Multi-conductor transmission line distribution parameter calculation method, readable storage medium and electronic equipment

Abstract

The invention relates to the technical field of electronic design automation, and discloses a multi-conductor transmission line distribution parameter calculation method, a readable storage medium and electronic equipment. The multi-conductor transmission line distribution parameter calculation method comprises the steps of obtaining multi-conductor transmission line parameters of a printed circuit board to be simulated; for a conductor transmission line with a rectangular cross section, a first type Chebyshev polynomial is used as an expansion function to unfold charge density distribution on the surface of a conductor, the zero point of the first type Chebyshev polynomial is a Gaussian-Chebyshev integral point, discretization processing is carried out on an integral equation, and the integral equation is converted into a linear equation set; and solving the linear equation set to obtain a charge distribution coefficient, and determining charge distribution on the surface of the conductor according to the coefficient. According to the technical scheme, the Chebyshev polynomial is adopted as the primary function to expand and represent the to-be-solved charge density on the segments, a traditional primary function is replaced, the calculation precision is high, and the calculation amount is small.

Description

Technical Field

[0001] This application relates to the field of electronic design automation technology, and in particular to a method for calculating the distributed parameters of a multi-conductor transmission line, a readable storage medium, and an electronic device. Background Technology

[0002] Accurate numerical simulation of board-level circuits on printed circuit boards (PCBs) plays a crucial role in PCB design. To accurately simulate various electromagnetic parameters on a PCB, it is first necessary to extract parameters from the transmission lines of interest. A transmission line is a structure that conducts electromagnetic waves. For a given transmission line, the parameters of interest are typically the inductance, capacitance, conductance, and resistance per unit length. For a multi-conductor transmission line system consisting of n+1 conductors, these parameters are given in the form of an n×n matrix. As PCB circuit systems become increasingly complex, accurate analysis of various transmission lines on the board has become a prerequisite for PCB board-level circuit design.

[0003] For all types of transmission lines, the fundamental assumption for their analysis is that the electromagnetic field surrounding the conductor has a transverse electromagnetic (TEM) structure. In a TEM mode field, there are no electric or magnetic field components along the axial direction. One important corollary of the TEM mode field is that it allows for the definition of voltage and current between transmission lines, even if the field varies with time or a non-uniform medium exists around the conductor; however, these effects are small. In these cases, the modes propagating in the transmission line can be considered quasi-TEM modes. The cutoff frequency of TEM modes is DC. For higher-order propagation modes in the transmission line, they decay rapidly below the cutoff frequency, maintaining sufficient computational accuracy when analyzing transmission lines at lower frequencies. In existing techniques for analyzing transmission line parameters, uniform transmission lines can usually be analyzed and calculated analytically. However, transmission lines on PCBs are typically non-uniform, lacking analytical formulas, and can only be calculated using numerical methods. The unit length parameters of inductance, capacitance, and conductance are obtained by solving the Laplace equation or Poisson equation for an ideal conductor in the transverse plane of the electrostatic field. These equations can be solved by various methods, such as the finite difference method, the method of moments, and the finite element method.

[0004] In existing methods, inductance and conductance parameters can generally be obtained by calculating the capacitance parameters of the transmission line, making the accuracy of capacitance calculation crucial. The capacitance per unit length on a conductor is defined by the ratio of surface charge to potential per unit length of the transmission line. The unknown parameter to be determined is the charge density, which is solved by expanding the surface charge using basis functions. Different basis functions used to expand the charge result in varying degrees of accuracy. For numerical methods, the key to both accuracy and efficiency lies in using appropriate basis functions to expand the unknown. A common expansion method is the stepped expansion, which defines the charge as a constant at equal intervals. This method is relatively simple, but its accuracy depends on the number of partitions, requiring a large number of partitions to obtain accurate results. Furthermore, the sampling points used to expand the unknown also significantly impact the calculation accuracy. Therefore, overcoming the problems of numerical instability and low accuracy at conductor edges, and the large computational burden due to the need for extensive partitioning to achieve the required accuracy, inherent in traditional pulse basis function combined with equidistant sampling point expansion methods, is crucial for achieving efficient and high-precision extraction of distributed parameters from PCB transmission lines. Summary of the Invention

[0005] To address the technical problems of numerical instability and low calculation accuracy at conductor edges caused by the traditional pulse basis function combined with equidistant sampling point expansion method in the prior art, and the large amount of computation required to achieve the required accuracy through extensive domain division, this invention provides a method for calculating the distributed parameters of multi-conductor transmission lines, a readable storage medium, and an electronic device.

[0006] The technical solution of this application uses Chebyshev polynomials as basis functions to expand and represent the piecewise charge density to be determined, replacing the traditional basis functions, which has high calculation accuracy and low computational cost.

