Radio frequency device equivalent modeling method for optimizing vector fitting technology based on peak searching method

Abstract

The invention discloses a radio frequency device equivalent modeling method for optimizing a vector fitting technology based on a peak searching method. The method adopts a vector fitting technology combined with a peak searching method, and is used for accelerating convergence and fitting processes of complex frequency domain response data. According to the method, the characteristics of frequency domain data of a radio frequency device are analyzed, initial pole distribution is optimized, the efficiency of a vector fitting algorithm is greatly improved, and a rational fitting form of the minimum pole number meeting the error tolerance set by a system is returned under the condition that the maximum pole number is searched and set in combination with a dichotomy. The vector fitting technology combined with the peak searching method significantly improves the generation efficiency and quality of the equivalent model, and is especially suitable for complex frequency domain response modeling of a radio frequency device. The method provides important support for simulation and optimization design of an efficient radio frequency system.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing and computer-aided design (CAD), and in particular relates to a radio frequency device equivalent modeling method based on a peak-finding method to optimize a vector fitting technology. Background Art

[0002] A major challenge in transient modeling of RF devices and power systems is ensuring that time-domain simulations accurately reflect frequency-dependent effects. These effects are typically caused by parasitic effects in RF devices, eddy currents in conductive materials in power systems, and relaxation phenomena in dielectrics, resulting in dynamic variations in the impedance, inductance, and capacitance matrices in the frequency domain. In practical applications, frequency-dependent responses are characterized by discrete frequency functions obtained through calculation or measurement. Equivalent modeling of RF devices and linear modeling of power system components can both be expressed as the convolution of terminal quantities (such as port voltages or node voltages) with the model's dynamic impulse response to include frequency-dependent effects in time-domain simulations. However, fully numerical convolution methods are computationally inefficient, especially when simulations require a large number of time steps. Therefore, using low-order rational functions to approximate the frequency-domain response has become an important means of improving computational efficiency.

[0003] In RF device equivalent modeling, rational function forms typically include polynomial, pole-residue, and pole-zero forms. When fitting wideband and complex frequency-domain response data, the polynomial form, due to the presence of high-order powers, can easily lead to severe data scaling, resulting in poor condition numbers when solving linear equations and limited fitting performance, often only providing low-order approximations. In contrast, rational function fitting using pole-residue or pole-zero forms is more suitable for such applications. The pole-residue form, in particular, is widely used in RF device parameter extraction and equivalent modeling due to its computational convenience and simple structure.

[0004] However, rational fitting in the form of pole residues also introduces challenges. Due to the nonlinear characteristics of its fitting function, it cannot be directly converted into the form of a linear system of equations. Through the vector fitting method (VF), the nonlinear fitting problem can be converted into a linear problem by setting the initial poles and scaling factor functions, and then the fitting accuracy can be optimized by iteratively updating the pole positions. The vector fitting algorithm adjusts the pole positions and residue values ​​of the model based on the least squares method to minimize the fitting error. This method can handle complex frequency domain response data and is particularly suitable for fitting data with multiple resonant peaks. It can be used for RF device parameter extraction and the establishment of equivalent models.

[0005] However, applying vector fitting methods to model RF devices still presents several challenges. First, the choice of initial poles significantly impacts the fitting performance and convergence speed. When the initial poles are far from the target location, the algorithm may converge more slowly or even become trapped in a local optimum. Second, the selection of the number of initial poles often requires empirical judgment, and different choices can lead to different fitting results.

[0006] Based on this, the present invention proposes optimizing the initial pole distribution by combining a peak-finding algorithm. This algorithm analyzes the characteristics of the RF device's frequency-domain response data, identifies resonant peaks, and distributes the initial poles near these peaks, thus avoiding the blindness of traditional uniform distribution strategies. Experiments have shown that combining the peak-finding algorithm with vector fitting technology significantly improves convergence speed and accuracy when fitting the multi-resonant peak data of RF devices.

