An electromagnetic parameter extraction method based on the non-conformal partial element equivalent circuit method

Abstract

The object of the present invention is to provide an electromagnetic parameter extraction method based on the non-conformal partial element equivalent circuit method, belonging to the technical field of computational electromagnetics. The method of the present invention divides a multi-scale electromagnetic structure into different regions according to the difference in size, and each region is meshed with triangular prism meshes of corresponding sizes. At the same time, h-SPV basis functions are defined at the non-conformal junctions to ensure the continuity of the current at the non-conformal junctions. During the calculation of the multi-scale structure problem, the present invention uses non-conformal meshing to avoid a large number of transition mesh elements at the interfaces of different regions. By establishing a current continuity boundary condition at the interface ports, while ensuring the calculation accuracy, the calculation complexity is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational electromagnetics, and particularly relates to an electromagnetic parameter extraction method based on a non-conformal partial element equivalent circuit method. Background Art

[0002] As a mainstream method for electromagnetic parameter extraction, the partial element equivalent circuit method (PEEC) has a core idea of discretizing a three-dimensional conductor structure into an interconnected network of resistors, inductors, and capacitors, and solving the frequency-domain response of the conductor system through circuit node equations. This method expands the conductor surface current through basis functions and enforces the current continuity condition to satisfy the law of conservation of charge. In traditional PEEC implementations, the basis functions need to be strictly configured on conformal tetrahedral or triangular prism element meshes to ensure that adjacent elements share a common edge or face, so as to maintain the normal continuity of the current density through the overlapping integral of the basis functions. This constraint can be efficiently implemented in simple geometric structures, but it faces significant challenges in multi-scale complex structures.

[0003] Multi-scale electromagnetic structures usually contain components with significantly different characteristic sizes, and their conformal mesh discretization requirements will lead to two types of problems:

[0004] (1) To meet the grid resolution of local fine features, it is necessary to insert transition elements between adjacent regions, which will sharply increase the number of grids and the matrix solution dimension;

[0005] (2) Non-conformal grid regions often appear at the cross-scale connection points. If traditional continuous basis function configuration is still forced, the normal component of the current density at the interface will be discontinuous. This non-physical truncation phenomenon essentially violates the current continuity equation, causing problems such as charge pseudo-accumulation, port impedance calculation deviation, and high-frequency resonance peak shift. Summary of the Invention

[0006] Aiming at the problems existing in the background art, the purpose of the present invention is to provide an electromagnetic parameter extraction method based on a non-conformal partial element equivalent circuit method. The method of the present invention divides the multi-scale electromagnetic structure into different regions according to the size difference, each region is meshed with triangular prism grids of corresponding sizes, and at the same time, h-SPV basis functions are defined at the non-conformal junctions, ensuring the continuity of the current at the non-conformal junctions and also avoiding a large number of transition grid elements at the interfaces between different regions, realizing the efficient solution of the multi-scale electromagnetic structure.

[0007] To achieve the above purpose, the technical solution of the present invention is as follows:

[0008] An electromagnetic parameter extraction method based on a non-conformal partial element equivalent circuit method, comprising the following steps:

[0009] Step 1. Perform domain modeling on the multi-scale structure: Decompose the multi-scale structure into several sub-regions according to different sizes, and each sub-region is meshed with triangular prism grid elements with appropriate sizes;

[0010] Step 2. Discretize the current of the target: Use the standard SPV basis function to characterize the equivalent volume current in the conductor within each sub-region, and introduce the h-SPV basis function at the non-conformal interface between sub-regions to characterize the equivalent volume current in the conductor; at the same time, apply equivalent boundary condition constraints to make the current continuous at the sub-region interface, and obtain the equivalent volume current and the potential at any point in space ;

[0011] Step 3. Substitute the expressions of the equivalent volume current and the potential at any point in space obtained in Step 2 into the volume electric field integral equation, and derive the expressions of partial resistance, partial inductance, and partial capacitance through the Galerkin test method;

[0012] Step 4. Combine Kirchhoff's current and voltage laws and boundary conditions to construct a partial element circuit equation set, establish a matrix equation based on the partial element circuit equation set, and then solve the matrix equation to obtain the voltage and the current corresponding to the basis function;

[0013] Step 5. Calculate and solve the required electromagnetic parameters through the voltage and the current corresponding to the basis function obtained in Step 4.