[0007] To achieve the above objectives, a first aspect of the present invention provides a method for calculating the distributed parameters of a multi-conductor transmission line, wherein the distributed parameters include the capacitance, inductance, and conductance parameters per unit length of the multi-conductor transmission line, and the method includes: Obtain the multi-conductor transmission line parameters of the printed circuit board to be simulated. The transmission line parameters include at least the geometric parameters and excitation voltage related to the multi-conductor transmission line. Based on the aforementioned geometric parameters, an integral equation is established to describe the relationship between the surface charge density and potential of the conductor; For a rectangular cross-section conductor transmission line, its edges are divided into multiple segments, and the charge density distribution on each segment is an unknown function. The unknown function is expanded using a set of basis functions in its domain space. , For the expansion function, we use the Chebyshev polynomial of the first kind as the expansion function. To visualize the charge density distribution on the conductor surface, The value is the order of the Chebyshev polynomial. For the unknown charge density distribution coefficient, the zeros of the Chebyshev polynomial of the first kind are the Gauss-Chebyshev integration points. The integral equation is discretized, transforming it into a system of linear equations. The constant terms of this system are determined based on the excitation voltage, and the solution to this system is the charge density distribution coefficient. ; Solving the system of linear equations yields the charge distribution coefficient. And determine the charge distribution on the surface of the conductor based on the coefficient; Calculate the total charge on the conductor surface based on the charge distribution; Calculate the capacitance per unit length of the multi-conductor transmission line based on the total charge and excitation voltage; Based on the capacitance parameters per unit length and the dielectric distribution around the multi-conductor transmission line, calculate the inductance parameters per unit length and the conductance parameters per unit length.

[0008] In one possible implementation of the first aspect, the geometric parameters include the conductor's linewidth, thickness, spacing, dielectric layer thickness, and conductor length. In one possible implementation of the first aspect, the transmission line parameters further include material electromagnetic parameters, which include dielectric constant, permeability, conductivity, and loss tangent.

[0009] In one possible implementation of the first aspect, when the medium surrounding the multi-conductor transmission line is a homogeneous medium, the inductance parameter per unit length is... Capacitance per unit length C, Conductivity per unit length magnetic permeability Dielectric constant and conductivity The following relationship must be satisfied: , as well as .

[0010] In one possible implementation of the first aspect, when the medium surrounding the multi-conductor transmission line is a non-uniform medium, the inductance parameter and conductance parameter per unit length are calculated in the following manner: The effective dielectric constant is calculated based on the dielectric layer thickness and conductor width in the geometric parameters, in order to convert the non-uniform dielectric into a uniform dielectric, and the complex dielectric constant is calculated based on the loss tangent. The complex capacitance parameters are determined based on the complex permittivity. The actual capacitance parameters per unit length are obtained from the real part of the complex capacitance parameters. The imaginary part of the complex capacitance parameters is multiplied by the angular frequency corresponding to the excitation voltage to calculate the conductance parameters per unit length. By removing the dielectric portion from the non-uniform medium to place the multi-conductor transmission line in an environment where the permeability is approximately equal to that of vacuum, the capacitance parameter per unit length in free space is calculated, and the inductance parameter per unit length is calculated based on the physical relationship between the inductance parameter per unit length and the capacitance parameter per unit length in free space.

[0011] In one possible implementation of the first aspect, the capacitance parameter per unit length of the multi-conductor transmission line is determined by an n×n capacitance matrix. Characterization, the capacitance matrix The charge distribution per unit length on the conductor surface is correlated with the voltage distribution of the conductor relative to a reference conductor using the following formula:

[0012] Where n is the number of signal conductors, V j q represents the voltage of the j-th signal conductor relative to the reference conductor. i This represents the unit length charge on the i-th signal conductor obtained by solving the system of linear equations.

[0013] In one possible implementation of the first aspect, the method further includes: Obtain the physical length of the preset signal traces in the layout of the printed circuit board to be simulated; The calculated inductance and capacitance parameters per unit length are multiplied by the physical length to obtain the total inductance and total capacitance of the preset signal trace.

[0014] In one possible implementation of the first aspect, the order of the Chebyshev polynomial is third or fourth.

[0015] In one possible implementation of the first aspect, the multi-conductor transmission line comprises a microstrip line or stripline on the printed circuit board to be simulated.

[0016] In a second aspect, this application provides a computer-readable storage medium storing instructions that, when executed on an electronic device, cause the electronic device to perform a method for calculating the distributed parameters of a multi-conductor transmission line as described in the first aspect and any possible implementation thereof.

[0017] Thirdly, this application provides an electronic device, comprising: A memory for storing instructions, and one or more processors, which, when the instructions are executed by the one or more processors, perform a method for calculating the distributed parameters of a multi-conductor transmission line as described in the first aspect above and any possible implementation thereof.

