A method for estimating the order of S-parameter fitting

Abstract

This invention discloses a method for estimating the order of S-parameter fitting. By analyzing the trajectory characteristics of S-parameters on the Smith chart and counting the number of clockwise rotations of adjacent sampling points, combined with smoothing filtering and non-causal sampling point filtering, the minimum order, order increment step size, and maximum order are automatically estimated, providing initial order settings for subsequent vector fitting. This invention effectively reduces the number of order attempts, improves fitting efficiency and stability, ensures that the passively repaired macromodel simultaneously satisfies causality and passivity, and enhances the accuracy and convergence of circuit time-domain simulation. It can be widely applied in electromagnetic field simulation and system-level link simulation processes.

Description

Technical Field

[0001] This invention relates to the fields of radio frequency circuit design automation and signal integrity analysis technology, and in particular to a method for estimating the order of S-parameter fitting. Background Technology

[0002] In RF, microwave, and high-speed circuit design, S-parameters are widely used to characterize the frequency response of devices and interconnect structures. A typical design flow usually includes: building a circuit schematic based on design specifications, replacing ideal devices with actual passive device models, and importing the S-parameters obtained from passive device simulations into a complete circuit containing active devices for SPICE (Simulation Program with Integrated Circuit Emphasis) simulation. Similarly, in signal integrity and power integrity analysis, electromagnetic simulations of connectors, power networks, interconnects, and signal networks are required to obtain S-parameters, and key performance indicators such as eye diagrams, crosstalk, and power noise are evaluated in system-level link simulations. In practical engineering applications, S-parameters can be obtained either through electromagnetic field simulations or through actual measurements using a vector network analyzer (VNA).

[0003] Electromagnetic field solvers, based on Maxwell's equations, typically obtain S-parameters as discrete, finite-bandwidth frequency domain data. In circuit simulation, time-domain simulation is often required in addition to frequency-domain analysis. There are two main methods for time-domain analysis of frequency-domain S-parameters: 1) The Inverse Fourier Transform (IFFT) method: This method converts the S-parameters into a time-domain impulse response, performs causality correction, and then convolves it with the input signal to obtain the time-domain output response. While performing causality correction, this method struggles to guarantee passivity, potentially leading to non-convergence issues in subsequent circuit simulations. 2) The Passive Macromodeling method: This method performs vector fitting on the discrete S-parameters to obtain a pole-residue model, and uses passive correction to ensure both causality and passivity are satisfied. Since the inverse Fourier transform of rational functions has an analytical form, it can efficiently perform convolution operations with time-domain signals, thus gradually becoming the mainstream approach in engineering practice.

[0004] In passive macro modeling, vector fitting is a crucial step in determining model quality, and its accuracy directly affects the effectiveness of passive repair and the accuracy of circuit simulation. Traditional vector fitting algorithms typically rely on user-inputted initial pole positions and iterative optimization to gradually converge to a model that meets error requirements. While there is considerable literature discussing initial pole setting methods, the selection of the fitting order still largely depends on manual experience or repeated trial and error. This blind experimentation has several drawbacks: strong subjectivity in order selection and a lack of unified standards; the need for multiple repeated fitting steps, resulting in high computational resource consumption; and insufficient model accuracy due to an excessively low order, while an excessively high order can easily lead to numerical instability and overfitting.

[0005] The order required for S-parameter vector fitting is influenced by various factors, including the complexity of the device or interconnect structure, the operating frequency range, the number of resonant modes, propagation delay characteristics, and the electromagnetic properties of the material. For different types of passive networks, or even the same type of network under different structural parameters and frequency bandwidths, the complexity of its frequency response may vary, leading to different orders required for vector fitting. Therefore, accurately obtaining the physical order of the S-parameters typically requires a complex system identification process, resulting in high computational costs and making real-time applications difficult. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for estimating the order of S-parameter fitting. By analyzing the trajectory characteristics of S-parameters on the Smith chart and counting the number of clockwise rotations of adjacent sampling points, combined with smoothing filtering and non-causal sampling point filtering, the minimum order, order increment step size, and maximum order are automatically estimated, providing initial order settings for subsequent vector fitting. This invention effectively reduces the number of order attempts, improves fitting efficiency and stability, ensures that the passively repaired macromodel simultaneously satisfies causality and passivity, and enhances the accuracy and convergence of circuit time-domain simulation. It can be widely applied in electromagnetic field simulation and system-level link simulation processes. This invention does not aim to absolutely accurately reproduce the physical order, but rather serves as a rapid estimation method. Under the premise of meeting engineering accuracy requirements, it quickly provides a reasonable minimum order (min_order), order increment step size (increment), and maximum order (max_order), thereby achieving a balance between efficiency and accuracy and providing reliable input for subsequent vector fitting.

