CN106372348A

CN106372348A - Vector fitting model order reduction method based on error control in linear system

Info

Publication number: CN106372348A
Application number: CN201610808296.9A
Authority: CN
Inventors: 谢树果; 张卫东; 苏东林; 阎照文
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2016-09-07
Filing date: 2016-09-07
Publication date: 2017-02-01
Anticipated expiration: 2036-09-07
Also published as: CN106372348B

Abstract

The invention discloses a method for reducing the order of a vector fitting model based on error control in a linear system. Aiming at traditional vector fitting under a wide frequency band, especially a highly dynamic linear system with a resonance point, the order of the established pole-residue model is The numbers are often high. The present invention introduces the error control function to select the data containing the important characteristics of the linear system through continuous iteration, and ignores the small change data at some representative details, thereby effectively reducing the order of the built model while sacrificing a certain modeling accuracy. number. Under the condition that the modeling accuracy requirements are met, the low-order pole-residue macromodel is obtained. Then the pole-residue macromodel is further transformed into a state-space model, and then passivity is processed, and finally the established pole-residue macromodel is output. The invention realizes the balance between model accuracy and complexity, and improves the simulation efficiency of electromagnetic compatibility electromagnetic emission.

Description

A Vector Fitting Model Order Reduction Method Based on Error Control in Linear Systems

技术领域technical field

本发明涉及一种线性系统中基于误差控制的矢量拟合模型降阶方法，属于电磁兼容技术领域，为实现电磁兼容量化设计仿真奠定基础。The invention relates to a vector fitting model reduction method based on error control in a linear system, belongs to the technical field of electromagnetic compatibility, and lays a foundation for realizing quantitative design and simulation of electromagnetic compatibility.

背景技术Background technique

随着电子系统向着高频率、高速化、小型化、多功能化和集成化的方向发展，电磁兼容性问题在电子系统设计过程中也越来越突出，已经成为制约电子系统研制的关键问题之一。With the development of electronic systems in the direction of high frequency, high speed, miniaturization, multi-function and integration, the problem of electromagnetic compatibility has become more and more prominent in the process of electronic system design, and has become one of the key issues restricting the development of electronic systems. one.

准确有效的电磁发射模型是进行电子系统电磁兼容性预测仿真及量化设计的关键。目前比较流行的基于矢量拟合的建模方法，能够快速地根据线性系统网络参数如S参数的测量或者仿真数据建立宽带等效模型。但是对于宽频带线性系统按照传统的矢量拟合所建模型往往阶数较高，仿真效率不高。电子系统的电磁兼容问题大多是由电路或元器件的带外特性导致的，所以急需建立干扰电路或元器件的含带外特性的宽带电磁兼容模型。因此，有必要在一定精度下，建立低阶模型，提高电磁兼容电磁发射的仿真效率。An accurate and effective electromagnetic emission model is the key to the prediction, simulation and quantitative design of electronic system electromagnetic compatibility. The currently popular modeling method based on vector fitting can quickly establish a broadband equivalent model based on the measurement or simulation data of linear system network parameters such as S parameters. However, for broadband linear systems, the model built by traditional vector fitting is often of high order, and the simulation efficiency is not high. The electromagnetic compatibility problems of electronic systems are mostly caused by the out-of-band characteristics of circuits or components, so it is urgent to establish a broadband electromagnetic compatibility model including out-of-band characteristics of interfering circuits or components. Therefore, it is necessary to establish a low-order model with a certain accuracy to improve the simulation efficiency of EMC electromagnetic emission.

发明内容Contents of the invention

本发明的目的是：克服现有技术的不足，提供一种线性系统中基于误差控制的矢量拟合模型降阶方法，进而得到低阶高精度模型，实现模型精度和复杂度的平衡，提高电磁兼容电磁发射的仿真效率。The purpose of the present invention is: to overcome the deficiencies of the prior art, to provide a vector fitting model reduction method based on error control in a linear system, and then to obtain a low-order high-precision model, to achieve a balance between model accuracy and complexity, and to improve electromagnetic Compatible with the simulation efficiency of electromagnetic emissions.

本发明一种线性系统中基于误差控制的矢量拟合模型降阶方法。通过引入误差控制函数采用不断迭代的方式选取出含有线性系统重要传输特性的数据，通过忽略某些代表细节处的微小变化数据，从而在牺牲很小建模精度情况下有效地降低所建模型的阶数。具体实现步骤如下：The invention relates to a vector fitting model reduction method based on error control in a linear system. By introducing an error control function, the data containing the important transmission characteristics of the linear system are selected in an iterative manner, and by ignoring the small change data at some representative details, the model is effectively reduced at the expense of small modeling accuracy. Order. The specific implementation steps are as follows:

步骤一：获取网络参数Step 1: Obtain network parameters

通过全波仿真软件，如HFSS、CST或者Microwave Office对建模对象进行仿真，获取宽频带内不同频点处的端口网络参数S(散射)参数值s_i＝j2πf_i。Simulate the modeling object through full-wave simulation software, such as HFSS, CST or Microwave Office, and obtain the S (scattering) parameter values of the port network parameters at different frequency points within a wide frequency band s _i =j2πf _i .

