Collaborative simulation method for FPC high-frequency signal integrity

Abstract

The invention relates to the technical field of signal simulation, in particular to a co-simulation method for FPC high-frequency signal integrity, which comprises the following steps of: according to an FPC laminated structure design file, identifying spatial geometric positions of a rigid connector and a flexible strip line, dividing the whole simulation space into a three-dimensional structure area and a layered transmission area, generating geometric region segmentation data, calling the geometric region segmentation data, and generating interface grid node coordinates. According to the invention, the overall simulation space is geometrically cut along the structure and morphology abrupt change part, and the complex FPC assembly is decomposed into the three-dimensional structure area and the layered transmission area, so that the whole link is prevented from being processed by a single three-dimensional full-wave method with huge computing resource consumption; and meanwhile, collaborative analysis of the three-dimensional discontinuity effect of the connector and the long-distance transmission characteristic of the flexible wire is realized, and the calculation time and the memory occupation are reduced while the simulation result is ensured to be highly close to physical actual measurement.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of signal simulation, in particular to a FPC high-frequency signal integrity cooperative simulation method. BACKGROUND

[0002] The signal simulation technology mainly utilizes computer software and numerical calculation methods to model, analyze and predict the transmission behavior of electric signals in circuits, interconnection channels and systems. The existing signal simulation technology adopts a three-dimensional full-wave electromagnetic field solver to perform overall subdivision and calculation on the entire model. For a flexible strip line region with relatively simple structure, the same level of grid subdivision is also applied to the complex connector region, resulting in a geometric growth of the number of grid elements, and further causing a huge amount of calculation and memory requirement. Therefore, improvement is needed. SUMMARY

[0003] The application aims to solve the problems in the prior art and provides a FPC high-frequency signal integrity cooperative simulation method.

[0004] In order to achieve the above-mentioned purpose, the application adopts the following technical scheme, a FPC high-frequency signal integrity cooperative simulation method, comprising the following steps: According to the FPC laminated structure design file, the spatial geometric positions of the rigid connector and the flexible strip line are identified, the overall simulation space is divided into a three-dimensional structure region and a layered transmission region, geometric region division data is generated, the geometric region division data is called, and interface grid node coordinates are generated; According to the working frequency and the conductive rate parameter of the rolled copper foil, a surface roughness erosion ratio value is calculated and generated, the surface roughness erosion ratio value is compared with a preset judgment threshold value in a numerical interval, and a frequency-variable loss correction coefficient is obtained; According to the geometric region division data and the frequency-variable loss correction coefficient, connector region three-dimensional field distribution data is calculated and generated, the flexible strip line region in the signal transmission channel is solved, the propagation characteristics of the voltage and current along the line are calculated, and flexible line region transmission characteristic data is generated; According to the connector region three-dimensional field distribution data and the flexible line region transmission characteristic data, a transmission boundary equation including tangential electric field and magnetic field information is constructed at the interface grid node coordinate position, interface energy exchange convergence data is generated, the error value of the interface energy exchange convergence data is monitored, when the error value is lower than a preset limit value, the voltage-to-current ratio at the input and output port impedance is extracted, and full-link signal integrity S parameters are generated.

[0005] Preferably, the interface grid node coordinate acquisition step is: Based on the FPC stacked structure design documents, the spatial geometric positions of the rigid connector and the flexible strip are marked. Cutting lines are set at the abrupt changes in morphology to perform geometric cutting. The overall simulation space is divided into a three-dimensional structural region and a layered transmission region, and geometric region segmentation data is generated. Based on the geometric region segmentation data, the mesh vertex information at the cutting surface is extracted. Lagrange multipliers are introduced for non-overlapping nodes at the interface to complete the mapping and matching process. The boundary position of electromagnetic energy exchange between regions is determined based on the matched node pairs, thus forming the boundary position of the interface. Based on the boundary position of the interface, the mesh vertex information at the cutting surface is called, the node pairs at the boundary position are traversed and deduplicated according to the coordinate order, the mesh node coordinate sequence that satisfies the continuity of the interface is selected, and the interface mesh node coordinates are generated.

[0006] Preferably, the step of obtaining the surface roughness erosion ratio value is as follows: Based on the operating frequency and the conductivity parameters of the rolled copper foil, combined with the vacuum permeability and relative permeability, the current penetration depth of the conductor surface is calculated, and the attenuation distance of the current density along the conductor thickness direction is defined as the standard skin depth, thus generating the standard skin depth. The surface roughness erosion ratio is calculated based on the standard skin depth.

[0007] Preferably, the step of obtaining the frequency-varying loss correction coefficient is as follows: The surface roughness erosion ratio is compared with a preset threshold range. If the surface roughness erosion ratio falls within the range of a smooth zone, a transition zone, or a deep erosion zone, the corresponding surface impedance calculation formula coefficients in the preset database are indexed to generate frequency-varying loss correction coefficients.

[0008] Preferably, the steps for acquiring the three-dimensional field distribution data of the connector area are as follows: Based on the geometric region segmentation data and the frequency-varying loss correction coefficient, a three-dimensional computational domain is constructed in the rigid connector region. Mesh elements are generated according to the geometric region segmentation data, and metal and dielectric surfaces are labeled. A surface impedance model is applied to the conductor boundary, and the frequency-varying loss correction coefficient is substituted into the port boundary conditions. The steady-state field solution under port excitation is calculated, and three-dimensional field distribution data of the connector region is generated.

