A rational fraction modeling method for S-parameters based on parallel vector fitting calculation

Abstract

The present invention discloses a method for rational fraction modeling of S parameters based on parallel vector fitting calculations, belonging to the field of integrated circuits and the technical field of inference or counting. The method comprises: starting a corresponding parallel pool according to the number of cores in the operating device, parallel processing of input files, and reading and saving S parameter data into a three-dimensional transfer matrix. An initial order range is set, the transfer matrix and the corresponding order are assigned to each core for vector fitting, initial poles are created, and poles and residues are iteratively calculated based on the initial poles to obtain a corresponding pole-residue model. The model calculation error and K value of each core's final output are calculated, and the model with the smallest K value is selected as the output result. Finally, the output result is verified. If the corresponding error meets the requirements, it is output; if not, the order range is increased, and the above steps are repeated until the error meets the requirements, and the final fitting model is output. This improves the calculation speed of vector fitting, thereby improving the accuracy and operational efficiency of rational fraction modeling of S parameters.

Description

Technical Field

[0001] The present invention belongs to the field of integrated circuits, and in particular relates to an S-parameter rational fraction modeling method based on parallel vector fitting calculation. Background Art

[0002] Actual circuit simulations involve a wide variety of devices. When the operating frequency of a circuit reaches radio frequency, frequency-dependent effects such as eddy currents in conductive materials and relaxation phenomena in dielectrics become increasingly pronounced. These effects ultimately translate into frequency-domain variations in the resistance, inductance, and capacitance matrices within the transient model equations, causing these matrices to change in the frequency domain. In this scenario, traditional lumped circuit elements (such as resistors, inductors, and capacitors) are unable to adequately describe the behavior of these complex devices. As the operating frequencies and signal speeds of modern devices continue to increase, the impact of packaging and interconnects on overall signal integrity becomes increasingly significant, necessitating the characterization of the complex electromagnetic behavior of these complex devices.

[0003] S-parameters (scattering parameters) are network parameters defined based on the relationship between incident and reflected waves. They are typically used to describe signal transmission between ports in a circuit. In circuit simulation, S-parameters are primarily used for frequency-domain analysis and are widely used to describe the frequency response characteristics of passive components (such as capacitors, inductors, and transmission lines). They are typically obtained through electromagnetic field simulation, actual measurements, or physical models. In some circuit simulations, in order to embed passive components into a larger circuit system, it is often necessary to equate them to a subcircuit. However, S-parameters defined in the frequency domain cannot be directly used in time-domain simulations, so S-parameter modeling is necessary.

[0004] Current research focuses on improving modeling efficiency and ensuring the passivity of rational fraction models. To achieve both improved modeling efficiency and improved fitting accuracy, the selection of initial poles must be carefully considered, and fitting issues in the presence of multiple noises must be properly addressed. Furthermore, to accelerate model building, parallel computing techniques are needed to improve modeling efficiency. Summary of the Invention

[0005] This invention aims to overcome the shortcomings of existing technologies and improve modeling efficiency. It provides an S-parameter rational fraction modeling method based on parallel vector fitting. This method creates a parallel computing pool, enabling parallel reading of S-parameters and storing them as a three-dimensional transfer matrix. After setting the initial order range to 5:5n (with a step size of 5), the transfer matrix and order are distributed to each computing core for vector fitting, significantly reducing iteration time while preserving data characteristics. Each core simultaneously creates initial poles, iteratively calculates the residue, and outputs a pole-residual model. Using the zero-frequency S-parameters as constraints, a quadratic programming optimization method is used to reconstruct the state-space model, effectively correcting the model's zero-frequency behavior. The error and K value (order × error) of the DC-corrected model are calculated, and the model with the lowest K value is selected for output. Parallel computing and multiple optimization checks are used to output the optimal result, effectively improving modeling efficiency while ensuring accuracy.