[0007] To further optimize fitting efficiency, the present invention also introduces QR decomposition technology during the initial pole update process, reducing the memory consumption of solving the linear equation system and accelerating the calculation speed. In addition, the number of poles is dynamically adjusted through bisection to ensure that the minimum number of poles is used while meeting the fitting error standard, thereby simplifying the complexity of the equivalent model. This vector fitting technology combined with the peak-finding algorithm greatly improves the efficiency of RF device parameter extraction and equivalent modeling, providing key support for efficient RF system simulation and optimization design. Summary of the Invention

[0008] In order to solve the problems of slow fitting speed and initial pole order selection in traditional vector fitting when fitting multi-resonance peak curves, the present invention proposes an equivalent modeling method for RF devices based on the peak-finding method to optimize the vector fitting technology. The initial pole position is set by using the dichotomy method and peak distribution, thereby realizing rapid fitting of the resonance curve.

[0009] The technical solution adopted in the present invention is as follows:

[0010] The equivalent modeling method of a radio frequency device based on the peak-finding method and optimized vector fitting technology includes the following steps:

[0011] Step 1: Measure and obtain the frequency domain response data of the RF device, and record the frequency response data at this time as the original data;

[0012] Step 2: Set the maximum number of poles and initialize N right and N left , combined with the peak-finding algorithm to optimize the setting of the initial extreme point;

[0013] Step 3: Construct the scaling factor based on the initial poles, generate the pole re-identification matrix, and solve the zero point of the scaling factor. The zero point of the scaling factor is the new pole of the iteration.

[0014] Step 4: Calculate the residue of the fitting function under the new extreme point to construct the rational fraction form of the fitting;

[0015] Step 5: Substitute the frequency of the original data into the current rational fraction form and calculate the residual between the fitted data and the original data;

[0016] Step 6: Determine whether the residual is less than the preset tolerance value. If it is less than the tolerance value, set N right = N, and jump to step 8, otherwise use the current pole as the new initial pole and proceed to step 7;

[0017] Step 7: Determine whether the current number of iterations is less than the maximum number of iterations. If so, proceed to step 3. If the current number of iterations is greater than the maximum number of iterations, set N left =N, proceed to step 8;

[0018] Step 8: Set the initial number of poles N = ceil((N left +N right ) / 2), where ceil(·) represents rounding up. If the initial number of poles N remains unchanged, the algorithm is exited; otherwise, it jumps to step 2.

[0019] Step 9: Output the fitted rational polynomial structure corresponding to the minimum number of poles, calculate the time domain response function and frequency domain response function, and complete the modeling of the RF device.

[0020] In the above technical solution, further, by default, the number N of initial poles is the number N of peaks in the frequency domain response data. peak It also supports customizing the number of initial poles N and adopts a peak-finding algorithm to select the initial poles for vector fitting. The frequency point where the peak is found is used as the candidate point for the initial pole.

[0021] Furthermore, if the set number of initial poles is greater than the number of peaks, the excess poles are evenly distributed in the frequency domain to include all peak points and evenly distributed conjugate complex pairs of poles. If the number of peaks is greater than the set number of initial poles, only the first N peak positions are selected as initial poles.

[0022] Furthermore, the peak finding algorithm uses the findpeaks function to smooth the data through a moving average filter, then calculates the first-order derivative of the smoothed data to obtain the rate of change of the data, finds the positive and negative change points of the first-order derivative, and filters out unimportant peaks by setting a threshold, retaining peaks that exceed the threshold.

[0023] Furthermore, the scaling factor σ(s) and the initial poles {a n}Convert the nonlinear fitting equation into a linear equation and set the zero point of the scaling factor σ(s) As the pinnacle of iterative updates The linear equation to be solved is Ax=b,

[0024]

[0025] b=[f(s1)…f(s Ns )]

[0026] Among them A k is the k-th row element of A, s k s=jω, is the Laplace domain, ω is the angular frequency, {a n} is a known pole, {c m} is the residue, {f(s k )} is the original data to be fitted, is the residue corresponding to the fitting factor σ(s).