[0007] This invention provides the following solutions:

[0008] This invention provides a method for predicting the order of S-parameter fitting, the method comprising the following steps:

[0009] S1. Obtain the S-parameters of the multi-port passive network;

[0010] S2, filter sampling points whose amplitude is less than the threshold TOL;

[0011] S3. Smooth the filtered S-parameter curve;

[0012] S4. Calculate the number of clockwise rotations for each S-parameter curve;

[0013] S5. Take the average number of rotations for all S-parameter curves;

[0014] S6. Calculate the minimum order, the order increment step, and the maximum order based on the average number of rotations.

[0015] Furthermore, the multi-port S-parameters of the passive network obtained in step S1 are denoted as S(f k )={S ij (f k )}, i,j=1,...,p,k=1,...,N s Where p is the number of ports, N s S represents the number of frequency sampling points. ij (f k ) represents the complex S-parameter value at the k-th frequency sampling point from the i-th port to the j-th port.

[0016] Furthermore, step S2 includes the following process: for any S-parameter curve S ij Based on the preset amplitude threshold TOL, sampling point data with excessively small amplitudes are filtered out, resulting in the filtered S-parameter curve G. ij .

[0017] Furthermore, the amplitude threshold TOL is set to 10. -5 .

[0018] Furthermore, in step S3, let the window length of the smoothing filter be w, and for the filtered complex sequence G of the S-parameter curve... ij ={g1,g2,...,g M ,},M≤N s The complex sequence H of the S-parameter curve after smoothing filtering ij The k-th data h k Represented as:

[0019] ,

[0020] Among them, Ω k |Ω represents a local sampling window centered at the k-th sampling point and with a length not exceeding w. k | indicates the number of sampling points within this window.

[0021] Furthermore, w is set to 13.

[0022] Furthermore, step S4 includes the following processes:

[0023] S4.1, the complex sequence H of the smoothed and filtered S-parameter curves ij Mapped to the complex plane, i.e. the trajectory plane corresponding to the Smith chart, for any three adjacent sampling points h k h k+1 and h k+2 Construct two adjacent vectors v k =h k -h k+1 and v k+1 =h k+1 -h k+2 , where h k h k+1 and h k+2 The real and imaginary parts are respectively used as two-dimensional plane coordinates;

[0024] S4.2 Calculate the vector v k to vector v k+1 Directed rotation angle θ k ;

[0025] S4.3, For all directed rotation angles θ greater than 0 k Summing yields the S-parameter curve S. ij The corresponding number of clockwise rotations:

[0026] ,

[0027] Among them, T ij This represents the number of clockwise rotations of the S-parameter curve from port i to port j on the Smith chart.

[0028] Furthermore, the directed rotation angle described in step S4 is calculated using the vector dot product and cross product:

[0029] ,

[0030] Where, d k c is the result of the dot product of adjacent vectors. k The atan2(.) function is used to calculate the directional rotation angle, which is the result of the two-dimensional cross product of adjacent vectors.

[0031] Furthermore, step S5 obtains the average number of rotations T using the following formula. m :

[0032] .

[0033] Furthermore, step S6 calculates the minimum order (min_order), the order increment step size (increment), and the maximum order (max_order) using the following formulas:

[0034] ,

[0035] Where ceilEven(x) represents the smallest even number not less than x, α, β and γ are the first proportionality coefficient, the second proportionality coefficient and the third proportionality coefficient respectively, 1.0≤α≤1.5, 0.4≤β≤0.6, 4.0≤γ≤7.0.

[0036] The beneficial effects of this invention based on its technical solution are as follows:

[0037] (1) This invention can automatically set the order of S-parameter vector fitting, thereby improving computational efficiency. By counting the number of clockwise rotations of the S-parameters on the Smith chart, this invention automatically estimates the minimum order, order increment step size, and maximum order required for vector fitting, avoiding the problem of relying on manual experience to repeatedly calculate the order in traditional methods. This reduces the number of fitting attempts and improves the automation level and overall computational efficiency of the vector fitting process.

[0038] (2) The present invention can improve the stability and robustness of the order prediction effect. Before calculating the number of rotations, the present invention filters out sampling points with too small amplitude and smooths the S-parameter curve. At the same time, it filters out the counterclockwise rotation angle caused by noise, insufficient sampling or local disturbance, thereby reducing the influence of measurement noise and electromagnetic field simulation numerical error on the order estimation result, making the obtained order prediction result more stable and reliable.

