S parameter time domain modeling method, device and system based on vector fitting and medium

Abstract

The invention discloses an S parameter time domain modeling method, device, medium and system based on vector fitting, and belongs to the field of microwave radio frequency device modeling and emulation.The method comprises the steps that a frequency domain response function is constructed based on a device S parameter, a residue and a pole value are approximated step by step through iterative optimization and a least square solution method, and the frequency domain response function is obtained; and finally, carrying out time domain convolution on the input signal based on the transfer function, and carrying out conversion of the output signal through the time domain convolution. According to the method, the simulation efficiency of the broadband microwave array system link time domain signal flow is improved.

Description

Technical Field

[0001] This invention relates to the field of microwave radio frequency device modeling and simulation, and more specifically, to a method, apparatus, medium, and system for S-parameter time-domain modeling based on vector fitting. Background Technology

[0002] The core challenge of link simulation for broadband microwave array systems lies in the coordination of interdisciplinary models and time-domain signal flow analysis. This system needs to bridge the boundaries between antennas, microwave circuits, and digital modules, achieving overall performance evaluation through parametric modeling of heterogeneous devices. However, traditional single-discipline modeling methods have limitations. Antenna modules rely on three-dimensional electromagnetic field finite element analysis, while microwave circuits employ frequency domain circuit analysis. This discrete modeling approach makes it difficult to directly utilize the numerical descriptions of each module in link-level time-domain signal flow simulation. Constructing a unified model architecture that supports time-domain simulation has become a key breakthrough for improving the accuracy of system analysis.

[0003] Multiport network S-parameter models offer a crucial entry point for addressing the aforementioned problems. This model characterizes the frequency domain transmission characteristics of devices through measured S-parameters, providing a more accurate description of the frequency response features of actual devices compared to idealized formula models. Although the classical definition of S-parameters is a linear mapping between the incident and reflected waves at the port, from a system simulation perspective, it can be analytically represented as the frequency domain transfer function of the modulated signal. This modeling approach based on actual test data not only reduces the difficulty of parameter acquisition but also improves computational efficiency through frequency domain matrix operations.

[0004] Directly embedding S-parameter models into time-domain simulations leads to severe computational bottlenecks. Each iteration requires performing a time-frequency transformation on the broadband signal: first, the time-domain excitation is transformed into a frequency-domain convolution with the S-parameter matrix, and then the result is transformed back into the time domain. When system-level simulations involve dozens of devices, this repeated transformation process results in exponentially increasing computational power consumption. More seriously, frequency-domain discretization can cause high-order harmonic folding, leading to spectral aliasing distortion of the time-domain waveform. This poses a fundamental constraint on the simulation of microwave array systems with stringent fidelity requirements for broadband signals. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, device, medium and system for S-parameter time-domain modeling based on vector fitting, which improves the simulation efficiency of time-domain signal flow of broadband microwave array system links.

[0006] The objective of this invention is achieved through the following solution: A time-domain modeling method for S-parameters based on vector fitting includes the following steps: The frequency domain response function is constructed based on the device's S-parameters. Then, the residue and pole values ​​are gradually approximated through iterative optimization and least squares solution to obtain a well-fitted transfer function equation. Finally, the input signal is convolved in the time domain based on the transfer function, and the output signal is transformed through the time domain convolution.

[0007] Furthermore, the construction of the frequency domain response function based on the device S-parameters specifically includes the following sub-steps: First, map the original S-parameters to digital angular frequencies: (1); in, These are the frequency values ​​of the original S-parameters, where s is the complex frequency in the complex domain and j is the imaginary number. Angular frequency; At the same time, the following conversions are performed on the dB and MA type S-parameters: (2); in, Let (i,j) be the (i,j)th element in the S-parameter matrix. To convert the amplitude into decibels, For angle; At this point, the original S-parameters are expressed as equation (3), where Number of ports of the device: (3); Then, the frequency response of the original S-parameters is approximated by constructing the transfer function of the vector fitting algorithm. The form of the transfer function is shown in equation (4). In equation (4), For transfer functions, The coefficients of the denominator polynomial, Let be the coefficients of the numerator polynomial, m be the order of the denominator polynomial, and n be the order of the numerator polynomial; by fractionally expanding the transfer function, it approximates the form shown in equation (5), where , It is a residue matrix. These are the poles of the transfer function. For constant terms, For a first-order linear term, The transfer function form is used as the polynomial part of the approximate fit of the transfer function, where N is the number of polynomials. These are extreme values; (4); (5).

