Integrated circuit stripline electric field distribution simulation method, device, equipment and medium

Abstract

The present application discloses a method, device, equipment and medium for simulating the electric field distribution of an integrated circuit stripline. The method comprises: dividing the stripline of the integrated circuit into a plurality of segments, obtaining the electric field of the current of each segment to the observation point, superimposing the electric field of the current of each segment to the observation point, and obtaining the overall electric field of the stripline to any position observation point of the integrated circuit, thereby avoiding the finite element segmentation in the entire airspace of the package substrate and the circuit board, and only needs to segment the stripline in the problem structure, thereby saving a large amount of computer storage space, and greatly reducing large and super-large matrix operations, reducing the calculation time, and realizing the segmentation of only the conductor without segmenting the entire space domain, thereby reducing the number of variables and the matrix scale, greatly reducing the amount of calculation, and enabling the overall problem to be simulated quickly.

Description

Technical Field

[0001] The present application relates to the technical field of integrated circuit simulation, and in particular to a method, device, equipment and medium for simulating electric field distribution of integrated circuit striplines. Background Art

[0002] Stripline structures are high-frequency transmission conductors placed between dielectrics between two parallel ground planes (or power planes). With the rapid development of the integrated circuit industry, circuit designs are becoming more and more complex, so the demand for simulating larger and more complex interconnect circuits has also increased. A rigorous full-wave approach is needed to fully consider all interconnect phenomena, such as crosstalk, and distortion. Since full-wave analysis considers all higher-order modes in addition to transmission line modes (i.e., transverse electromagnetic (TEM) modes), the results they provide simulate the physical properties of complex 3-D interconnects more accurately than traditional 2-D analysis tools. Among them, how to calculate and simulate the electric field in the package substrate and circuit board is crucial, which is a necessary condition for calculating the crosstalk between interconnect wires.

[0003] Among the simulation technologies in the related art, the finite element method (FEM) is a relatively common method. FEM technology discretizes the entire problem space. Therefore, if the problem space becomes larger, the simulator requires a large amount of memory to store variables, and it also takes a long time to solve a very large-scale matrix. This is a problem existing in large-scale 3-D simulators in the related art.

[0004] The above statements are only used to provide background information related to the present application and do not necessarily constitute prior art. Summary of the invention

[0005] The purpose of the present application is to provide a method, device, apparatus and medium for simulating the electric field distribution of integrated circuit striplines. In order to have a basic understanding of some aspects of the disclosed embodiments, a simple summary is given below. This summary is not a general review, nor is it intended to identify key / important components or describe the scope of protection of these embodiments. Its only purpose is to present some concepts in a simple form as a preface to the detailed description that follows.

[0006] According to one aspect of an embodiment of the present application, a stripline electric field distribution simulation method of an integrated circuit board is provided, comprising:

[0007] Dividing the stripline of the integrated circuit into multiple segments;

[0008] Obtaining the electric field of the current of each segment relative to an observation point;

[0009] The electric field of each segment current to an observation point is superimposed to obtain the overall electric field of the strip line to any observation point at the integrated circuit.

[0010] In some embodiments of the present application, obtaining the electric field of the current of each segment relative to the observation point includes:

[0011] Based on the introduced electric potential energy and magnetic potential energy, the relationship between electric field and electric potential energy and magnetic potential energy is derived;

[0012] Decompose the electric field into the sum of the TMz modes at each level and the superposition of the sum of the TEz modes at each level;

[0013] Obtain the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates;

[0014] The double integral in the polar coordinates is converted into the sum of the function values ​​at all poles contained in the lower half plane.

[0015] In some embodiments of the present application, the relationship between the electric field and the electric potential energy and the magnetic potential energy derived from the introduced electric potential energy and magnetic potential energy includes:

[0016] Electric potential energy and magnetic potential energy are introduced, and combined with Maxwell's equations of electric field, the relationship between electric field and electric potential energy and magnetic potential energy is derived.

[0017] In some embodiments of the present application, the electric potential energy and magnetic potential energy are introduced, and the relationship between the electric field, the electric potential energy and the magnetic potential energy is derived by combining the Maxwell equations of the electric field, including:

[0018] Introduce electric potential energy and magnetic potential energy, use magnetic vector potential to solve Maxwell's equations and obtain the magnetic field strength;

[0019] Applying the Lorentz norm to the magnetic field intensity to obtain the Lorentz normed magnetic field intensity;

[0020] The electric field intensity is obtained based on the Lorentz-normalized magnetic field intensity, the Helmholtz wave equation of the magnetic vector potential, and the Helmholtz wave equation of the electric vector potential.

