A lumped port normalized impedance s-parameter calculation method based on tfe

Abstract

The application belongs to the field of electromagnetic numerical methods, and provides a TFE-based lumped port normalized impedance S parameter calculation method. First, based on the definition of the super limit element method, the electric field and magnetic field distribution at the port boundary under the normalized modal field is constructed for the port boundary, and the port power and port impedance are calculated. Then, based on the characteristics of the lumped port, the normalized electric field and magnetic field are obtained through the normalized port impedance formula, and on this basis, a complete electromagnetic boundary value problem is established, and the corresponding matrix equation is derived. Finally, the matrix equation is solved, and the S parameter result is read from the solution matrix. Through the method, the application can directly extract the S parameter at the port boundary, avoid the secondary calculation link in the traditional method, ensure the parameter accuracy, and significantly improve the calculation efficiency. Meanwhile, through strict port normalization processing, the application ensures the generality and calculation stability under different port impedance conditions.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic numerical methods, specifically providing a method for calculating the S-parameters of lumped-port normalized impedance based on TFE. Background Technology

[0002] S-parameters are core indicators describing the transmission and reflection characteristics between ports in microwave networks. They play an irreplaceable role in the design and analysis of complex electromagnetic systems such as radio frequency integrated circuits (RFICs), monolithic microwave integrated circuits (MMICs), high-speed interconnect structures, and antenna feed networks. Accurate and efficient calculation of S-parameters is a crucial prerequisite for device performance prediction, system co-simulation, and optimized design. In electromagnetic simulation, the choice of port normalized impedance directly affects the values ​​of S-parameters. To perform matching analysis with the target system, it is usually necessary to obtain S-parameter results based on a specific normalized impedance.

[0003] Currently, the calculation of S-parameters in electromagnetic simulation software mainly relies on full-wave numerical algorithms, such as the finite element method (FEM) and the method of moments (MoM). These methods can accurately simulate the behavior of electromagnetic fields in complex structures by solving Maxwell's equations. The conventional S-parameter calculation process typically begins with a simulation using the software's default characteristic impedance (usually 50 ohms) as a reference to obtain an initial S-parameter matrix. When the user requires S-parameters for other normalized impedances (such as 75 ohms or complex impedances), subsequent mathematical transformations using network parameter conversion formulas are necessary. Therefore, when dealing with arbitrary normalized impedance problems, the above-mentioned technical solutions suffer from error propagation due to indirect process flow. How to avoid error propagation caused by indirect process flow and improve the accuracy of normalized impedance S-parameters is a crucial problem that needs to be solved in the S-parameter calculation process. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the normalized impedance S-parameters of lumped ports based on TFE, in order to solve the problem that existing methods for calculating S-parameters of lumped ports cannot achieve high efficiency and high accuracy. This invention uses the Transfinite Element (TFE) technique in the simulation solution process. Compared with traditional simulation solution methods, it avoids the secondary calculation from non-normalized S-parameters to normalized S-parameters, thereby improving the accuracy of S-parameter calculation.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating the S-parameters of lumped-port normalized impedance based on TFE, characterized by the following steps:

[0007] Step 1: Based on the definition of TFE, construct the electric field at the port boundary. Expressions and magnetic fields expression;

[0008] Step 2, based on the electric field Expressions and magnetic fields The expression calculates the port power and the port impedance;

[0009] Step 3: Based on the lumped port characteristics, obtain the normalized electric field according to the normalized port impedance formula. and magnetic field ;

[0010] Step 4: Apply a first-order absorbing boundary condition to the conductor boundary, and apply the normalized electric field... and magnetic field Establish the electromagnetic boundary value problem and construct the initial finite element matrix equations;

[0011] Step 5: Solve the finite element matrix equations to obtain the solution vector. Based on the definition of TFE, directly read the S-parameters from the solution vector.

[0012] Furthermore, in step 1, the electric field Expressions and magnetic fields The expression is as follows:

[0013] ,

[0014] ,

[0015] in, This represents the total number of edges in the grid. Indicates the number of edges on the port boundary. Describes the basis functions of the finite element method. This represents the coefficient of the m-th edge element; Indicates the number of port intrinsic modes. This represents the coefficient of the nth pattern. This represents the electric field eigenmode of the nth mode; This represents the magnetic field eigenmode of the nth mode. This indicates magnetic field excitation.