步骤二：建立低阶极点-留数宏模型Step 2: Establish a low-order pole-residue macromodel

具体的建模流程图如图1所示。图中σ代表均方根误差，误差控制函数δ定义为：The specific modeling flow chart is shown in Figure 1. In the figure, σ represents the root mean square error, and the error control function δ is defined as:

$δ δ (({s the s}_{i i})) = = \frac{| | | | {H h}_{R R a a w w} (({s the s}_{i i})) | | - - | | {H h}_{F f i i t t} (({s the s}_{i i})) | | | |}{| | {H h}_{R R a a w w} (({s the s}_{i i})) | |}$

其中H_Raw(s_i)代表仿真得到的散射参数数据，H_Fit(s_i)代表矢量拟合所建宏模型,i＝1,2,...K.；σ₀为预先设置的均方根误差，δ₀为预先设置的误差控制函数阈值。Among them, H _Raw (s _i ) represents the scattering parameter data obtained by simulation, H _Fit (s _i ) represents the macromodel built by vector fitting, i=1,2,...K.; σ ₀ is the pre-set mean square root error, δ ₀ is the preset error control function threshold.

建模部分包括两个迭代循环，第一个迭代循环为矢量拟合算法建模迭代循环，另一个是选取建模数组迭代循环。建模数组就是从H_Raw(s_i)中选出代表建模对象重要传输特性的数据。The modeling part consists of two iterative loops, the first iterative loop for vector fitting algorithm modeling iterative loop, the other is selection modeling array iterative loop. The modeling array is to select the data representing the important transmission characteristics of the modeling object from H _Raw (s _i ).

1)矢量拟合算法建模迭代循环1) Vector fitting algorithm modeling iterative loop

第一步：在整个宽频带内从步骤一中获取的S散射参数中均匀地选取几对数据作为初始建模数组。Step 1: Uniformly select several pairs of data from the S-scattering parameters obtained in step 1 in the entire broadband frequency band as the initial modeling array.

第二步：采用传统的矢量拟合算法进行建模Step 2: Modeling using traditional vector fitting algorithms

通过仿真或者测量得到线性系统的频域散射参数 Obtain the frequency domain scattering parameters of the linear system by simulation or measurement

假设待建立的极点-留数宏模型为H_Fit(s)，其数学表达式为：Assuming that the pole-residue macromodel to be established is H _Fit (s), its mathematical expression is:

${H h}_{F f i i t t} ((s the s)) = = {Σ Σ}_{m m = = 11}^{N N} \frac{{r r}_{m m}}{s the s - - {p p}_{m m}} + + d d - - - - - - ((11))$

式中，s＝jω表示复频率变量，ω为角频率，r_m，p_m分别为待辨识宏模型的第m个留数和极点，d是常数项值。矢量拟合的目的就是要求出式(1)中的极点p_m、留数r_m以及d的值。In the formula, s=jω represents the complex frequency variable, ω is the angular frequency, r _m and p _m are respectively the mth residue and pole of the macromodel to be identified, and d is the value of the constant term. The purpose of vector fitting is to obtain the values of pole p _m , residue r _m and d in formula (1).

极点的辨识：Identification of poles:

设初始极点同时引入尺度因子σ(s)。set initial pole At the same time, the scale factor σ(s) is introduced.

$σ σ ((s the s)) = = {Σ Σ}_{m m = = 11}^{N N} \frac{{\overset{~ ~}{r r}}_{m m}}{s the s - - {\overset{&OverBar; &OverBar;}{p p}}_{m m}} + + 11 - - - - - - ((22))$

其中，表示尺度因子σ(s)的第m个留数值。in, Indicates the mth residual value of the scaling factor σ(s).

