matrix may lead to dimensional mismatch. By introducing voltage gain coefficients and current gain coefficients, the impedance difference is correctly mapped to the voltage / current ratio in the circuit matrix, ensuring the numerical accuracy and physical consistency of the compensation term.

[0069] In one embodiment, step S170 specifically includes: filling the negative of the corrected and compensated self-impedance into the intersection of the row where the via current equation is located and the column where the target via current segment is located in the global matrix; when the target via current segment is the current via, then the diagonal elements of the global matrix are corrected; if the target via current segment is an adjacent via, then the off-diagonal elements of the global matrix are corrected.

[0070] The global matrix is ​​a unified sparse matrix composed of the electromagnetic field and circuit components in the 2.5D field-circuit coupled frequency domain simulation. The electromagnetic field component is solved using the finite element method, while the circuit component is constructed using an improved nodal analysis method. In this improved nodal analysis method, each via is treated as an independent circuit branch, corresponding to a via branch current unknown. This via branch current unknown occupies an independent row and column in the global matrix. The row represents the voltage balance equation for the via branch, and the column represents the contribution of the via branch current to the current balance equations of each node.

[0071] The row containing the via current equation refers to the row of equations in the global matrix corresponding to the current variable of the via branch. The physical meaning of this row is that the difference between the voltage at the positive and negative terminals of the via, minus the total voltage drop across the via branch, equals zero. The matrix elements in this row corresponding to each current unknown are the coefficients of the corresponding current terms in the voltage equation for that via branch.

[0072] The column containing the target via current segment refers to the column of unknowns in the global matrix corresponding to the target via current segment. The target via current segment can be the current via itself, or an adjacent via or field current variable that is electromagnetically coupled to the current via. When the target via current segment is the current via, the matrix element corresponding to this column is located in the diagonal position of the global matrix; when the target via current segment is an adjacent via, the matrix element corresponding to this column is located in the off-diagonal position of the global matrix.

[0073] The corrected self-impedance is the compensated impedance value after passive correction. In the via branch voltage equation, this compensated impedance term appears as a voltage drop, meaning the product of the compensated impedance and the corresponding current in the equation has a negative sign. Therefore, when filling the global matrix with this compensated impedance as a matrix element, the value to be filled is the negative of the corrected self-impedance. Specifically, at the intersection of the row containing the via current equation and the column containing the target via current segment, the negative is added to the existing value at that position through the element addition interface provided by the sparse matrix solver. This operation is a matrix element accumulation, retaining the matrix coefficients originally generated by the mesh discretization, only adding the correction component brought by the compensation, and does not cover the impedance-related matrix elements obtained from the original mesh solution.

[0074] When the target via current segment is the current via, the fill position is a diagonal element. The physical significance of diagonal element correction is to correct the coefficients related to the current via's own current in the current via branch voltage equation, and by superimposing compensation components, to make the equivalent self-impedance approximate the physical self-impedance corresponding to the true physical radius from the numerical self-impedance after mesh discretization. When the target via current segment is an adjacent via, the fill position is a non-diagonal element. The physical significance of non-diagonal element correction is to correct the coefficients related to the adjacent via current in the current via branch voltage equation, so that the equivalent mutual impedance tends to be consistent with the physical true value.

[0075] Through the separate corrections to the diagonal and off-diagonal elements, the coefficients related to each current unknown in the via branch equations of the global matrix are compensated, thus automatically incorporating the via radius error caused by mesh discretization during matrix solving. Since the compensation terms are filled with negative numbers, consistent with the sign convention of the voltage drop term in the improved nodal analysis method, the strict correspondence between the matrix equations and the physical circuit is ensured, preventing solution deviations caused by sign errors.

[0076] In practice, the above filling operation is accomplished by traversing the sparse structure of the global matrix. For each via, the row index of its via current equation and the column index of each target via current segment are determined during the construction phase. During filling, the element addition interface of the sparse matrix solver is directly called, and the negative of the self-impedance after correction and compensation is accumulated at the specified row and column positions. This process does not change the dimension of the matrix, does not add new unknowns, and does not destroy the sparse structure and symmetry of the matrix; therefore, its impact on the solution time is negligible.

[0077] Compared to existing error suppression methods that refine the mesh around vias, this invention does not require adding mesh elements or solving for new unknowns. Error correction is achieved through matrix-level impedance compensation on the existing mesh, and the simulation scale remains unchanged.