[0016] Furthermore, in step 2, the port power is specifically as follows:

[0017] ,

[0018] in, Indicates port power. Indicates the port face;

[0019] The port impedance is specifically , or , respectively represented as:

[0020] ,

[0021] ,

[0022] ,

[0023] in, This represents the port impedance calculated from voltage V and current Ii. The port impedance is used to calculate the current Ii and power P. This represents the port impedance calculated from voltage V and power P. Indicates the electric field integration line on the port. Indicates a port loop. Indicates the port face.

[0024] Furthermore, in step 3, the normalized electric field and magnetic field Specifically:

[0025] ,

[0026] in, Indicates port impedance. This indicates the preset complex reference impedance.

[0027] Furthermore, the specific process of step 4 is as follows:

[0028] According to TFE theory, the electric field and magnetic field Substituting into the weak form of the Helmholtz equation and applying the Galerkin method, For the test function, integration yields the finite element equation:

[0029] ,

[0030] in, Indicates frequency, Indicates permeability, Indicates wave impedance, Represents a unit vector. This represents the internal computational domain of the port model. Represents the relative permittivity. Represents the vacuum permittivity. Represents the imaginary unit;

[0031] Will Combining the equations into a matrix, we get:

[0032] ,

[0033] in, Represents the matrix of the finite element system. Represents the coupling matrix;

[0034] Substituting the normalized electric and magnetic fields, we get Q, Transformed into:

[0035] ,

[0036] Therefore, we can conclude that: ;

[0037] by As a test function, the matrix equation is obtained:

[0038] ,

[0039] in, For the modal system matrix, Represents the identity matrix. Represents the activation vector;

[0040] Substituting the normalized electric and magnetic fields, then , Transformed into:

[0041] ,

[0042] Therefore, we can conclude that: ;

[0043] The final finite element matrix equation is obtained as follows: .

[0044] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0045] This invention provides a method for calculating the S-parameters of lumped-port normalized impedance based on the transfinite element method (TFE). First, based on the definition of the transfinite element method, the electric and magnetic field distributions at the port boundary under a normalized modal field are constructed, and the port power and impedance are calculated. Then, based on the characteristics of the lumped port, the normalized electric and magnetic fields are obtained through the normalized port impedance formula. A complete electromagnetic boundary value problem is then established, and the corresponding matrix equations are derived. Finally, the matrix equations are solved, and the S-parameter results are read from the solution matrix. This method enables direct S-parameter extraction at the port boundary, avoiding the secondary calculation steps in traditional methods, thus ensuring parameter accuracy and significantly improving computational efficiency. Furthermore, the rigorous port normalization process ensures universality and computational stability under different port impedance conditions. Attached Figure Description

[0046] Figure 1This is a flowchart illustrating the method for calculating the S-parameters of lumped-port normalized impedance based on TFE in this invention.

[0047] Figure 2 This is a schematic diagram of the solution domain for the port model of the microwave device in this invention.

[0048] Figure 3 This is a schematic diagram of a patch antenna model in an embodiment of the present invention.

[0049] Figure 4 The diagram shows the S-parameter results obtained by the TFE-based lumped-port normalized impedance S-parameter calculation method in this embodiment of the invention.

[0050] Figure 5 This is an S-parameter error curve obtained by the TFE-based lumped port normalized impedance S-parameter calculation method in this embodiment of the invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0052] This embodiment provides a method for calculating the S-parameters of lumped-port normalized impedance based on TFE, the process of which is as follows: Figure 1 As shown, the specific steps include:

[0053] Step 1: Based on the definition of TFE, construct the electric field at the port boundary. Expressions and magnetic fields expression;

[0054] Suppose a... Figure 2 The port model of the microwave device shown is... Indicates the first-type absorbing boundary. This refers to a port, that is, a disconnect from the outside world, represented by a port. For example, the boundary of the computational domain Simplified to ;

[0055] Assuming the computational domain is discretized using tetrahedral elements, the electric and magnetic fields at the port boundaries are expanded as follows:

[0056] (1)

[0057] (2)

[0058] in, This represents the total number of edges in the grid. Indicates port boundary The number of sides on, Describes the basis functions of the finite element method. This represents the coefficient of the m-th edge element; Indicates the number of port intrinsic modes. This represents the coefficient of the nth pattern. This represents the electric field eigenmode of the nth mode. Indicates electric field excitation; This represents the magnetic field eigenmode of the nth mode. Indicates magnetic field excitation;

[0059] By adding the incident electric field mode to the mode summation, i.e. This allows for the simplification of equations (1) and (2) above. The simplified expressions for the electric and magnetic fields are as follows:

[0060] (3)

[0061] (4)

[0062] Step 2, based on the electric field Expressions and magnetic fields The expression calculates the port power and the port impedance;

[0063] The corresponding port power can be calculated using the electric and magnetic fields obtained above.