[0006] The present invention adopts the following technical solutions to achieve the above-mentioned purpose:

[0007] The S-parameter rational fraction modeling method based on parallel vector fitting calculation includes the following steps:

[0008] Step 1: Create a parallel pool (including n cores) based on the number of cores n detected on the running device, start n cores to process the input file in parallel, and save the S-parameter data into a three-dimensional transfer matrix.

[0009] Step 2: Set the initial order range and perform task allocation. Assign the transfer matrix generated in step 1 and the corresponding order to the core for vector fitting.

[0010] In step 3, each core simultaneously creates initial poles for the input data, performs pole iteration by solving an overdetermined linear equation Ax=b, calculates the residue, and outputs the final pole-residue model.

[0011] Step 4: Using the zero-frequency S parameters as constraints, perform quadratic programming optimization to adjust the model parameters. By adjusting the parameters of the state-space model, we ensure that its zero-frequency behavior is more accurate.

[0012] Step 5: Based on the output model after DC correction in step 4, analyze the results using the error and K value calculation formula, and select the result with the lowest K value for output.

[0013] Step 6: Verify the optimal output result in step 5. If the error is less than 10%, save and output the fitted model; if the error is greater than 10%, expand the end range and repeat the steps until the final error is less than 10%.

[0014] Preferably, the method of establishing a parallel pool and reading the S parameters in the input file and storing them in the transfer matrix in step 1 is:

[0015] Obtain the number of cores, n, running on the device, start a parallel pool (containing n cores), and perform data distribution preprocessing. Read the input file, iterate through all rows, and call the MATLAB function parpool(n) to start the parallel pool. Use the parfor function to sequentially distribute each row of the file to the cores, assigning n at a time. Store the read S-parameter data into the pre-set 3D transfer matrix.

[0016] Preferably, the method for setting the initial order range and the allocation of parallel processing data tasks in step 2 is:

[0017] Set the initial order range to 5:5n with a step size of 5. Using the parallel pool started in step 1, distribute the transfer matrix containing the S-parameter information and the n increasing orders generated in step 1 to the n cores one by one. Input the transfer matrix H and the corresponding order q into the vector fit function for processing. For S-parameter storage, a two-dimensional transfer matrix of size Nc!*Ns is suitable for vector fitting. For each desired port, the S-parameters for all frequencies are stored in a single row for easy access.

[0018] Preferably, the method for creating initial poles and calculating residues in step 3 of vector fitting is:

[0019] Based on the task allocation in step 2, each core synchronously performs vector fitting on the input transfer matrix, determines the number of poles according to the order of the input, and performs rapid iteration to create the initial poles. Here, within the range of F, q / 2 values ​​are linearly selected as the imaginary part of the pole, and then the real part is generated with a fixed depth (the ratio of the real part to the imaginary part). The resulting complex number and its conjugate total q poles. Here, if q is an odd number, q / 2 is rounded down, and an additional pole needs to be generated. This pole is obtained by averaging the first and last frequency points. Based on the initial poles created, solve an overdetermined linear equation:

[0020]

[0021] Perform pole iteration and solve another overdetermined linear equation based on the poles produced by the last iteration:

[0022]

[0023] The residue is calculated in this way, and the pole-residue model is finally output. to is the frequency point in the complex frequency domain, to For the extreme, to For the remainder, to To introduce the residue of the auxiliary function, to is the S parameter corresponding to the frequency point.

[0024] As an S-parameter rational fraction modeling method based on parallel vector fitting calculation, the method for performing DC verification on the vector fitting model output by each core in step 4 is as follows:

[0025] To make the pole-residue model more accurate at zero frequency, the original model needs to be calibrated. This is typically done by using the zero-frequency S parameters as constraints, using quadratic programming optimization to adjust the model parameters to achieve a more realistic zero-frequency response. The goal of the optimization process is to minimize the error at zero frequency. By adjusting the state-space model parameters, the zero-frequency behavior is ensured to be more accurate.