[0027] Furthermore, in order to obtain the residue corresponding to σ(s) Then, the zero point corresponding to the zero-pole form of the scaling factor σ(s) is calculated by the following formula Expressed in H:

[0028]

[0029] Where eig is the eigenvalue function, A is the extreme point {a n} is a diagonal matrix, when the extreme points {a n}When all are real poles, b is an all-one vector, is the residue vector.

[0030] Furthermore, for the relocation of complex poles, the real and imaginary part separation technology is used to perform conjugate processing on the complex poles, so that the complex poles finally solved are always conjugate symmetric. It is necessary to replace A, b, for:

[0031]

[0032] Where A is a diagonal matrix composed of poles, in which the real part a′ and imaginary part a″ of the conjugate complex pair poles a1, a2 are redistributed, b is originally a unit vector, and the position of the conjugate complex pair poles is replaced by [2,0] T , is the residue corresponding to the scaling factor σ(s), decomposing the residue corresponding to the complex pole into real and imaginary parts, and H represents the zero point of the scaling factor σ(s) solved by the final iteration It is also the pinnacle of iterative updates The new extreme

[0033] The present invention adopts a dichotomy method to search for a minimum pole expression that meets a fitting error standard under a given maximum pole number.

[0034] The vector fitting method (VF) has become an important tool for constructing equivalent models of RF devices due to its powerful frequency domain data fitting capabilities. The traditional vector fitting algorithm constructs a scaling factor function through the initial poles, and calculates the zero point of the scaling factor function as the new pole of the iteration, with the goal of minimizing the fitting residual. However, the distribution of the initial poles greatly affects the efficiency and effect of the fitting. Usually, the traditional method adopts uniformly distributed initial poles. Although this strategy is simple, it cannot fully utilize the characteristics of the data to be fitted, especially when processing complex frequency domain curves, it often exhibits a slower convergence speed. As a result, more poles and iterations are required to achieve the ideal fitting effect, which is not conducive to quickly and accurately generating an equivalent model. Therefore, the present invention proposes the above-mentioned scheme, which adopts a vector fitting technology combined with a peak-finding method to accelerate the convergence and fitting process of complex frequency domain response data. This method optimizes the initial pole distribution by analyzing the characteristics of the frequency domain data of the RF device, thereby greatly improving the efficiency of the vector fitting algorithm.

[0035] The vector fitting method based on the peak-finding algorithm to optimize the initial poles proposed in the present invention has the following characteristics. First, the peak-finding algorithm is used to obtain the characteristics of the original data and set them as the initial poles of the vector fitting. The initial poles of the traditional vector fitting adopt a simple uniform distribution strategy, which ignores the characteristics of the fitting data. For complex multi-resonance peak curves, its iteration speed is slow and the performance is poor. However, the vector fitting using the peak-finding algorithm can use fewer poles and faster iteration speed to meet the fitting error requirements. Second, the vector fitting algorithm converts nonlinear fitting into a process of solving a system of linear equations and iteratively updating the initial poles by introducing a scaling factor σ(s). In the process of iterating the initial poles, since the unknown number of the equation to be solved only needs the residue of the scaling factor σ(s) to be the part of interest, direct calculation will lead to a waste of computing resources. Therefore, the QR decomposition technology is adopted to simplify the matrix calculation, save computing cost and speed up the solution. Third, traditional vector fitting calculations require human experience to determine the optimal number of poles, while the present invention only needs to set the maximum number of poles and use the binary search method to search for fitting results, which can quickly output the rational form of fitting corresponding to the minimum number of poles that meets the fitting error requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the peak distribution vector fitting algorithm of the present invention;