[0018] Compared with the prior art, the beneficial effects of this application are as follows: This application obtains the geometric parameters and excitation voltage of the PCB transmission line to be simulated, providing a data foundation for subsequent calculations of capacitance, inductance, and conductance. Then, based on these geometric parameters, an integral equation describing the relationship between charge density and potential is established, thus providing a physical model for high-precision parameter calculations. By segmenting the conductor profile, Chebyshev polynomials are used as basis functions to approximate the charge density, and the integral equations are discretized using the zeros of these polynomials as collocation points. This transforms a continuous physical problem into a system of linear equations. Utilizing the high-precision approximation characteristics of Chebyshev polynomials and their advantage of eliminating Runge's phenomenon through zero collocation points, stable numerical solutions are fundamentally guaranteed even at the conductor edges where charge distribution changes drastically. Despite having significantly fewer unknowns than traditional methods, high computational accuracy is still achieved, resolving the inherent contradiction between accuracy and efficiency in traditional calculation methods. This application obtains a high-precision charge distribution coefficient by solving the aforementioned linear equations, and uses this coefficient to determine the charge distribution on the conductor surface, thus providing reliable source data for subsequent parameter calculations. Based on this, the total charge is calculated from the charge distribution, and the capacitance parameter per unit length is obtained by combining this with the excitation voltage. Finally, the inductance and conductance parameters are derived based on the dielectric distribution, thus completing the entire calculation process from electromagnetic field solution to circuit parameter output. This achieves efficient and high-precision extraction of distributed parameters for multi-conductor transmission lines on PCBs, providing crucial and reliable data support for accurate numerical simulation of board-level circuits. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 According to some embodiments of this application, a flowchart of a method for calculating the distributed parameters of a multi-conductor transmission line is shown; Figure 2 According to some embodiments of this application, a transmission line is shown; Figure 3 According to some embodiments of this application, a structural block diagram of an electronic device is shown. Detailed Implementation

[0021] The illustrative embodiments of this application include, but are not limited to, a method for calculating the distributed parameters of a multi-conductor transmission line, a readable storage medium, and an electronic device.

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0023] As mentioned earlier, the existing technology has technical problems such as numerical instability and low calculation accuracy at the conductor edge due to the traditional pulse basis function combined with the equidistant sampling point expansion method, and the need for a large number of domains to achieve the required accuracy, resulting in a large amount of computation.

[0024] In view of this, the present invention provides a method for calculating the distributed parameters of a multi-conductor transmission line, a readable storage medium, and an electronic device. The technical solution of this application uses Chebyshev polynomials as basis functions to expand and represent the piecewise charge density to be determined, replacing traditional basis functions, resulting in high calculation accuracy and low computational cost.

[0025] To achieve the above objectives, this invention provides a method for calculating the distributed parameters of a multi-conductor transmission line. The distributed parameters include the capacitance, inductance, and conductance per unit length of the multi-conductor transmission line. (Refer to...) Figure 1 The method for calculating the distributed parameters of a multi-conductor transmission line provided by this invention includes the following steps: Step S10: Obtain the multi-conductor transmission line parameters of the printed circuit board to be simulated. The transmission line parameters include at least the geometric parameters and excitation voltage related to the multi-conductor transmission line.

[0026] In some embodiments, the geometric parameters include the conductor's linewidth, thickness, spacing, dielectric layer thickness, and conductor length. By specifying these key dimensions, such as the conductor's linewidth, thickness, spacing, dielectric layer thickness, and conductor length, complete and necessary physical geometric information is provided for establishing accurate integral equations. This ensures a high degree of consistency between the constructed transmission line numerical model and the actual physical structure, thereby guaranteeing the accuracy of subsequent parameter extraction and calculation from the outset.

[0027] In some embodiments, the transmission line parameters further include material electromagnetic parameters, including dielectric constant, permeability, conductivity, and loss tangent. By introducing material electromagnetic parameters including dielectric constant, permeability, conductivity, and loss tangent, this method can accurately characterize the electromagnetic properties of the medium surrounding the conductor. This provides crucial physical property inputs for accurately calculating the inductance and conductivity per unit length under different medium distribution conditions (uniform or non-uniform), significantly enhancing the universality of the method and the reliability of the calculation results.

[0028] Step S20: Establish an integral equation based on the geometric parameters to describe the relationship between the surface charge density and potential of the conductor.

[0029] Step S30: For a rectangular cross-section conductor transmission line, divide its edges into multiple segments, where the charge density distribution on each segment is an unknown function. The unknown function is expanded using a set of basis functions in its domain space. , For the expansion function, we use the Chebyshev polynomial of the first kind as the expansion function. To visualize the charge density distribution on the conductor surface, The value is the order of the Chebyshev polynomial. For the unknown charge density distribution coefficient, the zeros of the Chebyshev polynomial of the first kind are the Gauss-Chebyshev integration points. The integral equation is discretized, transforming it into a system of linear equations. The constant terms of this system are determined based on the excitation voltage, and the solution to this system is the charge density distribution coefficient. ; Step S40: Solve the system of linear equations to obtain the charge distribution coefficient. And determine the charge distribution on the conductor surface based on the coefficient.