[0009] Preferably, the step of acquiring the transmission characteristic data of the flexible line area is as follows: Based on the three-dimensional field distribution data of the connector area, the tangential electric field component and tangential magnetic field component of the connector port are extracted. The field values ​​are rearranged according to the grid order of the port section and the coordinate system direction is unified. The data are mapped to the starting section of the flexible strip as the incident condition. The Green's function of the multilayer medium is called to solve the two-dimensional half-transmission equation and obtain the propagation characteristics of voltage and current along the line. Based on the propagation characteristics of voltage and current along the line, the phase constant and attenuation constant of each frequency point are read, the conductor surface impedance is updated according to the frequency-varying loss correction coefficient, and the propagation constant curve is corrected. The amplitude and phase distribution of voltage and current along the line are iteratively updated to form flexible line area transmission characteristic data.

[0010] Preferably, the step of obtaining the interface energy exchange convergence data is as follows: Based on the three-dimensional field distribution data of the connector area, the transmission characteristic data of the flexible line area, and the coordinates of the interface grid nodes, the tangential electric field component and the tangential magnetic field component are extracted at the coordinates of each interface grid node. The coordinate systems on both sides are unified according to the node number order and the phase reference is aligned. A node pair mapping list is established and the port affiliation and normal direction are marked. The coupling terms of the tangential electric field information and the tangential magnetic field information are written according to the node pair to generate the interface transmission boundary equation. According to the interface transmission boundary equation, the transmission characteristic data of the flexible line area is first injected into the boundary using the three-dimensional field distribution data of the connector area as the source, and then the three-dimensional field distribution data of the connector area is written back into the boundary using the transmission characteristic data of the flexible line area as the source. The tangential electric field information and tangential magnetic field information of the node pair are updated one by one, and the energy flux sequence and residual sequence after each exchange are recorded to generate the interface energy exchange convergence data.

[0011] Preferably, the steps for obtaining the end-to-end signal integrity S-parameters are as follows: Based on the convergence data of energy exchange at the interface, the maximum absolute difference of the energy flux difference sequence of adjacent iterations is calculated as the error value. The error value is compared with the preset limit. If the error value is less than the preset limit, the voltage-current ratio is extracted at the input port impedance and the voltage-current ratio is extracted at the output port impedance. The values ​​are rearranged according to the frequency point index and frequency domain transformation is performed to generate the full-link signal integrity S-parameters.

[0012] Compared with the prior art, the advantages and positive effects of the present invention are as follows: This invention geometrically divides the overall simulation space along abrupt changes in structural morphology, decomposing the complex FPC component into a three-dimensional structural region and a layered transmission region. This avoids using a single, computationally expensive three-dimensional full-wave method to process the entire link. At the interface of the division, Lagrange multipliers are introduced to map and match non-overlapping mesh nodes between different regions, solving the problem of physical field discontinuity caused by different meshing strategies and ensuring the accuracy of electromagnetic energy transfer between regions. Based on this, by calculating and integrating the root mean square roughness of the copper foil surface and the surface roughness erosion ratio of the relevant length, a frequency-varying loss model that is closer to the real physical morphology is constructed, ensuring the consistency and high fidelity of the loss analysis of the entire link. Finally, a transmission boundary equation is constructed at the interface, and bidirectional data exchange and iterative calculations are performed until the energy exchange converges. This achieves a collaborative analysis of the three-dimensional discontinuity effect of the connector and the long-distance transmission characteristics of the flexible line, reducing computation time and memory usage while ensuring that the simulation results closely approximate physical measurements. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the steps of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0015] Please see Figure 1 This invention provides a technical solution, a co-simulation method for FPC high-frequency signal integrity, comprising the following steps: Based on the FPC stacked structure design documents, the spatial geometric positions of the rigid connector and the flexible strip are identified, the overall simulation space is divided into a three-dimensional structural region and a layered transmission region, geometric region segmentation data is generated, and the interface mesh node coordinates are generated by calling the geometric region segmentation data. Based on the operating frequency and the conductivity parameters of the rolled copper foil, the surface roughness erosion ratio is calculated and generated. The surface roughness erosion ratio is then compared with a preset judgment threshold to obtain the frequency conversion loss correction coefficient. Based on the geometric region segmentation data and frequency conversion loss correction coefficient, the three-dimensional field distribution data of the connector area is calculated and generated. The flexible stripline region in the signal transmission channel is solved, and the propagation characteristics of voltage and current along the line are calculated to generate the transmission characteristic data of the flexible stripline region. Based on the three-dimensional field distribution data of the connector area and the transmission characteristic data of the flexible line area, a transmission boundary equation including tangential electric field and magnetic field information is constructed at the coordinate position of the interface grid node. The interface energy exchange convergence data is generated, and the error value of the interface energy exchange convergence data is monitored. When the error value is lower than the preset limit, the voltage-current ratio at the input and output port impedance is extracted to generate the full-link signal integrity S-parameter.