[0014] Furthermore, in Step 1, the appropriate size means that the size of the triangular prism grid element is proportional to the size of the sub-region. Larger triangular prism grid elements are used to mesh larger sub-regions, and smaller triangular prism grid elements are used to mesh smaller sub-regions.

[0015] Furthermore, in Step 2, the SPV basis function consists of a transverse SPV basis function and a longitudinal SPV basis function ; the h-SPV basis function consists of a transverse h-SPV basis function and a longitudinal h-SPV basis function and their expressions are respectively:

[0016] (1)

[0017] (2)

[0018] where represents a triangular prism element, represents the area of the interface being a triangle, represents the length of the intersection of the cross-sectional triangle and the boundary edge, Expressed as a triangular prism element The height, vector represents the vector from the free vertex of the cross-sectional triangle to any point inside the triangle, and the vector is the origin is the vector from the origin to any point inside the triangular prism element.

[0019] Furthermore, the specific process of discretizing the current of the target is as follows:

[0020] Equivalent volume current The discrete expression is

[0021] (3)

[0022] where represents the number of common quadrilateral faces of the triangular prism pair, represents the number of non-conformal quadrilateral faces on the regional interface, is the number of common triangular faces of the triangular prism pair, is the number of non-conformal triangular faces on the regional interface; are the sequence numbers of the transverse SPV basis function , transverse h-SPV basis function , longitudinal SPV basis function and longitudinal h-SPV basis function respectively; , , , are the discrete currents corresponding to the transverse SPV basis function , transverse h-SPV basis function , longitudinal SPV basis function and longitudinal h-SPV basis function respectively;

[0023] In the analysis of the surface charge distribution characteristics, the charge density of each discrete unit shows a spatially uniform distribution characteristic; based on this physical assumption, the surface charge density is discretized and expanded using a rectangular pulse basis function to obtain the discrete charge of the pulse basis function at the field point , and its mathematical expression is denoted as:

[0024] (4)

[0025] In the formula, is the area integral domain pulse function of the nth discrete unit at the field point, is the total charge of the nth discrete unit, N T is the total number of discrete units, is the volume of the triangular prism element;

[0026] According to the scalar potential theory of quasi-static fields, there is an integral relationship between the electric potential at any point in space and the surface charge distribution. This physical relationship can be mathematically characterized by the Green's function in free space and can be specifically expressed as:

[0027] (5)

[0028] where is the field point, is the source point; is the field geometric unit volume, is the source geometric unit volume; is the area integral domain pulse function of the nth discrete element of the source point, is the discrete charge of the pulse basis function of the source point, is the permittivity, N is the number of half basis function boundary surfaces, is the Green's function.

[0029] Furthermore, the specific process of step 3 is as follows:

[0030] The mixed potential form of the volume electric field integral equation can be expressed as:

[0031] (6)

[0032] where is the scattered electric field, and the vector magnetic potential is related to the electric potential at any point in space through the Green's function and the source distribution; represents the Laplacian operator, is the angular frequency, and j is the complex number symbol;

[0033] Applying the Galerkin test method, that is, using the basis function and the test function to be the same, taking the inner product operation on equation (6) gives:

[0034] (7)

[0035] Substituting the expressions of the SPV basis function discrete body current and the pulse basis function discrete charge into equation (7), expanding the three parts on the left side of the above equation respectively gives the partial resistance , the partial inductance and the partial potential coefficient expressions, which are respectively:

[0036] (8)

[0037] (9)

[0038] (10)

[0039] wherein, is the conductivity; is the permeability; is the Green's function; is the permittivity; is the quadrilateral area of the interface between two triangular prism elements which is a quadrilateral; is the expression of the basis function corresponding to the m-th source point, is the expression of the basis function corresponding to the n-th source point;

[0040] In addition, define the partial capacitance .

[0041] Furthermore, the electromagnetic parameters are port current, port voltage, port impedance, parasitic parameters RLC, power distribution, power consumption, and S-parameters equivalent through the port, etc.