[0021] In some embodiments of the present application, decomposing the electric field into the sum of each level of TMz mode and the superposition of the sum of each level of TEz mode includes:

[0022] TM z The expressions of the electric field in each direction under this mode are

[0023]

[0024]

[0025] TE z The expressions of the electric field in each direction under this mode are

[0026]

[0027] TE E z (x,y,z)=0;

[0028] Based on TM z The expressions of the electric field in each direction and TE z The expression of the electric field in each direction in the mode decomposes the electric field.

[0029] In some embodiments of the present application, obtaining the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates includes:

[0030] Perform a two-dimensional Fourier transform on the electric field of the TMz mode and the TEz mode, and map the spatial domain xy plane into k x k y frequency domain, forming k x k y Double integral in the frequency domain;

[0031] The k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinate transformation.

[0032] In some embodiments of the present application, the k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinates, including:

[0033] Using polar coordinates k x =k ρ cosθ,k y =k ρ sinθ, expand the lower limit of the integral from zero to negative infinity, and we get

[0034]

[0035] In some embodiments of the present application, obtaining the electric field of the current of each segment relative to the observation point further includes:

[0036] According to the residue theorem, the integral is converted into a series summation to obtain the closed-loop explicit expression of the electric field generated by the stripline.

[0037] According to another aspect of an embodiment of the present application, a simulation device for electric field distribution of an integrated circuit stripline is provided, comprising:

[0038] A stripline segmentation module, used to segment the stripline of the integrated circuit into a plurality of segments;

[0039] An electric field acquisition module, used for acquiring the electric field of each segmented current relative to an observation point;

[0040] The superposition module is used to superimpose the electric field of each segmented current on the observation point to obtain the overall electric field of the strip line on any position observation point of the integrated circuit.

[0041] According to another aspect of an embodiment of the present application, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for simulating the electric field distribution of an integrated circuit stripline as described in any embodiment of the present application.

[0042] According to another aspect of the embodiments of the present application, a computer-readable storage medium is provided, on which a computer program is stored, and the computer program is executed by a processor to implement the simulation method of the electric field distribution of the integrated circuit stripline described in any embodiment of the present application.

[0043] The technical solution provided by one aspect of the embodiments of the present application may have the following beneficial effects:

[0044] The integrated circuit stripline electric field distribution simulation method provided in the embodiment of the present application divides the stripline of the integrated circuit into multiple segments, obtains the electric field of the current of each segment to the observation point, superimposes the electric field of the current of each segment to the observation point, and obtains the overall electric field of the stripline to any observation point at any position of the integrated circuit, thereby avoiding finite element segmentation in the entire airspace of the packaging substrate and the circuit board. Only the stripline in the problem structure needs to be segmented, thereby saving a large amount of computer storage space, and greatly reducing large and ultra-large matrix operations, reducing calculation time, and realizing the segmentation of only conductors without segmenting the entire space domain, thereby reducing the number of variables and the matrix scale, greatly reducing the amount of calculation, and allowing the overall problem to be simulated quickly.

[0045] The above description is only an overview of the technical solution of the embodiment of the present application. In order to more clearly understand the technical means of the embodiment of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the embodiment of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1A flow chart of a method for simulating electric field distribution of an integrated circuit stripline according to an embodiment of the present application is shown.

[0048] Figure 2 A flowchart of the steps of obtaining the electric field of each segment's current versus observation point according to one embodiment of the present application is shown.

[0049] Figure 3 A schematic diagram of the structure of a multi-layer packaging substrate according to an embodiment of the present application is shown.

[0050] Figure 4 A schematic diagram of a stripline with horizontal surface current in one embodiment of the present application is shown.

[0051] Figure 5 A schematic diagram of the integral profile and pole positions of the residue theory applied in one embodiment of the present application is shown.

[0052] Figure 6 A schematic diagram showing the relationship between the contribution of each TM and TE mode in |Ex| and its observation position ρ in one embodiment of the present application.

[0053] Figure 7 A structural block diagram of an integrated circuit stripline electric field distribution simulation device according to an embodiment of the present application is shown.

[0054] Figure 8 A structural block diagram of an electronic device according to an embodiment of the present application is shown.

[0055] Fig. 9 A schematic diagram of a computer-readable storage medium according to an embodiment of the present application is shown. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.

[0057] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined as here.

