CN108108557B

CN108108557B - Adaptive fitting and simulation method for nport problem based on vector matching method

Info

Publication number: CN108108557B
Application number: CN201711391776.0A
Authority: CN
Inventors: 赵林; 吴大可; 程明厚; 李雷; 刘寅
Original assignee: Huada Empyrean Software Co Ltd
Current assignee: Shenzhen Huada Jiutian Technology Co ltd
Priority date: 2017-12-21
Filing date: 2017-12-21
Publication date: 2020-06-02
Anticipated expiration: 2037-12-21
Also published as: CN108108557A

Abstract

The invention provides an nport problem self-adaptive fitting and simulation method based on a vector matching method, which comprises the following steps: (1) carrying out self-adaptive fitting on the S parameter by using a vector matching method to obtain a fitting result S with optimal fitting order K and delay time d_ij(s), wherein i is greater than or equal to 1 and j is less than or equal to n; (2) transfer function S in frequency domain by inverse Laplace transform_ij(s) conversion to an excitation function s in the time domain_ij(t); (3) the convolution of the S parameters is computed by a recursive method, thus obtaining the algebraic equation of the nport model. The nport problem self-adaptive fitting and simulation method based on the vector matching method utilizes the vector matching method to carry out self-adaptive fitting on the S parameters and the recursive convolution method to quickly calculate the convolution of the S parameters, achieves higher fitting precision and better fitting effect, and provides a calculation format with simple form and higher precision by Taylor approximation.

Description

Adaptive fitting and simulation method for nport problem based on vector matching method

Technical Field

The invention relates to the technical field of circuit simulation, in particular to an nport problem adaptive fitting and simulation method based on a vector matching method.

Background

Vector matching is a stable and efficient fitting method proposed by b.gustavsen in the literature "Rational adaptation of frequency domain responses by vector matching" (published in "IEEE Transactions on power Delivery" volume 14, phase 3). The vector matching method is particularly suitable for modeling related S parameters (Y parameters or Z parameters) in circuit simulation, and has the following advantages compared with other fitting methods:

(1) the vector matching method is to give an initial pole in principle, solve two linear least square equations to obtain a modified pole, generally only need iteration of limited steps to obtain the pole meeting the requirements, and has high convergence speed;

(2) the actually measured S parameters generally only contain frequency response within a limited range, and the result fitted by a vector matching method can theoretically process the frequency response within any range;

(3) other fitting methods suffer from numerical problems when fitting a measured frequency response over a wide frequency range using high-order rational functions, especially in the case of noisy frequency responses, while the vector matching method is not affected.

The method adopts a rational function to approximately fit a network function H(s), and the partial sum form is as follows:

wherein r is a constant term, is a real number, p_kAnd q is_kRespectively pole and residue. The approximate fitting is realized by replacing the initial poles with a group of modified poles, the modified poles are obtained by a pole relocation method based on linear least square, and the fitting order is equal to the number of the initial poles. The selection of each pair of conjugate poles is as follows:

to ensure stability of the fit, the selected poles should all lie in the left half plane of the complex plane.

The recursive convolution method is a method for calculating convolution proposed by Shen Lin and Ernest S.Kuh in the literature, "transformation correlation of loss interconnection based on the recursive convolution transformation" (published in "EEETransductions on Circuits and Systems" journal No. 39, Vol. 11). When the convolution is calculated by the traditional method, in order to obtain the convolution of the current time, integration from zero time to the current time is required, and the convolution calculation is required to be subjected to reverse folding, moving, multiplying and adding, so that the convolution operation is very complicated, and the simulation time is difficult to bear. When the convolution of the current moment is calculated by the recursive convolution method, only the convolution result of the previous moment is needed to be utilized, so that the defect is avoided, and the calculation efficiency is greatly improved.

In rf circuit analysis, it is difficult to measure the current and voltage on each port directly, so the n-port network problem is usually described by the S-parameter. The scattering parameter is a network parameter based on the relationship between incident and reflected waves, and describes the network in terms of the reflected signal at a port of the device and the signal transmitted from that port to another port. The scattering matrix is a matrix reflecting the relationship between incident and reflected waves at the port. FIG. 1 shows a two-port network model, where A₁,A₂Is an incident wave, B₁,B₂Is a reflected wave, V₁,V₂Is the voltage, I₁,I₂Is the current. FIG. 2 shows an n-port network model, let A_i,B_iIncident wave and reflected wave, V, of the ith port_i,I_iRespectively, voltage and current, S ═ S_ij) I is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to n, and the incident wave and the reflected wave have the following relationship:

wherein,

R_iis a reference resistance.