[0016] The steps to obtain the coordinates of the mesh nodes at the interface are as follows: Based on the FPC stacked structure design documents, the spatial geometric positions of the rigid connector and the flexible strip are marked. Cutting lines are set at the abrupt changes in morphology to perform geometric cutting. The overall simulation space is divided into a three-dimensional structural region and a layered transmission region, and geometric region segmentation data is generated. Based on the geometric region segmentation data, the mesh vertex information at the cutting surface is extracted. Lagrange multipliers are introduced for non-overlapping nodes at the interface to complete the mapping and matching process. Based on the matched node pairs, the boundary position of electromagnetic energy exchange between regions is determined, thus forming the boundary position of the interface. Based on the boundary position of the interface, the mesh vertex information at the cutting surface is called, the node pairs at the boundary position are traversed and deduplicated according to the coordinate order, the mesh node coordinate sequence that satisfies the continuity of the interface is selected, and the interface mesh node coordinates are generated.

[0017] Specifically, based on the FPC stack-up structure design documents, the physical property parameters of the dielectric layer, copper foil layer, and cover film layer are analyzed. The thickness, relative permittivity, and loss tangent of each material layer are read. At the same time, the component package list in the design documents is traversed to retrieve the coordinates of the center point of the rigid connector in the layout coordinate system. In addition to the contour dimensions, the rate of change of the conductor width is scanned along the signal transmission path, and the first derivative of the width along the line is calculated. Locations where the absolute value of the derivative exceeds a preset width change threshold are marked as abrupt changes in shape. For example, a width change threshold is set. ,in Assuming an average linewidth of 0.15mm for the flexible strip, any abrupt change in linewidth exceeding 0.015mm is considered a morphological abrupt change point. A geometric cutting position is selected between the edge of the rigid connector and the morphological abrupt change point, and a cutting distance is set. The calculation formula is: ,in The safety margin factor is set to 0.05. To determine the wavelength in the medium corresponding to the highest operating frequency, if the highest frequency is 10 GHz and the dielectric constant of the medium is 3.5, the wavelength is approximately 16 mm. The calculated cutting distance is 0.8 mm. At this location, an equation is established for the cutting plane normal to the signal transmission direction. ,in For normal vector components, As a constant term, the entity Boolean operation algorithm is called to divide the geometry of the overall simulation model using the cutting plane. The part containing the connector is defined as the three-dimensional full-wave analysis region, and the straight and uniformly cross-sectional flexible line part is defined as the layered transmission line region. The geometric topology relationship of the two regions is reconstructed, and the face ID and the region identifier on the dividing plane are recorded to generate geometric region segmentation data.

[0018] Based on the geometric region segmentation data, index to the geometric surface marked as the cutting surface, traverse the vertex list generated by the finite element mesh on this surface, and obtain the set of mesh nodes on one side of the three-dimensional structural region. and the set of grid nodes on one side of the layered transmission region ,calculate Each node The two-dimensional coordinates projected onto the cutting plane are calculated simultaneously. Each node Two-dimensional coordinates on the same plane, for and Non-conformal node pairs whose spatial coordinates do not completely coincide, introducing Lagrange multipliers. To enforce the continuity constraint on the tangential component of the electromagnetic field, an interface coupling integral equation is constructed. ,in Represents the interface area. The Lagrange multiplier vector to be solved is used to characterize the equivalent surface current density on the interface. Let be the tangential electric field vector on one side of the three-dimensional structure region. The tangential electric field vector is located on one side of the layered transmission region. For the differential area element, set a threshold distance for determining node matching. This threshold is set to one-tenth of the average side length of the grid. For example, when the average side length of the grid is 0.2 mm, Set the value to 0.02 mm and calculate the Euclidean distance between any two nodes. ,like Then it is determined to be a directly overlapping node. The basis function interpolation method is used to establish a mapping relationship. The field quantity on the three-dimensional side is projected to the node position on the layered side through shape functions. All the node index pairs that establish the association and their corresponding weighting coefficients are recorded to lock the physical window range of energy exchange and form the interface boundary position.

[0019] Based on the interface boundary position, the list of vertex information of the cutting surface mesh stored in memory is read. This list contains the three-dimensional coordinates of all discrete points involved in the calculation. Sort the node coordinates in the list, first by Z-axis coordinate from smallest to largest, then sort by Z-axis coordinate from smallest to largest. If the difference in Z-axis coordinates is less than the coordinate tolerance... Sort by the Y-axis, then by the X-axis; coordinate tolerance is specified here. Set as To eliminate the impact of floating-point calculation errors, an adjacent item comparison is performed in the sorted sequence. It checks if the coordinate distance between two consecutive nodes is less than the coordinate tolerance. If it is, the node is considered a duplicate and the subsequent item is removed, retaining only the unique node identifier. Then, a topological continuity check is performed on the deduplicated node sequence, and the total area of ​​the facets formed by all adjacent nodes is calculated. And calculate the theoretical geometric cross-sectional area enclosed by the cutting profile. Construct area coverage index The coverage pass threshold is set at 0.99. If the value is greater than or equal to 0.99, it is determined that the grid nodes are continuously distributed on the interface without holes, which can meet the numerical transfer requirements of the electromagnetic field boundary conditions. The nodes that pass the verification are renumbered according to their spatial position order, and a structured array containing the node index, spatial coordinates and the ID of the grid cell to which it belongs is established to generate the coordinates of the grid nodes at the interface.