[0026] As an S-parameter rational fraction modeling method based on parallel vector fitting calculation, the method of calculating the error and K value of the vector fitting model output by each core and selecting the optimal result output in step 5 is as follows:

[0027] Based on the DC check results from step 4, calculate the error and K value for each core's vector fitting model output. K is a set result judgment factor used to determine the balance between error and order of the fitting model. Compare the K values ​​of all cores and save and output the fitting model with the smallest K value.

[0028] As an S-parameter rational fraction modeling method based on parallel vector fitting calculation, the method for verifying the fitting model results and ensuring that the error is less than 10% in step 6 is as follows:

[0029] According to the optimal result finally output in step 5, check whether the corresponding error err is less than 10%, and make the following judgment: if it is less than 10%, output the corresponding fitting model and save it to the output file; if it is greater than 10%, further expand the order range and set it to 5[(m-1)*n+1]:5*m*n (m is the number of times the range is expanded, and the maximum value of m is 10), with a step size of 5, and repeat the above steps until the final result error is less than 10%, then output the corresponding fitting model and save it to the output file.

[0030] The present invention adopts the above technical solution and has the following beneficial effects:

[0031] (1) The present invention proposes an S-parameter rational fraction modeling method based on parallel vector fitting calculation. The method starts a parallel pool containing n cores, performs a pre-processing step for data processing according to the number of cores n of the device, distributes each row of data to the core in turn, and stores it in a three-dimensional transfer matrix. Subsequently, an initial order range is set, and the generated transfer matrix with increasing order is distributed to different cores for vector fitting. When each core processes the data, the number of poles is gradually determined, and rapid iteration is performed to create the initial poles. Subsequently, iterative operations are performed based on these poles to generate a pole-residual model, and a DC check is performed on the model output by each core. The zero-frequency response is adjusted through secondary optimization to make the model more consistent with the actual data. Finally, the model error is confirmed. The above process is repeated for multiple iterations for models with an error greater than 10%. Finally, a rational fraction model with a smaller error is obtained, while significantly improving the efficiency and accuracy of S-parameter modeling.

[0032] (2) The present invention introduces parallel computing in vector fitting calculations and distributes tasks to multiple cores, so that each core can perform vector fitting calculations at the same time. The creation of a parallel pool enables tasks to be distributed according to the number of cores, allowing multiple calculations of increasing orders to be attempted simultaneously. In particular, in DC passivity correction, the model parameters can be adjusted more accurately through the parallel computing of multiple cores to achieve the purpose of optimizing the zero-frequency response. Ultimately, the hardware resources are fully utilized, and the appropriate pole and residual models can be quickly determined. In the face of tasks of different scales, the number of cores can be flexibly adjusted without overall reconstruction of the model. Compared with traditional vector fitting algorithms, the efficiency of S-parameter modeling is improved while also being more flexible. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the S-parameter rational fraction modeling method based on parallel vector fitting calculation of the present invention;

[0034] Figure 2 It is a detailed explanation diagram of the allocation of tasks and parallel processing in the process of reading and processing data in the present invention;

[0035] Figure 3 This is an explanatory diagram of the transfer matrix storage process in vector fitting. The three-dimensional matrix containing S parameters is read from the input file. Nc is the number of ports and Ns is the number of frequency points. The first figure shows the S parameter storage format in the input file. The second figure extracts the S parameters corresponding to each frequency point and converts the stored data size from Nc*Nc to Nc!.

[0036] Figure 4It is a data netlist diagram in the vector fitting process, in spectre format, reflecting the temporary variable values ​​in the calculation process, namely the state space variables G. All values ​​are stored in the form of a matrix;

[0037] Figure 5 This is a schematic diagram of the DC correction process and a comparison of the effects. A three-port input file is used as an example. The constraint in the figure is a constraint.

[0038] Figure 6 This is the final fitting effect diagram, using a 4-port S-parameter file as the input file. The magnitude in the figure is the amplitude, and the frequency is the frequency. DETAILED DESCRIPTION

[0039] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0040] To make the objectives, technical features, and advantages of the present invention more readily apparent, the following detailed description of the specific embodiments of the present invention is provided in conjunction with the accompanying drawings. It is apparent that the embodiments described are only a portion of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative effort should fall within the scope of protection of the present invention.