Thus, there is a formula in the frequency domain

Conversion to have in time domain

Wherein the convolution

s_ij(t)＝L^-1(S_ij) Is an excitation function, L^-1Representing the inverse Laplace transform. Substitution into

To the above formula, get the formula

Simplifying to obtain a model equation of the ith port:

note that the key to solving the above model equation is how to compute the excitation function s_ijIs performed. The conventional method transforms S parameters (fitting parameters) in the frequency domain into excitation functions in the time domain by Fourier inverse transform, and then calculates convolution by numerical discrete method. When the convolution is performed by using the method, in order to obtain the convolution of the current time, integration from zero time to the current time is required, so that the longer the simulation time is, the greater the cost for calculating the convolution of the current time is, and the calculation time is usually intolerable.

In order to reduce the time of convolution calculation, it is often considered to calculate the convolution using a recursive method. The recursive method has the advantages that in the convolution, in order to obtain the convolution at the current moment, only the convolution result at the previous moment is needed, so that the complex calculation is avoided, and the calculation efficiency is greatly improved. Moreover, compared with the conventional method, the recursive method does not need to perform causal correction (causal correction) but only needs to perform passive correction (passive correction) when calculating the convolution of the S parameter. Reference is made to the document "Passionbased Sample Selection and Adaptive vector matching Algorithm for policy-response Modeling of spark Frequency Domain Data" (behavial Modeling and mapping Conference,2004.Proceedings of the2004IEEE International).

The general procedure for solving the nport problem by the recursion method is that a rational formula is fitted to the S parameters in a given discrete frequency domain by a vector matching method, then an expression of the S parameters in a time domain is solved, and finally the convolution of the S parameters in the time domain is calculated by the recursion method, so that an algebraic equation of the nport model (1) is obtained.

The nport model also typically takes into account the delay effect, i.e., the time delay (timedelay) that a signal experiences as it passes through an nport device, which appears in the frequency domain as a shift in the amplitude and phase of the signal. The delay effect is related to the properties of the nport device and the frequency of the input signal. In practical applications, we usually assume that the delay time is constant. Such an assumption is reasonable over a range of frequencies.

When solving the nport problem by using a recursion method, how to effectively extract the delay time of the S parameter and solve the rational-factorial fitting of the optimal order and how to combine the circuit simulation characteristics and quickly calculate the convolution by using the recursion method have very important significance for improving the simulation precision and speed of the nport problem.

Disclosure of Invention

In order to solve the defects in the prior art, the invention provides an nport problem self-adaptive fitting and simulation method based on a vector matching method. When the S parameter is fitted, a rational fraction fitting type with higher precision is obtained by automatically selecting a fitting order and extracting the optimal delay time; meanwhile, when the convolution of the S parameter is calculated, a recursive calculation format with simple form and high precision is obtained through Taylor approximation according to the characteristics of circuit simulation.

In order to achieve the above purpose, the nport problem adaptive fitting and simulation method based on the vector matching method of the invention comprises the following steps:

(1) carrying out self-adaptive fitting on the S parameter by using a vector matching method to obtain a fitting result S with optimal fitting order K and delay time d_ij(s), wherein i is greater than or equal to 1 and j is less than or equal to n;

(2) transfer function S in frequency domain by inverse Laplace transform_ij(s) conversion to an excitation function s in the time domain_ij(t)；

(3) The convolution of the S parameters is computed by a recursive method, thus obtaining the algebraic equation of the nport model.

Further, the step (1) further comprises:

for S parameter S_ijCarrying out passive correction, wherein i is more than or equal to 1, and j is more than or equal to n;

let the delay time d be 0 and K be 2, 4_maxFitting S by K order vector matching method_ijCalculating the fitting error of the K-order vector matching method, and selecting K with the smallest fitting error or meeting the precision requirement firstly;

if the fitting error does not meet the accuracy requirement, assume delay time d>0, order

For M1, 2, 1_mCalculating an extraction delay time d_mLast S parameter

And to

Carrying out passive correction, and fitting by using K-order vector matching method

Calculating the fitting error

The delay time with the smallest fitting error is selected.