[0020] The steps for obtaining the surface roughness erosion ratio are as follows: Based on the operating frequency and the conductivity parameters of the rolled copper foil, combined with the vacuum permeability and relative permeability, the current penetration depth of the conductor surface is calculated, and the attenuation distance of the current density along the conductor thickness direction is defined as the standard skin depth, thus generating the standard skin depth. The surface roughness erosion ratio is calculated based on the standard skin depth using the following formula: ; in, This represents the surface roughness erosion ratio. denoted as the root mean square roughness of the copper foil surface profile. For standard skin depth, The length of the copper foil surface profile. The fitting coefficients are for the additional loss magnitude. This is the steepness adjustment coefficient. Pi is a constant. It is the arctangent function. For hyperbolic tangent function, standard skin depth The calculation formula is: , The resistivity of rolled copper foil, Angular frequency, , where is the permeability.

[0021] Specifically, based on the operating frequency and the conductivity parameters of the rolled copper foil, combined with the vacuum permeability and relative permeability, a predefined frequency scan list in the simulation settings is invoked. This list covers the high-frequency communication band from 1 GHz to 20 GHz, and discrete frequency point data is extracted in 0.1 GHz increments. For each frequency point, the conductivity value in the material properties of the rolled copper foil is read, for example, the conductivity of typical rolled copper is taken. S / m, while introducing vacuum permeability H / m and the relative permeability of the copper foil The physical field calculations are focused on the extremely thin outermost region of the conductor. Based on the propagation law of electromagnetic fields in good conductors, the exponential decay characteristics of electromagnetic waves after entering the conductor are derived using Maxwell's equations, thus attenuating the current density amplitude to the amplitude of the surface current density. The depth corresponding to approximately 36.8% is defined as the characteristic penetration distance. Numerical substitution is performed for each discrete frequency point. Considering the significance of the skin effect at high frequencies, this depth is usually on the order of micrometers or even submicrometers. By establishing an inverse mapping relationship between frequency and depth, a depth data sequence that dynamically changes with frequency is constructed to quantify the distribution concentration of high-frequency current on the conductor cross section and generate a standard skin depth.

[0022] In the numerical calculation formula for surface roughness erosion ratio, a combination of arctangent and hyperbolic tangent functions is introduced to model the low-frequency roughness profile and high-frequency micro-undulations of the copper foil surface, respectively. The arctangent term corrects for the increased current path effect caused by the large-scale profile, while the hyperbolic tangent term, combined with a kurtosis adjustment coefficient, characterizes the additional scattering loss of surface resistance due to abrupt changes in micromorphology. This is achieved through parameter... and The coordinated adjustment of the two can more accurately fit the nonlinear loss growth trend of FPC rolled copper foil in the millimeter wave band, overcoming the problem of insufficient correction of the traditional Hammerstad model in the high frequency band. parameter and The steps to obtain the data are as follows: obtain the angular frequency parameters of the current scan from the test settings of the vector network analyzer, and set the test frequency. GHz, using the formula Calculate the angular frequency and obtain rad / s, while selecting the vacuum permeability constant H / m, relative permeability is set based on the non-magnetic characteristics of rolled copper. The absolute permeability of the conductor was calculated. H / m; parameter The acquisition steps are as follows: A four-probe resistivity meter is used to measure the surface resistivity of the rolled copper foil sample used in the FPC. In a standard laboratory environment at 25 degrees Celsius, multiple measurements are taken at various points on a 10cm × 10cm copper foil sample, and the average value is calculated to obtain the volume resistivity data for this batch of materials. The resistivity of the rolled copper foil is then obtained through measurement. This parameter reflects the conductivity of the material itself and directly affects the magnitude of ohmic loss and the significance of the skin effect when current is transmitted inside the conductor. parameter The steps for obtaining it are as follows: based on the resistivity obtained above... angular frequency and permeability Using the physical definition of the skin depth of a good conductor Perform the calculation and substitute the values ​​to obtain... The value inside the square root is approximately m After opening the prescription, the standard skin depth was obtained. m, which is approximately 0.661 This value characterizes the thickness of the surface layer where the current is mainly concentrated at a frequency of 10 GHz; parameter and The acquisition steps are as follows: The smooth and rough surfaces of the rolled copper foil are scanned using an atomic force microscope, with the scanning area set as follows: The sampling resolution is 256×256 points. The height matrix is ​​extracted from the generated 3D topographic point cloud data, and the root mean square roughness is obtained by calculating the standard deviation of the height distribution using statistical methods. After measurement Simultaneously, autocorrelation function analysis is performed on the surface profile data to decay the autocorrelation function back to its initial value. The corresponding horizontal distance is defined as the length of the copper foil surface profile. Calculated To ensure dimensional consistency in the formula, these two parameters are converted to the standard international unit, the meter. m, m; parameter and The steps for obtaining the data are as follows: First, a set of standard transmission line test templates with different roughness levels are fabricated. Then, the insertion loss per unit length is measured using a vector network analyzer. The measurement results are compared with simulation results based on smooth surfaces, for example, to extract the additional loss component caused by roughness. Finally, a network is constructed based on this roughness. and Using the error function as the variable, a nonlinear curve fitting method is performed using the least squares method to minimize the sum of squared residuals between the theoretically calculated erosion ratio curve and the measured loss increase ratio curve. Under the material system of this example, the fitting coefficient of the additional loss amplitude is obtained through fitting calculation. Steepness adjustment coefficient ; Calculations based on parameters: First, calculate the dimensionless ratio of roughness to skin depth: ; Calculate the squared term in the first part of the formula: ; Calculate the arctangent function term (result in radians): ; Calculate the total value within the parentheses in the first part: ; Calculate the independent variable of the hyperbolic tangent function (note) (Meters are also required) ; Calculate the hyperbolic tangent function value: ; Calculate the product term in the second part of the formula: ; Adding the two parts together gives the final surface roughness erosion ratio: ; The results show that at a working frequency of 10 GHz, due to the presence of surface roughness in the copper foil, the actual surface resistance will be 1.3874 times that of an ideal smooth surface. This value quantifies the enhancing effect of roughness on high-frequency signal transmission loss. This ratio will be used to correct the surface impedance boundary conditions of the conductor in the future, so as to accurately reflect the real conductor loss characteristics in electromagnetic field simulation.