[0058] The meanings of the symbols in this article are shown in the following table:

[0059]

[0060]

[0061] In view of the problems existing in the related art that when the problem space becomes larger, the simulator needs a large amount of memory to store variables, and it takes a long time to solve a very large-scale matrix, the embodiment of the present application provides a stripline electric field distribution simulation method for an integrated circuit board, which divides the stripline of the integrated circuit into multiple segments, obtains the electric field of the current of each segment to the observation point, superimposes the electric field of the current of each segment to the observation point, and obtains the overall electric field of the stripline to any observation point at the position of the integrated circuit, thereby avoiding the finite element FEM (Finite Element Method) segmentation in the entire airspace of the packaging substrate and the circuit board. Only the stripline in the problem structure needs to be segmented, thereby saving a large amount of computer storage space, and greatly reducing large and very large matrix operations, reducing calculation time, and realizing the segmentation of only conductors without segmenting the entire space domain, thereby reducing the number of variables and the matrix scale, greatly reducing the amount of calculation, and enabling the overall problem to be simulated quickly.

[0062] The following describes an integrated circuit stripline electric field distribution simulation method, device, equipment and medium proposed according to an embodiment of the present application in conjunction with the accompanying drawings.

[0063] refer to Figure 1 As shown, an embodiment of the present application provides a method for simulating electric field distribution of an integrated circuit stripline, comprising steps S10 to S30:

[0064] S10, dividing the stripline of the integrated circuit into a plurality of segments;

[0065] S20, obtaining the electric field of the current of each segment relative to the observation point;

[0066] S30, superimposing the electric field of each segmented current to an observation point to obtain the overall electric field of the strip line to any observation point at a position of the integrated circuit.

[0067] An integrated circuit may include a package substrate or a circuit board.

[0068] refer to Figure 2 As shown, in some embodiments, obtaining the electric field of the current of each segment relative to the observation point may include:

[0069] S201, deriving a relationship between electric field and electric potential energy and magnetic potential energy based on the introduced electric potential energy and magnetic potential energy;

[0070] S202, decomposing the electric field into the sum of TMz modes at each level and the superposition of the sum of TEz modes at each level;

[0071] S203, obtaining the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates;

[0072] S204: Convert the double integral in polar coordinates into the sum of function values ​​at all poles included in the lower half plane.

[0073] In some embodiments, the relationship between the electric field and the electric potential energy and the magnetic potential energy is derived based on the introduced electric potential energy and magnetic potential energy, including: introducing the electric potential energy and the magnetic potential energy, combining the Maxwell equations of the electric field, and deriving the relationship between the electric field and the electric potential energy and the magnetic potential energy.

[0074] In some embodiments, electric potential energy and magnetic potential energy are introduced, and the relationship between electric field, electric potential energy and magnetic potential energy is derived by combining Maxwell equations of electric field, which may include:

[0075] Introduce electric potential energy and magnetic potential energy, use magnetic vector potential to solve Maxwell's equations and obtain the magnetic field strength;

[0076] Applying the Lorentz norm to the magnetic field intensity to obtain the Lorentz normed magnetic field intensity;

[0077] The electric field intensity is obtained based on the Lorentz-normalized magnetic field intensity, the Helmholtz wave equation of the magnetic vector potential, and the Helmholtz wave equation of the electric vector potential.

[0078] In some embodiments, decomposing the electric field into the sum of each level of TMz mode and the superposition of the sum of each level of TEz mode may include:

[0079] TM z The expressions of the electric field in each direction under this mode are

[0080]

[0081] TE z The expressions of the electric field in each direction under this mode are

[0082]

[0083] TE E z (x,y,z)=0;

[0084] Based on TM z The expressions of the electric field in each direction and TE z The expression of the electric field in each direction in the mode decomposes the electric field.

[0085] In some embodiments, obtaining the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates comprises:

[0086] S2031, perform a two-dimensional Fourier transform on the electric field of the TMz mode and the TEz mode, and map the spatial domain xy plane into k x k y frequency domain, forming k x k y Double integral in the frequency domain;

[0087] S2032, the k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinate transformation.

[0088] For example, the k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinate transformation, which can include:

[0089] Using polar coordinates k x =k ρ cosθ,k y =k ρ sinθ, expand the lower limit of the integral from zero to negative infinity, and we get

[0090]

[0091] Exemplarily, obtaining the electric field of the current of each segment relative to the observation point may also include: converting the integral into a series sum according to the residue theorem to obtain a closed-loop explicit expression of the electric field generated by the stripline.