[0008] Furthermore, the method of iterative optimization and least squares solution to gradually approximate the residue and extreme values ​​to obtain a well-fitted transfer function equation specifically includes the following sub-steps: First, construct the scalar fitting function: (8); in, For the fitting function, The value at the zero point. The extreme value, d For constant terms, se It is a first-order term; Specify initial pole set Given the initial poles, equation (8) is solved as an overdetermined linear least squares problem: (9); in, Residue; Zero point is obtained by the following formula: (11); in, It's midnight. It contains poles diagonal matrix, It is a column vector where all elements are 1. This includes residues. ; Substituting the obtained zeros into equation (9) as new initial poles, and through continuous iteration, the poles are located from their initial positions to better positions. The final convergence condition is as follows: (12); Thus, the residue matrix in equation (5) is obtained. constant term First-order linear term .

[0009] Furthermore, provided that the accuracy allows, the iteration can be terminated before convergence is complete, and the final residue can be obtained by equation (8).

[0010] Furthermore, the step of performing temporal convolution on the input signal based on the transfer function, and then transforming the output signal through temporal convolution, specifically includes the following sub-steps: The time-domain form of the transfer function is the system's impulse response. Time-domain filtering is achieved using time-domain convolution. First, the transfer function... It can be represented in the following form: (13); in and These are the Laplace transforms of the system output and input, respectively; Express the impulse response function as the inverse Laplace transform of the transfer function: (14);

[0011] Then the time-domain output signal Input signal With impulse response Convolution: (15); in, This is the delay amount.

[0012] An electronic device for S-parameter time-domain modeling based on vector fitting includes a processor and a memory, wherein the memory stores a computer program that, when loaded by the processor, executes the method described in any of the preceding claims.

[0013] A computer-readable storage medium storing a computer program that, when loaded by a processor, executes the method described in any of the preceding claims.

[0014] An S-parameter time-domain modeling electronic system based on vector fitting includes the S-parameter time-domain modeling electronic device based on vector fitting as described above.

[0015] The beneficial effects of this invention include: This invention addresses the low simulation efficiency caused by repeated time-frequency transformations required when directly calling the frequency-domain S-parameter model in time-domain signal flow simulation of broadband microwave array systems. It constructs a frequency-domain response function based on the device's S-parameters, gradually approximating the residue and pole values ​​through iterative optimization and least-squares solutions, ultimately obtaining a well-fitting transfer function equation. Finally, time-domain convolution is used to convert the output signal. In signal flow-driven microwave array system link simulation, using the vector fitting model constructed in this invention to replace the original frequency-domain S-parameter model of the device avoids repeated time-frequency transformations at each simulation time step, thereby effectively improving the simulation efficiency of time-domain signal flow in broadband microwave array system links.

[0016] This invention proposes a vector fitting-based S-parameter time-domain modeling method. It constructs a vector fitting transfer function that conforms to the frequency response of the device's S-parameters, and then performs time-domain convolution on the input signal based on this transfer function. Compared with the original frequency-domain S-parameter model, the model constructed in this invention directly calculates the input signal in the time domain, avoiding repeated time-frequency transformations in each simulation step. This can effectively improve the simulation efficiency of the time-domain signal flow of broadband microwave array system links, and has significant advantages over traditional methods. 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the method according to an embodiment of the present invention; Figure 2 The result is the amplitude vector fitting of the S-parameters of the bandpass filter; Figure 3 The result is the phase vector fitting of the S-parameters of the bandpass filter; Figure 4 The power spectrum of the input signal to the bandpass filter; Figure 5 The power spectrum of the bandpass filter output signal; Figure 6 The result is the amplitude vector fitting of the S-parameters of the low-noise amplifier; Figure 7 The results are the phase vector fitting results for the S-parameters of the low-noise amplifier; Figure 8 The power spectrum of the input signal to the low-noise amplifier; Figure 9 This is the power spectrum of the output signal of the low-noise amplifier. Detailed Implementation

[0019] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.