[0039] (3) This invention supports parallel computing and can quickly complete the order prediction. This invention independently performs amplitude filtering, smoothing and clockwise rotation statistics on each curve in the multi-port S-parameter. There is no computational dependency between the curves. Therefore, parallel computing can be used to process the S-parameter curves of the fruit bar at the same time. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a flowchart illustrating a method for estimating the order of S-parameter fitting provided in this embodiment.

[0042] Figure 2 This is a schematic diagram illustrating the application of the order prediction results in vector fitting.

[0043] Figure 3This is a schematic diagram comparing the original S12 curve with the result after amplitude filtering and smoothing.

[0044] Figure 4 This is a schematic diagram comparing the original S22 curve with the result after amplitude filtering and smoothing.

[0045] Figure 5 This is a schematic diagram of the processed S22 curve on the Smith chart.

[0046] Figure 6 This is a schematic diagram comparing the original S12 curve with the results of vector fitting.

[0047] Figure 7 This is a schematic diagram comparing the original S22 curve with the results of vector fitting. Detailed Implementation

[0048] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the protection scope of the embodiments of the present invention.

[0049] This embodiment provides a method for estimating the order of S-parameter fitting, referring to... Figure 1 The method includes the following steps:

[0050] S1. Obtain the multi-port S-parameters of the passive network, denoted as S(f k )={S ij (f k )}, i,j=1,...,p,k=1,...,N s Where p is the number of ports, N s S represents the number of frequency sampling points. ij (f k ) represents the complex S-parameter value at the k-th frequency sampling point from the i-th port to the j-th port.

[0051] S2. Filtering sampling points with amplitudes less than the threshold TOL includes the following process: For any S-parameter curve S ij Based on the preset amplitude threshold TOL, sampling point data with excessively small amplitudes are filtered out, resulting in the filtered S-parameter curve G. ij In this embodiment, the amplitude threshold TOL is set to 10. -5 .

[0052] S3. Smooth the filtered S-parameter curves. Let the window length of the smoothing filter be w. For the complex sequence G of the filtered S-parameter curves... ij={g1,g2,...,g M ,},M≤N s The complex sequence H of the S-parameter curve after smoothing filtering ij The k-th data h k Represented as:

[0053] ,

[0054] Among them, Ω k |Ω represents a local sampling window centered at the k-th sampling point and with a length not exceeding w. k | indicates the number of sampling points within the window. In this embodiment, w is set to 13.

[0055] S4. Calculate the number of clockwise rotations for each S-parameter curve, including the following steps:

[0056] S4.1, the complex sequence H of the smoothed and filtered S-parameter curves ij Mapped to the complex plane, i.e. the trajectory plane corresponding to the Smith chart, for any three adjacent sampling points h k h k+1 and h k+2 Construct two adjacent vectors v k =h k -h k+1 and v k+1 =h k+1 -h k+2 , where h k h k+1 and h k+2 The real and imaginary parts are respectively used as two-dimensional plane coordinates;

[0057] S4.2 Calculate the vector v k to vector v k+1 Directed rotation angle θ k The directed rotation angle is calculated using the dot product and cross product of vectors:

[0058] ,

[0059] Where, d k c is the result of the dot product of adjacent vectors. k The atan2(.) function is used to calculate the directional rotation angle, which is the result of the two-dimensional cross product of adjacent vectors.

[0060] S4.3, For all directed rotation angles θ greater than 0 k Summing yields the S-parameter curve S. ij The corresponding number of clockwise rotations:

[0061] ,

[0062] Among them, T ij This represents the number of clockwise rotations of the S-parameter curve from port i to port j on the Smith chart.

[0063] S5. Take the average number of rotations (T) for all S-parameter curves. m It is calculated using the following formula:

[0064] .

[0065] S6. Calculate the minimum order (min_order), the order increment step size (increment), and the maximum order (max_order) using the following formulas:

[0066] ,

[0067] Where ceilEven(x) represents the smallest even number not less than x, α, β, and γ are the first, second, and third proportionality coefficients, respectively, with 1.0 ≤ α ≤ 1.5, 0.4 ≤ β ≤ 0.6, and 4.0 ≤ γ ≤ 7.0. After obtaining the minimum order min_order, increment step size increase, and maximum order max_order, they can be used as initial configuration parameters for applications such as... Figure 2 The vector fitting process is shown below. The specific fitting process is not the focus of this invention and will not be elaborated upon.

[0068] For a passive network layout with 26 ports, its multi-port S-parameters are obtained through simulation using an electromagnetic field solver. Following the steps outlined in this embodiment, the following can be obtained: Figure 3 4 and Figure 5 The results are shown. The S-parameters of the 26-port port contain 26*26=676 curves.