[0023] The steps for obtaining the frequency-varying loss correction coefficient are as follows: Based on the surface roughness erosion ratio value, it is compared with the range of the preset judgment threshold. If the surface roughness erosion ratio value falls within the range of the smooth area, the transition area, or the deep erosion area, the corresponding surface impedance calculation formula coefficient in the preset database is indexed to generate the frequency-varying loss correction coefficient.

[0024] Specifically, based on the surface roughness erosion ratio, a judgment threshold system based on signal integrity design specifications is established. Two key critical thresholds are set to delineate different loss-affected areas. By analyzing the correlation between a large amount of PCB board cross-section test data and S-parameter attenuation, the judgment threshold for smooth areas is defined. The threshold for defining a deep erosion zone is 1.15. The calculated surface roughness erosion ratio is 1.80. Compare the numerical range with these two thresholds, if If the frequency point is in a smooth region, then the roughness has little effect on the loss, and the loss is mainly dominated by the DC resistance of the conductor; if If the skin effect and surface roughness work together, the loss increases nonlinearly. If the surface roughness is found to be in a deep erosion zone, then the surface roughness becomes the dominant loss factor. Based on the area identification code generated by the determination result, an index search is performed in the pre-set material electromagnetic parameter database. This database stores the correction coefficient table for different roughness levels at various frequency bands. The polynomial coefficients in the surface impedance correction algorithm of the corresponding area are extracted, and the accurate correction factor at the current frequency is obtained by using the interpolation algorithm to generate the frequency-varying loss correction coefficient.

[0025] The steps for obtaining the three-dimensional field distribution data of the connector area are as follows: Based on the geometric region segmentation data and frequency-varying loss correction coefficient, a three-dimensional computational domain is constructed in the rigid connector region. Mesh elements are generated according to the geometric region segmentation data, and metal and dielectric surfaces are labeled. A surface impedance model is applied to the conductor boundary, and the frequency-varying loss correction coefficient is substituted into the port boundary conditions. The steady-state field solution under port excitation is calculated, and three-dimensional field distribution data of the connector region is generated.

[0026] Specifically, based on the geometric region segmentation data and frequency-varying loss correction coefficients, a three-dimensional computational domain is constructed in the rigid connector region. The geometry engine is called to read the boundary of the connector's solid model, and the air background region is expanded outward from this center, with the edge distance of the background region set. The calculation formula is: ,in The speed of light in a vacuum. The starting frequency of the simulation band was set to 1 GHz, and the calculated extension distance was 75 mm. To ensure that the radiation boundary conditions did not interfere with the near-field distribution, a mesh generation algorithm was used to generate a tetrahedral mesh, and the maximum mesh size was set. The control formula is in The highest simulation frequency is 20GHz. Given a relative permittivity of 3.5 for the dielectric, the maximum side length of the mesh is calculated to be approximately 2.5 mm. The conductor surface is then refined with a finer mesh, identifying all geometric surfaces marked as metallic. The frequency-dependent loss correction coefficient obtained in the preceding steps is then applied. Applying the modified surface impedance boundary condition, its impedance value The calculation formula is: ,in The imaginary unit, Pi This represents the current solution frequency. Take the permeability of the copper conductor as H / m, Take the conductivity of copper as S / m, the calculated impedance value is assigned to the corresponding mesh surface, wave ports are set at the signal input and output positions, and the finite element solution matrix equation is established. ,in The stiffness matrix includes both geometric and material properties. Let be the electric field distribution vector to be solved. Given the port excitation source vector, start the iterative solver to perform calculations, and set the convergence criterion as the magnitude error of the S-parameters. Its calculation formula is ,in The magnitude of the S-parameters in the current iteration step. The threshold value for the previous step is set to 0.02, meaning that the calculation is terminated when the error between adjacent iterations is less than 2%. The finally converged electric and magnetic field data are extracted to generate the three-dimensional field distribution data of the connector region.