将σ(s)乘以H_Fit(s)得到一个新极点-留数宏模型Multiply σ(s) by H _Fit (s) to get a new pole-residue macromodel

${Σ Σ}_{m m = = 11}^{N N} \frac{{\overset{^^}{r r}}_{m m}}{s the s - - {\overset{&OverBar; &OverBar;}{p p}}_{m m}} + + \overset{^^}{d d} = = {H h}_{F f i i t t} ((s the s)) (({Σ Σ}_{m m = = 11}^{N N} \frac{{\overset{~ ~}{r r}}_{m m}}{s the s - - {\overset{&OverBar; &OverBar;}{p p}}_{m m}} + + 11)) - - - - - - ((33))$

其中，表示新极点-留数宏模型的第i个留数值，表示新极点-留数宏模型的常数项值。通过移项，进一步可以得到：in, Indicates the ith residue value of the new pole-residue macromodel, represents the value of the constant term of the new pole-residue macromodel. By shifting terms, we can further get:

${Σ Σ}_{m m = = 11}^{N N} \frac{{\overset{^^}{r r}}_{m m}}{s the s - - {\overset{&OverBar; &OverBar;}{p p}}_{m m}} + + \overset{^^}{d d} - - {H h}_{F f i i t t} ((s the s)) {Σ Σ}_{m m = = 11}^{N N} \frac{{\overset{~ ~}{r r}}_{m m}}{s the s - - {\overset{&OverBar; &OverBar;}{p p}}_{m m}} = = {H h}_{F f i i t t} ((s the s)) - - - - - - ((44))$

公式(4)中，将看作是未知量，在离散频点s_i＝jω_i处，i＝1,2,...K且K＞2(N+1)，并用H_Raw(s_i)的近似取代H_Fit(s_i)，最终可以得到如下线性方程组。In formula (4), the As an unknown quantity, at the discrete frequency point s _i =jω _i , _i =1,2,...K and K>2(N+1), and _{replace H Fit} ₍ s _i ), and finally the following linear equations can be obtained.

AX＝b (5)AX=b (5)

线性方程组中的矩阵A和矢量X，b定义分别如下：The matrix A and vector X, b in the linear equation system are defined as follows:

$A A = = [\begin{matrix} \frac{11}{{jω jω}_{11} - - {\overset{&OverBar; &OverBar;}{p p}}_{11}} & ... ... & \frac{11}{{jω jω}_{11} - - {\overset{&OverBar; &OverBar;}{p p}}_{N N}} & 11 & \frac{- - {H h}_{R R a a w w} (({jω jω}_{11}))}{{jω jω}_{11} - - {\overset{&OverBar; &OverBar;}{p p}}_{11}} & ... ... & \frac{- - {H h}_{R R a a w w} (({jω jω}_{11}))}{{jω jω}_{11} - - {\overset{&OverBar; &OverBar;}{p p}}_{N N}} \\ ... ... & ... ... & ... ... & ... ... & ... ... & ... ... & .. .. \\ \frac{11}{{jω jω}_{K K} - - {\overset{&OverBar; &OverBar;}{p p}}_{11}} & ... ... & \frac{11}{{jω jω}_{K K} - - {\overset{&OverBar; &OverBar;}{p p}}_{N N}} & 11 & \frac{- - {H h}_{R R a a w w} (({jω jω}_{K K}))}{{jω jω}_{K K} - - {\overset{&OverBar; &OverBar;}{p p}}_{11}} & ... ... & \frac{- - {H h}_{R R a a w w} (({jω jω}_{K K}))}{{jω jω}_{K K} - - {\overset{&OverBar; &OverBar;}{p p}}_{N N}} \end{matrix}] - - - - - - ((66))$

$X x = = {(({\overset{^^}{r r}}_{11},, {\overset{^^}{r r}}_{22},, ... ... {\overset{^^}{r r}}_{N N},, \overset{^^}{d d},, {\overset{~ ~}{r r}}_{11},, {\overset{~ ~}{r r}}_{22},, ... ... {\overset{~ ~}{r r}}_{N N}))}^{T T} - - - - - - ((77))$

b＝(H_Raw(jω₁),...,H_Raw(jω_K))^T (8)b＝(H _Raw (jω ₁ ),...,H _Raw (jω _K )) ^T (8)

方程(5)是一个超定线性方程组，可以通过最小均方差准则求解未知变量X。新的极点值可以通过计算得到，其中A为包含初始极点的的对角矩阵，b为单位列向量，为包含的行向量。通过几次迭代，当尺度因子σ(s)接近于1时，终止迭代，输出最终的极点值p_m(m＝1,…,N)。Equation (5) is an overdetermined linear equation system, which can be solved for the unknown variable X by the minimum mean square error criterion. New pole values can be obtained by Calculated, where A is the initial pole containing the Diagonal matrix of , b is a unit column vector, to contain row vector of . After several iterations, when the scale factor σ(s) is close to 1, the iteration is terminated, and the final pole value p _m (m=1,...,N) is output.