[0064] (5)

[0065] in, Indicates port power. Indicates the port face;

[0066] After obtaining the port electric field, magnetic field, and corresponding port power, the corresponding port impedance can be calculated; port impedance is divided into... , , Let V and Ii represent the port impedance calculated using voltage V and current Ii, the port impedance calculated using current Ii and power P, and the port impedance calculated using voltage V and power P, respectively; these can be expressed using the following formulas:

[0067] (6)

[0068] (7)

[0069] (8)

[0070] in, Indicates the electric field integration line on the port. Indicates a port loop. Indicates the port face;

[0071] Step 3: Based on the lumped port characteristics, obtain the normalized electric field according to the normalized port impedance formula. and magnetic field ;

[0072] The lumped port is placed inside the model and has a user-defined complex reference impedance. Typically, it is 50 ohms; to normalize the port impedance to the user-defined value, the port impedance calculated in the previous step needs to be multiplied by a corresponding coefficient, so that the port impedance is... For example, the normalized port impedance is expressed as:

[0073] (9)

[0074] in, Indicates the normalized port impedance. Indicates port impedance, here expressed as port impedance. For example, then ;

[0075] As can be seen above, by scaling the electric field, the port impedance can be normalized to the user-defined value; using the same method, the magnetic field can also be scaled accordingly. The normalized electric and magnetic fields are denoted as:

[0076] (10)

[0077] After normalizing the electric and magnetic fields, the port power remains unchanged:

[0078] (11)

[0079] Step 4: Apply a first-order absorbing boundary condition (ABC) to the conductor boundary, based on the normalized electric field. and magnetic field Establish the electromagnetic boundary value problem and construct the initial finite element matrix equations;

[0080] According to TFE-related theories, the electric field and magnetic field Substituting into the weak form of the Helmholtz equation and applying the Galerkin method, For the test function, integration yields the finite element equation:

[0081] (12)

[0082] in, Indicates frequency, Indicates permeability, Indicates wave impedance, Represents a unit vector. This represents the internal computational domain of the port model. Represents the relative permittivity. Represents the vacuum permittivity. Represents the imaginary unit;

[0083] because The edge elements on the surface have been excluded from the expansion of the electric field vector, therefore in Above The above Combining these equations into a matrix, we can obtain:

[0084] (13)

[0085] in, Represents the matrix of the finite element system. The coupling matrix is ​​represented by the following expression:

[0086] (14)

[0087] (15)

[0088] in, Indicates relative permeability;

[0089] express A vector composed of the coefficients of the edge elements.

[0090] This represents a vector consisting of the modal field expansion coefficients;

[0091] Substituting the normalized electric and magnetic fields obtained in step 3 into equation (13), we get matrix Q and the modal field expansion coefficient vector. Transformed into:

[0092] (16)

[0093] Then equation (13) can be rewritten as:

[0094] (17)

[0095] Using a similar method, the electric field and magnetic field Substituting into the weak form of the Helmholtz equation, As a test function, and integrated over the computational domain, based on the orthogonality of the patterns, the following form can be constructed:

[0096] (18)

[0097] in, This represents the transpose of the coupling matrix. For the modal system matrix, The identity matrix is ​​represented by f; the excitation vector is represented by f, where all elements except the row element corresponding to the excitation mode k are 0, and the non-zero elements take values ​​of 0, ... ;

[0098] The expression is:

[0099] (19)

[0100] Substituting the normalized electric and magnetic fields obtained in step 3 into equation (18), the matrix R and the excitation term f are transformed as follows:

[0101] (20)

[0102] Then equation (18) can be rewritten as:

[0103] (twenty one)

[0104] Combining equations (17) and (21), we obtain the final finite element matrix equation:

[0105] (twenty two)

[0106] Step 5: Solve the finite element matrix equations to obtain the solution vector. Based on the definition of TFE, directly read the S-parameters from the solution vector.

[0107] Solving the above matrix equation yields the solution vector. Assume the excitation port is k, where, The i-th element ( The S-parameter represents the transmission coefficient of the i-th port. ;like According to transmission theory, the S-parameters are... .

[0108] The beneficial effects of the present invention will be explained in detail below with reference to simulation tests.