[0037] Figure 2This is an amplitude graph comparing a simple case of the peak distribution vector fitting algorithm described in the present invention with the Matlab result;

[0038] Figure 3 This is a phase diagram comparing a simple case of the peak distribution vector fitting algorithm described in the present invention with the Matlab result;

[0039] Figure 4 It is the amplitude and phase diagram of the multi-peak curve fitted by the traditional vector fitting algorithm described in the present invention;

[0040] Figure 5 It is the amplitude and phase diagram of the multi-peak curve fitted by the peak distribution vector fitting algorithm of the present invention;

[0041] Figure 6 This is a comparison of the iterative convergence speed of the peak distribution vector fitting algorithm described in the present invention and the traditional vector fitting algorithm in fitting the multi-resonance peak curve.

[0042] Figure 7 This is the amplitude diagram of the S21 parameters of the real device fitted by the traditional vector fitting algorithm described in the present invention;

[0043] Figure 8 This is the amplitude diagram of the S21 parameters of the real device fitted by the peak distribution vector fitting algorithm described in the present invention;

[0044] Figure 9 is a frequency response diagram of the peak distribution vector fitting algorithm of the present invention;

[0045] Figure 10 It is the time domain response diagram of the peak distribution vector fitting algorithm described in the present invention. DETAILED DESCRIPTION

[0046] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] RF devices play a key role in communications, radar, and sensing systems, and accurate modeling of their performance is crucial for system analysis and optimization. RF device equivalent modeling typically relies on frequency-domain responses (such as S-parameters, impedance, or admittance data) and uses mathematical models to parametrically describe them, supporting time-domain simulations or system-level design analysis. Vector fitting (VF) methods, due to their powerful frequency-domain data fitting capabilities, have become an important tool for constructing RF device equivalent models. Traditional vector fitting algorithms construct a scaling factor function using initial poles and then calculate the zeros of the scaling factor function as new poles for iteration, optimizing the algorithm with the goal of minimizing the fitting residual. However, the distribution of initial poles significantly impacts the efficiency and effectiveness of the fitting. Traditional methods typically use a uniform distribution of initial poles. While simple, this strategy fails to fully exploit the characteristics of the data being fitted, often exhibiting slow convergence, particularly when dealing with complex frequency-domain curves. Consequently, a larger number of poles and iterations are required to achieve an ideal fitting result, hindering the rapid and accurate generation of equivalent models. To solve this problem, the present invention proposes a vector fitting technology combined with a peak-finding method to accelerate the convergence and fitting process of complex frequency-domain response data. This method analyzes the characteristics of the frequency-domain data of RF devices, optimizes the initial pole distribution, and greatly improves the efficiency of the vector fitting algorithm. At the same time, combined with the bisection method, it searches for the maximum number of poles set and returns a rational fitting form with the minimum number of poles that meets the error tolerance set by the system. The vector fitting technology combined with the peak-finding method significantly improves the generation efficiency and quality of the equivalent model, and is particularly suitable for complex frequency-domain response modeling of RF devices. This method provides important support for efficient RF system simulation and optimization design.

[0048] According to a specific embodiment of the present invention, a RF device equivalent modeling method based on a peak-finding method and optimized vector fitting technology is provided. Figure 1 As shown, the specific steps include:

[0049] Step 1: Use a network analyzer (Vector Network Analyzer, VNA) to measure and obtain the frequency domain response data of the device or use electromagnetic simulation tools (such as CST, HFSS) to obtain the frequency domain response data of the device. The frequency response data at this time is recorded as the original data. According to the set maximum number of poles N max , set the initial number of poles N = N max , and initialize N right =N max and N left =0, N left 、N right is the number of poles in the left and right half planes of the complex plane.