[0041] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0042] Embodiment: The present invention will be further described below with reference to the accompanying drawings. Figure 1 As shown, including S1~S6.

[0043] S1. Use the MATLAB function feature('numcores') to return the number of processor cores (n) available on the device (including physical and logical cores). Use the parpool function to start a parallel pool (containing n cores) based on this number of cores for data distribution preprocessing. Open the input file, iterate over all rows, and use the parfor function to sequentially allocate each row to n cores at a time. Store the read S-parameter data into the pre-set 3D transfer matrix until all rows have been processed.

[0044] S2. Set the initial order range to 5:5n with a step size of 5, and use the parallel pool started in S1 to distribute tasks. The transfer matrix containing S parameter data generated in S1 and n increasing orders are distributed to n cores one by one through the parfor function for parallel vector fitting processing. Here, the storage method of the transfer matrix is: the transfer matrix suitable for vector fitting is a two-dimensional matrix of size Nc!*Ns. For each required port, the S parameters of all frequency points are saved in one row for easy call. The storage process of the transfer matrix is ​​shown in the attached figure. Figure 3 As shown in the figure, the original vector fitting method reads the transfer function saved from the touchstone file as a three-dimensional matrix of size Nc*Nc*Ns, resulting in a double waste of time and space. However, for small-port input files, data comparison revealed that their S parameters are not symmetrical. Therefore, the S parameters of small-port input files are not processed as described above, and the three-dimensional matrix of size Nc*Nc*Ns is directly saved as the transfer matrix.

[0045] S3, as an S-parameter rational fraction modeling method based on parallel vector fitting calculation, step S3 synchronously performs vector fitting on the input transfer matrix based on the task allocation in S2, determines the number of poles, and quickly iterates to create initial poles. Based on the created initial poles, solve the overdetermined linear equation:

[0046] ,

[0047] Get the residue to By rewriting the fitting model into the form of fractions, the residue can be converted into the form of zero points. In this case, the zero point is the extreme point, thus realizing the extreme point iteration. According to the extreme point generated by the last iteration, another simpler overdetermined linear equation is solved again:

[0048] ,

[0049] Calculate more accurate residues and finally output the pole-residue model.

[0050] S4. In order to make the pole-residue model more accurate at zero frequency, the method of correcting the original model is to use the S parameters of the zero frequency point as constraints, perform quadratic programming, and reconstruct the state space model. The process is shown in the attached figure. Figure 4As shown in Figure 1. The constraints are: Aeq*x=beq, where Aeq = kron(-G.B'*inv(GA)',eye(m)) is a matrix constructed through Kronecker product, relating the system's dynamics to the optimization variables. Beq represents the difference between the desired response and the current model output. By optimizing the variable x (i.e., the vectorized form of the matrix GC), we adjust the model's poles and residues to ensure that the zero-frequency response meets the desired S-parameters. Ultimately, the new pole-residue model derived through quadratic programming more accurately reflects the system's behavior at zero frequency and provides a more reliable low-frequency response.

[0051] S5. For the accuracy analysis of the fitting model, the error formula is set here:

[0052] ,

[0053] A higher order results in more poles in the final fit, making the vector fit model more complex and unfavorable for model call and operation. Therefore, a result judgment factor, K, is set to satisfy the following: K = err * q. The smaller the K value, the better the balance between error and order in the fitting model. Selecting the fitting model corresponding to the smallest K value essentially means finding a vector fit model with small errors and a relatively simple model. Based on the pole-residue model output by each core in S4 after DC calibration, the error and K value corresponding to each model are calculated, compared and judged, and the model with the smallest K value is selected as the final output.

[0054] S6. Based on the optimal output result in S5, check whether the error corresponding to the fitting model is less than 10%. If it is less than 10%, output the corresponding fitting model and save it to the output file. If it is greater than 10%, further expand the order range. The order range satisfies: 5[(m-1)*n+1]:5*m*n (m is the number of times the range is expanded, and the maximum value of m is 10), with a step size of 5. Repeat the above steps until the final result error is less than 10%, and then output the corresponding fitting model and save it to the file.