[0078] In one specific embodiment, when performing passive correction on the compensated self-impedance, if the real part of the compensated self-impedance is negative, the real part is forcibly set to zero. It should be noted that the passive correction is only performed on the compensated impedance; the original numerical self-impedance is retained, and the corrected physical self-impedance remains unchanged. This is because the numerical self-impedance originates from a mesh discretization solution, while the corrected physical self-impedance originates from a physical analytical formula, and both inherently satisfy the passive condition. The negative real part only appears in the compensated impedance term after the impedance difference is mapped through the field-path coefficients; therefore, only the compensated impedance needs to be trimmed, avoiding disruption of the original physical meaning of the physical analytical impedance.

[0079] In this embodiment, near the resonant point, the difference between the corrected physical self-impedance and the numerical self-impedance may have a negative real component. A negative real part corresponds to negative resistance, meaning that the system experiences non-physical energy gain at this frequency, potentially leading to divergence in the matrix iterative solution or rendering the results meaningless. Forcing the negative real part to zero ensures that the real part of the corrected self-impedance is non-negative, guaranteeing the passivity of the system matrix. The imaginary part represents the reactance component and does not involve the positive or negative nature of energy dissipation; therefore, it remains unchanged to maintain the frequency response characteristics of the impedance. The introduction of negative resistance would disrupt the positive definiteness or semi-positive definiteness of the matrix, preventing the iterative solver from converging. By simply setting the real part to zero, simulation divergence is effectively avoided while maintaining computational efficiency, and the reactance compensation information carried by the imaginary part is not lost.

[0080] In one specific embodiment, during the 2.5D field-circuit coupled frequency domain simulation, the electromagnetic field part is solved using the finite element method, while the circuit part uses an improved nodal analysis method to construct a global matrix. The impedance characteristics of vias are solved using the via branch current equations and the remaining circuit elements in the improved nodal analysis method matrix, forming a unified solution system.

[0081] The following detailed explanation, with reference to specific embodiments, illustrates the process of the via mesh radius compensation method in 2.5D full-wave simulation of the present invention. This method is applied to... Figure 2 In the process of extracting S-parameters of a signal network in the multilayer PCB structure shown, the via model is integrated into the field-path hybrid global sparse matrix system using the modified node analysis method.

[0082] Step 1: Define the unknown quantity of via current.

[0083] First, in the process of constructing the sparse matrix of the 2.5D field-path hybrid simulation system, the electrical connection relationship of the vias must first be identified by nodes and the variables defined.

[0084] 1. Node Identification: Traverse the via model object to identify the connection location of the via in the circuit network. Specifically: For Figure 3The via shown is named via01. Obtain the globally unique index number of the positive end node p of the via in the solver, denoted as pos_node_number; obtain the globally unique index number of the negative end node n of the via, denoted as neg_node_number.

[0085] 2. Branch Current Definition: Branch current is introduced as an additional unknown in the MNA system. A globally unique identifier for the via branch current is obtained in the solver, denoted as current_node_number. This variable represents the current passing through the via.

[0086] 3. Field Correlation: Identify electromagnetic field unknowns that overlap with or are adjacent to the physical location of the via. These unknowns will be used as controlled source variables in subsequent matrix construction.

[0087] Step 2: Establish the topological equations for Kirchhoff's current law and voltage law.

[0088] Based on the modified node analysis method, the basic circuit constraint equations of the vias are filled into the global sparse matrix to form the initial matrix structure. The basic topological constraints for the connection between the vias and the external circuits are constructed by combining Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL), as shown in the above topological equation formulas.

[0089] In the rows corresponding to the positive and negative nodes of the via, establish the current inflow / outflow relationship respectively: in the pos_node_number row, the current_node_number column, the fill factor +1.0 indicates that the current flows out of the via and into the positive node; in the neg_node_number row, the current_node_number column, the fill factor -1.0 indicates that the current flows into the via from the negative node.

[0090] Referring to the topology equation formula, a voltage balance relationship is constructed in the row corresponding to the via branch current variable `current_node_number`: in the `current_node_number` row, the fill factor is +1.0 in the `pos_node_number` column; in the `current_node_number` row, the fill factor is -1.0 in the `neg_node_number` column. At this point, the equation in this row expresses... The relationship with other impedance terms is included, but the impedance characteristics of vias are not yet included.

[0091] Step 3: Extract the electromagnetic parameters of the dielectric layer and the via radius.