[0092] A specific example of a stripline electric field distribution simulation method for an integrated circuit board is a fast simulation method for the electric field distribution of a package substrate and a circuit board stripline based on spatial Fourier transform. The method of this example can be applied to Figure 3 The package substrate shown, Figure 3 shows a schematic structural diagram of a multi-layer packaging substrate, Figure 3 ① represents a via, ② represents a metal plate, and ③ represents a stripline signal line. The method of this example may include the following steps:

[0093] 1) Under the premise of the known current spatial distribution on the stripline, divide the stripline into small segments along the length direction. The length of each small segment is one tenth of its frequency wavelength at the highest frequency required for simulation, that is, λ / 10. In this way, the current of the known stripline is decomposed into the superposition of the known currents of each small segment. If the electric field spatial distribution of any small segment current is obtained and superimposed, the electric field spatial distribution of the known stripline is obtained.

[0094] 2) Calculate the electric field of each small current segment on the observation point.

[0095] 2a) Introduce the physical quantities of electric potential energy and magnetic potential energy, and derive the relationship between electric field and electric potential energy and magnetic potential energy based on Maxwell's equations for electric field.

[0096] 2b) Since the package substrate and circuit board are stacked structures in the z direction, the electric field is decomposed into the sum of TMz modes at each level and the superposition of the sum of TEz modes at each level to facilitate decoupling calculation.

[0097] 2c) Perform a two-dimensional Fourier transform on the electric field Maxwell equations of the TMz and TEz modes above, and map the spatial domain xy plane into k x k y frequency domain, forming a double integral.

[0098] 2d) Then k x k y The double integral in the frequency domain is transformed into polar coordinates, k x =k ρ cosθ,k y =k ρ sinθ, converted to k ρ and the double integral of the angle θ.

[0099] 2e) The polar coordinate k above ρ The integral of is converted into the sum of function values ​​at all poles contained in the lower half plane by the Cauchy residue theorem. This Sommerfield integral is analytically evaluated by applying residue theory. Summing the residues at the poles in the complex plane leads to a fast and computable modal series expansion that does not require any numerical integration. The special functions that appear in the modal series expansion are fast and computable Bessel functions. This method greatly improves the computational efficiency compared to numerical integration.

[0100] 2f) The above angular integral is in the form of a Hankel function, whose value can be calculated using a ready-made formula.

[0101] 3) The electric fields of each of the above-mentioned small currents at the observation point are superimposed to obtain the overall electric field of the strip line at any observation point at the package substrate and the circuit board.

[0102] This method avoids the finite element FEM (Finite Element Method) segmentation in the entire airspace of the package substrate and circuit board. It only needs to segment the strip lines in the problem structure, thereby saving a lot of computer storage space and avoiding large and super-large matrix operations.

[0103] In this example, the problem of large amount of integral calculation is solved through the above step 2). Since it is easy to calculate and does not require any numerical integration, the calculation time is greatly reduced. Therefore, by only dividing the conductor instead of the entire space domain, the number of variables and the matrix size are reduced, the amount of calculation is greatly reduced, and the use of highly oscillating and slowly converging numerical integration on the computer is avoided, so that the overall problem can be quickly simulated.

[0104] Through step 2), the electric field distribution caused by the current source can be obtained, that is, the electric field vector at any point in the space is obtained under the premise of knowing the position and strength of the current source. Specifically, step 2) may include the following specific steps:

[0105] The geometry of the horizontal current source is Figure 4 So, it is located at (x 0 ,y 0 ,z 0 ) is a tiny current source between two ground planes (z = 0, z = d), which are perfectly conductive top and bottom ground planes that constrain the layered dielectric material ( μ, see the table in the previous article for professional terms). Given the current source strength, it is necessary to obtain the electric field expression at any point (x, y, z) in space.

[0106] Choose to use TM z and TE z The field can be solved by combining two modes because the z-direction is perpendicular to the layered surfaces of a layered dielectric. Therefore, TM z and TE z The modes will be decoupled, greatly simplifying the electric field solution. The relationship between the potential and the field is given by Maxwell's equations. In the previous table, all the symbols used before writing Maxwell's equations are listed. Using the symbols already defined, Maxwell's equations can be written as

[0107]

[0108] For the case where only current flows on the interconnect surface, the magnetic vector potential is chosen To solve Maxwell's equations:

[0109]

[0110] After applying the Lorentz gauge

[0111]

[0112] The electric field can be expressed as

[0113]

[0114] Substituting (2.8) into (2.9) and using the identity get

[0115]

[0116] Combining (2.2) and (2.7) into (2.10), we obtain the Helmholtz wave equation for the magnetic vector potential

[0117]

[0118] in

[0119] By using the duality principle, the Helmholtz wave equation for the electric vector potential is obtained. This expression is useful for modeling situations where the structure involves multiple ground planes. For such aperture problems, the equivalent magnetic current flowing in the aperture is obtained and the electric vector potential is chosen to be used.

