A method for fast calculating broadband electromagnetic performance of microstrip line and microstrip-like two-port structure

Abstract

This invention discloses a rapid calculation method for the broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures. It relates to the fields of electromagnetic calculation and electromagnetic compatibility-aided design technology, and includes: acquiring and preprocessing the layout data of the microstrip port conductor to be tested, generating a binary layout image; inputting the binary layout image into a pre-trained convolutional neural network, outputting a real-valued encoded prediction vector of the complex mode eigenvalues ​​of the dominant mode at a preset sampling frequency; denormalizing and decoding the prediction vector to obtain complex mode eigenvalue samples; identifying the complex mode eigenvalue samples based on a second-order analytical model and analytically extending them to obtain the broadband modal impedance of the target frequency band; obtaining the port impedance matrix according to the reconstruction relationship, and converting and outputting broadband scattering parameters and electromagnetic performance results. This invention can significantly reduce the computational overhead of full-wave frequency sweep and improve the simulation efficiency of microstrip lines and the iteration speed of EMC design.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic calculation and electromagnetic compatibility-aided design technology, and more specifically to a method for rapid calculation of the broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures. Background Technology

[0002] Microstrip lines and microstrip-like structures are widely used in high-speed interconnects on printed circuit boards, RF front-ends, and microwave passive devices. In engineering design, it is usually necessary to evaluate their impedance matching, insertion loss, and resonance characteristics over a wide frequency band. In the EMC design phase, these electromagnetic properties often directly affect the system's transmission, reflection, and out-of-band leakage of interference energy. Therefore, it is necessary to conduct broadband electromagnetic evaluation and screening of a large number of layout variants.

[0003] Traditional methods typically rely on full-wave electromagnetic simulation for dense frequency scanning to obtain broadband Z / S parameters. However, this process is computationally expensive and time-consuming during parameter scanning, structural topology variant selection, and optimization iteration. On the other hand, some surrogate models rely on manual low-dimensional parameterization, which is difficult to cover irregular corners, stepped impedance segments, gradient segments, and complex suppression structures in actual layouts. Directly predicting the full-band port response, on the other hand, leads to high output dimensionality, unstable training, and difficulty in ensuring physical consistency.

[0004] Existing research has proposed a broadband fast reconstruction approach based on analytical extension of modal eigenvalues: extracting modal eigenvalues ​​of the port impedance matrix at a small number of frequency points, extending the modal eigenvalues ​​to the full frequency range through an analytical model of the equivalent circuit, and then reconstructing the port parameters. However, this type of method still requires accurate modal eigenvalue samples at the sampling frequency points; if sampling point data is still obtained through full-wave simulation, there is still a significant computational overhead when screening a large number of layout variants.

[0005] Therefore, there is a need to design a fast electromagnetic calculation method that can take the layout as a direct input, avoid the dependence on full-wave solution of sampling points, and quickly reconstruct the broadband response based on only a small amount of frequency information. Summary of the Invention

[0006] In view of this, the present invention provides a method for rapid calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures. This method can maintain the accuracy of broadband prediction while significantly reducing the computational overhead of traditional full-wave broadband frequency scanning during the EMC design and evaluation of microstrip lines and microstrip-like structures, thereby enabling rapid calculation and screening of broadband electromagnetic performance of microstrip structures.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A fast calculation method for the broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures includes: Step 1: Acquire the conductor layout data of the microstrip port structure under test and preprocess it to generate a binary layout image; Step 2: Input the binary layout image into the pre-trained convolutional neural network, and output the real-valued encoded prediction vector of the complex modal feature values ​​of the dominant mode at the preset sampling frequency point; Step 3: Perform inverse normalization and decoding on the real-number encoded prediction vector to obtain the complex mode feature value samples of the dominant mode at the sampling frequency point; Step 4: Based on the second-order analytical model, perform parameter identification and analytical extension on the complex modal eigenvalue samples to obtain the broadband modal impedance at any frequency point within the target frequency band; Step 5: Based on the reconstruction relationship between broadband modal impedance and port quantities, reconstruct the port impedance matrix in the target frequency band, and obtain broadband scattering parameters from the port impedance matrix. Output the broadband scattering parameters to obtain the broadband electromagnetic performance calculation results.