[0069] Figure 3 This shows a comparison between the original S12 curve and the result after amplitude filtering and smoothing. The solid red line represents the original S12 curve, and the dashed blue line represents the result after filtering out S-parameters below TOL (-100dB) and smoothing. It can be seen that the blue curve has fewer sampling points than the red curve; these are the filtered-out data points.

[0070] Figure 4 The comparison between the original S22 curve and the result after amplitude filtering and smoothing is shown. Since the amplitude of the S22 curve is relatively large and no small spikes are visible, the processed curve is close to the original S22 curve. Figure 5 The effect of the processed S22 curve on the Smith chart is shown.

[0071] The final calculation yields the average number of clockwise rotations, T.m =1.027, and further obtained min_order=2, increment=2, max_order=18. Referring to these three metrics, the vector fitting algorithm obtains a rational function model through column fitting, with a root mean square error (RMSE) of 5.725e compared to the original S-parameters. -5 The average order of each column is 9.76.

[0072] Figure 6 and Figure 7 The original S12 (S22) curve and the results after vector fitting are shown respectively.

[0073] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0075] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for predicting the order of S-parameter fitting, characterized in that, The method includes the following steps: S1. Obtain the multi-port S-parameters of the passive network; S2, filter sampling points whose amplitude is less than the threshold TOL; S3. Smooth the filtered S-parameter curve; S4. Calculate the number of clockwise rotations for each S-parameter curve; S5. Take the average number of rotations for all S-parameter curves; S6. Calculate the minimum order, the order increment step, and the maximum order based on the average number of rotations.

2. The method for predicting the order of S-parameter fitting according to claim 1, characterized in that: The multi-port S-parameters of the passive network obtained in step S1 are denoted as S(f k )={S ij (f k )}, i,j=1,...,p,k=1,...,N s Where p is the number of ports, N s S represents the number of frequency sampling points. ij (f k ) represents the complex S-parameter value at the k-th frequency sampling point from the i-th port to the j-th port.

3. The method for predicting the order of S-parameter fitting according to claim 1, characterized in that: Step S2 includes the following process: For any S-parameter curve S ij Based on the preset amplitude threshold TOL, sampling point data with excessively small amplitudes are filtered out, resulting in the filtered S-parameter curve G. ij .

4. The method for predicting the order of S-parameter fitting according to claim 3, characterized in that: Amplitude threshold TOL is set to 10 -5 .

5. The method for predicting the order of S-parameter fitting according to claim 3, characterized in that: In step S3, let the window length of the smoothing filter be w, and for the filtered complex sequence G of the S-parameter curve... ij ={g1,g2,...,g M ,},M≤N s The complex sequence H of the S-parameter curve after smoothing filtering ij The k-th data h k Represented as: ， Among them, Ω k |Ω represents a local sampling window centered at the k-th sampling point and with a length not exceeding w. k | indicates the number of sampling points within this window.

6. The method for predicting the order of S-parameter fitting according to claim 5, characterized in that: w is set to 13.

7. The method for predicting the order of S-parameter fitting according to claim 1, characterized in that: Step S4 includes the following processes: S4.1, the complex sequence H of the smoothed and filtered S-parameter curves ij Mapped to the complex plane, i.e. the trajectory plane corresponding to the Smith chart, for any three adjacent sampling points h k h k+1 and h k+2 Construct two adjacent vectors v k =h k -h k+1 and v k+1 =h k+1 -h k+2 , where h k h k+1 and h k+2 The real and imaginary parts are respectively used as two-dimensional plane coordinates; S4.2 Calculate the vector v k to vector v k+1 Directed rotation angle θ k ; S4.3, For all directed rotation angles θ greater than 0 k Summing yields the S-parameter curve S. ij The corresponding number of clockwise rotations: ， Among them, T ij This represents the number of clockwise rotations of the S-parameter curve from port i to port j on the Smith chart.

8. The method for predicting the order of S-parameter fitting according to claim 7, characterized in that: The directed rotation angle mentioned in step S4 is calculated using the vector dot product and cross product: ， Where, d k c is the result of the dot product of adjacent vectors. k Given the result of the two-dimensional cross product of adjacent vectors, the atan2(.) function is used to calculate the directional rotation angle.

9. The method for predicting the order of S-parameter fitting according to claim 1, characterized in that: Step S5 obtains the average number of rotations T using the following formula. m : 。 10. The method for predicting the order of S-parameter fitting according to claim 1, characterized in that: Step S6 calculates the minimum order (min_order), the order increment step size (increment), and the maximum order (max_order) using the following formulas: ， Where ceilEven(x) represents the smallest even number not less than x, α, β and γ are the first proportionality coefficient, the second proportionality coefficient and the third proportionality coefficient respectively, 1.0≤α≤1.5, 0.4≤β≤0.6, 4.0≤γ≤7.0.

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