[0120]

[0121] The electric field strength For TM z model,

[0122]

[0123] TM H z (x,y,z)=0.(2.18)

[0124] For TE z model,

[0125]

[0126] TE E z (x,y,z)=0;(2.21)

[0127]

[0128] The two-dimensional Fourier transform pair is defined as

[0129]

[0130] Perform Fourier transform in x and y directions.

[0131] Therefore, TM z The electric field can be expressed in the frequency domain as follows

[0132]

[0133] in,

[0134]

[0135] Similarly, TE z The electric field can be expressed in the frequency domain as

[0136]

[0137] in,

[0138]

[0139] In common packaging substrates and circuit boards, the dielectric between each layer is uniform. 1 =μ 2 =μ and The region between the plates is divided into upper and lower regions at the locations of the surface current sources. By making this separation, boundary conditions can be applied more easily. In general, the solutions to (2.35) and (2.42) can be written as:

[0140]

[0141] Among them, B 1TM ,B 2TM ,B 1TE ,B 2TE C 1TM ,C 2TM ,C 1TE and C 2TE are coefficients determined by applying boundary conditions.

[0142] The boundary conditions of the horizontal current source problem are as follows: Since the metal plate is an ideal conductor, at z e =d,

[0143]

[0144] In z e =d,

[0145]

[0146] In z e =0,

[0147]

[0148] In z e =0,

[0149]

[0150] As well as the electrical continuity characteristics at the junction of conductor lines, that is, the characteristics of electric field continuity and magnetic field continuity, and the boundary characteristics of surface current,

[0151] In z e =z o ,

[0152] In z e =z o ,

[0153] In z e =z o ,

[0154] In z e =z o .

[0155] Substituting (2.41)-(2.46) into (2.47)-(2.54) and solving the resulting equations yields the values ​​of the coefficients:

[0156] B 1TE =B 2TE =0, (2.55)

[0157] C 1TM =C 2TM =0, (2.56)

[0158]

[0159] Among them, k ρ 2 =k x 2 +k y 2 =k 2 -k z 2 . (2.61)

[0160] Finally, substituting (2.55)-(2.60) into (2.29)-(2.42), we obtain the spectral domain electric and magnetic fields of the horizontal current source:

[0161]

[0162] Total electric field in x direction

[0163]

[0164] Total electric field in y direction

[0165]

[0166] For convenience, z is defined i and z ni, i=1,2 is the area where the observation point is located, whether it is zone 1 or zone 2:

[0167] z 1 =dz e ,z 2 =z e , (2.72)

[0168] and z n1 =z o ,z n2 =dz o . (2.73)

[0169] The || symbol in the above equation indicates that the field is excited by a horizontal current.

[0170] After obtaining the expression of the electric field in the frequency domain, a two-dimensional inverse Fourier transform is performed to obtain the electric field expression in the spatial domain.

[0171] This article shows the x-component of the TMz electric field, and the other electric field components are similar to this x-component.

[0172] This paper shows that z Taking the x component of the mode electric field as an example, we perform a two-dimensional inverse Fourier transform on it.

[0173]

[0174] Express the above formula in polar coordinates, k x =k ρ cosθ,k u =k ρ sinθ, and extending the lower limit of the integral from zero to negative infinity, we get

[0175]

[0176] Substituting (2.62) into the above formula, we get

[0177]

[0178] in is the Green's function, which is defined as

[0179]

[0180] z n1 =z o ,z n2 =dz o ,z 1 =dz,z 2 = z,

[0181]

[0182] Il=1, where the second kind of Hankel function is a deformation of the special function Bessel function:

[0183]

[0184] To calculate the integral, residue theory is used to calculate the integral in, for example, equation (10) to obtain an explicit expression for the electric field, thereby obtaining the required modal series expansion.

[0185]

[0186] where the desired pole is the Green's function The extreme point.