[0050] Step 2: Find the peak of the fitted data according to the set number of poles N, and use the peak-finding algorithm to find all the peak points and peak positions of the original data. When the number of peak points is greater than or equal to the number of poles, the initial pole is selected as the peak frequency position of the first N peak points; when the peak point is less than the number of poles, the initial pole difference number is evenly distributed within the corresponding frequency range. The evenly distributed poles exist in the form of conjugate complex pairs:

[0051] a n =-α+jβa n+1 =-α-jβ

[0052] α=β / 100

[0053] Where β is the frequency domain value of the points evenly distributed within the frequency domain.

[0054] Step 3: Construct the scaling factor σ(s) and the pole re-identification matrix, and solve the linear equation system Ax=b to obtain the residue of the scaling factor σ(s)

[0055] The original fitting form is as follows:

[0056]

[0057] where {a n} is the extreme point, {c n} is the residue, d and h are real constants, s = 2πω represents the Laplace domain, and ω is the frequency point data of the original data;

[0058] The scaling factor σ(s) can be written as follows:

[0059]

[0060] The right side of the first equation is the extreme residue form of the scaling factor σ(s), is the residue corresponding to the scaling factor σ(s), and the right side of the second equation is the zero-pole form of the scaling factor σ(s). is the zero point of the scaling factor σ(s);

[0061] Multiplying the scaling factor σ(s) by the fitted data f(s) yields the following equation:

[0062]

[0063] where {a n} is the known initial pole, f(s) is the known data to be fitted, s=jω is the Laplace variable, and ω represents the frequency domain point data. Then the unknown variables only include the residue and two constants d and h.

[0064] The corresponding linear equation system Ax=b is as follows:

[0065]

[0066] b=[f(s1)…f(s Ns )]

[0067] Where s = jω, is the Laplace domain, ω is the angular frequency, {a n} is a known pole, {f(s k )} is the original data to be fitted; is the residue corresponding to the fitting factor σ(s). Pole re-identification only needs to be applied to the residue of the fitting factor σ(s), while other variables {c k}, d, and h are not needed. Therefore, QR decomposition can be used to speed up matrix calculation.

[0068] In finding the residue corresponding to σ(s) After that, we now know the overall expression of the scaling factor σ(s), including the corresponding extreme points {a n} and residue The zero point corresponding to the zero-pole form of the scaling factor σ(s) is calculated by the following formula

[0069]

[0070] Where eig is the eigenvalue function, A is the extreme point {a n}, b is an all-one vector, is the residue vector. When the extreme point {a n When there are conjugate complex poles, it is necessary to replace the corresponding complex pole matrix A, coefficient vector b, and residue vector Rewrite it as follows:

[0071]

[0072] Where a′, a″ are the real and imaginary parts of the corresponding complex poles, and c′, c″ are the real and imaginary parts of the corresponding residues. Then we can get Represent the real and imaginary parts of the zero point respectively, so the complex zero point corresponds to This reconstructs the conjugate complex number pair.

[0073] Step 4: Obtain the new pole a by solving the linear equation system Ax=b as follows new (That is, the zero point of the scaling factor σ(s) ) under the residue c new and constant terms d, h.

[0074]

[0075] x=[c new1 …c newN dh] T

[0076] b=[f(s1)…f(s N )] T

[0077] The fitting rational fraction constructed at this time is as follows:

[0078]

[0079] Step 5: Calculate the fitting data f fit The residual δ between (s) and the original data f(s):

[0080]

[0081] Step 6: Determine whether the residual δ is less than the preset tolerance value. If the residual δ is less than the tolerance value, set N right = N, and jump to step 8; if the residual δ is greater than the tolerance value, proceed to step 7.

[0082] Step 7: Determine whether the current number of iterations is less than the maximum number of iterations. If the current number of iterations is less than the maximum number of iterations, use the current extreme point as the new initial extreme point and jump to step 3; if the current number of iterations is greater than the maximum number of iterations, set N left =N, proceed to step 8.