Further, the pair K is 2, 4_maxFitting S by K order vector matching method_ijThe calculation formula of (2) is as follows:

in the formula, r_ij,KIs a constant term, being a real number, p_ij,kAnd q is_ij,kRespectively pole and residue.

Further, a calculation formula of the fitting error of the K-order vector matching method is as follows:

fitting error of K order vector matching method:

further, the S parameter after the delay time is calculated and extracted

The calculation method comprises the following steps:

at port i, j and frequency s_lValue of (A)

Further, in step (2), the transfer function S in the frequency domain is transformed by inverse Laplace transform_ij(s) conversion to an excitation function s in the time domain_ij(t)。

Let the transfer function S_ij(s) is fitted with

Then conversion is made to the time domain with an excitation function

Where δ (·) denotes a dirac function, and d is a delay time.

Further, the step (3) of calculating the convolution of the S parameter by using a recursive method, Y_ij(t)＝s_ij(t)*X_j(t) recursive computation format:

Y_ij(t)＝r_ijX_j(t-d)+Z_ij(t)

wherein,

X_j(t)＝V_j(t)+R_jI_j(t)

d is the delay time for extraction.

The invention mainly considers two aspects involved in calculating nport problem by using a recursion method: fitting by a vector matching method and recursive computation of convolution. The nport problem self-adaptive fitting and simulation method based on the vector matching method has the following advantages: (1) compared with the common vector matching method for fixing the fitting order, the self-adaptive fitting method can automatically select the order, so that the fitting accuracy is higher; meanwhile, the delay effect of the S parameter is considered, and the fitting effect is better by extracting the delay time. (2) When the convolution of the S parameter is calculated by a recursion method, a calculation format with simple form and high precision is provided by Taylor approximation in consideration of the fact that the time step of the common simulation is small.

Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

Drawings

The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:

FIG. 1 is a diagram of a two-port network model according to the prior art;

FIG. 2 is a schematic diagram of a prior art n-port network model according to the present invention;

FIG. 3 is a flow chart of an nport problem adaptive fitting and simulation method based on a vector matching method according to the present invention.

Detailed Description

The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.

Fig. 3 is a flowchart of the nport problem adaptive fitting and simulation method based on the vector matching method according to the present invention, and the nport problem adaptive fitting and simulation method based on the vector matching method according to the present invention will be described in detail with reference to fig. 3.

First, in step 101, the S parameter is adaptively fitted by using a vector matching method. The actually measured S parameters have a rational formula sum form theoretically after being fitted by a vector matching method. In practical applications, we generally have a fitting form in consideration of the delay effect in the time domain

Wherein i is more than or equal to 1 and less than or equal to n, j is more than or equal to 1 and less than or equal to n, r_ijIs a constant term (real number), p_kAnd q is_kRespectively the pole and the residue, K_ijOrder of rational fraction, d_ijIs a delay time, and r_ijIs a real number, p_kAnd q is_kEither real or respectively complex conjugates occurring in pairs. K_ijIs a positive integer (K is always set in the vector matching method)_ijEven number), d_ijAre non-negative real numbers. In practical applications, we can assume K_ijAnd d_ijThe value at each port being the same, i.e. K_ij＝K,d_ijD (for all i, j), where K is a positive even number and d is a non-negative real number.

Let L denote the total number of samples in the S parameter, S_lIndicates the frequency(s) of the l-th sample point_l＝2πf_l，f_lDenotes the frequency, 1. ltoreq. l.ltoreq.L), S_ij,lRepresents the value of S parameter, S, corresponding to the ith sampling point_ij(s_l) Expressing rational components fitted according to the vector matching method at s_lThe calculated value is processed.

Suppose that the vector matching method is used for the S parameter S of the i, j port_ijFitting results having the form:

definition of S_ijRelative error of fit:

relative error e_ijTo measure the accuracy of the fit. Theoretically, the greater the fitting order K is, the higher the fitting accuracy is; however, the larger K is, the more calculation load is required for calculating convolution by the recursive method, and the slower the calculation is. Therefore, a balance needs to be maintained when selecting the fitting order K. We use the tolerance tol to control the order of the fit.