留数和常数项辨识Residue and constant term identification

当极点辨识完成之后，得到p_m(m＝1,…,N)，此时留数r_m(m＝1,…,N)和常数项d可以通过方程(9)进行辨识。After the pole identification is completed, p _m (m=1,...,N) is obtained. At this time, the residue r _m (m=1,...,N) and the constant term d can be identified through equation (9).

A'x'＝b' (9)A'x'=b' (9)

其中：in:

${A A}^{' '} = = [[\begin{matrix} \frac{11}{{jω jω}_{11} - - {p p}_{11}} & ... ... & \frac{11}{{jω jω}_{11} - - {p p}_{N N}} & 11 \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ \frac{11}{{jω jω}_{K K} - - {p p}_{11}} & ... ... & \frac{11}{{jω jω}_{K K} - - {p p}_{N N}} & 11 \end{matrix}]]$

x'＝[r₁,r₂,…,r_N,d]^T x'＝[r ₁ ,r ₂ ,…,r _N ,d] ^T

b'＝[H_Raw(jω₁),…,H_Raw(jω_K)]^T b'＝[H _Raw (jω ₁ ),…,H _Raw (jω _K )] ^T

此时，就可以得到极点-留数宏模型。At this point, the pole-residue macromodel can be obtained.

第三步：计算采用矢量拟合所建模型与建模数组之间的均方根误差σ，若σ≤σ₀，则输出矢量拟合模型。否则，增加阶数，重复第二步，直到满足σ≤σ₀。Step 3: Calculate the root mean square error σ between the model built by vector fitting and the modeling array. If σ≤σ ₀ , output the vector fitting model. Otherwise, increase the order and repeat the second step until σ≤σ ₀ is satisfied.

2)选取建模数组迭代循环2) Select the modeling array iteration loop

第一步：在得到矢量拟合模型后，计算误差函数δ(s_i)；Step 1: After obtaining the vector fitting model, calculate the error function δ(s _i );

其中，H_Raw(s_i)代表仿真得到的散射参数数据，H_Fit(s_i)代表矢量拟合所建宏模型,i＝1,2,...K。Among them, H _Raw (s _i ) represents the scattering parameter data obtained by simulation, H _Fit (s _i ) represents the macromodel built by vector fitting, i=1,2,...K.

第二步：若max(δ(s_i))≤δ₀则输出宽频带的极点-留数模型，进入3)无源性判定及强。若max(δ(s_i))＞δ₀，则增加新的数据到建模数组，重新进入1)矢量拟合算法建模迭代循环。其中所增加的新数据选取在δ(s_i)最大处。The second step: if max(δ(s _i ))≤δ ₀ , output the pole-residue model of broadband, and enter into 3) passivity judgment and strength. If max(δ(s _i ))>δ ₀ , add new data to the modeling array, and re-enter 1) vector fitting algorithm modeling iteration cycle. The added new data is selected at the point where δ(s _i ) is maximum.

经过多次迭代循环，预先设置的建模精度σ₀和δ₀都被满足，则输出的极点-留数宏模型为：After multiple iteration cycles, the preset modeling accuracy σ ₀ and δ ₀ are both satisfied, then the output pole-residue macromodel is:

${H h}_{F f i i t t} ((s the s)) = = {Σ Σ}_{m m = = 11}^{N N} \frac{{r r}_{m m}}{s the s - - {a a}_{m m}} + + d d$

其中，s＝jω。ω为角频率，a_m为极点-留数宏模型H_Fit(s)的第m个极点值，r_m为极点-留数宏模型H_Fit(s)的第m个留数值，d为常数项值，N表示极点-留数宏模型H_Fit(s)的阶数。where s=jω. ω is the angular frequency, a _m is the mth pole value of the pole-residue macromodel H _Fit (s), r _m is the mth residue value of the pole-residue macromodel H _Fit (s), and d is a constant Item value, N represents the order of the pole-residue macromodel H _Fit (s).

3)无源性判定及增强。3) Passivity judgment and enhancement.

将得到极点-留数宏模型转化为状态空间模型：Convert the resulting pole-residue macromodel to a state-space model:

其中，x为状态变量，u为输入向量，y为输出向量，表示对x求导，A、B、C、和D为状态方程系数矩阵。 Among them, x is the state variable, u is the input vector, y is the output vector, Indicates the derivative of x, and A, B, C, and D are the state equation coefficient matrices.

由状态方程系数矩阵构建无源性判定矩阵J＝(A-B(D-I)^-1C)(A-B(D+I)^-1C)；计算矩阵J的特征值λ_i，若λ_i为负实数，则状态空间模型不满足无源性；反之，状态空间模型满足无源性。Construct passivity judgment matrix J=(AB(DI) ^-1 C)(AB(D+I) ^-1 C) by state equation coefficient matrix; calculate the eigenvalue λ _i of matrix J, if λ _i is a negative real number, Then the state-space model does not satisfy the passivity; on the contrary, the state-space model satisfies the passivity.