[0055] The above specific implementation methods and examples are specific support for the technical ideas proposed in the present invention, and cannot be used to limit the scope of protection of the present invention. Any equivalent changes or equivalent modifications made on the basis of the technical solution of the present invention in accordance with the technical ideas proposed in the present invention still fall within the scope of protection of the technical solution of the present invention.

Claims

1. An S-parameter rational fraction modeling method based on parallel vector fitting calculation, characterized in that: The following steps are involved: Step 1: Create a parallel pool according to the number of cores n of the detected running device, where the parallel pool contains n cores, reads the S parameters in the input file in parallel and stores them into a three-dimensional transfer matrix; Step 2: Set the initial order range, assign the transfer matrix generated in step 1 and the corresponding order to the core, and perform parallel vector fitting; Step 3: Each core creates the initial poles for the input data, performs pole iteration, calculates the residue, and outputs the final pole-residual model. Step 4: By setting the S parameters of the zero-frequency point as constraints, perform quadratic programming to reconstruct the state space model and adjust the poles and residues so that the response of the model at zero frequency is as close as possible to the desired S parameters; Step 5: Based on the output model after DC correction in step 4, analyze the results using the error and K value calculation formula, and select the result with the lowest K value for output; Step 6: Verify the optimal output result in step 5. If the error is less than 10%, save and output the fitted model. If the error is greater than 10%, expand the end range and repeat the steps until the final error is less than 10%.

2. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1, characterized in that: The method for creating a parallel pool and parallel processing the S parameter data of the input file in step 1 is as follows: obtaining the number of cores n of the detected running device, starting the parallel pool, where the parallel pool contains n cores, performing data distribution preprocessing, reading the input file, traversing all rows, and distributing each row to the core in sequence, distributing n at a time, and storing the read S parameter data in a set three-dimensional transfer matrix.

3. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1, characterized in that: The method for setting the initial order range and parallel data processing task allocation in step 2 is: setting the initial order range to 5:5n, the step size to 5, and continuing to use the parallel pool started in step 1, and allocating the transfer matrix containing S parameter information and n increasing orders generated in step 1 to n cores one by one for processing operations, that is, vector fitting.

4. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1, characterized in that: The method for creating initial poles and calculating residues in the vector fitting in step three is as follows: based on the task allocation in step two, vector fitting is performed on the input transfer matrix synchronously on each core, the number of poles is determined according to the order of the input, and initial poles are created by rapid iteration. Pole iteration is performed based on the created initial poles, and residues are calculated based on the model generated by the last iteration, and a pole-residue model is output.

5. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1, characterized in that: The method for performing DC calibration on the output models on all cores in step 4 is as follows: In order to make the pole-residue model more accurate at zero frequency, the original model needs to be corrected. Usually, the S parameters of the zero-frequency point are used as constraints to perform quadratic programming optimization to adjust the parameters of the model so that it is more realistic in zero-frequency response. During the optimization process, the goal is to minimize the error at the zero-frequency point. By adjusting the parameters of the state-space model, its zero-frequency behavior is ensured to be more accurate.

6. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1, characterized in that: The method for calculating the error and K value and selecting the optimal model output in step five is: according to the final output model of each core after DC verification in step five, the error and K value of each model fitting are calculated, where the K value is the product of the order and the error, and the fitting model corresponding to the minimum K value is selected as the final output result.

7. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1, characterized in that: The method for verifying the model results in step 5 and ensuring that the error is less than 10% is as follows: based on the optimal output result in step 5, detect whether its error is less than 10%. If it is less than 10%, output the corresponding fitting model and save it to a file; if it is greater than 10%, further expand the order range and set it to 5[(m-1)*n+1]:5*m*n, where m is the number of times the range is expanded, the maximum value of m is 10, and the step size is 5. Repeat the above steps until the final result error is less than 10%, and then output the corresponding fitting model and save it to a file.

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