[0042] Furthermore, the specific process of step 5 is as follows:

[0043] When extracting electromagnetic parameters using the PEEC algorithm, apply the current source current at the port to obtain the port voltage , or apply the voltage source voltage at the port to obtain the port current ;

[0044] Then the expression of the port input impedance is or ;

[0045] The expression of the S-parameter is: ; wherein is the reference impedance;

[0046] The expression of the ohmic loss is ; I u is the current of the basis function with the serial number u, R u is the resistance of the basis function with the serial number u, and U is the total number of basis functions inside the conductor.

[0047] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0048] During the calculation process of the multi-scale structure problem of the present invention, by establishing the current continuity boundary condition at the interface port, while ensuring the calculation accuracy, the use of non-conformal grid meshing avoids the buffer grid and reduces the calculation complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flow chart for extracting electromagnetic parameters by the partial element equivalent circuit method of the volume electric field integral equation based on the SPV basis function with non-conformal triangular prism meshes.

[0050] Figure 2 Schematic diagram of the transverse SPV basis function defined on the common quadrilateral surface of a pair of triangular prism meshes.

[0051] Figure 3 Schematic diagram of the longitudinal SPV basis function defined on the common triangular surface of a pair of triangular prism meshes.

[0052] Figure 4 Schematic diagram for handling the interface current in the non-conformal grid region.

[0053] Figure 5 Schematic diagram of the transverse h-SPV basis function defined on a single triangular prism mesh.

[0054] Figure 6 Schematic diagram of the longitudinal h-SPV basis function defined on a single triangular prism mesh.

[0055] Figure 7 Schematic diagram of the topological relationship of the dissection grid for the two-dimensional simplification of the conductor.

[0056] Figure 8 Schematic diagram of a thin-layer lossy conductor.

[0057] Figure 9 Comparison diagram of the AC resistance and AC inductance of the thin-layer lossy conductor varying with frequency between NC-PRI-VIE-PEEC and VIE-PPEC;

[0058] Among them, (a) is the comparison diagram of NC-PRI-VIE-PEEC and VIE-PPEC for the AC resistance; (b) is the comparison diagram of NC-PRI-VIE-PEEC and VIE-PPEC for the AC inductance.

[0059] Figure 10 Multi-scale structure model and excitation method.

[0060] Figure 11 Schematic diagrams of non-conformal triangular prism mesh dissection and conformal triangular prism mesh dissection;

[0061] Among them, (a) is the schematic diagram of non-conformal triangular prism mesh dissection; (b) is the schematic diagram of conformal triangular prism mesh dissection. Detailed implementation manners

[0062] To make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the implementation manners and the accompanying drawings.

[0063] The present invention provides an electromagnetic parameter extraction method based on the non - conformal partial - element equivalent - circuit method. This method innovatively uses non - conformal triangular - prism grid elements to discretize and separate lossy conductors, and uses SPV basis functions defined on the triangular - prism grid elements to characterize the equivalent volume current in the conductors, and uses pulse basis functions to characterize the potential within the volume elements. Then, by defining semi - SPV basis functions on the non - conformal boundaries of the conductors, the continuity of the volume current on the conductor boundaries is achieved. Next, the expressions of the discrete current and potential are substituted into the volume electric - field integral equation, and a matrix equation is obtained through the Galerkin test method. Finally, by solving the matrix equation, the equivalent resistance and voltage inside the conductor are obtained. The main electromagnetic parameters obtained by the present invention are the current, voltage, power distribution, power consumption in the circuit, and the S - parameter network equivalent through the ports.

