S parameter rational fraction modeling method based on parallel vector fitting calculation

Abstract

The invention discloses an S parameter rational fraction modeling method based on parallel vector fitting calculation, which belongs to the technical field of integrated circuits and calculation or counting, and comprises the following steps of: starting a corresponding parallel pool according to the core number of running equipment, performing parallel processing on an input file, and reading and storing S parameter data into a three-dimensional transfer matrix. Setting an initial order range, distributing the transfer matrix and the corresponding order to each core for vector fitting, creating an initial pole, and calculating the pole and the residue according to the initial pole in a loop iteration manner to obtain a corresponding pole-residue model; and calculating an error and a K value according to the final output model of each core, and selecting the model with the minimum K value as an output result. And finally, an output result is verified, and if a corresponding error meets a requirement, output is carried out. And if the error does not meet the requirement, the order range is increased, the steps are repeated until the error meets the requirement, and a final fitting model is output, so that the calculation speed of vector fitting is improved, and the precision and the operation efficiency of rational fraction modeling on the S parameter are improved.

Description

Technical Field

[0001] The 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] In actual circuit simulation, various types of devices are involved. When the operating frequency of the circuit reaches radio frequency, frequency-related effects such as eddy current effects in conductive materials and relaxation phenomena in dielectrics become more and more obvious, and eventually become changes in the resistance, inductance and capacitance matrices in the transient model formula in the frequency domain, resulting in changes in the resistance, inductance and capacitance matrices in the frequency domain. In this case, traditional lumped circuit elements (such as resistors, inductors, and capacitors) cannot fully describe the behavior of these complex devices. As the operating frequency and signal speed of modern devices continue to increase, the impact of packaging and interconnection on overall signal integrity becomes more and more important, and the complex electromagnetic behavior of these complex devices must be characterized.

[0003] S parameters (scattering parameters) are network parameters defined based on the relationship between incident waves and reflected waves, and are usually used to describe the signal transmission between ports in a circuit. In circuit simulation, S parameters are mainly used for frequency domain analysis and are widely used to describe the frequency response characteristics of passive devices (such as capacitors, inductors, transmission lines, etc.). They are usually obtained through electromagnetic field simulation, actual measurements, or physical models. In some circuit simulations, in order to embed passive devices 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 for time domain simulation, so S parameters must be modeled.

[0004] The current research focuses on improving modeling efficiency and ensuring the passivity of rational fraction models. In order to improve modeling efficiency and fitting accuracy at the same time, the selection of initial poles must be fully considered and the fitting problem under multi-noise conditions must be properly handled. In addition, in order to accelerate the model building process, parallel computing technology needs to be introduced to improve modeling efficiency. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art, speed up the modeling efficiency, provide an S parameter rational fraction modeling method based on parallel vector fitting calculation, create a parallel calculation pool, realize the parallel reading of S parameters and store them as a three-dimensional transfer matrix, and set the initial order range to 5:5n (step length is 5) on the basis of assigning the transfer matrix and order to each calculation core for vector fitting, thereby significantly reducing the iteration time under the premise of retaining the data characteristics. Each core synchronously creates the initial pole, iteratively calculates the residue and outputs the pole-residual model, and uses the zero-frequency S parameter as a constraint to optimize the reconstruction of the state space model through quadratic programming, which effectively corrects the zero-frequency behavior of the model. By calculating the error and K value (order × error) of the DC corrected model, the one with the lowest K value is selected for output, and the optimal result is output by using parallel calculation and multiple optimization verification, effectively improving the modeling efficiency while ensuring accuracy.

[0006] The present invention adopts the following technical solutions to achieve the above-mentioned invention object: The S-parameter rational fraction modeling method based on parallel vector fitting calculation includes the following steps: Step 1: Create a parallel pool (including n cores) based on the detected number of cores n of the running device, start the n cores to process the input file in parallel, and save the S parameter data into a three-dimensional transfer matrix.

[0007] Step 2: Set the initial order range and perform task allocation. Allocate the transfer matrix generated in step 1 and the corresponding order to the core for vector fitting.

[0008] 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.

[0009] Step 4: Use the zero-frequency S parameters as constraints to perform quadratic programming optimization to adjust the model parameters. By adjusting the parameters of the state-space model, its zero-frequency behavior is ensured to be more accurate.