[0030] Step S50: Calculate the total charge on the conductor surface based on the charge distribution.

[0031] Step S60: Calculate the capacitance per unit length of the multi-conductor transmission line based on the total charge and excitation voltage.

[0032] Step S70: Calculate the inductance and conductance per unit length based on the capacitance per unit length and the dielectric distribution around the multi-conductor transmission line.

[0033] It is understood that the execution order of steps S10 to S70 above is only an illustration. In other embodiments, other execution orders may be used, and some steps may be split or combined. This is not limited here.

[0034] This application obtains the geometric parameters and excitation voltage of the PCB transmission line to be simulated, providing a data foundation for subsequent calculations of capacitance, inductance, and conductance. Then, based on these geometric parameters, an integral equation describing the relationship between charge density and potential is established, thus providing a physical model for high-precision parameter calculations. By segmenting the conductor profile, Chebyshev polynomials are used as basis functions to approximate the charge density, and the integral equations are discretized using the zeros of these polynomials as collocation points. This transforms a continuous physical problem into a system of linear equations. Utilizing the high-precision approximation characteristics of Chebyshev polynomials and their advantage of eliminating Runge's phenomenon through zero collocation points, stable numerical solutions are fundamentally guaranteed even at the conductor edges where charge distribution changes drastically. Despite having significantly fewer unknowns than traditional methods, high computational accuracy is still achieved, resolving the inherent contradiction between accuracy and efficiency in traditional calculation methods. This application obtains a high-precision charge distribution coefficient by solving the aforementioned linear equations, and uses this coefficient to determine the charge distribution on the conductor surface, thus providing reliable source data for subsequent parameter calculations. Based on this, the total charge is calculated from the charge distribution, and the capacitance parameter per unit length is obtained by combining this with the excitation voltage. Finally, the inductance and conductance parameters are derived based on the dielectric distribution, thus completing the entire calculation process from electromagnetic field solution to circuit parameter output. This achieves efficient and high-precision extraction of distributed parameters for multi-conductor transmission lines on PCBs, providing crucial and reliable data support for accurate numerical simulation of board-level circuits.

[0035] PCB models are generally layered structures. Multi-conductor transmission line structures may exist in different layers. Multi-conductor transmission lines mainly include microstrip lines or striplines on the printed circuit board to be simulated. Microstrip lines are open structures, existing on the surface and back of the PCB, with conductors exposed to air. Their layered structure is: Signal Layer, Medium Layer, and Ground Layer. Striplines are closed structures, existing within the PCB layer stack, with conductors embedded in the dielectric. Their layered structure is: Top Layer, Medium Layer, Signal Layer, Medium Layer, and Ground Layer. Both structures require parameters including the dielectric constant, loss tangent, conductivity, permeability, layer thickness, metal layer roughness model, conductor width, and other physical and electrical parameters of the layer stack. The input lumped voltage also needs to be determined. Numerical calculations are required for each transmission line to obtain the distributed parameters of all transmission lines.

[0036] The following section introduces the derivation of the basic equations of the method of moments by combining the obtained geometric parameters and excitation voltage of the transmission line of the PCB to be simulated.

[0037] The calculation method of this invention is based on the method of moments. It is known that the fundamental assumption of all transmission line analysis methods is that the electromagnetic field around the conductor has a TEM structure. Based on this assumption, we consider the differential form of Maxwell's equations after the lateral decomposition of the transmission line on the PCB:

[0038] In the transverse plane, equations (1.1) and (1.2) are the same as the electrostatic field equations. In the transverse plane, the distribution of the TEM field is the same as that of the electrostatic field under DC excitation. The electric field intensity E of the electrostatic field in the transverse plane (xy) can be defined as an auxiliary scalar field. Gradient in the horizontal plane:

[0039] To determine the unit-length parameters of inductance, capacitance, and conductance, we need to obtain them from the solution of an ideal conductor in the transverse plane of the electrostatic field. This means that we must solve the Laplace or Poisson equations in a two-dimensional transverse plane: At a unit charge density of Within the region, electrostatic potential Satisfies the Poisson equation:

[0040] This equation can be solved using many methods, and the known solution to this problem can be obtained as follows:

[0041] For the problem above, the typical interest lies in determining the electric potential at a specific point in a defined region, and thus the charge distribution that generates that potential. This requires defining basis functions to expand the unknowns for solution. For a two-dimensional cross-sectional structure of an ideal conductor on a PCB, there exists a position current density on the surface of the i-th conductor. (C / m 2 If the charge distribution on the surface of the i-th conductor is expanded as follows:

[0042] This basis function expansion is called the impulse expansion method. In each sub-segment, the charge distribution is assumed to be constant, although the specific value is unknown, and is determined by the coefficients... The decision was made to use a stepped distribution to approximate the true charge distribution, which is the basic principle of the method of moments.