[0083] Step 8: Reset the number of poles N = ceil((N right +N left ) / 2). When the number of poles N remains unchanged, the algorithm is exited and the fitting rational fraction form corresponding to the minimum number of poles is output. Otherwise, the new number of poles N is substituted into step 2.

[0084] Step 9: Fit the original data using the best fitting rational fraction form function, calculate the frequency response and time domain response under the vector fitting form, and complete the simulation modeling.

[0085] Figure 2 and Figure 3Shown are the fitting amplitude and phase diagrams obtained by running a simple case on the MWork platform, and compared with the fitting results of Matlab. The algorithm proposed in this patent is better than the fitting results of Matlab in this example, using fewer poles and the fitting results are closer to the original data. The method of the present invention can be used to accurately model RF devices and transmission lines. In view of the complex frequency domain response curves of RF devices in reality, a vector fitting algorithm combining a peak-finding algorithm to set the initial poles is proposed. Different from the traditional vector fitting algorithm, the core technology has three points: First, the initial pole optimization technology, which uses the peak-finding algorithm to obtain the characteristics of the fitting data and sets it as the initial pole of the vector fitting. The traditional method adopts a simple uniform distribution strategy and ignores the data characteristics, resulting in a slow iteration speed and poor performance when processing complex multi-resonance peak curves. The vector fitting method optimized by the peak-finding algorithm can use fewer poles and a faster iteration speed to meet the fitting error requirements. Figure 4 and Figure 5 The final effect of the multi-resonance peak curve fitting with a fixed number of poles is shown when the initial pole strategy is uniformly distributed and peak distribution. By comparing the two figures, it can be clearly concluded that the vector fitting technology using the peak distribution initial pole can better fit the multi-resonance peak curve. Figure 6 A comparison chart of the convergence speed of the two initial pole assignment algorithms is shown. Second, the QR decomposition technology is applied to speed up the pole iteration rate. The vector fitting algorithm transforms the nonlinear fitting problem into a problem of solving a set of linear equations and iteratively updating the initial poles by introducing a scaling factor σ(s). In the process of iterating the initial poles, direct calculation may lead to a waste of computing resources, so the QR decomposition technology is used to simplify the matrix calculation. This not only saves computing costs, but also speeds up the solution speed. Third, automatically determine the optimal number of poles. Traditional vector fitting calculations need to rely on experience to judge the optimal number of poles, while the present invention only needs to set the maximum number of poles, search for the fitting results through bisection, and quickly output the fitting rational form corresponding to the minimum number of poles that meets the fitting error requirements. This feature makes this method more efficient and reliable when dealing with complex systems. The method of the present invention can better fit real data, such as Figure 7 and Figure 8 As shown, the vector fitting using uniform distribution of initial poles cannot completely fit the original data, while the vector fitting using the peak distribution of the present invention can better fit the data of the real device. Figure 9 Shown is the frequency domain response calculated from the results of vector fitting. Figure 10 The figure shows the time-domain response plot for a square wave input calculated using the vector fit function. This result demonstrates that the vector fit function can abstract the characteristics of real RF devices into mathematical expressions, facilitating subsequent simulation modeling.

[0086] The embodiments described above are merely some preferred embodiments of the present invention and are not intended to limit the present invention. Persons skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent substitution or equivalent transformation falls within the scope of protection of the present invention.