Constants in the fit are taken as follows. Tolerance tol 1.0e-3, maximum fitting order K_max64, maximum delay time d_max10ns (1ns 1e-9 s). For maximum delay time d_maxMaking M times of equal division (no taking M as 100), and recording delta d as d_maxand/M. Note K_opt,d_optRespectively, are the best values of the fit.

The basic method for carrying out self-adaptive fitting on the S parameter by using a vector matching method is as follows: (1) without first considering the time delay (i.e. d)_m0), directly fitting the S parameter by a vector matching method, and gradually increasing the fitting order K from 2 to K_maxIf the fitting precision meets the requirement in the process, the fitting is successful; if K is equal to K_maxIf the fitting precision still does not meet the requirement, selecting the K with the maximum fitting precision (not setting

) And (2) turning to fitting by a vector matching method with time delay; (2) let delay time d increase gradually from 0 to d_maxFor each d, use

Fitting by an order vector matching method, wherein if the fitting precision in the process meets the requirement, the fitting is successful; if d ═ d_maxIf the fitting precision still does not meet the requirement, the d with the maximum fitting precision is selected (no setting is made)

) Outputting fitting results

The following describes a specific implementation process of the nport problem adaptive fitting method based on the vector matching method in detail with reference to specific embodiments.

Step 1 for S parameter S_ij(i is more than or equal to 1, j is less than or equal to n) to carry out passive correction, an initial value m is set to be 0, and a delay time d is assumed_m＝0。

Step 2, K is 2, 4_max，

(2.1) fitting S by K-order vector matching method_ij(1. ltoreq. i, j. ltoreq. n) to obtain

(2.2) calculation of S_ijError of fit

Then the fitting error of the K order vector matching method is calculated as

(2.3) if e_KNot more than tol, successful fitting, K_optAnd (4) quitting when the key is K.

Otherwise: if K is<K_maxAnd K is K +2, turning to step (2.1); if K is equal to K_maxGo to step 3.

Step 3 order

For M1, 2, 1_m＝mΔd,

(3.1) calculating the S parameter after the extraction delay time

At port i, j and frequency s_lHas a value of

(3.2) pairs

Performing passive correction, and using

Fitting by order vector matching method, calculating fitting error

(3.3) if

The fitting is successful and the fitting is successful,

d_opt＝d_mand exiting.

Otherwise: if m is<M, then M ═ M +2, d_mTurning to step (3.1) when m is equal to Δ d;

if M is equal to M, then take

And (6) exiting.

Then the fitting error of the K order vector matching method is calculated as

The above implementation steps are explained as follows:

(1) in the above step, when the S parameter is fitted in step 2, the S parameters S of all ports_ij(1. ltoreq. i, j. ltoreq. n) with exactly the same fitting order. If S parameter S of different ports is assumed_ij(i is more than or equal to 1, j is less than or equal to n) has different orders, and only the step 2 needs to be changed as follows: fix i, j, to parameter S_ijRespectively with K_ij(2≤K_ij≤K_max) Fitting by order vector matchingFind out the relative error e_ij,KMinimum (or first satisfied with e)_ij,KNot more than tol) of_ijAs S_ijThe fitting result of (1).

(2) In the above step, when the delay time of the S parameter is extracted in step (3.1), it is assumed that S parameters S of all ports_ij(1. ltoreq. i, j. ltoreq. n) with identical delay times. This has the advantage of facilitating passive correction (since the S-parameters of all ports need to be used simultaneously when passive correction is done before fitting by vector matching). If S parameter S of different ports is assumed_ijExtracted delay time d_ijDifferent from each other, then before the delay time of each port i, j is extracted, a passive correction is made, so that the fitting efficiency is reduced (especially when the number of ports is large).

(3) In the above process, if the given S parameter has no time delay (i.e. d is 0), a more accurate fitting result can be obtained quickly through step 1 and step 2.

(4) In the fitting process, the constant K_max,d_maxM, etc. can be determined autonomously according to the particular problem.

(5) The fitting process described above mainly considers how to autonomously select the fitting order and the delay time. In practical application, the fitting order and the delay time are key factors for restricting the fitting accuracy, and other factors, such as the properties of devices, instruments for measuring S parameters and the like, also influence the fitting result, so that the thought method can be used together with other technical means.