[0092] 1. Medium Parameter Extraction: For the location of the via segment, the associated unknown field quantities in the numerical simulation mesh are first located using the via data structure. Then, the corresponding medium RLGC parameter objects for this region are extracted. Next, a pre-defined electromagnetic parameter mapping table is searched, using the RLGC objects as indexes to match the corresponding physical parameter set. Electromagnetic physical parameters include the dielectric constant. , magnetic permeability μ and thickness h.

[0093] 2. Via Radius Extraction: The physical radius of the via is read from the via model data structure and denoted as... Read the current grid distribution from the field unknown data structure (e.g.) Figure 4 The equivalent numerical radius of the via (as shown) is denoted as . The equivalent numerical radius of the via reflects the geometric characteristics after the mesh is discretized.

[0094] Step 4: Calculate the numerical self-impedance of the via.

[0095] Based on the geometric features after mesh discretization, the numerical impedance of the via in the current mesh is calculated as a reference. The analytical impedance calculation formula is then used, with the medium parameters of the current field element input. (μ,h), simulation frequency f, and numerical radius The numerical self-impedance of the via under mesh discretization is calculated and denoted as . The via numerical self-impedance includes the effect of mesh size on impedance calculation, and usually deviates from the actual physical impedance.

[0096] Step 5: Calculate the physical self-impedance of the via and the reciprocity correction.

[0097] Based on real physical geometric characteristics, the theoretical physical radius of the via is calculated, considering reciprocity constraints. Using the analytical impedance calculation formula, the dielectric parameters, simulation frequency f, and via physical radius are input. The theoretical physical self-impedance is calculated and denoted as . This physical impedance represents the input impedance of an ideal cylindrical via in an infinitely large parallel plate or a specific medium.

[0098] When multiple via segments or adjacent via coupling exist, the physical self-impedance is symmetrically corrected to ensure electromagnetic reciprocity. The impedance is geometrically averaged to ensure the symmetry of the impedance terms in the matrix and to avoid non-physical energy transfer directions.

[0099] Step 6: Calculate the via self-impedance compensation value and passive correction.

[0100] The complex difference between the corrected physical self-impedance and the numerical self-impedance is calculated to obtain the basic compensation impedance. This basic compensation impedance is then multiplied by the field-circuit coupling gain coefficient to obtain the corrected compensation self-impedance. This step is to correctly map the impedance difference calculated in the field domain to the voltage / current ratio of the circuit matrix.

[0101] After checking the real part of the self-impedance after compensation, if the real part is less than 0, it indicates that mesh compensation may cause non-physical energy gain in the system, i.e., negative resistance. In this case, a passivity correction is performed, forcibly setting the real part of ΔZij to zero or adjusting it to a non-negative value. This step ensures that the corrected system matrix satisfies the passivity condition, guaranteeing the convergence and physical rationality of the simulation solution.

[0102] Step 7: Fill in the matrix values.

[0103] Determine the row containing the via branch current variable current_node_number, and the column containing the coupled field current variable or via segment variable branch_current_node_id. Call the sparse matrix solver element addition interface, and subtract the compensation impedance value from the position in the current_node_number row and the branch_current_node_id column. At the same time, if there are mutual inductance terms, fill the mutual inductance impedance to the corresponding off-diagonal position.

[0104] After the above filling, the behavioral equation corresponding to the via in the global sparse matrix becomes: This equation precisely expresses the via voltage-current relationship after considering mesh compensation.

[0105] in, The voltage at the positive terminal node p of the via; The voltage at the negative terminal node n of the via; The voltage difference between the external nodes at both ends of a via is derived from the KVL constraints of the circuit topology. Characterizing the branch current of the via itself The fundamental impedance voltage drop generated on the via includes the contribution of the via's physical inherent impedance. The compensation impedance term introduced in this invention, The compensation impedance is after reciprocity symmetry correction and passive correction. The field-correlated equivalent current is used to offset the impedance calculation deviation caused by the inconsistency between the grid discrete equivalent numerical radius and the real physical radius. It is the core manifestation of the grid radius compensation effect of this invention. The self-impedance of the via is numerical. This represents the current in other coupled via current segments, reflecting the original electromagnetic coupling effect between multiple vias and their current segments. The voltage drop corresponding to the original numerical impedance is characterized by the result of mesh discretization. The equivalent field voltage term obtained by mapping the two-dimensional parallel plate waveguide field is derived from the 2.5D full-wave finite element field solution and reflects the field-induced voltage contribution of the plane field at the via connection location.