Claims

1. A radio frequency device equivalent modeling method based on peak-finding method to optimize vector fitting technology, characterized in that: The steps include: Step 1: Measure and obtain the frequency domain response data of the RF device, and record the frequency response data at this time as the original data; Step 2: Set the maximum number of poles, the initial number of poles, and initialize N right and N left , combined with the peak-finding algorithm to optimize the setting of the initial extreme point; Step 3: Construct the scaling factor based on the initial poles, generate the pole re-identification matrix, and solve the zero point of the scaling factor. The zero point of the scaling factor is the new pole of the iteration. Step 4: Calculate the residue of the fitting function under the new extreme point to construct the rational fraction form of the fitting; Step 5: Substitute the frequency of the original data into the current rational fraction form and calculate the residual between the fitted data and the original data; Step 6: Determine whether the residual is less than the preset tolerance value. If it is less than the tolerance value, set N right = N, and jump to step 8, otherwise use the current pole as the new initial pole and proceed to step 7; Step 7: Determine whether the current number of iterations is less than the maximum number of iterations. If so, proceed to step 3. If the current number of iterations is greater than the maximum number of iterations, set N left =N, proceed to step 8; Step 8: Set the initial number of poles N = ceil((N left +N right ) / 2), where ceil(·) represents rounding up. If the initial number of poles N remains unchanged, the algorithm is exited; otherwise, it jumps to step 2. Step 9: Output the fitted rational polynomial structure corresponding to the minimum number of poles and calculate the time domain response function and frequency domain response function for modeling RF devices.

2. The radio frequency device equivalent modeling method based on peak search method optimization vector fitting technology according to claim 1 is characterized in that: According to the number N of initial poles initially set, a peak-finding algorithm is used to select the initial poles of the vector fitting, and the frequency point where the peak value is found is used as the initial pole candidate point to optimize the setting of the initial pole.

3. The RF device equivalent modeling method based on peak-finding method optimization vector fitting technology according to claim 2, characterized in that: If the number of initial poles set is greater than the number of peaks, the excess poles are evenly distributed in the frequency domain to include all peak points and evenly distributed conjugate complex pairs of poles. If the number of peaks is greater than the number of initial poles set, only the first N peak positions are selected as initial poles.

4. The method for equivalent modeling of radio frequency devices based on peak-finding method optimization vector fitting technology according to claim 2, characterized in that: The peak finding algorithm uses the findpeaks function to smooth the data through a moving average filter, then calculates the first-order derivative of the smoothed data to obtain the rate of change of the data, finds the positive and negative change points of the first-order derivative, and filters out unimportant peaks by setting a threshold, retaining peaks that exceed the threshold.

5. The radio frequency device equivalent modeling method based on peak search method optimization vector fitting technology according to claim 1 is characterized in that: Using the scaling factor σ(s) and setting the initial poles {a n }Convert the nonlinear fitting equation into a linear equation and set the zero point of the scaling factor σ(s) As the pinnacle of iterative updates The linear equation to be solved is Ax=b, b=[f(s1)…f(s Ns )] Among them A k is the k-th row element of A, s k s=jω, is the Laplace domain, ω is the angular frequency, {a n } is a known pole, {c m } is the residue, {f(s k )} is the original data to be fitted, is the residue corresponding to the fitting factor σ(s).

6. The radio frequency device equivalent modeling method based on peak-finding method optimization vector fitting technology according to claim 5 is characterized in that: In finding the residue corresponding to σ(s) Then, the zero point corresponding to the zero-pole form of the scaling factor σ(s) is calculated by the following formula Expressed in H: Where eig is the eigenvalue function, A is the extreme point {a n } is a diagonal matrix, when the extreme points {a n }When all are real poles, b is an all-one vector, is the residue vector.

7. The radio frequency device equivalent modeling method based on peak-finding method optimization vector fitting technology according to claim 5, characterized in that: For complex pole relocation, the real and imaginary part separation technology is used to perform conjugate processing on the complex poles, so that the complex poles finally solved are always conjugate symmetric. It is necessary to replace A, b, for: Where A is a diagonal matrix composed of poles, in which the real part a′ and imaginary part a″ of the conjugate complex pair poles a1, a2 are redistributed, b is originally a unit vector, and the position of the conjugate complex pair poles is replaced by [2,0] T , is the residue corresponding to the scaling factor σ(s), decomposing the residue corresponding to the complex pole into real and imaginary parts, and H represents the zero point of the scaling factor σ(s) solved by the final iteration It is also the pinnacle of iterative updates The new extreme

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