当状态空间模型不满足无源性时，通过对留数r_m和常数项d进行扰动处理增强其无源性。When the state-space model does not satisfy the passivity, its passivity is enhanced by perturbing the residue r _m and the constant term d.

${ΔH ΔH}_{F f i i t t} ((s the s)) = = {Σ Σ}_{m m = = 11}^{N N} \frac{{Δr Δr}_{m m}}{s the s - - {a a}_{m m}} + + Δ Δ d d &cong; &cong; 00$

其中，Δr_m为极点留数宏模型H_Fit(s)第m个留数r_m的微扰动值，Δd为极点留数宏模型H_Fit(s)常数项d的微扰动值，N表示宏模型的阶数。Among them, Δr _m is the microperturbation value of the mth residue r _m of the pole residue macromodel H _Fit (s), Δd is the microperturbation value of the constant term d of the pole residue macromodel H _Fit (s), and N represents the macro The order of the model.

使得无源性判定矩阵J的特征值λ_i不存在负实数。经过多次迭代修正后最终可以保证模型满足无源性要求。最后输出高精度低阶极点-留数宏模型H_Fit。So that the eigenvalue λ _i of the passivity judgment matrix J does not have negative real numbers. After multiple iterative corrections, the model can finally be guaranteed to meet the passivity requirements. Finally, the high-precision low-order pole-residue macromodel H _Fit is output.

本发明的优点和积极效果在于：Advantage and positive effect of the present invention are:

①针对线性电路系统太过庞大复杂时，在不掌握系统具体电路及任何参数的情况下，当发生电磁兼容问题时，如果进行宽带建模分析，采用传统的矢量拟合算法所建模型的复杂度往往会非常高。本发明提出的方法，可以建立高精度的低阶等效模型，提高仿真效率。① When the linear circuit system is too large and complex, if the electromagnetic compatibility problem occurs without knowing the specific circuit and any parameters of the system, if the broadband modeling analysis is performed, the model built by the traditional vector fitting algorithm will be complicated. is often very high. The method proposed by the invention can establish a high-precision low-order equivalent model and improve simulation efficiency.

②本发明对仿真数据进行建模时，只需要较少的仿真数据，就可以建立原线性系统的低阶宽带模型，准确度高，且无需知道电路内部结构和具体参数。② When the present invention models the simulation data, only a small amount of simulation data is needed to establish a low-order broadband model of the original linear system with high accuracy and without knowing the internal structure and specific parameters of the circuit.

③本发明相较于其他模型降阶方法，在相同阶数下具有更高的建模精度，尤其对于极小值点处。更适合应用到具有大量谐振点的线性系统建模。③Compared with other model reduction methods, the present invention has higher modeling accuracy at the same order, especially for the minimum point. It is more suitable for modeling linear systems with a large number of resonance points.

附图说明Description of drawings

图1是本发明中基于误差控制的矢量拟合模型降阶方法流程图；Fig. 1 is the flow chart of the vector fitting model reduction method based on error control in the present invention;

图2是验证实例微带滤波器的三维立体模型图；Fig. 2 is a three-dimensional model diagram of a verification example microstrip filter;

图3是验证实例滤波器电路原理图；Fig. 3 is the schematic diagram of the verification example filter circuit;

图4是验证实例滤波器尺寸示意图；Figure 4 is a schematic diagram of the size of the verification example filter;

图5是传统矢量拟合所建模型与测量数据的对比图；Fig. 5 is a comparison diagram of the model built by traditional vector fitting and the measured data;

图6是经典的平衡截断模型降阶方法所建模型与测试数据的对比图；Fig. 6 is a comparison chart of the model built by the classic balanced truncated model reduction method and the test data;

图7是本发明所建模型与测试数据的对比图。Fig. 7 is a comparison diagram between the model built by the present invention and the test data.

具体实施方式detailed description

下面将结合附图和实施例对本发明做进一步的详细说明。The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

本发明提供的基于误差控制的矢量拟合模型降阶方法，首先通过仿真获取一定带宽下线性系统端口网络参数，如散射(S)参数。通过引入误差控制函数通过不断迭代的方式选取出包含线性系统重要特性的数据，通过忽略某些代表细节处的微小变化数据，从而在牺牲一定建模精度情况下有效地降低所建模型的阶数。在得到满足建模精度要求的情况下，获得低阶极点-留数宏模型。然后将极点-留数宏模型进一步转化为状态空间模型，然后再进行无源性处理，最后输出所建极点-留数宏模型。The error control-based vector fitting model reduction method provided by the present invention first obtains the port network parameters of a linear system under a certain bandwidth through simulation, such as scattering (S) parameters. By introducing the error control function, the data containing the important characteristics of the linear system are selected through continuous iteration, and by ignoring the small change data at some representative details, the order of the built model can be effectively reduced at the expense of a certain modeling accuracy. . Under the condition that the modeling accuracy requirements are met, the low-order pole-residue macromodel is obtained. Then the pole-residue macromodel is further transformed into a state-space model, and then passivity is processed, and finally the established pole-residue macromodel is output.