[0020] The specific implementation process of this invention is as follows: In a preferred embodiment, the present invention specifically proposes a vector fitting-based S-parameter time-domain modeling method. This method utilizes a vector fitting algorithm to fit the S-parameters, constructing a corresponding transfer function. The time-domain form of the transfer function represents the system's impulse response, and then time-domain filtering is achieved using time-domain convolution. The flow of the method described in this invention is as follows: Figure 1 As shown, it mainly includes the following steps: Step 1: Construct the frequency domain response function based on S-parameters S-parameters are usually represented by analog frequencies, while transfer functions in system model analysis are usually represented by digital angular frequencies. Therefore, to construct the frequency response function, it is first necessary to map the original S-parameters to digital angular frequencies.

[0021] (1); in, These are the frequency values ​​of the original S-parameters.

[0022] Meanwhile, since the poles and residues of the vector fitting algorithm are real numbers or conjugate complex pairs, they are more suitable for RI-type S-parameters. Therefore, the following transformations are required for dB and MA-type S-parameters: (2); At this point, the original S-parameters can be expressed as equation (3), where This represents the number of ports on the device.

[0023] (3); To fit arbitrary frequency response characteristics of radio frequency microwave devices, this invention constructs a transfer function of a vector fitting algorithm to approximate the frequency response of the original S-parameters. The general form of the transfer function is shown in equation (4). To facilitate iterative fitting and solution, the transfer function is partially expanded fractionally, approximating the form shown in equation (5). In equation (5), It is a residue matrix. These are the poles of the transfer function. For constant terms, It is a first-order linear term. The transfer function form is widely used in the fields of circuits and electrical engineering. In this invention, it serves to approximate the polynomial part of the transfer function.

[0024] (4); (5); This polynomial model requires pole stability, and that the poles and residues are real numbers or conjugate complex pairs. Furthermore, passive devices have requirements regarding singular values ​​because: (6); in, It is a collection of singular values For a diagonal matrix, passive devices require all singular values ​​to be less than 1, i.e.: (7); Step 2: Iterative optimization and least squares solution The core of the vector fitting algorithm is to iteratively adjust the poles and residues. First, fix the poles and optimize the residues; then fix the residues and optimize the poles; repeat this iterative process until convergence. The specific steps are as follows: First, construct the scalar fitting function: (8); Specify initial pole set Given the initial poles, equation (8) is solved as an overdetermined linear least squares problem: (9); Another expression for equation (9) is shown in equation (10): (10); By expressing the sum of the two fractional parts of equation (9) as the product of the zeros and poles, it can be seen that... The extreme point must equal The zero point can be obtained by the following formula: (11); in, It contains poles diagonal matrix, It is a column vector where all elements are 1. This includes residues. The vector.

[0025] Substituting the obtained zeros into equation (9) as new initial poles, and through continuous iteration, the poles are located from their initial positions to better positions. The final convergence condition is as follows: (12); In practical applications, if the accuracy allows, the iteration can often be terminated before convergence (e.g., 100 iterations), and the final residue can be obtained by equation (8).

[0026] Therefore, the residue matrix in equation (5) can be obtained. constant term First-order linear term .

[0027] Step 3: Perform temporal convolution on the input signal based on the transfer function. The time-domain form of the transfer function is the system's impulse response. Time-domain filtering can be achieved using time-domain convolution. Generally, the transfer function... It can be represented in the following form: (13); in and These are the Laplace transforms of the system output and input, respectively.