[0027] The steps for obtaining transmission characteristic data of flexible line areas are as follows: Based on the three-dimensional field distribution data of the connector area, the tangential electric field component and tangential magnetic field component of the connector port are extracted. The field values ​​are rearranged according to the grid order of the port section and the coordinate system direction is unified. The data are mapped to the starting section of the flexible strip as the incident condition. The Green's function of the multilayer medium is called to solve the two-dimensional half-transmission equation and obtain the propagation characteristics of voltage and current along the line. Based on the propagation characteristics of voltage and current along the line, the phase constant and attenuation constant of each frequency point are read, the conductor surface impedance is updated according to the frequency-varying loss correction coefficient, and the propagation constant curve is corrected. The amplitude and phase distribution of voltage and current along the line are iteratively updated to form the transmission characteristic data of the flexible line area.

[0028] Specifically, based on the three-dimensional field distribution data of the connector area, the tangential electric field component and tangential magnetic field component of the connector port are extracted, the cross-sectional mesh nodes at the connection between the connector and the flexible plate are locked, and the three-dimensional electric field vector on each node is read. and magnetic field vector Calculate the unit normal vector of the cross section. Using the formula Extract the tangential electric field, where The dot product operation represents vectors, and similarly, the formula is used. The tangential magnetic field is extracted, and the unstructured tetrahedral mesh field data is mapped onto a two-dimensional uniform rectangular mesh, with the interpolation resolution set to [value missing]. As the incident source term in the subsequent transmission equation, the two-dimensional semi-wave equation is solved using the multilayer dielectric Green's function library, and the voltage is defined. The formula for calculating the path integral is as follows: ,in The integral path is the one that runs vertically from the center of the signal line towards the reference ground plane. Define the current as the path differential vector. The formula for calculating the loop integral is as follows: ,in To form a closed loop that closely adheres to the surface of the signal conductor, by varying the propagation distance... By solving the slice at the point, the distribution sequence of voltage and current along the line is obtained, and the propagation characteristics of voltage and current along the line are obtained.

[0029] Based on the propagation characteristics of voltage and current along the transmission line, the phase constant and attenuation constant at each frequency point are read, and the complex propagation constant in transmission line theory is analyzed. Its defining formula is ,in The attenuation constant is used to characterize the attenuation of signal amplitude. To characterize the phase constant of the phase delay, the frequency-varying loss correction coefficient is read. resistance per unit length Make corrections, the correction formula is as follows ,in For static skin resistance without roughness correction, maintain inductance per unit length Electrical conductivity and capacitor The propagation constant remains unchanged; it is then recalculated using the corrected resistance. The calculation formula is: ,in Given the angular frequency, the voltage and current along the transmission line are iteratively updated using the transmission line equations. The voltage recursion formula is as follows: ,in The distance from the walking distance along the line is taken as 1 / 20 of the wavelength. The characteristic impedance is calculated using the following formula: After completing the recursion over the entire length, the relative error between the terminal voltage amplitude and the preset theoretical value is calculated. The formula is ,in The terminal voltage obtained by recursion, Assuming the theoretical lossless transmission voltage, the error threshold is set to... If the error exceeds the limit, the distribution parameters are fine-tuned and the process is repeated until the convergence requirement is met. The final stable amplitude and phase data along the line are recorded to form the transmission characteristic data of the flexible line area.

[0030] The steps for obtaining convergence data of energy exchange at the interface are as follows: Based on the three-dimensional field distribution data of the connector area, the transmission characteristic data of the flexible line area, and the coordinates of the interface grid nodes, the tangential electric field component and the tangential magnetic field component are extracted at the coordinates of each interface grid node. The coordinate system directions on both sides are unified and the phase reference is aligned according to the node number order. A node pair mapping list is established and the port affiliation and normal direction are marked. The coupling terms of the tangential electric field information and the tangential magnetic field information are written according to the node pair to generate the interface transmission boundary equation. Based on the boundary equation of the interface transmission, the boundary injection of the transmission characteristic data of the flexible line area is first performed using the three-dimensional field distribution data of the connector area as the source, and then the boundary write-back of the three-dimensional field distribution data of the connector area is performed using the transmission characteristic data of the flexible line area as the source. The tangential electric field information and tangential magnetic field information of the node pair are updated one by one, and the energy flux sequence and residual sequence after each exchange are recorded to generate the interface energy exchange convergence data.

[0031] Specifically, based on the three-dimensional field distribution data of the connector area, the transmission characteristic data of the flexible line area, and the coordinates of the interface grid nodes, a dynamic mapping table is constructed in memory to store the correspondence between physical quantities on both sides of the interface. Each recorded interface grid node coordinate is traversed, and its spatial index value is used to read the corresponding electric and magnetic field vectors from the three-dimensional field distribution dataset, and the corresponding voltage and current values ​​from the transmission characteristic dataset. For each node position, the normal vector of its tangential plane is calculated, and the tangential components of the electric and magnetic fields parallel to the tangential plane are extracted through vector dot product operations. The direction of the local coordinate systems on the rigid connector side and the flexible stripline side is checked according to the right-hand screw rule. If the normal definition on one side is detected to be opposite to the global reference direction, then the normal vector on that side is extracted. The magnetic field component values ​​are multiplied by negative one to achieve directional unification. At the same time, based on the difference in the phase reference plane position between the two regions during meshing, a phase compensation factor is introduced to align the phase of the frequency domain field data. Subsequently, based on the principle of minimizing the node spatial distance, the surface mesh nodes of the three-dimensional region are paired with the cross-sectional nodes of the layered transmission region to construct a node pair mapping list containing node ID, coordinate deviation, and region identifier. According to the boundary condition of the continuity of the tangential component of the electromagnetic field, a coupling relationship expression is constructed for each pair of nodes. The voltage and current on the flexible line side are converted into equivalent tangential fields and an equation is established with the tangential field on the connector side. These equations are assembled into a linear equation system in sparse matrix form. The port affiliation and energy transfer direction corresponding to the unknowns in the equations are clearly marked to generate the interface transmission boundary equation.