线性系统端口散射参数的仿真软件为：AWR公司的Microwave Office仿真软件。仿真得到线性端口的散射参数s_i＝j2πf_i，f_i代表频率点。然后采用Matlab软件按照流程图1进行建模，最终得到低阶极点-留数宏模型。The simulation software for the scattering parameters of the linear system port is: Microwave Office simulation software of AWR Company. Simulation to get the scattering parameters of the linear port s _i =j2πf _i , where f _i represents a frequency point. Then use Matlab software to model according to the flow chart 1, and finally get the low-order pole-residue macromodel.

下面以0～8GHz微带低通滤波器为建模对象进行说明：The following takes the 0-8GHz microstrip low-pass filter as the modeling object to illustrate:

如图2所示为所采用的验证实例微带滤波器的三维立体模型图，从图中可以看出，此微带滤波器为对称结构。图4为所采用的验证实例微带滤波器的具体尺寸示意图，其具体尺寸值如表1所示，其中L代表微带线的长度，W代表微带线的宽度。Figure 2 shows the three-dimensional model diagram of the microstrip filter used in the verification example. It can be seen from the figure that the microstrip filter has a symmetrical structure. Figure 4 is a schematic diagram of the specific dimensions of the microstrip filter used in the verification example, and its specific dimension values are shown in Table 1, wherein L represents the length of the microstrip line, and W represents the width of the microstrip line.

表1验证实例微带滤波器尺寸值表(单位mm)Table 1 Verification example microstrip filter size value list (unit: mm)

L_A _LA L_B L _B L_C L _C L_D L _D L_E L _E L_F L _F 2.5402.540 1.7761.776 2.0322.032 1.1181.118 1.9811.981 2.7432.743 W_A W _A W_B W _B W_C W _C W_D W _D W_E W _E W_F W _F 0.38100.3810 0.2540.254 0.13970.1397 0.17780.1778 0.35560.3556 0.25400.2540

采用AWR公司Microwave Office软件对0～8GHz低通滤波器进行仿真得到2～10GHz的S11参数，图3所示为所采用的验证实例微带滤波器在Microwave office仿真软件中的仿真模型。本发明是一种基于误差控制的矢量拟合模型降阶方法，包括以下步骤一至四。Use Microwave Office software of AWR Company to simulate the 0-8GHz low-pass filter to obtain the S11 parameters of 2-10GHz. Figure 3 shows the simulation model of the verification example microstrip filter used in the Microwave office simulation software. The present invention is a vector fitting model reduction method based on error control, comprising the following steps 1 to 4.

步骤一：网络参数获取Step 1: Obtain network parameters

通过AWR公司的Microwave Office仿真软件对建模对象低通滤波器进行端口散射参数仿真，获取2～10GHz频段的S11参数数据其中s_i对应仿真数据的频点，H_Raw(s_i)表示相应频点下散射S12参数，K表示频点个数。Through the Microwave Office simulation software of AWR Company, the port scattering parameter simulation of the low-pass filter of the modeling object is carried out, and the S11 parameter data of the 2-10GHz frequency band is obtained Among them, s _i corresponds to the frequency point of the simulation data, H _Raw ( _si ) represents the scattering S12 parameter at the corresponding frequency point, and K represents the number of frequency points.

步骤二：建立低阶宏模型。Step 2: Establish a low-level macro model.

分别设置均方根误差σ₀和误差控制函数阈值δ₀，σ₀＝1.000dB和δ₀＝3dB。The root mean square error σ ₀ and the error control function threshold δ ₀ are respectively set, σ ₀ =1.000dB and δ ₀ =3dB.

建模部分包括两个迭代循环，第一个迭代循环为矢量拟合算法建模迭代循环，另一个为建模数据选取迭代循环。The modeling part consists of two iterative loops, the first iterative loop for the vector fitting algorithm modeling iterative loop, and the other iterative loop for the modeling data selection iterative loop.

第一步：在整个2～10GHz宽频带内从步骤一种获取的S参数中均匀地选取四个数据作为初始建模数组。Step 1: S-parameters obtained from step 1 in the entire 2-10 GHz wide frequency band Four data are uniformly selected as the initial modeling array.