[0109] This embodiment uses a patch antenna as an example, and the antenna model is as follows: Figure 3 As shown; firstly, based on the definition of the superfinite element method, the port boundary is analyzed, as follows. Figure 2As shown, the electric and magnetic field distributions at the port boundary under normalized modal fields are constructed. Then, the port power is calculated and normalized, and the port impedance characteristics are further calculated. Next, based on the lumped port characteristics, the normalized electric and magnetic field distributions are obtained by calculating the normalized port impedance. Based on this, a complete electromagnetic boundary value problem is established, and the corresponding matrix equation is derived. Finally, by solving this matrix equation, the S-parameter results are directly read from the solution matrix. By comparing the results with those obtained using HFSS fast frequency sweep, and using the finite element method as a comparative example, the S-parameter results and error curves are shown below. Figure 4 , Figure 5 As shown in the figure, the present invention can effectively improve the accuracy of S-parameters by solving the lumped port S-parameters through TFE.

[0110] In summary, based on the above technical solutions, this invention enables the direct extraction of S-parameters at the port boundary, avoiding the secondary calculation step in traditional methods, thus ensuring parameter accuracy and significantly improving computational efficiency. At the same time, this invention ensures universality and computational stability under different port impedance conditions through strict port normalization processing.

[0111] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A method for calculating the S-parameters of lumped-port normalized impedance based on TFE, characterized in that, Includes the following steps: Step 1: Based on the definition of TFE, construct the electric field at the port boundary. Expressions and magnetic fields expression; Step 2, based on the electric field Expressions and magnetic fields The expression calculates the port power and the port impedance; Step 3: Based on the lumped port characteristics, obtain the normalized electric field according to the normalized port impedance formula. and magnetic field ; Step 4: Apply a first-order absorbing boundary condition to the conductor boundary, and apply the normalized electric field... and magnetic field The electromagnetic boundary value problem is established, and the initial finite element matrix equations are constructed. The specific process is as follows: According to TFE theory, the electric field and magnetic field Substituting into the weak form of the Helmholtz equation and applying the Galerkin method, For the test function, , This represents the total number of edges in the grid. The number of edges on the port boundary is represented by the equation, and integration yields the finite element equation: ， in, Indicates frequency, Indicates permeability, Indicates wave impedance, Represents a unit vector. This represents the internal computational domain of the port model. Represents the relative permittivity. Represents the vacuum permittivity. Represents the imaginary unit; Describes the basis functions of the finite element method. This represents the coefficient of the m-th edge element; Indicates the number of port intrinsic modes. This represents the coefficient of the nth pattern. This represents the electric field eigenmode of the nth mode; This represents the magnetic field eigenmode of the nth mode. Indicates magnetic field excitation; Will Combining the equations into a matrix, we get: ， in, Represents the matrix of the finite element system. Represents the coupling matrix; Substituting the normalized electric and magnetic fields, then Q, Transformed into: ， in, Indicates port impedance. Indicates the preset complex reference impedance; Therefore, we can conclude that: ; by As a test function The matrix equation is obtained as follows: ， in, For the modal system matrix, Represents the identity matrix. Represents the activation vector; Substituting the normalized electric and magnetic fields, then , Transformed into: ， Therefore, we can conclude that: ; The final finite element matrix equation is obtained as follows: ; Step 5: Solve the finite element matrix equations to obtain the solution vector. Based on the definition of TFE, directly read the S-parameters from the solution vector.

2. The method for calculating the S-parameters of lumped-port normalized impedance based on TFE according to claim 1, characterized in that, In step 1, the electric field Expressions and magnetic fields The expression is as follows: ， ， in, This represents the total number of edges in the grid. Indicates the number of edges on the port boundary. Describes the basis functions of the finite element method. This represents the coefficient of the m-th edge element; Indicates the number of port intrinsic modes. This represents the coefficient of the nth pattern. This represents the electric field eigenmode of the nth mode; This represents the magnetic field eigenmode of the nth mode. This indicates magnetic field excitation.

3. The method for calculating the S-parameters of lumped-port normalized impedance based on TFE according to claim 2, characterized in that, In step 2, the port power is specifically as follows: ， in, Indicates port power. Indicates the port face; The port impedance is specifically , or , respectively represented as: ， ， ， in, This represents the port impedance calculated from voltage V and current Ii. The port impedance is used to calculate the current Ii and power P. This represents the port impedance calculated from voltage V and power P. Indicates the electric field integration line on the port. Indicates a port loop. Indicates the port face.

4. The method for calculating the S-parameters of lumped-port normalized impedance based on TFE according to claim 3, characterized in that, In step 3, the normalized electric field and magnetic field Specifically: ， in, Indicates port impedance. This indicates the preset complex reference impedance.

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