[0187]

[0188] Because we defined it before: n1 =z o ,z n2 =dz o ,z 1 =dz,z 2 = z,

[0189]

[0190] Il=1,

[0191] When the observation area i = 1, z ni =z n1 =z o ,

[0192]

[0193] When the observation area i = 2, z ni =z n2 =dz o ,

[0194]

[0195] Therefore, the required pole is sin(k z d), that is, sin(k z d)=nπ,n=0,1,2,…

[0196] Since the relation k ρ 2 =k 2 -k z 2 ,

[0197] get

[0198] The application of the residue theorem, its integration path and the location of the poles are detailed in Figure 5 shown.

[0199] (11) and k ρ = 0 are the branch point contributions associated with the integral. They are given by Figure 5 The required deformation contours, poles and branch point singularities are as follows: Figure 5 As shown in the figure. As will be shown later, the branch point contributions of the TEz and TMz modes are equal in magnitude but 180 degrees out of phase, so they cancel analytically when the TEz and TMz modes are added to obtain the total field. Therefore, the branch point contribution is an analytical additional product of the separation of the field into TEz and TMz modes and does not affect the amplitude and phase of the total electric field.

[0200] This formula is a closed-loop explicit expression of the electric field generated by the stripline. It is expressed as the sum of a series of Hankel functions at the poles from an infinite integral. Since the Hankel function can be calculated quickly, the electric field can be calculated very quickly.

[0201] like Figure 6 As shown, in the uniform case, a horizontal source does not excite TEM modes. The total field consists mainly of TM1 modes, except very close to the source, where TMz modes come into play. Since all TEz and TMz modes decay very quickly with increasing distance from the source, the total field also decays very quickly with increasing distance. This behavior indicates that there is almost no coupling between horizontal traces in a uniform structure, while a sparse reaction matrix is ​​expected in uniformly filled stripline applications. Therefore, horizontal traces will couple only when they are very close to each other. Figure 6 The x-direction dipole |E x | and r q Relationship curve graph, Figure 6 TE and TM branch point contributions are shown in FIG.

[0202] exist Figure 6 The x-component of the total electric field is plotted in , which is a superposition of all the important TEz and TMz modes, as well as the branch point contributions associated with the TEz and TMz fields. The results for all closed-form field expressions are verified by comparison with those obtained by directly applying numerical integration routines in Matlab to the integrals, such as Eq. (10). The excellent agreement obtained for these results indicates that all the important poles have been included.

[0203] The above description of various embodiments tends to emphasize the differences between the various embodiments. The same or similar aspects can be referenced to each other, and for the sake of brevity, they will not be repeated herein.

[0204] refer to Figure 7 As shown, another embodiment of the present application provides a simulation device for electric field distribution of an integrated circuit stripline, comprising:

[0205] A stripline segmentation module, used to segment the stripline of the integrated circuit into a plurality of segments;

[0206] An electric field acquisition module, used for acquiring the electric field of each segmented current relative to an observation point;

[0207] The superposition module is used to superimpose the electric field of each segmented current on the observation point to obtain the overall electric field of the strip line on any position observation point of the integrated circuit.

[0208] Exemplarily, the electric field acquisition module is further specifically used for:

[0209] Based on the introduced electric potential energy and magnetic potential energy, the relationship between electric field and electric potential energy and magnetic potential energy is derived;

[0210] Decompose the electric field into the sum of the TMz modes at each level and the superposition of the sum of the TEz modes at each level;

[0211] Obtain the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates;

[0212] The double integral in the polar coordinates is converted into the sum of the function values ​​at all poles contained in the lower half plane.

[0213] Exemplarily, the relationship between the electric field, the electric potential energy and the magnetic potential energy derived from the introduced electric potential energy and magnetic potential energy includes:

[0214] Electric potential energy and magnetic potential energy are introduced, and combined with Maxwell's equations of electric field, the relationship between electric field and electric potential energy and magnetic potential energy is derived.

[0215] Exemplarily, the introduction of electric potential energy and magnetic potential energy, combined with Maxwell's equations for electric field, derives the relationship between electric field and electric potential energy and magnetic potential energy, including:

[0216] Introduce electric potential energy and magnetic potential energy, use magnetic vector potential to solve Maxwell's equations and obtain the magnetic field strength;

[0217] Applying the Lorentz norm to the magnetic field intensity to obtain the Lorentz normed magnetic field intensity;

[0218] The electric field intensity is obtained based on the Lorentz-normalized magnetic field intensity, the Helmholtz wave equation of the magnetic vector potential, and the Helmholtz wave equation of the electric vector potential.