第二步：采用传统矢量拟合算法进行建模Step 2: Modeling with traditional vector fitting algorithm

具体过程请参见具体实现步骤中关于传统矢量拟合建模的介绍。For the specific process, please refer to the introduction of traditional vector fitting modeling in the specific implementation steps.

第三步：计算采用矢量拟合所建模型与建模数组之间的均方根误差σ，若σ≤σ₀，则进入2)。否则，增加阶数，重复第二步，直到满足σ≤σ₀。Step 3: Calculate the root mean square error σ between the model built by vector fitting and the modeling array. If σ≤σ ₀ , go to 2). Otherwise, increase the order and repeat the second step until σ≤σ ₀ is satisfied.

2)建模数据选取迭代循环2) Modeling data selection iterative cycle

第一步：矢量拟合算法所建模型与建模数组之间的均方根误差满足σ≤σ₀后，计算误差函数 Step 1: Calculate the error function after the root mean square error between the model built by the vector fitting algorithm and the modeling array satisfies σ≤σ ₀

第二步：判断是否满足δ＝max(δ_i)≤δ₀。若满足，则输出宽频带的极点-留数宏模型，进行无源性加强。若不满足，则增加新的数据到建模数组，重新进入1)矢量拟合算法建模迭代循环。其中所增加的新数据选取在δ_i最大处。The second step: judging whether δ=max(δ _i )≤δ ₀ is satisfied. If it is satisfied, the pole-residue macromodel of wide frequency band is output for passivity enhancement. If not satisfied, add new data to the modeling array, and re-enter 1) vector fitting algorithm modeling iteration cycle. The added new data is selected at the point where δ _i is the largest.

最终输出的极点-留数宏模型为：The final output pole-residue macromodel is:

其中，s＝jω表示复频率变量。ω为角频率，a_m为极点-留数宏模型H_Fit(s)的第m个极点值，r_m为极点-留数宏模型H_Fit(s)的第m个留数值，d为常数项值，N表示极点-留数宏模型H_Fit(s)的阶数。Among them, s=jω represents a complex frequency variable. ω is the angular frequency, a _m is the mth pole value of the pole-residue macromodel H _Fit (s), r _m is the mth residue value of the pole-residue macromodel H _Fit (s), and d is a constant Item value, N represents the order of the pole-residue macromodel H _Fit (s).

步骤三：无源性判定及增强。Step 3: Passivity determination and enhancement.

当状态空间模型不满足无源性时，通过对留数r_m和常数项d进行微扰动处理保证其无源性。When the state-space model does not satisfy the passivity, the passivity is ensured by slightly perturbing the residue r _m and the constant term d.

使得无源性判定矩阵J的特征值λ_i不存在负实数。经过多次迭代修正后最终可以保证模型满足无源性要求。最后输出低阶极点-留数宏模型H_Fit，如图6所示。从图6中可以看出，最终得到的14阶极点留数宏模型在谐振点4.5GHz处具有0.1336dB的误差。So that the eigenvalue λ _i of the passivity judgment matrix J does not have negative real numbers. After multiple iterative corrections, the model can finally be guaranteed to meet the passivity requirements. Finally, the low-order pole-residue macromodel H _Fit is output, as shown in FIG. 6 . It can be seen from Figure 6 that the final 14th-order pole residue macromodel has an error of 0.1336dB at the resonance point of 4.5GHz.

为了体现本发明的优越性，采用了传统的矢量拟合算法对实例中的微带滤波器S11进行了建模，模型为45阶时如图5所示。从图5中可以看出，45阶极点留数宏模型在谐振点4.5GHz处具有5.195dB的误差。之后，采用经典的平衡截断模型降阶法对传统的矢量拟合算法建立的45阶极点留数宏模型进行模型降阶，为了对比，同样降阶到14阶，但是在谐振点处具有16.590dB的误差，如图7所示。通过与传统矢量拟合建模方法和平衡截断模型降阶方法相对比，本发明在极小值点处所建极点-留数宏模型具有更高的建模精度，实现模型精度和复杂度的平衡，大大提高了电磁兼容电磁发射的仿真效率。In order to reflect the superiority of the present invention, the traditional vector fitting algorithm is used to model the microstrip filter S11 in the example, as shown in Figure 5 when the model is 45th order. It can be seen from Figure 5 that the 45th-order pole residue macromodel has an error of 5.195dB at the resonance point of 4.5GHz. Afterwards, the classic balance truncated model reduction method is used to reduce the model order of the 45th-order pole residue macromodel established by the traditional vector fitting algorithm. For comparison, the order is also reduced to the 14th order, but there is a 16.590dB at the resonance point error, as shown in Figure 7. Compared with the traditional vector fitting modeling method and the balance truncation model reduction method, the pole-residue macromodel built by the present invention at the minimum point has higher modeling accuracy, and realizes the balance between model accuracy and complexity. Balance, greatly improving the simulation efficiency of EMC electromagnetic emission.