[0008] Preferably, the preprocessing of the conductor layout data includes: embedding the top metal conductor layout of the microstrip port structure to be tested into a fixed design window, and discretizing it into a single-channel binary image of a fixed size on a uniform grid to obtain a binary layout image. The pixel values ​​of the binary layout image are 0 or 1, which are used to indicate whether there is a metal conductor in the corresponding grid cell.

[0009] Preferably, step 2 specifically includes: Construct and use a pre-trained convolutional neural network, taking the binary layout image as input, to predict the complex modal feature values ​​of at least two dominant modes at preset sampling frequency points. , Where n is the modal index. Sampling frequency; Each complex modal feature value of the output of the pre-trained convolutional neural network is jointly encoded with logarithmic magnitude and phase information, and converted into a value containing... The phase information is encoded in real numbers, and the encoding results of all modes and all sampling frequencies are concatenated into a real-number encoded prediction vector.

[0010] Preferably, the phase information adopts and It means that, among them The phase angle of the complex modal feature value of the dominant mode at the sampling frequency point is used; the real number encoded prediction vector is standardized and destandardized according to the training set statistics to obtain the complex modal feature value sample of the dominant mode at the sampling frequency point.

[0011] Preferably, a second-order analytical model equation is established based on the complex modal eigenvalue samples, and the parameters of the second-order analytical model equation are solved to obtain the broadband modal eigenvalues ​​or broadband modal impedances at any frequency point within the target frequency band.

[0012] Preferably, the parameters for solving the second-order analytical model equations specifically include: The equivalent inductance or capacitance parameters are determined based on the imaginary part approximation equation, and then the equivalent resistance or conductance parameters are linearly solved using the real part approximation equation, as shown in the following expression: Approximate expression for the admittance of cascaded sub-blocks:

[0013] Approximate expression for the impedance of parallel sub-blocks:

[0014] in, For the first The modality of the first Equivalent admittance of each cascaded sub-block; For the first The modality of the first The equivalent impedance of each parallel sub-block; Angular frequency; , , , These are the equivalent resistance, equivalent inductance, equivalent conductance, and equivalent capacitance parameters of the corresponding sub-blocks; Analytical calculation of bandwidth at any frequency point This allows us to obtain broadband modal eigenvalues ​​or broadband modal impedances.

[0015] Preferably, step 5 specifically includes: Based on the reconstruction relationship between modal and port quantities, broadband is utilized. and the corresponding eigenvector matrix Reconstruct the port impedance matrix within the target frequency band The scattering parameters are obtained through the standard transformation relationship. The expression is as follows: Port impedance matrix at sampling frequency The modal decomposition is as follows: ; ; in, The eigenvector matrix, The characteristic value of modal impedance, To sample frequency Place and No. Eigenvectors corresponding to the modal impedance eigenvalues; Output port impedance matrix and scattering parameters Broadband electromagnetic performance indicators used for rapid evaluation of return loss, insertion loss, impedance matching degree, and resonant peak location and amplitude.

[0016] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for fast calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures, with the following beneficial effects: 1. Using fixed-size binary layout images as a unified input reduces the dependence on fixed topology and manual low-dimensional parameterization, and adapts to multiple microstrip structure variants (such as uniform microstrip lines, gradient microstrip structures, microstrip low-pass filter structures, etc.). 2. Neural networks only need to predict modal feature values ​​at a small number of sampling frequency points (and use...) Encoding reduces regression difficulty, and the output dimension is significantly reduced, which is conducive to stable training and points to the more physically meaningful intermediate quantity of "modality". 3. Second-order eigenvalue analytical extension uses a second-order equivalent RLC analytical model to analytically reconstruct modal eigenvalues / modal impedances across the entire frequency band, which can obtain the Z / S parameters of the ports across the entire frequency band with extremely low computational cost, avoiding traditional dense frequency scanning; 4. It is particularly suitable for rapid pre-evaluation and scheme selection in the EMC design phase, which can significantly reduce the number of repeated full-wave simulations and the overall iteration cycle. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 The method flowchart provided by the present invention.