[0064] Embodiment 1

[0065] An electromagnetic parameter extraction method based on the non - conformal partial - element equivalent - circuit method, the schematic flow diagram of which is as Figure 1 shown, includes the following steps:

[0066] Step 1. Perform domain - based modeling on the multi - scale structure: Decompose the multi - scale target into several independent sub - regions according to different sizes, and perform non - conformal meshing on different sub - regions using triangular - prism grid elements of different sizes. Use larger triangular - prism grid elements for meshing larger sub - regions and smaller triangular - prism grid elements for meshing smaller sub - regions;

[0067] Step 2. Discretize the current of the target: Use standard SPV basis functions to characterize the equivalent volume current in the conductors within each sub - region, and introduce h - SPV basis functions at the non - conformal interfaces between sub - regions to characterize the equivalent volume current of the conductors. At the same time, apply equivalent boundary - condition constraints to ensure current continuity at the sub - region interfaces, and obtain the equivalent volume current and the potential at any point in space ;

[0068] The form and properties of the SPV basis functions are closely related to the geometric structure of the triangular prism. The characteristics of the transverse SPV basis functions are closely related to the geometric shape of the cross - section of the triangular prism, while the longitudinal SPV basis functions depend on the height of the triangular prism and the longitudinal structure. The schematic diagram of the definition of the transverse SPV basis function is as Figure 2 shown, the conformal region is a pair of parallelograms, one of which is positive and the other is negative; the schematic diagram of the definition of the longitudinal SPV basis function is as Figure 3As shown, the conformal region is a pair of triangles, one positive and the other negative. This inherent connection endows the SPV basis functions with excellent geometric adaptability to triangular prisms, enabling them to exhibit unique advantages when solving electromagnetic problems related to triangular prism structures. The SPV basis functions construct a complete set of functions within the triangular prism. This indicates that for any physically valid electric field and current distributions within the triangular prism, they can be accurately expressed through the linear combination of SPV basis functions. This completeness property lays an important foundation for accurately solving electromagnetic problems. Under specific conditions, the SPV basis functions possess orthogonality. This property enables the interaction between different basis functions during electromagnetic calculations to be handled through simple inner product operations, greatly simplifying the complex calculation process.

[0069] According to the structural characteristics of the triangular prism, the standard SPV basis functions can be divided into transverse SPV basis functions and longitudinal SPV basis functions , and their expressions are respectively:

[0070] (1)

[0071] (2)

[0072] where, is the length of the intersection of the cross-sectional triangle and the boundary edge, and represent the positive and negative triangle areas corresponding to the cross-sectional triangle respectively, denotes the vector from the triangular field point to the free vertex of the positive triangle, denotes the vector from the free vertex of the negative triangle to the field point ; denotes the vector from the top surface of the positive triangular prism to the field point and parallel to the edge, denotes the vector from the field point to the free top surface of the negative triangular prism and parallel to the edge, represents the height of the positive triangular prism corresponding to the basis function, represents the height of the negative triangular prism corresponding to the basis function; represents the positive triangular prism unit, represents the negative triangular prism unit;

[0073] The h-SPV basis functions are composed of transverse h-SPV basis functions and longitudinal h-SPV basis functions . The schematic diagram of the transverse h-SPV basis function defined on a single triangular prism grid is as shown in Figure 5 , and the schematic diagram of the longitudinal h-SPV basis function defined on a single triangular prism grid is as shown inFigure 6 As shown, their expressions are respectively:

[0074] (3)

[0075] (4)

[0076] Among them, represents a triangular prism element, represents the area of the interface with a triangular shape, represents the height of the triangular prism element The vector represents the vector from the free vertex of the cross-sectional triangle to any point inside the triangle, and the vector is the origin The vector to any point inside the tetrahedron.

[0077] In the low-frequency PEEC algorithm, the current conservation characteristic requires that the current density of the conductor conduction path satisfies the continuity condition. If non-conformal meshing is adopted, the mesh topology mismatch at the interface will lead to numerical truncation of the current path, thus destroying the global consistency of the physical model. Therefore, it is necessary to enforce the Kirchhoff's Current Law (KCL) on the currents on both sides of the interface through the cross-region current continuity constraint condition to ensure equivalence with the solution of the global conformal mesh.

[0078] Taking Figure 4 the lossy conductor region Ω shown as an example, it is divided by the interface Γ into and two sub-domains. At the interface Γ, by introducing the flux balance equation of the current density ;

[0079] (5)

[0080] Then the current at the boundary should satisfy the expression:

[0081] (6)

[0082] Among them, represents the current density corresponding to the q-th basis function at the interface Γ of the t-th sub-domain. This equation enforces the sum of the normal fluxes of the current densities on both sides of the interface to be zero, ensuring the global conservation of the current path under non-conformal discretization.