[0219] Exemplarily, the electric field is decomposed into the sum of each level of TMz mode and the superposition of the sum of each level of TEz mode, including:

[0220] TM z The expressions of the electric field in each direction under this mode are

[0221]

[0222] TE z The expressions of the electric field in each direction under this mode are

[0223]

[0224] TE E z (x,y,z)=0;

[0225] Based on TM z The expressions of the electric field in each direction and TE z The expression of the electric field in each direction in the mode decomposes the electric field.

[0226] Exemplarily, obtaining the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates includes:

[0227] Perform a two-dimensional Fourier transform on the electric field of the TMz mode and the TEz mode, and map the spatial domain xy plane into k x k y frequency domain, forming k x k y Double integral in the frequency domain;

[0228] The k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinate transformation.

[0229] For example, the k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinates, including:

[0230] Using polar coordinates k x =k ρ cosθ,k y =k ρ sinθ, expand the lower limit of the integral from zero to negative infinity, and we get

[0231]

[0232] Exemplarily, the double integral in polar coordinates is converted into the sum of function values ​​at all poles included in the lower half plane by using the Cauchy residue theorem.

[0233] The simulation device of the electric field distribution of the integrated circuit stripline of the embodiment of the present application divides the stripline of the integrated circuit into multiple segments, obtains the electric field of the current of each segment to the observation point, superimposes the electric field of the current of each segment to the observation point, and obtains the overall electric field of the stripline to any position observation point of the integrated circuit. Thus, it is avoided to perform finite element segmentation on the entire airspace of the package substrate and the circuit board, and only the stripline in the problem structure needs to be segmented, thereby saving a lot of computer storage space, and greatly reducing large and super-large matrix operations, reducing calculation time, and realizing the segmentation of only the conductor without segmenting the entire space domain, thereby reducing the number of variables and the matrix scale, greatly reducing the amount of calculation, and enabling the overall problem to be quickly simulated.

[0234] The above description of various embodiments tends to emphasize the differences between the various embodiments. The same or similar aspects can be referenced to each other, and for the sake of brevity, they will not be repeated herein.

[0235] Another embodiment of the present application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method of any of the above embodiments.

[0236] refer to Figure 8 As shown, the electronic device 10 may include: a processor 100, a memory 101, a bus 102 and a communication interface 103, and the processor 100, the communication interface 103 and the memory 101 are connected via the bus 102; the memory 101 stores a computer program that can be run on the processor 100, and when the processor 100 runs the computer program, it executes the method provided in any of the aforementioned embodiments of the present application.

[0237] The memory 101 may include a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk storage. The communication connection between the device network element and at least one other network element is realized through at least one communication interface 103 (which may be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. may be used.

[0238] The bus 102 may be an ISA bus, a PCI bus, or an EISA bus, etc. The bus may be divided into an address bus, a data bus, a control bus, etc. The memory 101 is used to store a program, and the processor 100 executes the program after receiving an execution instruction. The method disclosed in any implementation of the aforementioned embodiment of the present application may be applied to the processor 100, or implemented by the processor 100.

[0239] The processor 100 may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in the processor 100 or an instruction in the form of software. The above processor 100 may be a general-purpose processor, which may include a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in the embodiments of the present application can be directly embodied as a hardware decoding processor for execution, or a combination of hardware and software modules in the decoding processor for execution. The software module may be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory 101, and the processor 100 reads the information in the memory 101 and completes the steps of the above method in combination with its hardware.

[0240] The electronic device provided in the embodiment of the present application and the method provided in the embodiment of the present application are based on the same inventive concept and have the same beneficial effects as the method adopted, operated or implemented by them.

[0241] Another embodiment of the present application provides a computer-readable storage medium, on which a computer program is stored, and the computer program is executed by a processor to implement the method of any of the above embodiments. Fig. 9 As shown, the computer-readable storage medium shown is a CD 20 on which a computer program (ie, a program product) is stored. When the computer program is run by a processor, the method provided by any of the aforementioned embodiments will be executed.

[0242] It should be noted that examples of computer-readable storage media may also include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other optical or magnetic storage media, which are not listed here one by one.

[0243] The computer-readable storage medium provided in the above-mentioned embodiments of the present application and the method provided in the embodiments of the present application are based on the same inventive concept and have the same beneficial effects as the method adopted, run or implemented by the application program stored therein.

[0244] It should be noted that:

[0245] The term "module" is not intended to be limited to a specific physical form. Depending on the specific application, a module can be implemented as hardware, firmware, software, and / or a combination thereof. In addition, different modules can share common components or even be implemented by the same components. There may or may not be clear boundaries between different modules.