[0019] Figure 2 A schematic diagram of the microstrip structure conductor layout and its binary image representation provided by the present invention.

[0020] Figure 3 This is a schematic diagram of the structure of the convolutional neural network for regressing modal feature value encoding vectors from binary layout images, as provided by the present invention.

[0021] Figure 4 This is a schematic diagram of parameter identification and broadband reconstruction of the second-order eigenvalue analytical extension AEE provided by the present invention.

[0022] Figure 5 This is a schematic diagram comparing broadband S-parameters in the embodiments provided by the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] This invention is particularly applicable to the EMC-aided design of microstrip interconnect / suppression structures on printed circuit boards for power electronic controllers (domain controllers) in new energy vehicles. It relates to a method for rapidly calculating the broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures. Specifically, it involves: discretizing the microstrip conductor layout into a fixed-size binary image; using a convolutional neural network to predict the complex modal eigenvalues ​​(modal impedance eigenvalues) of the dominant mode at a preset small number of sampling frequencies; and combining this with second-order eigenvalue analytic extension (AEE) to perform broadband analytical reconstruction of the modal eigenvalues, thereby rapidly obtaining broadband port impedance parameters and scattering parameters.

[0025] Example 1: This invention discloses a method for rapidly calculating the broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures, including: Step 1: Acquire the conductor layout data of the microstrip port structure under test and preprocess it to generate a binary layout image; Step 2: Input the binary layout image into the pre-trained convolutional neural network, and output the real-valued encoded prediction vector of the complex modal feature values ​​of the dominant mode at the preset sampling frequency point; Step 3: Perform inverse normalization and decoding on the real-number encoded prediction vector to obtain the complex mode feature value samples of the dominant mode at the sampling frequency point; Step 4: Based on the second-order analytical model, perform parameter identification and analytical extension on the complex modal eigenvalue samples to obtain the broadband modal impedance at any frequency point within the target frequency band; Step 5: Based on the reconstruction relationship between broadband modal impedance and port quantities, reconstruct the port impedance matrix in the target frequency band, and obtain broadband scattering parameters from the port impedance matrix. Output the broadband scattering parameters to obtain the broadband electromagnetic performance calculation results.

[0026] Specifically, the preprocessing of the conductor layout data includes: embedding the top metal conductor layout of the microstrip port structure under test into a fixed design window, and discretizing it into a single-channel binary image of a fixed size on a uniform grid, thereby avoiding reliance on manual low-dimensional parameterization; obtaining a binary layout image, wherein the pixel value of the binary layout image is 0 or 1, which is used to indicate whether there is a metal conductor in the corresponding grid cell.

[0027] Specifically, step 2 includes: Construct and use a pre-trained convolutional neural network, taking the binary layout image as input, to predict the complex modal feature values ​​of at least two dominant modes at preset sampling frequency points. , Where n is the modal index. Sampling frequency; Each complex modal feature value of the output of the pre-trained convolutional neural network is jointly encoded with logarithmic magnitude and phase information, and converted into a value containing... The phase information is encoded in real numbers, and the encoding results of all modes and all sampling frequencies are concatenated into a real-number encoded prediction vector.

[0028] Specifically, the phase information adopts and It means that, among them The phase angle of the complex modal feature value of the dominant mode at the sampling frequency point is used; the real number encoded prediction vector is standardized and destandardized according to the training set statistics to obtain the complex modal feature value sample of the dominant mode at the sampling frequency point.

[0029] In a specific embodiment of the present invention, in order to reduce the difficulty of complex regression and avoid the influence of phase jump, this embodiment preferably adopts the following real number encoding (writing complex numbers as...). ):

[0030] The encoding results of all modalities and all sampling frequencies are concatenated to form the network output vector, and the components are standardized / de-standardized according to the statistics of the training set.

[0031] Specifically, a second-order analytical model equation is established based on the complex modal eigenvalue samples, and the parameters of the second-order analytical model equation are solved to obtain the broadband modal eigenvalues ​​or broadband modal impedances at any frequency point within the target frequency band.