[0106] This equation integrates circuit topology constraints, via impedance, mesh analytical compensation terms, multi-via coupling terms, and two-dimensional planar field contributions into a single equation, achieving field-circuit coupling between the field solution and the circuit solution. It's important to note that this equation is a row equation of the MNA global sparse matrix, and the compensation terms within the equation... In the aforementioned matrix filling step, the negative of the compensation impedance is written into the matrix coefficients. Through the transformation of the linear equation, the equivalent expression in the algebraic equation is finally presented. Its compensatory effect.

[0107] Compared to the original via equation without compensation, this equation adds... The compensation component does not require local mesh refinement around the vias; it corrects mesh aperture errors simply by adding compensation terms at the matrix level. Furthermore, because reciprocal symmetry correction is performed during the impedance compensation calculation stage, diagonal and off-diagonal elements are filled simultaneously, ensuring the global sparse matrix maintains reciprocal or structural symmetry. Therefore, it can be solved directly using a symmetric sparse matrix solver without incurring additional solution overhead. Additionally, the passive correction process prevents the compensation terms from introducing non-physical active gains corresponding to negative resistance, ensuring the physical rationality and iterative convergence of simulations in high-frequency and resonant scenarios.

[0108] By incorporating this equation into the complete global linear equation system AX=b and solving the global sparse matrix, we can simultaneously obtain the voltages at each circuit node, the currents in the via branches, and the unknowns in the two-dimensional planar field. Furthermore, we can solve for the output via impedance, S-parameters, and other PDN simulation results. In the 1MHz-5GHz simulation frequency band, the simulation results corresponding to this equation show higher consistency with the output results of commercial electromagnetic simulation software compared to the uncompensated scheme, with a particularly significant improvement in accuracy in the high-frequency range.

[0109] Using the via mesh radius compensation method of the present invention in 2.5D full-wave simulation and without using the via mesh radius compensation method of the present invention, the S-parameters of a signal network in the same PCB structure were extracted and compared with the results of commercial three-dimensional full-wave simulation software. Figure 5 and Figure 6Two sets of comparative curves are presented. The solid line, case_std.s4p, represents the commercial standard simulation reference result; the dashed line, case_comp.s4p, represents the simulation result after applying the via impedance compensation correction of this invention; and the dotted line, case_no_comp.s4p, represents the original mesh discretization simulation result without compensation correction. The results show that the S-parameter curve with mesh compensation correction is closer to the commercial software reference curve in the 1MHz to 5GHz frequency range compared to the result without mesh compensation correction. The low-frequency range is less affected by via impedance errors, and the three sets of simulation results show little difference. However, in the mid-to-high frequency range, the via impedance error caused by mesh discretization is amplified, and the S-parameters without mesh compensation correction show significant amplitude and depth deviations at the resonant frequency. In terms of computational resources, the mesh size using the mesh compensation correction method is the same as the uncompensated case, and the matrix solution time is almost the same. Therefore, after impedance compensation processing according to the present invention, there is no need to refine the mesh, the S-parameter curve remains highly consistent with the commercial standard reference results, effectively compensates for the simulation deviation introduced by the equivalent numerical radius, and improves the accuracy of high-frequency simulation while maintaining the original simulation scale.

[0110] The principle and technical effects of a via mesh radius compensation method in 2.5D full-wave simulation according to the present invention will be explained below.

[0111] This invention does not modify the via geometry model or perform mesh refinement. Error correction is achieved through matrix-level impedance compensation. The overall processing flow is as follows: First, the equivalent numerical radius and physical radius are substituted into the via impedance analytical formula to calculate the numerical self-impedance and the original physical self-impedance. To satisfy the reciprocity theorem for passive electromagnetic systems, a reciprocal symmetric correction is performed on the original physical self-impedance to obtain the corrected physical self-impedance. The difference between the corrected physical self-impedance and the numerical self-impedance is calculated; this difference characterizes the impedance deviation introduced by mesh discretization. The difference is multiplied by the field-circuit coupling coefficient to obtain the compensated impedance. The field-circuit coupling coefficient is used to complete the transition from the field solution space to the MNA circuit matrix space. Dimensional mapping; passive correction is performed on the compensation impedance. When the real part of the compensation impedance is negative, the real part is forced to zero to eliminate non-physical active gain; based on the transposition relationship of the via branch voltage balance equation, the negative value of the passively corrected compensation impedance is taken and filled into the corresponding row and column intersection position of the global sparse matrix by numerical accumulation; when the target via current segment is the current via, the diagonal elements of the correction matrix realize self-impedance compensation; when the target via current segment is another via current segment, the off-diagonal elements of the correction matrix realize mutual impedance compensation; after the matrix filling is completed, the global linear equation system AX=b is solved, and the unknown quantities of voltage and current fields are output, thereby obtaining simulation results such as via impedance and S-parameters.