[0043] Assuming the ground plane is an infinitely large reference ground, the integral equation for the surface potential of the conductor is:

[0044] Formula (1.7) above is a general integral equation describing physical laws. In actual calculations, it needs to be instantiated according to the specific geometric parameters of the PCB transmission line to be simulated, such as line width, thickness, and spacing. In some embodiments, establishing an integral equation describing the relationship between charge density and potential on a specific conductor surface based on geometric parameters is achieved in the following way: the geometric parameters uniquely determine two key elements in the integral equation: the integration region and the relationship between the source point and the field point. The conductor surface profile defined by the geometric parameters determines the integration region in formula (1.7), that is, the physical path where the charge distribution exists. This integration region is the entire region where the charge distribution exists, i.e. The region comprised of all source points (x', y') ≠ 0. The relative positions of the conductors, defined by geometric parameters such as spacing, determine the distance between the source point (x′, y′) and the field point (x, y) in the integration kernel. The specific calculation method is as follows. For example, for a rectangular cross-section conductor with width W and thickness T, its integration region is the perimeter of the rectangle; for a multi-conductor system, the center distance between conductors will directly affect the calculation of the distance between the source point and the field point on different conductors. Thus, the general integral equation (1.7) is transformed into a solvable integral equation for a specific transmission line structure.

[0045] It should be noted that, due to The above-mentioned ground plane is assumed to be an infinitely large reference ground, and it is known that... ,so .

[0046] The above integration method can be rewritten as a matrix equation based on the method of moments, which can be expressed as:

[0047] Dimension A is × The elements can be represented as ; Dimensions B is determined by the excitation voltage. Sure; Dimensions , representing the unknown coefficients in the charge expansion. The capacitance between the conductor and the reference ground is known to satisfy the following equation:

[0048] The surface charge formula can be expressed as the integral of the surface charge over the contour of a two-dimensional cross-section of a conductor:

[0049] At this point, the matrix equation satisfied by the multi-conductor transmission line based on the method of moments has been obtained. The next step is to expand the unknowns to be solved based on the properties of the transmission line on the PCB and substitute them into the matrix equation to solve the problem.

[0050] The following describes the specific process of establishing an integral equation based on geometric parameters, using Chebyshev polynomials as basis functions to expand the expression of the piecewise charge density, and using the zeros of the Chebyshev polynomials as collocation points (interpolation points) to transform the integral equation into a system of linear equations. In other words, it involves establishing the Chebyshev polynomial, obtaining its sampling points, and using the Chebyshev polynomial to expand the surface charge.

[0051] First, let's introduce the Chebyshev polynomial, the most typical representative of the triangular family of orthogonal polynomials, whose definition is as follows:

[0052] The following are some of the first items for reference:

[0053]

[0054] Chebyshev polynomials satisfy the following recurrence relation:

[0055] In some embodiments, the Chebyshev polynomial has an order of third or fourth. That is, this invention only uses the highest order fourth Chebyshev polynomial, corresponding to the polynomial in the above formula. Since the Chebyshev polynomial has an order of third or fourth, a good balance is achieved between computational complexity and computational accuracy. This is based on the inventors' in-depth research and experimental verification, which shows that at this order, the typical charge distribution of PCB transmission lines can be sufficiently approximated, thus ensuring high computational accuracy while avoiding the unnecessary computational burden caused by using excessively high orders, thereby optimizing computational efficiency.

[0056] In the domain [-1, 1], an n-order Chebyshev polynomial corresponds to n zeros and poles, and the zero formula is as follows:

[0057] It should also be noted that the domain of the polynomial needs to be transformed in actual calculations, and the transformed elements satisfy the following equation:

[0058] The commonly used expansion function is the impulse function shown in equation (1.6). However, this function is relatively simple and uses a step approximation to fit the unknown function. If a large amount of meshing is required to obtain better computational accuracy, it will affect both computational efficiency and computational accuracy.

[0059] To improve the accuracy and efficiency of solving transmission line distributed parameters, considering the actual charge distribution on the conductive strips of the PCB, polynomial interpolation is more reasonable for fitting the charge distribution on the conductor surface. Chebyshev polynomials can be used for interpolation. It is known that if equidistant interpolation is used, Runge's phenomenon can easily occur at the function edges, resulting in large errors at these edges. Using Chebyshev points as sampling points can largely avoid this phenomenon. Since the actual charge distribution on the PCB conductive strip surface reaches its peak at the edges, the accuracy of the polynomial fitting at these edges is particularly important. Among all nth-degree polynomials, the Chebyshev approximation has the smallest maximum error within its domain.

[0060] This invention fits the conductive band by segmenting the cross-sectional contour. Therefore, when performing polynomial fitting, it can be considered as fitting on a one-dimensional straight line. The charge distribution is on the surface of the two-dimensional rectangular cross-section of the conductor. The surface contour of each conductor is divided into multiple segments, for example, the conductor surface contour is divided into N segments. A third-order Chebyshev polynomial is used to fit the charge distribution of the conductive band. The Chebyshev series on each segment i is as follows:

[0061] coefficient The following formula is used to derive:

[0062] The surface charge is then expressed by the following formula:

[0063] At this point, the Chebyshev polynomial fitting is complete. Substituting the above equation as the basis function for the surface charge expansion into the matrix equation (i.e., the linear equation system) (1.8) established by the method of moments, and solving the matrix, we obtain the matrix of the unknown coefficients of the charge expansion, which is also the matrix of the charge distribution coefficients of the linear equation system: .