[0032] Specifically, the parameters for solving the second-order analytical model equations include: The equivalent inductance or capacitance parameters are determined based on the imaginary part approximation equation, and then the equivalent resistance or conductance parameters are linearly solved using the real part approximation equation, as shown in the following expression: Approximate expression for the admittance of cascaded sub-blocks:

[0033] Approximate expression for the impedance of parallel sub-blocks:

[0034] in, For the first The modality of the first Equivalent admittance of each cascaded sub-block; For the first The modality of the first The equivalent impedance of each parallel sub-block; Angular frequency; , , , These are the equivalent resistance, equivalent inductance, equivalent conductance, and equivalent capacitance parameters of the corresponding sub-blocks; Analytical calculation of bandwidth at any frequency point This allows us to obtain broadband modal eigenvalues ​​or broadband modal impedances.

[0035] In a specific embodiment of the present invention, sparse mode samples at sampling frequency points are... A second-order AEE equivalent circuit analytical model is used for broadband extension. AEE classifies modes into C-type and L-type based on their low-frequency behavior, and characterizes their frequency behavior using series / parallel RLC forms respectively. Preferably, the first-order model can be expressed as: C-type (tandem RLC form):

[0036] L-type (parallel RLC configuration):

[0037] in R, L, G, and C are equivalent parameters.

[0038] To accommodate wider frequency bands and situations involving multi-resonance behavior, this invention preferably employs a second-order model consisting of two RLC sub-blocks. Expressed in N-order generalization form (preferably N=2 in this invention): C-type (Nth-order series model, equivalent admittance superposition):

[0039] L-type (Nth-order parallel model, equivalent impedance superposition):

[0040] Considering the common frequency-dependent behavior of conductor and dielectric losses, the following form is preferred to reduce unknowns and improve stability:

[0041] Parameter extraction and extension strategy: in small loss approximation Under these conditions, the imaginary part approximation relation can be used to solve the problem first. And then Given the real part, establish a linear equation and solve it. Correspondingly, the imaginary / real part of the second-order model sub-block can be approximated as follows (used for constructing the equation "imaginary part determines LC, real part solves RG"): Series subblock admittance approximation:

[0042] Approximate impedance of parallel sub-blocks:

[0043] Therefore, second-order AEE parameter identification can be completed with only a small number of sampling frequencies, and the bandwidth can be analytically calculated for any frequency. This allows us to obtain broadband modal eigenvalues ​​or broadband modal impedances.

[0044] Specifically, step 5 includes: Based on the reconstruction relationship between modal and port quantities, broadband is utilized. and the corresponding eigenvector matrix Reconstruct the port impedance matrix within the target frequency band The scattering parameters are obtained through the standard transformation relationship. The expression is as follows: Port impedance matrix at sampling frequency The modal decomposition is as follows: ; ; in, The eigenvector matrix, The characteristic value of modal impedance, To sample frequency Place and No. Eigenvectors corresponding to the modal impedance eigenvalues; Output port impedance matrix and scattering parameters Broadband electromagnetic performance indicators used for rapid evaluation of return loss, insertion loss, impedance matching degree, and resonant peak location and amplitude.

[0045] Example 2

[0046] like Figures 1-4 As shown, this embodiment provides a fast method for calculating the broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures. The method includes offline dataset construction and network training, as well as online fast inference and broadband reconstruction.

[0047] (a) Graphical representation of the map

[0048] A top-level metal conductor layout of the microstrip structure to be evaluated is obtained. This layout is then embedded into a preset rectangular design window and discretized according to a preset grid resolution to generate a fixed-size binary layout image. The pixel values ​​of the binary image are used to indicate whether a metal conductor exists in the corresponding grid cell. This binary image is then used as input to a subsequent convolutional neural network.

[0049] To improve the stability of network training and inference, the input image can be normalized according to the global mean and standard deviation of the training set.