[0032] Based on the interface transmission boundary equation, a bidirectional iterative solver controller is initialized. The initial excitation source is set at the input port of the rigid connector. The tangential electric field distribution calculated in the connector region is forcibly applied to the initial section of the flexible stripline as a first-type boundary condition. The transmission line solver is then activated to calculate the voltage and current response along the line, obtaining the reflected voltage and current at the flexible line port. The reflected voltage and current are then converted back into a tangential magnetic field distribution using the transmission line mode function, and this is written back to the output port section of the rigid connector region as a second-type boundary condition. This triggers the three-dimensional full-wave solver to update the internal field distribution. After completing one full "field-path-field" data exchange cycle, at the end of each cycle, the electric field vector and conjugate magnetic field vector of all grid nodes on the interface are cross-multiplied, the Poynting vector is calculated and numerically integrated along the cross-sectional area to obtain the instantaneous energy flux value passing through the interface. This flux value is stored in an array according to the iteration order. At the same time, the absolute value of the difference between the energy flux of the current iteration step and the previous iteration step is calculated and recorded in the residual monitoring sequence. The above injection, solution, write-back and update steps are continuously executed until the system state tends to stabilize and the interface energy exchange convergence data is generated.

[0033] The steps for obtaining the S-parameters of end-to-end signal integrity are as follows: Based on the convergence data of energy exchange at the interface, the maximum absolute difference of the energy flux difference sequence between adjacent iterations is calculated as the error value. The error value is compared with the preset limit. If the error value is less than the preset limit, the voltage-current ratio is extracted at the input port impedance and the voltage-current ratio is extracted at the output port impedance. The values ​​are then rearranged according to the frequency index and frequency domain transformation is performed to generate the full-link signal integrity S-parameters.

[0034] Specifically, based on the interface energy exchange convergence data, the latest data in the residual monitoring sequence is called to set the preset limit required for convergence determination. The setting of this limit is based on the accuracy requirements of the signal link power budget. For example, the limit is set to one ten-thousandth of the total input power, that is, when the input power is normalized to 1W, the preset limit is [value missing]. W is used to calculate the difference in energy flux values ​​between two adjacent iterations, yielding the iteration error value. For example, if the flux in the Nth iteration is 0.9502W and in the (N-1)th iteration it is 0.9505W, then the error value is... W. The error value is compared with a preset limit. If the error value is greater than the preset limit, it is determined that convergence has not yet occurred and the iteration continues. If the error value is less than the preset limit, it is determined that the energy exchange at the interface has reached a steady state. At this time, the voltage and current distribution of the entire link is locked. The total voltage phasor and total current phasor are extracted at the signal input port of the rigid connector, and their ratio is calculated to obtain the input impedance. Similarly, the voltage-current ratio is extracted at the output port of the flexible stripline to obtain the load impedance. According to microwave network theory, the mismatch between the calculated port impedance and the system characteristic impedance (e.g., 50 ohms) is used to solve for each element in the scattering parameter matrix. For example, the return loss is calculated by dividing the difference between the input impedance and the characteristic impedance by their sum. Following the order of the frequency scan list, the complex values ​​of the S-parameters calculated for each frequency point are rearranged, and the frequency domain data is converted to the time domain through inverse fast Fourier transform for causality checks. After eliminating spurious response components that violate physical causality, the data is transformed back to the frequency domain to generate the full-link signal integrity S-parameters.

[0035] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A co-simulation method for FPC high-frequency signal integrity, characterized in that, Includes the following steps: Based on the FPC stacked structure design documents, the spatial geometric positions of the rigid connector and the flexible strip are identified, the overall simulation space is divided into a three-dimensional structural region and a layered transmission region, geometric region segmentation data is generated, and the interface mesh node coordinates are generated by calling the geometric region segmentation data. Based on the operating frequency and the conductivity parameters of the rolled copper foil, a surface roughness erosion ratio is calculated and generated. The surface roughness erosion ratio is then compared with a preset judgment threshold to obtain a frequency conversion loss correction coefficient. Based on the geometric region segmentation data and the frequency conversion loss correction coefficient, the three-dimensional field distribution data of the connector area is calculated and generated. The flexible stripline region in the signal transmission channel is solved, and the propagation characteristics of voltage and current along the line are calculated to generate the transmission characteristic data of the flexible stripline region. Based on the three-dimensional field distribution data of the connector area and the transmission characteristic data of the flexible line area, a transmission boundary equation including tangential electric field and magnetic field information is constructed at the coordinate position of the interface grid node. Interface energy exchange convergence data is generated, and the error value of the interface energy exchange convergence data is monitored. When the error value is lower than the preset limit, the voltage-to-current ratio at the input and output port impedance is extracted to generate the full-link signal integrity S-parameter.