[0064] In some embodiments, when the medium surrounding the multi-conductor transmission line is a uniform medium, the inductance parameter L per unit length and the capacitance parameter per unit length are... Conductivity per unit length The permeability μ, permittivity ε, and conductivity σ satisfy the following relationship:

[0065] The above relationship only applies to the case where the transmission line is surrounded by a uniform medium. For the case of a non-uniform medium, the complex permittivity can be used. Since the inductance depends only on the permeability of the medium surrounding the conductor and is independent of the permittivity of the medium, the medium surrounding the conductor can be removed and replaced with free space. The distributed capacitance C0 of the conductor in free space can be solved, and the distributed inductance L0 can be solved using the above relationship.

[0066] When the medium surrounding a multi-conductor transmission line is a homogeneous medium, the inductance and conductance parameters can be efficiently and accurately derived directly from the obtained capacitance parameters by utilizing the known and definite physical relationships between the inductance parameter L, capacitance parameter C, conductance parameter G per unit length and the permeability μ, permittivity ε, and conductivity σ. This simplifies the calculation process, improves calculation efficiency, and ensures calculation accuracy in the typical scenario of a homogeneous medium.

[0067] In some embodiments, when the medium surrounding the multi-conductor transmission line is a non-uniform medium, the inductance parameter and conductance parameter per unit length are calculated as follows: The effective dielectric constant is calculated based on the dielectric layer thickness and conductor width in the geometric parameters to approximate the non-uniform medium as a uniform medium, and the complex dielectric constant is calculated using the loss tangent; the complex capacitance parameter is determined based on the complex dielectric constant, the actual capacitance parameter per unit length is obtained from the real part of the complex capacitance parameter, and the imaginary part of the complex capacitance parameter is multiplied by the angular frequency corresponding to the excitation voltage to calculate the conductance parameter per unit length; the dielectric portion in the non-uniform medium is removed to place the multi-conductor transmission line in an environment where the permeability is approximately equal to the permeability of vacuum, the capacitance parameter per unit length in free space is calculated, and the inductance parameter per unit length is calculated based on the physical relationship satisfied by the inductance parameter per unit length and the capacitance parameter per unit length in free space.

[0068] When the conductor is surrounded by a non-uniform dielectric layer, a situation primarily seen in microstrip lines, occurs where the conductor is exposed to air while its lower surface is encased in a dielectric layer. In such cases, it is necessary to determine the relative permittivity. The problem needs to be addressed. It is known that in this case, the electric field lines exist partly in the air and partly within the dielectric. If this non-uniform dielectric (air and dielectric) is replaced with a dielectric material having an effective dielectric constant… The effective dielectric constant is: (The dielectric constant is replaced by a homogeneous medium.)

[0069]

[0070] In the above formula, h is the thickness of the dielectric layer, and w is the width of the conductor. For skin depth.

[0071] For non-uniform dielectrics, a loss tangent exists in the dielectric region, allowing the complex permittivity to be used in calculations to uniquely determine the capacitance.

[0072] In the above formula, the complex capacitance is the coefficient obtained by solving the matrix. Let the effective conductance and capacitance be:

[0073]

[0074] In the above formula ω is the angular frequency. When the dielectric is non-uniform, the non-uniformity and loss are equivalently handled by calculating the effective dielectric constant and complex dielectric constant, and the conductance is calculated based on the complex capacitance parameters. Simultaneously, the free-space capacitance is calculated by removing the dielectric portion, and the inductance is then calculated using the physical relationships within free space. This method provides a precise and dedicated computational path for handling the complex scenario of non-uniform dielectrics, ensuring its effectiveness and accuracy in environments closer to real-world PCB applications.

[0075] For n+1 conductors, one conductor needs to be chosen as the reference conductor, and the voltage of each of the other conductors relative to the reference conductor is V. j In some embodiments, the capacitance per unit length of a multi-conductor transmission line is determined by an n×n capacitance matrix. Characterization, capacitance matrix The charge distribution per unit length on the conductor surface is correlated with the voltage distribution of the conductor relative to a reference conductor using the following formula: Where n is the number of signal conductors, V j q represents the voltage of the j-th signal conductor relative to the reference conductor. i This represents the charge per unit length on the i-th signal conductor obtained by solving a system of linear equations.