[0028] The impulse response function can be expressed as the inverse Laplace transform of the transfer function: (14); Then the time-domain output signal It can be represented as an input signal With impulse response Convolution: (15); Furthermore, the present invention verifies the vector fitting-based S-parameter time-domain modeling method provided in the above embodiments through the following two examples: Example 1: A bandpass filter A certain bandpass filter has S-parameters with a frequency range of 100MHz to 10GHz, an operating frequency band of 1.3 to 2.3GHz, and an input signal of... , , Insertion loss ≤ 2.8dB, out-of-band rejection ≥ 27dB, in-band ripple ≤ 1.4dB.

[0029] Step 1: Construct the frequency domain response function based on S-parameters According to the original The original S-parameters are transformed into the matrix shown in Equation (3) through linear interpolation. The transfer function shown in Equation (5) is initially constructed to prepare for the least squares solution.

[0030] Step 2: Iterative optimization and least squares solution The iteration count was set to 100. The extreme points were iteratively optimized, and the transfer function was solved using least squares. The magnitude fitting curve of the transfer function was compared with the original S-parameters. The results are as follows: Figure 2 As shown, the green curve represents the error, indicating a good fit. The phase fitting curve of the transfer function is shown below. Figure 3 As shown, the phases are basically consistent, which meets the requirements for time-domain modeling.

[0031] Step 3: Perform temporal convolution on the input signal based on the transfer function. Based on the vector-fit transfer function obtained in step two, the input signal is convolved in the time domain. The effective portion of the convolution result is then truncated to obtain the output signal. Power spectrum analysis is performed on the input and output signals, and the results are as follows. Figure 4 , Figure 5 As shown, the in-band signal at 2 GHz is retained, while the out-of-band signal at 3.6 GHz is filtered out.

[0032] Example 2: A low-noise amplifier A certain low-noise amplifier has an S-parameter frequency range of 100MHz to 26.5GHz, an operating frequency band of 0.7 to 5GHz, and an input signal of... , , Power gain ≥14dB, noise figure ≤2.2dB, output power ≥20dBm.

[0033] Step 1: Construct the frequency domain response function based on S-parameters According to the original The original S-parameters are transformed into the matrix shown in Equation (3) through linear interpolation. The transfer function shown in Equation (5) is initially constructed to prepare for the least squares solution.

[0034] Step 2: Iterative optimization and least squares solution The iteration count was set to 100. The extreme points were iteratively optimized, and the transfer function was solved using least squares. The magnitude fitting curve of the transfer function was compared with the original S-parameters. The results are as follows: Figure 6 As shown, the green curve represents the error, indicating a good fit. The phase fitting curve of the transfer function is shown below. Figure 7 As shown, the phases are basically consistent, which meets the requirements for time-domain modeling.

[0035] Step 3: Perform temporal convolution on the input signal based on the transfer function. Based on the vector-fit transfer function obtained in step two, the input signal is convolved in the time domain. The effective portion of the convolution result is then truncated to obtain the output signal. Power spectrum analysis is performed on the input and output signals, and the results are as follows. Figure 8 , Figure 9 As shown, there is a significant difference in amplification factor between the 3GHz signal within the operating frequency band and the 6.2GHz signal outside the operating frequency band.

[0036] In other aspects of the invention, an electronic device for S-parameter time-domain modeling based on vector fitting is also provided, comprising a processor and a memory, wherein the memory stores a computer program that, when loaded by the processor, executes the method as described in any of the preceding claims.

[0037] In other aspects of the invention, an S-parameter time-domain modeling electronic system based on vector fitting is also provided, including the S-parameter time-domain modeling electronic device based on vector fitting as described above.

[0038] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0039] According to one aspect of the present invention, a computer program product or computer program is provided, the computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and executes the computer instructions, causing the computer device to perform the methods provided in the various optional implementations described above.

[0040] In another aspect, embodiments of the present invention also provide a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods described in the above embodiments.

Claims

1. A vector fitting based S-parameter time domain modeling method, characterized in that, The method comprises the following steps: The frequency domain response function is constructed based on the device S parameters, and the residue and pole values are gradually approached by means of iterative optimization and least square solution, so that a fitted transfer function equation is obtained, and finally the input signal is subjected to time domain convolution based on the transfer function, and the output signal is converted through time domain convolution.