[0050] (II) Construction of Training Data and Supervised Labels

[0051] For multiple sets of different microstrip structure samples (e.g., uniform microstrip transmission lines, graded microstrip structures, microstrip low-pass filter structures, etc.), full-wave electromagnetic simulation is used to obtain the two-port scattering parameters of each sample in the target frequency band. The port impedance matrix is ​​obtained by standard transformation. In a preset set of a small number of sampling frequency points Take the corresponding port impedance matrix. And solve its eigenvalue problem to obtain the modal impedance eigenvalues ​​(also known as modal impedance intrinsic values) of the two dominant modes:

[0052] in The characteristic value of the complex modal impedance. This represents the corresponding modal current eigenvector.

[0053] The real and imaginary parts of the two modal feature values ​​at the sampling frequency point are concatenated in a fixed order to form the supervision label vector, as shown in the following expression: (III) Label Encoding and Network Training To avoid training instability caused by direct regression of complex numbers, this embodiment uses each complex modal feature value... The encoding is a triple of "logarithmic amplitude + phase sine and cosine", that is:

[0054] The target vector (dimension is proportional to the number of sampling frequencies) is obtained by concatenating the two modes and all sampling frequencies, and the components of each dimension are standardized according to the statistics of the training set.

[0055] Convolutional neural networks are constructed, with a single-channel binary image as input. The network consists of a convolutional feature extraction backbone and two regression output heads: after extracting geometric features through a shared backbone, the two regression heads output two modalities at all sampling frequencies. The encoding amount; the two outputs are concatenated to form the final prediction vector. During training, regression loss functions such as SmoothL1 Loss are used, and the optimizer can be Adam. Early stopping based on the validation set loss can be performed to obtain a model with better generalization performance.

[0056] (iv) Online inference: Directly predict modal eigenvalue samples at sampling frequency points from the layout.

[0057] During the inference phase, only a binary layout image of the new microstrip structure to be evaluated needs to be input. The input image is normalized according to the mean and standard deviation from the training phase and then fed into the convolutional neural network to obtain the predicted normalized encoding vector. Denormalization is then performed on this vector, and it is decoded according to the encoding rules to recover the complex eigenvalue samples of the two modes at the sampling frequency points. .

[0058] (v) Second-order AEE: Identifying the modal equivalent circuit parameters from the sampling points and reconstructing the full frequency response analytically.

[0059] Input the two modal eigenvalue sampling points obtained in step (iv) into the second-order eigenvalue analytical extension (AEE) module.

[0060] Second-order AEE classifies modes into two categories based on their low-frequency behavior: C-type (capacitive) mode: Low-frequency capacitive dominance, which can be represented by a second-order series RLC modal equivalent circuit; L-type (inductive) mode: dominated by low-frequency inductance, which can be represented by a second-order parallel RLC mode equivalent circuit.

[0061] For each mode, AEE is based on the sampling frequency point. The imaginary part characteristics are used to identify reactance-related parameters (such as equivalent L / C parameters), and loss-related parameters (such as R / G parameters) are obtained through linear solutions, thus yielding the set of second-order equivalent circuit parameters for this mode. Subsequently, the broadband eigenvalues ​​of this mode can be calculated analytically at any frequency point in the target frequency band. This enables efficient extension and reconstruction from sparse sampling points to the full frequency range.

[0062] (vi) Reconstruct port parameters and output broadband electromagnetic performance

[0063] Obtaining the broadband eigenvalues ​​of two modes Then, based on the mode decomposition relation, the modal quantities are reconstructed into a port impedance matrix. The scattering parameters are then obtained by standard transformation. The final output bandwidth is... or It is used to quickly evaluate broadband electromagnetic performance indicators such as return loss, insertion loss, impedance matching degree, and resonant peak of microstrip structures, thereby reducing the computational overhead of traditional full-wave dense frequency scanning and improving the efficiency of scheme selection in the EMC design stage.

[0064] (vii) Comparative verification

[0065] To verify the broadband reconstruction effect of this invention, the broadband output of this embodiment can be used. Broadband obtained from full-wave electromagnetic simulation Compare, such as Figure 5 As shown, the consistency of amplitude and phase, as well as the degree of matching of key resonant behaviors, are evaluated.