[0083] For the definition of the conformal mesh, establish the SPV basis function, and use the transverse SPV basis function to discretize the transverse variation of the equivalent volume current in the region, and use the longitudinal SPV basis function to discretize the equivalent volume current Vertical variation. When dealing with the interface of the processing area, the transverse h-SPV basis function is used Equivalent volume current within the discrete region Transverse variation, using the longitudinal h-SPV basis function Equivalent volume current within the discrete region Vertical variation. Therefore, Can be discretely expressed as:

[0084] (7)

[0085] Among them, Respectively represent the number of common quadrilateral faces on the discrete triangular prism and the number of non-conformal quadrilateral faces on the interface of the region, Respectively represent the number of common triangular faces on the discrete triangular prism and the number of non-conformal triangular faces on the interface of the region;

[0086] Step 3. Substitute the expressions of the discrete current and potential obtained in Step 2 into the volume electric field integral equation, and further derive the expressions of partial resistance, partial inductance, and partial capacitance through the Galerkin test method;

[0087] The mixed potential form of the volume electric field integral equation can be expressed as:

[0088] (8)

[0089] Among them, the vector magnetic potential Is related to the electric potential At any point in space through the Green's function and the source distribution;

[0090] Apply the Galerkin test method, that is, with the basis function being the same as the test function, perform the inner product operation on the above formula to obtain:

[0091] (9)

[0092] Substitute the SPV basis function discrete volume current And the field point pulse basis function discrete charge Expressions into the above formula, expand the three parts on the left end of the above formula respectively to obtain the partial resistance 、Partial inductance And the partial potential coefficient Expressions, respectively:

[0093] (10)

[0094] (11)

[0095] (12)

[0096] The definition of partial capacitance .

[0097] Step 4. Combine Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL) to jointly establish some circuit equations, then establish a matrix equation and solve it to obtain the current corresponding to the basis function;

[0098] Figure 7 The schematic diagram of the topological relationship of the two-dimensional simplified mesh of the conductor is shown in Figure 1. The non-conformal interface should meet the boundary current continuity condition of the interface. Figure 7 As shown in the figure, if there are 6 grid units, then in the case of DC, according to the topological relationship in the grid, the KVL equation and the KCL equation can be established:

[0099] (13)

[0100] (14)

[0101] I u is the current of the basis function with serial number u, u=1,2,3,…,9; R ab is the coupling resistance of the basis function corresponding to serial number a and corresponding serial number b, a=1,2,3,…,9, b=1,2,3,…,9; is the electric potential at the grid or interface numbered w, w=1,2,3,…,9; is the current of the excitation current source;

[0102] Depend on Figure 7 The excitation port shown, combined with the interface boundary current continuity condition, can obtain the final matrix equation:

[0103] (15)

[0104] Solving the above matrix equation can obtain the current corresponding to the basis function inside the conductor The potential of the grid nodes , which is used for subsequent electromagnetic parameter calculations.

[0105] In the case of AC, the matrix equation corresponding to formula (15) is:

[0106] (16)

[0107] in is a matrix representing the topological relationship of the geometric grid. The superscript T represents the rank, and I represents the current corresponding to the basis function. represents the potential of the grid, represents the applied excitation source, C is the partial capacitance, and L is the inductance.

[0108] Step 5. The required electromagnetic parameters, such as port impedance, parasitic parameters RLC, power distribution, power consumption, and the S-parameter network equivalent through the port and potential distribution, can be obtained from the current, voltage, and some elements obtained in Step 4.

[0109] When extracting the port parameters of the packaged circuit by the PEEC algorithm, a current source current is applied at the port to obtain the port voltage , or a voltage source voltage is applied at the port to obtain the port current ; taking the current source as an example, the port input impedance is obtained by dividing the obtained port voltage by the current source current , and its expression is ; where the real part of the input impedance is the port resistance of the conductor, and the imaginary part is the port inductance of the conductor.

[0110] The expression of the input admittance is .

[0111] The expression of the S-parameter is: .

[0112] The expression of the ohmic loss is , where U is the total number of basis functions inside the conductor.