2. The vector fit based S-parameters time domain modeling method of claim 1, wherein, The frequency domain response function is constructed based on the device S parameters, and the residue and pole values are gradually approached by means of iterative optimization and least square solution, so that a fitted transfer function equation is obtained, and finally the input signal is subjected to time domain convolution based on the transfer function, and the output signal is converted through time domain convolution. The frequency domain response function is constructed based on the device S parameters, and the residue and pole values are gradually approached by means of iterative optimization and least square solution, so that a fitted transfer function equation is obtained, and finally the input signal is subjected to time domain convolution based on the transfer function, and the output signal is converted through time domain convolution. (1)； wherein is the frequency value of the original S parameter, s is a complex frequency in the complex domain, j is an imaginary number, is an angular frequency; Firstly, the original S parameters are mapped to digital angular frequency: (2)； wherein, is the (i,j)th element of the S parameter matrix, is the magnitude converted to decibels, is the angle; At this time, the original S parameter is expressed as Equation (3), where is the number of ports of the device: (3)； The frequency response of the original S parameter is approximated by constructing a transfer function of the vector fitting algorithm, and the form of the transfer function is shown in equation (4), in which, is the transfer function, is the denominator polynomial coefficient, is the numerator polynomial coefficient, m is the denominator polynomial order, and n is the numerator polynomial order; the transfer function is partially expanded, and is approximated in the form shown in equation (5), in which, is the residue matrix, is the pole of the transfer function, is the constant term, is the first-order linear term, and the transfer function form of is taken as the polynomial part of the approximate fitting transfer function, N is the number of polynomials, is the pole value; (4)； (5)。 3. The vector fit based S-parameters time domain modeling method of claim 2, wherein, Meanwhile, the following conversion is performed on the dB and MA type S parameters: The frequency domain response function is constructed based on the device S parameters, and the residue and pole values are gradually approached by means of iterative optimization and least square solution, so that a fitted transfer function equation is obtained, and finally the input signal is subjected to time domain convolution based on the transfer function, and the output signal is converted through time domain convolution. (8)； wherein is a zero value, is a zero value, is a pole value, d is a constant term, Firstly, a scalar fitting function is constructed: is a first order term; Specifying an initial set of poles With the initial poles known, solve equation (8) as an over-determined linear least squares problem: (9)； wherein is the number of leaves; The zero point is obtained by the following formula: (11)； in, It's midnight. It contains poles diagonal matrix, It is a column vector where all elements are 1. This includes residues. ; The obtained zero point is substituted into formula (9) as a new initial pole, and the pole is positioned from the initial pole position to a better position through continuous iteration, and the final convergence condition is as follows: (12)； Thus, the residue matrix in equation (5) is obtained as the constant term the first order linear term .

4. The vector fit based S-parameters time domain modeling method of claim 3, wherein, The iteration can be terminated before the convergence is completed under the premise of accuracy, and the final residue is obtained by formula (8).

5. The vector fit based S-parameters time domain modeling method of claim 3, wherein, The frequency domain response function is constructed based on the device S parameters, and the residue and pole values are gradually approached by means of iterative optimization and least square solution, so that a fitted transfer function equation is obtained, and finally the input signal is subjected to time domain convolution based on the transfer function, and the output signal is converted through time domain convolution. The time-domain form of the transfer function is the impulse response of the system, and time-domain filtering is implemented using time-domain convolution; first, the transfer function is expressed in the following form: (13)； wherein and are Laplace transforms of the system output and input, respectively; The impulse response function is expressed as the Laplace inverse transform of the transfer function: (14)； then the time domain output signal is the input signal convolved with the impulse response h(n). (15)； wherein, is the delay amount.

6. An electronic device for time-domain modeling of S-parameters based on vector fitting, characterized by The computer program is stored in the memory, and when the computer program is loaded by the processor and executes the method of any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, The computer program is stored in the computer readable storage medium, and the computer program is loaded by the processor and executes the method of any one of claims 1-5.

8. A vector fit based S-parameter time domain modeling electronic system, characterized by, The electronic device for S parameter time domain modeling based on vector fitting according to claim 6.

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