[0076] The voltage and charge relative to the reference ground are defined as follows:

[0077] By using an n×n capacitance matrix to characterize the capacitance parameter per unit length of a multi-conductor transmission line, and clarifying that it correlates charge distribution with voltage distribution through matrix equations, it can fully describe the mutual capacitance and self-capacitance effects between conductors in a multi-conductor system, thereby accurately characterizing the electromagnetic coupling between conductors. This provides crucial and comprehensive capacitance parameter information for analyzing the signal integrity of complex cable bundles.

[0078] In some embodiments, the method for calculating the distributed parameters of multi-conductor transmission lines provided in this application further includes: obtaining the physical length of a preset signal trace in the layout of the printed circuit board to be simulated; multiplying the calculated inductance and capacitance parameters per unit length by the physical length respectively to obtain the total inductance and total capacitance values ​​of the preset signal trace. By obtaining the physical length of the preset signal trace and converting the unit length parameters into total parameters, the total inductance and total capacitance values ​​required for circuit-level simulation can be directly obtained, improving the practicality and convenience of the output results of this method.

[0079] Figure 2 This diagram illustrates a transmission line, assuming that... Figure 2 The transmission line shown is defined as Trace1294. The distributed parameters of Trace1294, calculated using the multi-conductor transmission line distributed parameter calculation method provided by this invention, are shown in Table 1 below.

[0080] Table 1

[0081] Comparing the calculation results in Table 1 with those of some commercial software, the values ​​are basically consistent, indicating that the method described in this invention has achieved the calculation accuracy of commercial software.

[0082] This invention employs the Method of Moments (MoM), based on integral equations, which offers higher accuracy than other numerical methods. Furthermore, the MoM only requires dividing the conductor surface into surface or line meshes to solve for surface charge, avoiding the complex mesh generation required by the finite element method (FEA) and finite difference method (FD), thus improving the efficiency of model mesh extraction. In addition, this invention uses the zeros of Chebyshev polynomials as interpolation points to interpolate the conductor surface charge, resulting in better fitting effects. This not only avoids the Runge phenomenon but also reduces sampling points and improves computational speed. Simultaneously, using corresponding Chebyshev polynomials as interpolation basis functions to fit the unknown surface charge leads to even higher accuracy. By determining whether the surrounding medium is homogeneous, the inductance and capacitance parameters are calculated separately, and a mapping relationship between material properties and the conductor is established, simplifying the complexity of the entire numerical simulation process. This eliminates the need for special handling in structurally complex transmission lines, improving overall computational efficiency and reducing computational costs.

[0083] In summary, this invention combines the two methods—using the method of moments to construct the matrix equations of multi-conductor transmission lines and using Chebyshev polynomial expansion to determine the unknown charges in the matrix equations—to replace traditional basis functions and achieve computational accuracy consistent with commercial software.

[0084] In addition, this application also provides a computer-readable storage medium storing instructions that, when executed on an electronic device, cause the electronic device to perform a method for calculating the distribution parameters of a multi-conductor transmission line as described in any of the above embodiments.

[0085] In addition, this application also provides an electronic device, such as Figure 3 As shown, the electronic device 500 includes: a memory for storing instructions, and one or more processors, which, when the instructions are executed by the one or more processors, perform a method for calculating the distribution parameters of a multi-conductor transmission line as described in any of the above embodiments.

[0086] Figure 3 The electronic device 500 shown also includes a communication interface 503. The processor 502, memory 501, and communication interface 503 are connected via a communication bus and communicate with each other.

[0087] Processor 502 may be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits used to control the execution of programs in the above scheme.

[0088] Communication interface 503 is used to communicate with other devices or communication networks, such as Ethernet, Radio Access Network (RAN), Wireless Local Area Networks (WLAN), etc.

[0089] Memory 501 may be a read-only memory (ROM) or other type of static storage device capable of storing static information and instructions, random access memory (RAM) or other type of dynamic storage device capable of storing information and instructions, or electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital versatile optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto. Memory may exist independently and be connected to the processor via a bus. Memory may also be integrated with the processor. Various embodiments of the mechanisms disclosed in this application can be implemented in hardware, software, firmware, or combinations of these implementation methods. Embodiments of this application can be implemented as computer programs or program code executable on a programmable system, the programmable system including at least one processor, a storage system (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device.

[0090] In the accompanying drawings, some structural or methodological features may be shown in a specific arrangement and / or order. However, it should be understood that such a specific arrangement and / or order may not be necessary. Rather, in some embodiments, these features may be arranged in a manner and / or order different from that shown in the illustrative drawings. Furthermore, the inclusion of structural or methodological features in a particular figure does not imply that such features are required in all embodiments, and in some embodiments, these features may be omitted or may be combined with other features.

[0091] It should be noted that all units / modules mentioned in the device embodiments of this application are logical units / modules. Physically, a logical unit / module can be a physical unit / module, a part of a physical unit / module, or a combination of multiple physical units / modules. The physical implementation of these logical units / modules themselves is not the most important factor; the combination of functions implemented by these logical units / modules is the key to solving the technical problems proposed in this application. Furthermore, to highlight the innovative aspects of this application, the above-described device embodiments of this application have not introduced units / modules that are not closely related to solving the technical problems proposed in this application. This does not mean that the above-described device embodiments do not contain other units / modules.