[0113] Figure 8 This is a schematic diagram of the thin-layer lossy conductor to be dissected in this embodiment. As Figure 8 shown, for the thin-layer lossy conductor with a size of , a triangular prism dissection is performed, and the entire conductor is divided into two sub-regions. For the left sub-region, a triangular prism grid unit with a large size is used for dissection, and for the right sub-region, a triangular prism grid unit with a small size is used for dissection. The interface between the two sub-regions is the non-conformal region. The conductivity is set to , and a 1A current source excitation is set at both ends. Through the numerical calculation of the triangular prism non-conformal partial element equivalent circuit method of the present invention, its resistance is obtained as , and the error from the theoretical value is 1%.

[0114] At frequencies from 1 Hz to 10 GHz, in the non-conformal grid triangular prism volume integral partial element equivalent circuit method (NC-PRI-VIE-PEEC) and the conformal grid tetrahedron volume integral partial element equivalent circuit method (VIE-PEEC) modes of the present invention, the AC resistance and AC inductance are solved, and the results are compared as follows Figure 9 (a) and Figure 9As shown in Fig. (b), although there are small differences in resistance at high frequencies due to the differences in mesh quality, the overall agreement of the two electromagnetic parameters is good, meeting the solution accuracy.

[0115] Embodiment 2

[0116] For multi-scale structures such as Figure 10 shown in the figure, it is composed of a larger-sized cube (side length of 1 mm) spliced with a smaller-sized cylindrical conductor (radius of 0.1 mm). The material is set as copper (the conductivity is set as ), and a 1A current source excitation is added at the upper end of the cylinder and the lower end of the cube, and the port resistance is calculated by the NC-PRI-VIE-PEEC algorithm of the present invention.

[0117] As Figure 11 shown in Fig. (a), in the triangular prism meshing mode, the number of formed meshes is 920 triangular prisms, the number of calculated unknowns is 2242, and the calculation time is. At the same meshing size, as Figure 11 shown in Fig. (b), the number of meshes formed by non-conformal meshing in sub-regions is 450 triangular prisms, and the number of calculated unknowns is 1075.

[0118] Table 1 shows the comparison of the calculation results of the multi-scale structure of this embodiment by the NC-PRI-VIE-PEEC method of the present invention and the traditional VIE-PPEC method. Combining the data in Table 1, it can be seen that the non-conformal mesh improvement reduces the number of calculated unknowns by 108% and reduces the calculation time by 49%, while ensuring the accuracy of the calculation results. This can prove the effectiveness of the present invention.

[0119] Table 1

[0120] VIE-PEEC NC-PRI-VIE-PEEC R (mΩ) 0.6231 0.6105 L (nH) 0.9222 0.9025 Subdivided mesh 920 450 Unknowns 2242 1075 Computation time (s) 196.6 131.5