提供以上实施例仅仅是为了描述本发明的目的，而并非要限制本发明的范围。本发明的范围由所附权利要求限定。不脱离本发明的精神和原理而做出的各种等同替换和修改，均应涵盖在本发明的范围之内。The above embodiments are provided only for the purpose of describing the present invention, not to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent replacements and modifications made without departing from the spirit and principle of the present invention shall fall within the scope of the present invention.

Claims

1. An error control-based vector fitting model order reduction method in a linear system is characterized by comprising the following steps:

the method comprises the following steps: acquiring linear system port network parameters under a set bandwidth through simulation;

step two: uniformly selecting a plurality of pairs of data from the network parameters obtained in the step one in the whole set bandwidth as initial modeling arrays;

step three: modeling the modeling array by adopting a vector fitting algorithm;

step four: vector adopted for calculationThe root mean square error sigma between the model established by the quantity fitting algorithm and the modeling array is calculated, and if the root mean square error sigma is less than or equal to the sigma₀Then the vector fitting model, σ, is output₀The error is a preset root mean square error; otherwise, increasing the order, and repeating the third step until sigma is less than or equal to sigma₀；

Step five: after the vector fitting model is obtained, the error function(s) is calculated_i)；

Step six: if max ((s)_i))≤₀Outputting a pole-residue model of the wide frequency band, entering the passivity judgment and enhancement in the sixth step,₀is a preset value; if max ((s)_i))＞₀If so, adding new data to the modeling array, and re-entering the step three iteration loop; through an iterative loop, a predetermined value σ₀And₀all satisfied, the output pole-residue macro model is:

H_{F i t} (s) = Σ_{m = 1}^{N} \frac{r_{m}}{s - a_{m}} + d

wherein, s ═ j ω represents a complex frequency variable; omega is the angular frequency, a_mLeave a number of macro-models for poles H_Fit(s) mth extreme value, r_mLeave a number of macro-models for poles H_Fit(s) mth residue value, d is the pole residue macro model H_FitConstant term value of(s), N represents the pole residue macro model H_Fit(s) order;

step six: passivity judgment and enhancement are carried out, and model fullness is finally ensured after multiple iterative correctionsThe passivity requirement is satisfied; finally outputting a high-precision low-order pole-residue macro model H_Fit：

{ΔH}_{F i t} (s) = Σ_{m = 1}^{N} \frac{{Δr}_{m}}{s - a_{m}} + Δ d &cong; 0

Wherein, Δ r_mLeave a number of macro-models for poles H_Fit(s) mth residue r_mThe perturbation value of (1) is a pole residue macro model H_Fit(s) the perturbation value of the constant term d.

2. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: in the first step, full-wave simulation software HFSS, CST or Microwave Office is adopted to simulate.

3. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: in said step five, the error function(s)_i) The calculation formula of (a) is as follows:

δ (s_{i}) = \frac{| | H_{R a w} (s_{i}) | - | H_{F i t} (s_{i}) | |}{| H_{R a w} (s_{i}) |}

wherein H_Raw(s_i) Data representing the simulation-derived parameters of the linear system port network, H_Fit(s_i) Represents the macro model created by vector fitting, i ═ 1, 2.

4. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: in said step five, the new data added is selected in(s)_i) The maximum.

5. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: the sixth step is specifically realized as follows:

and (3) converting the obtained pole-residue macro model into a state space model:

wherein x is a state variable, u is an input vector, y is an output vector,expressing the derivation of x, A, B, C, and D as a matrix of state equation coefficients;

constructing an passivity judgment matrix J ═ (A-B (D-I) from the coefficient matrix of the state equation^-1C)(A-B(D+I)^-1C) (ii) a Calculating the eigenvalues λ of the matrix J_iIf λ_iIf the real number is negative, the state space model does not meet passivity; otherwise, the state space model satisfies passivity;

when the state space model does not satisfy passivity, the residue r is checked_mThe constant term d is subjected to disturbance treatment to enhance the passivity of the constant term d;

{ΔH}_{F i t} (s) = Σ_{m = 1}^{N} \frac{{Δr}_{m}}{s - a_{m}} + Δ d &cong; 0

make the eigenvalue lambda of the passivity decision matrix J_iThere are no negative real numbers; after multiple iterative corrections, the model is finally guaranteed to meet the passivity requirement; finally outputting a high-precision low-order pole-residue macro model H_Fit。