[0092] It should be noted that in the examples and description of this application, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0093] Although this application has been illustrated and described with reference to certain preferred embodiments thereof, those skilled in the art should understand that various changes in form and detail may be made thereto without departing from the spirit and scope of this application.

Claims

1. A method for calculating distributed parameters of a multi-conductor transmission line, characterized in that, The distributed parameters include the capacitance, inductance, and conductance per unit length of a multi-conductor transmission line, and the method includes: Obtain the multi-conductor transmission line parameters of the printed circuit board to be simulated. The transmission line parameters include at least the geometric parameters and excitation voltage related to the multi-conductor transmission line. Based on the aforementioned geometric parameters, an integral equation is established to describe the relationship between the surface charge density and potential of the conductor; For a rectangular cross-section conductor transmission line, its edges are divided into multiple segments, and the charge density distribution on each segment is an unknown function. The unknown function is expanded using a set of basis functions in its domain space. , For the expansion function, we use the Chebyshev polynomial of the first kind as the expansion function. To visualize the charge density distribution on the conductor surface, The value is the order of the Chebyshev polynomial. For the unknown charge density distribution coefficient, the zeros of the Chebyshev polynomial of the first kind are the Gauss-Chebyshev integration points. The integral equation is discretized, transforming it into a system of linear equations. The constant terms of this system are determined based on the excitation voltage, and the solution to this system is the charge density distribution coefficient. ; Solving the system of linear equations yields the charge density distribution coefficient. And determine the charge distribution on the surface of the conductor based on the coefficient; Calculate the total charge on the conductor surface based on the charge distribution; Calculate the capacitance per unit length of the multi-conductor transmission line based on the total charge and excitation voltage; Based on the capacitance parameters per unit length and the dielectric distribution around the multi-conductor transmission line, calculate the inductance parameters per unit length and the conductance parameters per unit length.

2. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 1, characterized in that, The geometric parameters include the conductor's linewidth, thickness, spacing, dielectric layer thickness, and conductor length.

3. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 2, characterized in that, The transmission line parameters also include material electromagnetic parameters, which include dielectric constant, permeability, conductivity, and loss tangent.

4. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 3, characterized in that, When the medium surrounding the multi-conductor transmission line is a uniform medium, the inductance parameter per unit length... Capacitance per unit length C, Conductivity per unit length magnetic permeability Dielectric constant and conductivity The following relationship must be satisfied: , as well as .

5. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 3, characterized in that, When the medium surrounding the multi-conductor transmission line is a non-uniform medium, the inductance and conductance per unit length are calculated as follows: The effective dielectric constant is calculated based on the dielectric layer thickness and conductor width in the geometric parameters, in order to convert the non-uniform dielectric into a uniform dielectric, and the complex dielectric constant is calculated based on the loss tangent. The complex capacitance parameters are determined based on the complex permittivity. The actual capacitance parameters per unit length are obtained from the real part of the complex capacitance parameters. The imaginary part of the complex capacitance parameters is multiplied by the angular frequency corresponding to the excitation voltage to calculate the conductance parameters per unit length. By removing the dielectric portion from the non-uniform medium, the multi-conductor transmission line is placed in free space. The capacitance parameter per unit length in free space is calculated, and the inductance parameter per unit length is calculated based on the physical relationship between the inductance parameter per unit length and the capacitance parameter per unit length in free space.

6. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 1, characterized in that, The capacitance per unit length of the multi-conductor transmission line is determined by an n×n capacitance matrix. Characterization, the capacitance matrix The charge distribution per unit length on the conductor surface is correlated with the voltage distribution of the conductor relative to a reference conductor using the following formula: Where n is the number of signal conductors. This represents the voltage of the j-th signal conductor relative to the reference conductor. This represents the unit length charge on the i-th signal conductor obtained by solving the system of linear equations.

7. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 1, characterized in that, The method further includes: Obtain the physical length of the preset signal traces in the layout of the printed circuit board to be simulated; The calculated inductance and capacitance parameters per unit length are multiplied by the physical length to obtain the total inductance and total capacitance of the preset signal trace.

8. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 1, characterized in that, The Chebyshev polynomial is of order three or four.

9. The method for calculating the distributed parameters of a multi-conductor transmission line according to claim 1, characterized in that, The multi-conductor transmission line includes microstrip lines or striplines on the printed circuit board to be simulated.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed on an electronic device, cause the electronic device to perform the method for calculating the distributed parameters of a multi-conductor transmission line as described in any one of claims 1-9.

11. An electronic device, characterized in that, include: A memory for storing instructions, and one or more processors, wherein when the instructions are executed by the one or more processors, the processors perform a method for calculating the distributed parameters of a multi-conductor transmission line as described in any one of claims 1-9.

Images