[0121] The above is only the specific implementation manner of the present invention. Any feature disclosed in this specification, unless specifically described, can be replaced by other equivalent or similar-purpose alternative features; all the features disclosed, or all the steps in any method or process, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. An electromagnetic parameter extraction method based on the non-conformal partial element equivalent circuit method, characterized in that Including the following steps: Step 1. Perform domain modeling on the multi-scale structure: Decompose the multi-scale structure into several sub-regions according to different sizes, and each sub-region is divided by triangular prism grid elements with appropriate sizes; Step 2. Discretize the current of the target: In each sub-region, the standard SPV basis function is used to characterize the equivalent volume current in the conductor, and the h-SPV basis function is introduced at the non-conformal interface between sub-regions to characterize the equivalent volume current in the conductor. At the same time, equivalent boundary conditions are applied to ensure current continuity at the sub-region interface, and the equivalent volume current is obtained. and the potential at any point in space ; The SPV basis functions are composed of transverse SPV basis functions and longitudinal SPV basis functions ; The h-SPV basis functions are composed of transverse h-SPV basis functions and longitudinal h-SPV basis functions ; Their expressions are respectively as follows: (1) (2) Among them, represents a triangular prism element, represents the area of the interface with a triangular shape, represents the length of the intersection of the cross-sectional triangle and the boundary edge, represents the triangular prism element height, vector represents the vector from the free vertex of the cross-sectional triangle to any point inside the triangle, vector is the origin vector to any point inside the triangular prism element; Step 3. Substitute the equivalent body current obtained in Step 2 and the potential at any point in space into the volume electric field integral equation, and derive the expressions of partial resistance, partial inductance, and partial capacitance through the Galerkin test method. The specific process is as follows: The mixed potential form of the volume electric field integral equation can be expressed as: (3) Among them, is the scattered electric field, and the vector magnetic potential is related to the electric potential at any point in space through the Green's function and the source distribution; represents the Laplacian operator, is the angular frequency, and j is the complex number symbol; Apply the Galerkin test method, that is, use the basis function and the test function to be the same, and perform the inner product operation on Equation (3) to obtain: (4) Discretize the body current of the SPV basis function The expression and the discrete charge of the pulse basis function at the field point Substitute the expressions into Equation (4), and expand the three parts on the left side of the above equation respectively to obtain the partial resistance , the partial inductance and the partial potential coefficient expressions, respectively: (5) (6) (7) Among them, is the conductivity; is the magnetic permeability; is the Green's function; is the permittivity; is the quadrilateral area where the interface between two triangular prism elements is a quadrilateral, is the expression of the basis function corresponding to the m-th source point, is the expression of the basis function corresponding to the n-th source point; In addition, define partial capacitance ; Step 4. Combine Kirchhoff's current and voltage laws and boundary conditions to construct a partial element circuit equation set, establish a matrix equation based on the partial element circuit equation set, and then solve the matrix equation to obtain the voltage and the current corresponding to the basis function; Step 5. Calculate and solve the required electromagnetic parameters through the voltage and the current corresponding to the basis function obtained in Step 4. The specific process is as follows: When extracting electromagnetic parameters using the PEEC algorithm, a current source current is applied at the port to obtain the port voltage , or a voltage source voltage is applied at the port to obtain the port current ; The port input impedance is expressed as or ; The S-parameter expression is: ; where is the reference impedance; The Ohmic loss expression is ; I u is the current of the basis function with serial number u, R u is the resistance of the basis function with serial number u, and U is the total number of basis functions inside the conductor.

2. The electromagnetic parameter extraction method according to claim 1, characterized in that In Step 1, being size-adapted means that the size of the triangular prism grid element is proportional to the size of the sub-region. Larger triangular prism grid elements are used to divide larger sub-regions, and smaller triangular prism grid elements are used to divide smaller sub-regions.

3. The electromagnetic parameter extraction method according to claim 1, characterized in that, The specific process of current discretization for the target is as follows: Equivalent body current The discrete expression is (8) Among them, represents the number of common quadrilateral faces of the triangular prism pair, represents the number of non-conformal quadrilateral faces on the regional interface, is the number of common triangular faces of the triangular prism pair, is the number of non-conformal triangular faces on the regional interface; are successively the serial numbers of the transverse SPV basis functions , transverse h-SPV basis functions , longitudinal SPV basis functions and longitudinal h-SPV basis functions respectively; are successively the discrete currents corresponding to the transverse SPV basis functions , transverse h-SPV basis functions , longitudinal SPV basis functions and longitudinal h-SPV basis functions respectively. The surface charge density is discretized and expanded in space using rectangular pulse basis functions to obtain the discrete charges of the pulse basis functions at the field points , and its mathematical expression is denoted as: (9) In the formula, is the area integral pulse function of the n-th discrete element of the field point, is the total charge of the n-th discrete element, and N T is the total number of discrete elements, is the volume of the triangular prism element; Then the electric potential at any point in space The specific expression can be constructed as follows: (10) Among them, is the field point, is the source point; is the area integral domain pulse function of the nth discrete unit of the source point, is the field geometric unit volume, is the source geometric unit volume, is the discrete charge of the pulse basis function of the source point; is the permittivity, N is the number of half basis function boundary surfaces, is the Green's function.

4. The electromagnetic parameter extraction method according to claim 1, wherein The electromagnetic parameters are port current, port voltage, port impedance, parasitic parameters RLC, power distribution, power consumption, and S parameters equivalent through the port.

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