2. The co-simulation method for FPC high-frequency signal integrity according to claim 1, characterized in that, The steps for obtaining the coordinates of the interface mesh nodes are as follows: Based on the FPC stacked structure design documents, the spatial geometric positions of the rigid connector and the flexible strip are marked. Cutting lines are set at the abrupt changes in morphology to perform geometric cutting. The overall simulation space is divided into a three-dimensional structural region and a layered transmission region, and geometric region segmentation data is generated. Based on the geometric region segmentation data, the mesh vertex information at the cutting surface is extracted. Lagrange multipliers are introduced for non-overlapping nodes at the interface to complete the mapping and matching process. The boundary position of electromagnetic energy exchange between regions is determined based on the matched node pairs, thus forming the boundary position of the interface. Based on the boundary position of the interface, the mesh vertex information at the cutting surface is called, the node pairs at the boundary position are traversed and deduplicated according to the coordinate order, the mesh node coordinate sequence that satisfies the continuity of the interface is selected, and the interface mesh node coordinates are generated.

3. The co-simulation method for FPC high-frequency signal integrity according to claim 1, characterized in that, The steps for obtaining the surface roughness erosion ratio are as follows: Based on the operating frequency and the conductivity parameters of the rolled copper foil, combined with the vacuum permeability and relative permeability, the current penetration depth of the conductor surface is calculated, and the attenuation distance of the current density along the conductor thickness direction is defined as the standard skin depth, thus generating the standard skin depth. The surface roughness erosion ratio is calculated based on the standard skin depth.

4. The co-simulation method for FPC high-frequency signal integrity according to claim 1, characterized in that, The steps for obtaining the frequency-varying loss correction coefficient are as follows: The surface roughness erosion ratio is compared with a preset threshold range. If the surface roughness erosion ratio falls within the range of a smooth zone, a transition zone, or a deep erosion zone, the corresponding surface impedance calculation formula coefficients in the preset database are indexed to generate frequency-varying loss correction coefficients.

5. The co-simulation method for FPC high-frequency signal integrity according to claim 1, characterized in that, The steps for obtaining the three-dimensional field distribution data of the connector area are as follows: Based on the geometric region segmentation data and the frequency-varying loss correction coefficient, a three-dimensional computational domain is constructed in the rigid connector region. Mesh elements are generated according to the geometric region segmentation data, and metal and dielectric surfaces are labeled. A surface impedance model is applied to the conductor boundary, and the frequency-varying loss correction coefficient is substituted into the port boundary conditions. The steady-state field solution under port excitation is calculated, and three-dimensional field distribution data of the connector region is generated.

6. The co-simulation method for FPC high-frequency signal integrity according to claim 1, characterized in that, The steps for obtaining the transmission characteristic data of the flexible line area are as follows: Based on the three-dimensional field distribution data of the connector area, the tangential electric field component and tangential magnetic field component of the connector port are extracted. The field values ​​are rearranged according to the grid order of the port section and the coordinate system direction is unified. The data are mapped to the starting section of the flexible strip as the incident condition. The Green's function of the multilayer medium is called to solve the two-dimensional half-transmission equation and obtain the propagation characteristics of voltage and current along the line. Based on the propagation characteristics of voltage and current along the line, the phase constant and attenuation constant of each frequency point are read, the conductor surface impedance is updated according to the frequency-varying loss correction coefficient, and the propagation constant curve is corrected. The amplitude and phase distribution of voltage and current along the line are iteratively updated to form flexible line area transmission characteristic data.

7. The co-simulation method for FPC high-frequency signal integrity according to claim 1, characterized in that, The steps for obtaining the interface energy exchange convergence data are as follows: Based on the three-dimensional field distribution data of the connector area, the transmission characteristic data of the flexible line area, and the coordinates of the interface grid nodes, the tangential electric field component and the tangential magnetic field component are extracted at the coordinates of each interface grid node. The coordinate systems on both sides are unified according to the node number order and the phase reference is aligned. A node pair mapping list is established and the port affiliation and normal direction are marked. The coupling terms of the tangential electric field information and the tangential magnetic field information are written according to the node pair to generate the interface transmission boundary equation. According to the interface transmission boundary equation, the transmission characteristic data of the flexible line area is first injected into the boundary using the three-dimensional field distribution data of the connector area as the source, and then the three-dimensional field distribution data of the connector area is written back into the boundary using the transmission characteristic data of the flexible line area as the source. The tangential electric field information and tangential magnetic field information of the node pair are updated one by one, and the energy flux sequence and residual sequence after each exchange are recorded to generate the interface energy exchange convergence data.

8. The co-simulation method for FPC high-frequency signal integrity according to claim 1, characterized in that, The steps for obtaining the end-to-end signal integrity S-parameters are as follows: Based on the convergence data of energy exchange at the interface, the maximum absolute difference of the energy flux difference sequence of adjacent iterations is calculated as the error value. The error value is compared with the preset limit. If the error value is less than the preset limit, the voltage-current ratio is extracted at the input port impedance and the voltage-current ratio is extracted at the output port impedance. The values ​​are rearranged according to the frequency point index and frequency domain transformation is performed to generate the full-link signal integrity S-parameters.

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