[0246] The algorithm and display provided herein are not inherently related to any specific computer, virtual device or other equipment. Various general devices can also be used together with examples based on this. According to the above description, it is obvious to construct the structure required for this type of device. In addition, the application is not directed to any specific programming language yet. It should be understood that various programming languages ​​can be utilized to realize the content of the application described herein, and the description made to specific languages ​​above is for the purpose of disclosing the best mode of implementation of the application.

[0247] It should be understood that, although the steps in the flowchart of the accompanying drawings are displayed in sequence as indicated by the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least a part of the steps in the flowchart of the accompanying drawings may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.

[0248] The above embodiments only express the implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A stripline electric field distribution simulation method for an integrated circuit board, characterized in that: include: Dividing the stripline of the integrated circuit into multiple segments; Obtaining the electric field of the current of each segment relative to an observation point; The electric field of each segment current to an observation point is superimposed to obtain the overall electric field of the strip line to any observation point at the integrated circuit.

2. The method according to claim 1, characterized in that The step of obtaining the electric field of each segmented current relative to an observation point comprises: Based on the introduced electric potential energy and magnetic potential energy, the relationship between electric field and electric potential energy and magnetic potential energy is derived; Decompose the electric field into the sum of the TMz modes at each level and the superposition of the sum of the TEz modes at each level; Obtain the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates; The double integral in the polar coordinates is converted into the sum of the function values ​​at all poles contained in the lower half plane.

3. The method according to claim 1, characterized in that The relationship between the electric field, the electric potential energy and the magnetic potential energy derived from the introduced electric potential energy and magnetic potential energy includes: Electric potential energy and magnetic potential energy are introduced, and combined with Maxwell's equations of electric field, the relationship between electric field and electric potential energy and magnetic potential energy is derived.

4. The method according to claim 3, characterized in that The electric potential energy and magnetic potential energy are introduced, combined with Maxwell's equations for electric field, to derive the relationship between electric field, electric potential energy and magnetic potential energy, including: Introduce electric potential energy and magnetic potential energy, use magnetic vector potential to solve Maxwell's equations and obtain the magnetic field strength; Applying the Lorentz norm to the magnetic field intensity to obtain the Lorentz normed magnetic field intensity; The electric field intensity is obtained based on the Lorentz-normalized magnetic field intensity, the Helmholtz wave equation of the magnetic vector potential, and the Helmholtz wave equation of the electric vector potential.

5. The method according to claim 4, characterized in that The decomposition of the electric field into the sum of the TMz modes at each level and the superposition of the sum of the TEz modes at each level comprises: TM z The expressions of the electric field in each direction under this mode are TE z The expressions of the electric field in each direction under this mode are TE E z (x,y,z)=0; Based on TM z The expressions of the electric field in each direction and TE z The expression of the electric field in each direction in the mode decomposes the electric field.

6. The method according to claim 2, characterized in that The step of obtaining the double integral of the electric field in the TMz mode and the TEz mode in polar coordinates includes: Perform a two-dimensional Fourier transform on the electric field of the TMz mode and the TEz mode, and map the spatial domain xy plane into k x k y frequency domain, forming k x k y Double integral in the frequency domain; The k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinate transformation.

7. The method according to claim 6, characterized in that The k x k y The double integral in the frequency domain is transformed into a double integral in polar coordinates through polar coordinates, including: Using polar coordinates k x =k ρ cosθ,k y =k ρ sinθ, expand the lower limit of integration from zero to negative infinity, and we get 8. The method according to claim 2, characterized in that: The step of obtaining the electric field of each segmented current relative to an observation point further includes: According to the residue theorem, the integral is converted into a series summation to obtain the closed-loop explicit expression of the electric field generated by the stripline.

9. A simulation device for electric field distribution of integrated circuit strip lines, characterized in that: include: A stripline segmentation module, used to segment the stripline of the integrated circuit into a plurality of segments; An electric field acquisition module, used for acquiring the electric field of each segmented current relative to an observation point; The superposition module is used to superimpose the electric field of each segmented current on the observation point to obtain the overall electric field of the strip line on any position observation point of the integrated circuit.

10. An electronic device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for simulating the electric field distribution of an integrated circuit strip line according to any one of claims 1 to 8.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program is executed by a processor to implement the method for simulating electric field distribution of an integrated circuit stripline according to any one of claims 1 to 8.

Images