[0112] This invention eliminates the need for mesh refinement, does not increase the number of unknowns to be solved, maintains the simulation scale, and preserves the computational efficiency of 2.5D simulation. Reciprocal symmetry processing, combined with simultaneous filling of diagonal and off-diagonal elements, ensures that the global matrix satisfies reciprocal symmetry, allowing the use of a highly efficient symmetric sparse matrix solver. Passive correction avoids non-physical negative resistance at resonant frequencies, preventing matrix iteration divergence. It also supports self-impedance and mutual impedance compensation, making it suitable for simulations of isolated vias, as well as printed circuit boards with multiple via segments, interconnected vias, and advanced packaged power distribution networks. The compensation benchmark is based on the full-wave analytical formula, preserving time-harmonic fluctuation effects and improving the accuracy of simulation results in high-frequency scenarios. This invention can accurately compensate for via radius errors caused by mesh discretization, maintain matrix symmetry, and is applicable to simulation methods for arbitrary via geometry within a 2.5D full-wave framework, meeting the accuracy and efficiency requirements of high-frequency and high-speed system design.

[0113] In addition, this invention also proposes a via mesh radius compensation device for 2.5D full-wave simulation, see [link to relevant documentation]. Figure 7 The device includes: The via variable definition module 701 is used to treat each via as an independent circuit branch during the 2.5D field-circuit coupled frequency domain simulation, assign unknown via current, and obtain the index of the positive terminal node, the index of the negative terminal node, and the index of the via current. Topology equation construction module 702 is used to establish the topology equation for the connection between vias and external circuits based on Kirchhoff's current law and voltage law, and to fill the contribution coefficients of current unknowns and voltage unknowns in the global matrix. The parameter acquisition module 703 is used to extract the electromagnetic parameters of the dielectric layer at the location of the via, and to obtain the via physical radius and the via equivalent numerical radius. The numerical self-impedance calculation module 704 is used to calculate the numerical self-impedance of the via corresponding to the mesh based on the via equivalent numerical radius and using the via impedance analytical formula. The physical self-impedance calculation module 705 is used to calculate the physical self-impedance of a via based on its physical radius using the via impedance analytical formula, and to perform symmetry correction on the physical self-impedance to obtain the corrected physical self-impedance. The self-impedance compensation module 706 is used to calculate the difference between the corrected physical self-impedance and the numerical self-impedance, multiply the difference by the field-circuit coupling coefficient to obtain the compensated self-impedance, and perform passive correction on the compensated self-impedance to obtain the corrected and compensated self-impedance. The matrix filling module 707 is used to fill the global matrix with the negative of the corrected and compensated self-impedance.

[0114] All relevant content of each step involved in the above method embodiments can be referenced from the functional description of the corresponding functional module, and will not be repeated here.

[0115] In other embodiments of the present invention, an electronic device is disclosed, see [link to relevant documentation]. Figure 8 The electronic device may include: one or more processors 801; a memory 802; a display 803; one or more application programs (not shown); and one or more computer programs 804. These devices may be connected via one or more communication buses 805. The one or more computer programs 804 are stored in the memory 802 and configured to be executed by the one or more processors 801. The one or more computer programs 804 include instructions that can be used to perform actions such as… Figure 1 and Figure 7 And the various steps in the corresponding embodiments.

[0116] Through the above description of the embodiments, those skilled in the art will clearly understand that, for the sake of convenience and brevity, only the division of the above functional modules is used as an example. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. The specific working process of the system, device, and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0117] In the various embodiments of this invention, the functional units can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0118] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as flash memory, portable hard disk, read-only memory, random access memory, magnetic disk, or optical disk.

[0119] While embodiments of the invention have been described in detail above, it will be apparent to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations fall within the scope and spirit of the invention as defined in the claims. Furthermore, the invention described herein may have other embodiments and can be implemented or carried out in various ways. Unless otherwise defined, the technical or scientific terms used herein should be understood in their ordinary sense by one of ordinary skill in the art to which this invention pertains. The terms "comprising" and similar expressions used herein mean that the element or object preceding the word encompasses the element or object listed following the word and its equivalents, but do not exclude other elements or objects.