[0010] Step 5: Based on the output model after DC correction in step 4, analyze the results through the error and K value calculation formula, and select the result with the lowest K value for output.

[0011] 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%.

[0012] 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: Get the number of cores n of the running device, start the parallel pool (including n cores), and perform data distribution preprocessing. Read the input file, traverse all lines, call the parpool(n) function in the matlab language to start the parallel pool, and use the parfor function to distribute each line of the above file to the core in sequence, each time n cores are distributed, and the read S parameter data is stored in the set three-dimensional transfer matrix.

[0013] Preferably, the method for setting the initial order range and the allocation of parallel processing data tasks in step 2 is: Set the initial order range to 5:5n, the step size to 5, and continue to use the parallel pool started in step 1. The transfer matrix containing S parameter information generated in step 1 and n increasing orders are distributed to n cores one by one. Input the transfer matrix H and the corresponding order q into the vector fitting function for processing. For the storage of S parameters, 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 its frequency points are saved in one row for easy call.

[0014] Preferably, the method for creating initial poles and residue calculation in the vector fitting in step 3 is: 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 input order, and performs fast 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), and the obtained 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:

[0015] Perform pole iteration and solve another overdetermined linear equation based on the poles produced by the last iteration:

[0016] The residue is calculated in this way, and finally the pole-residue model is output. to is the frequency point in the complex frequency domain, to For the extreme point, to For the remainder, to To introduce the residue of the auxiliary function, to is the S parameter corresponding to the frequency point.

[0017] As an S-parameter rational fraction modeling method based on parallel vector fitting calculation, the method of performing DC verification on the vector fitting model output by each core 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 at the zero frequency point are used as constraints to perform quadratic programming optimization to adjust the parameters of the model to make it more realistic in zero-frequency response. During the optimization process, the goal is to minimize the error at the zero frequency point and ensure that its zero-frequency behavior is more accurate by adjusting the parameters of the state-space model.

[0018] 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: According to the output results after DC verification in step 4, calculate the error and K value of the vector fitting model output by each core. The K value is the set result judgment factor, which is used to judge the balance of the fitting model for error and order. Compare the K values ​​of all cores, save and output the fitting model with the smallest K value.

[0019] As an S-parameter rational fraction modeling method based on parallel vector fitting calculation, the method of checking the fitting model results and ensuring that the error is less than 10% in step 6 is: According to the optimal result finally output in step five, 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 in 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%, and then output the corresponding fitting model and save it in the output file.

[0020] The present invention adopts the above technical solution and has the following beneficial effects: (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 preprocessing 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, and the above process is repeated for multiple iterations for models with errors greater than 10%. Finally, a rational fraction model with a smaller error is obtained, and the efficiency and accuracy of S-parameter modeling are significantly improved.

[0021] (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 parallel computing of multiple cores to achieve the purpose of optimizing the zero-frequency response. Ultimately, the hardware resources can be fully utilized to quickly determine the appropriate pole and residual model. In the face of tasks of different scales, the number of cores can be flexibly allocated without overall reconstruction of the model. Compared with the traditional vector fitting algorithm, it improves the efficiency of S-parameter modeling while also being more flexible. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] 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; 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; Figure 3 It is an explanatory diagram of the transfer matrix storage process in vector fitting. It reads the three-dimensional matrix containing S parameters in the input file. Nc is the number of ports and Ns is the number of frequency points. The first figure is the storage form of S parameters in the input file. The second figure extracts the S parameters corresponding to each frequency point and converts it from storing Nc*Nc data to storing Nc! data. Figure 4 It is a data netlist diagram in the vector fitting process, in the format of spectre, which reflects the temporary variable values ​​in the calculation process, that is, the state space variable G. All values ​​are stored in the form of a matrix; Figure 5This is a schematic diagram of the DC correction process and a comparison of the effects, taking a three-port input file as an example, where constraint is a constraint; Figure 6 This is the final fitting effect diagram, with 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

[0023] The present invention will be further explained below in conjunction with 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.

[0024] In order to make the purpose, technical features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should belong to the protection scope of the present invention.

[0025] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and 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.