[0066] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0067] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for rapid calculation of the broadband electromagnetic properties of microstrip lines and microstrip-like two-port structures, characterized in that, include: Step 1: Acquire the conductor layout data of the microstrip port structure under test and preprocess it to generate a binary layout image; Step 2: Input the binary layout image into the pre-trained convolutional neural network, and output the real-valued encoded prediction vector of the complex modal feature values ​​of the dominant mode at the preset sampling frequency point; Step 3: Perform inverse normalization and decoding on the real-number encoded prediction vector to obtain the complex mode feature value samples of the dominant mode at the sampling frequency point; Step 4: Based on the second-order analytical model, perform parameter identification and analytical extension on the complex modal eigenvalue samples to obtain the broadband modal impedance at any frequency point within the target frequency band; Step 5: Based on the reconstruction relationship between broadband modal impedance and port quantities, reconstruct the port impedance matrix in the target frequency band, and obtain broadband scattering parameters from the port impedance matrix. Output the broadband scattering parameters to obtain the broadband electromagnetic performance calculation results.

2. The method for rapid calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures according to claim 1, characterized in that, The preprocessing process for the conductor layout data includes: embedding the top metal conductor layout of the microstrip port structure under test into a fixed design window, and discretizing it into a single-channel binary image of a fixed size on a uniform grid to obtain a binary layout image. The pixel values ​​of the binary layout image are 0 or 1, which are used to indicate whether there is a metal conductor in the corresponding grid cell.

3. The method for rapid calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures according to claim 1, characterized in that, Step 2 specifically includes: Construct and use a pre-trained convolutional neural network, taking the binary layout image as input, to predict the complex modal feature values ​​of at least two dominant modes at preset sampling frequency points. , Where n is the modal index, Sampling frequency; Each complex modal feature value of the output of the pre-trained convolutional neural network is jointly encoded with logarithmic magnitude and phase information, and converted into a value containing... The phase information is encoded in real numbers, and the encoding results of all modes and all sampling frequencies are concatenated into a real-number encoded prediction vector.

4. The method for rapid calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures according to claim 3, characterized in that, The phase information is adopted and It means that, among them The phase angle of the complex modal feature value of the dominant mode at the sampling frequency point is used; the real number encoded prediction vector is standardized and destandardized according to the training set statistics to obtain the complex modal feature value sample of the dominant mode at the sampling frequency point.

5. The method for rapid calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures according to claim 4, characterized in that, Based on the complex modal eigenvalue samples, a second-order analytical model equation is established, and the parameters of the second-order analytical model equation are solved to obtain the broadband modal eigenvalues ​​or broadband modal impedances at any frequency point within the target frequency band.

6. The method for rapid calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures according to claim 5, characterized in that, The specific parameters for solving the second-order analytical model equations include: The equivalent inductance or capacitance parameters are determined based on the imaginary part approximation equation, and then the equivalent resistance or conductance parameters are linearly solved using the real part approximation equation, as shown in the following expression: Approximate expression for the admittance of cascaded sub-blocks: Approximate expression for the impedance of parallel sub-blocks: in, For the first The modality of the first Equivalent admittance of each cascaded sub-block; For the first The modality of the first The equivalent impedance of each parallel sub-block; Angular frequency; , , , These are the equivalent resistance, equivalent inductance, equivalent conductance, and equivalent capacitance parameters of the corresponding sub-blocks; Analytical calculation of broadband at any frequency point This allows us to obtain broadband modal eigenvalues ​​or broadband modal impedances.

7. The method for rapid calculation of broadband electromagnetic performance of microstrip lines and microstrip-like two-port structures according to claim 6, characterized in that, Step 5 specifically includes: Based on the reconstruction relationship between modal and port quantities, broadband is utilized. and the corresponding eigenvector matrix Reconstruct the port impedance matrix within the target frequency band The scattering parameters are obtained through the standard transformation relationship. The expression is as follows: Port impedance matrix at sampling frequency The modal decomposition is as follows: ； ； in, The eigenvector matrix, The characteristic value of modal impedance, To sample frequency Place and No. Eigenvectors corresponding to the modal impedance eigenvalues; Output port impedance matrix and scattering parameters Broadband electromagnetic performance indicators used for rapid evaluation of return loss, insertion loss, impedance matching degree, and resonant peak location and amplitude.

Images