Claims

1. A method for compensating the radius of via mesh in 2.5D full-wave simulation, characterized in that, The method includes: S110: In the 2.5D field-circuit coupled frequency domain simulation, each via is treated as an independent circuit branch, the unknown quantity of the via current is assigned, and the index of the positive terminal node of the via, the index of the negative terminal node of the via, and the index of the via current are obtained. S120: Based on Kirchhoff's current law and voltage law, establish the topological equation for the connection between the via and the external circuit, and fill the contribution coefficients of the unknown current and voltage in the global matrix. S130: Extract the electromagnetic parameters of the dielectric layer at the location of the via, and obtain the physical radius and equivalent numerical radius of the via; S140: Based on the equivalent numerical radius of the via, calculate the numerical self-impedance of the via corresponding to the mesh using the via impedance analytical formula. S150: Based on the physical radius of the via, calculate the physical self-impedance of the via using the via impedance analytical formula, and perform symmetry correction on the physical self-impedance to obtain the corrected physical self-impedance. S160: Calculate the difference between the corrected physical self-impedance and the numerical self-impedance, multiply the difference by the field-circuit coupling coefficient to obtain the compensated self-impedance, perform passive correction on the compensated self-impedance, and obtain the corrected compensated self-impedance. S170: Fill the global matrix with the negative of the corrected and compensated self-impedance.

2. The method according to claim 1, characterized in that, The analytical formula for the via impedance is: ； Where j is the imaginary unit; h is the via height; η is the dielectric impedance; and k is the wave number. It is a zero-order Hankel function of the second kind; It is a first-order Hankel function of the second kind; is the self-impedance; r is the via radius.

3. The method according to claim 1, characterized in that, The physical self-impedance is symmetrically corrected to obtain the corrected physical self-impedance, including: The physical self-impedance is reciprocally corrected using the numerical self-impedance to obtain the corrected physical self-impedance, such that the corrected physical self-impedance and the numerical self-impedance satisfy reciprocal symmetry.

4. The method according to claim 1, characterized in that, The field-circuit coupling coefficient includes the product of the voltage gain coefficient and the current gain coefficient.

5. The method according to claim 1, characterized in that, Step S170 specifically includes: The negative of the corrected and compensated self-impedance is filled into the intersection of the row containing the via current equation and the column containing the target via current segment in the global matrix; when the target via current segment is the current via, the diagonal elements of the global matrix are corrected; if the target via current segment is an adjacent via, the off-diagonal elements of the global matrix are corrected.

6. The method according to claim 1, characterized in that, When performing passive correction on the compensated self-impedance, if the real part of the compensated self-impedance is negative, the real part is forcibly set to zero.

7. The method according to claim 1, characterized in that, In the 2.5D field-circuit coupled frequency domain simulation, the electromagnetic field part is solved using the finite element method, while the circuit part uses an improved node analysis method to construct a global matrix.

8. A via mesh radius compensation device for 2.5D full-wave simulation, characterized in that, The device includes: The via variable definition module is used to treat each via as an independent circuit branch during 2.5D field-circuit coupled frequency domain simulation, assign unknown via current, and obtain the index of the positive terminal node, the index of the negative terminal node, and the index of the via current. The topology equation construction module is used to establish the topology equations for the connection between vias and external circuits based on Kirchhoff's current law and voltage law, and to fill the contribution coefficients of the unknown current and voltage in the global matrix. The parameter acquisition module is used to extract the electromagnetic parameters of the dielectric layer at the location of the via, and to obtain the physical radius and equivalent numerical radius of the via. The numerical self-impedance calculation module is used to calculate the numerical self-impedance of the via corresponding to the mesh based on the equivalent numerical radius of the via and using the via impedance analytical formula. The physical self-impedance calculation module is used to calculate the physical self-impedance of the via based on the physical radius of the via and using the via impedance analytical formula, and to perform symmetry correction on the physical self-impedance to obtain the corrected physical self-impedance. The self-impedance compensation module is used to calculate the difference between the corrected physical self-impedance and the numerical self-impedance, multiply the difference by the field-circuit coupling coefficient to obtain the compensated self-impedance, and perform passive correction on the compensated self-impedance to obtain the corrected and compensated self-impedance. The matrix filling module is used to fill the global matrix with the negative of the corrected and compensated self-impedance.

9. An electronic device, characterized in that, include: Processor and memory, wherein the memory is used to store computer programs; The processor is configured to execute a computer program stored in the memory to cause the electronic device to perform the method of any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

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