[0026] Embodiment: The present invention is further described below in conjunction with the accompanying drawings. Figure 1 As shown, including S1~S6.

[0027] S1. Use the feature('numcores') function in the matlab language to return the number of processor cores n (including physical cores and logical cores) available on the running device, and use the parpool function to start a parallel pool (including n cores) based on this number of cores n for data distribution preprocessing. Open the input file, traverse all rows, and use the parfor function to distribute each row to the core in sequence, distributing n cores each time, and store the read S parameter data into the set three-dimensional transfer matrix until all rows are processed.

[0028] S2. Set the initial order range to 5:5n and the step size to 5. Use the parallel pool started in S1 to allocate tasks. The transfer matrix containing S parameter data generated in S1 and n increasing orders are allocated to n cores one by one through the parfor function for parallel vector fitting. 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 original vector fitting method, the transfer function saved by reading the touchstone file is a three-dimensional matrix of size Nc*Nc*Ns, which causes a double waste of time and space. For the small port input file, after data comparison, it is found that its S parameters are not symmetrical. Therefore, the S parameters of the small port input file are not processed as above, and the three-dimensional matrix of size Nc*Nc*Ns is directly saved to the transfer matrix.

[0029] 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 creates initial poles through rapid iteration. Based on the created initial poles, solve the overdetermined linear equation: , 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 pole, thus realizing pole iteration. According to the pole generated by the last iteration, another simpler overdetermined linear equation is solved again: , Calculate more accurate residues and finally output the pole-residue model.

[0030] 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 at zero frequency as constraints, perform quadratic programming, and reconstruct the state space model. The process is shown in the attached figure. Figure 4As shown. The constraints are: Aeq*x=beq, where Aeq = kron(-G.B'*inv(GA)',eye(m)) is a matrix constructed by Kronecker product, which relates the dynamic relationship of the system to the optimization variables. And beq represents the difference between the expected response and the current model output. By optimizing the variable x (i.e., the vectorized form of the matrix GC), we adjust the poles and residues of the model to ensure that the response at zero frequency meets the expected S parameters. Ultimately, the new pole-residue model obtained by quadratic programming can more accurately reflect the behavior of the system at zero frequency and provide more reliable low-frequency response.

[0031] S5. For the accuracy analysis of the fitting model, the error formula is set here: , The higher the order, the more poles will be generated by the final fitting, and the vector fitting model will be more complex, which is not conducive to the call and operation of the model. Therefore, the result judgment factor K is set to satisfy: K=err*q. The smaller the K value, the better the balance between the error and the order of the fitting model. Selecting the fitting model corresponding to the smallest K value is to find a vector fitting model with a small error and relatively simple. Based on the pole-residue model output by each core in S4 after DC verification, calculate the error and K value corresponding to each model, compare and judge, and select the model with the smallest K value as the final result output.

[0032] 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 in the output file; if it is greater than 10%, further expand the order range, and 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), the step length 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 in the file.

[0033] The above specific implementation methods and examples are specific supports for the technical ideas proposed in the present invention, and cannot be used to limit the protection scope 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, creating a parallel pool according to the number of cores n of the detected running device, wherein the parallel pool contains n cores, and 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 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 parameter of the zero frequency point as a constraint, the state space model is reconstructed by performing quadratic programming, and the poles and residues are adjusted so that the response of the model at zero frequency is as close as possible to the expected S parameter; Step 5: Based on the output model after DC correction in step 4, analyze the results through 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: obtaining the number of cores n of the detected running device, starting the parallel pool, wherein 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 into the set three-dimensional transfer matrix.

3. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1 is 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, namely vector fitting.

4. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1 is characterized in that: The method for creating initial poles and residue calculation in the vector fitting of 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 is characterized in that: The method of performing DC verification 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 by taking the S parameters of the zero-frequency point as constraints and performing quadratic programming optimization to adjust the parameters of the model so that it is more in line with reality in terms of zero-frequency response. During the optimization process, the goal is to minimize the error of the zero-frequency point, and by adjusting the parameters of the state-space model, ensure that its zero-frequency behavior is more accurate.

6. The S-parameter rational fraction modeling method based on parallel vector fitting calculation according to claim 1 is 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, and 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 is 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 in 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 in a file.

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