Next, in step 102, the transfer function S in the frequency domain is transformed by inverse Laplace transform_ij(s) conversion to an excitation function s in the time domain_ij(t)。

Setting the vector matching method to match S parameter S_ijThe result of the adaptive fitting is

Conversion to the time domain of

Where δ (·) represents a dirac function.

Finally, the convolution of the S-parameters is computed in step 103 using a recursive method, resulting in the algebraic equation for the nport model (1). The recursive calculation format of the S-parameter convolution is given below.

In formula (1), let X_j(t)＝V_j(t)+R_jI_j(t), then the following convolution needs to be calculated:

s_ij(t)*(V_j(t)+R_jI_j(t))＝s_ij(t)*X_j(t)＝:Y_ij(t) (5)

Y_ijthe recursive computation format of (t) is derived as follows:

here, ,

let Δ t be the time step of the current time, then

The last step of the above equation uses Taylor approximation

e^x＝1+x+O(x²)(x→0)

Since the time step Δ t is small in the actual circuit simulation, the above approximation is reasonable; and e is approximated by 1+ x during computer operation^xIt would be calculated faster.

From (3) to (7), recursive calculation format

Y_ij(t)＝r_ijX_j(t-d)+Z_ij(t) (9)

Wherein,

and finally, substituting (9) - (10) into (1) to obtain an algebraic equation of the nport model.

The recursive calculation format for calculating the convolution of the S parameter is explained as follows:

(1) in deriving the above-mentioned recursion relationship, we assume that the delay times of the S-parameters at each port are the same, i.e., d_ijD (for all i, j). If d is_ijThe recursive format is also applicable to different values of i and j, and only the formula (9) is changed into

Y_ij(t)＝r_ijX_j(t-d_ij)+Z_ij(t)

Elsewhere, it is unchanged.

(2) In the above recursive relationship, we assume that the delay time d is constant regardless of the frequency of the incident wave. If the delay time d is related to the frequency of the incident wave, the above-mentioned recursive relation is no longer true, and the convolution cannot be accurately calculated by the recursive method.

(3) From the Taylor equation, we can also estimate the local stage error of equation (8). In fact, a Taylor approximation is made to the second term after the 3 rd equal sign in equation (8), which is

Thereby having an estimation

Therefore, the local truncation error of equation (8) is O ((Δ t)²)。

(4) The mode of calculating convolution by using a recursion method is mature, and the recursion format is different from other formats in that the delay time is considered, approximation is carried out when delta t is small, the recursion relation is simple, and meanwhile, the precision is high.

Those of ordinary skill in the art will understand that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An nport problem self-adaptive fitting and simulation method based on a vector matching method comprises the following steps:

(3) Calculating the convolution of the S parameter by a recursive method so as to obtain an algebraic equation of the nport model,

the step (1) further comprises:

let the delay time d be 0 and K be 2, 4, …, K_maxFitting S by K order vector matching method_ijCalculating the fitting error of the K-order vector matching method, and selecting K with the smallest fitting error or meeting the precision requirement firstly;

For M is 1,2, …, M, d_mCalculating an extraction delay time d_mLast S parameter

And to

The passive correction is carried out in such a way that,then fitting by using a K-order vector matching method

Calculating the fitting error

Selecting d with the smallest fitting error_m，

Calculating the convolution of the S parameter by using a recursion method in the step (3): y is_ij(t)＝s_ij(t)*X_j(t) a recursive convolution calculation format of

Y_ij(t)＝r_ijX_j(t-d)+Z_ij(t)

Wherein,

X_j(t)＝V_j(t)+R_jI_j(t)

d is the delay time of the extraction,

wherein, the nport problem is the simulation precision and speed of the serial server, the S parameter is the scattering parameter,

in the formula,

denotes the fitting error, Δ d denotes the maximum delay time d_maxDividing M times, and recording delta d as d_max/M，r_ijIs a constant term, p_ij,kAnd q is_ij,kRespectively the pole and the residue, K_ijOrder of rational formula, p_ij,kAnd q is_ij,kΔ t represents the time step at the current time, either as a real number or respectively as a complex conjugate number occurring in pairs.

2. The nport problem adaptive fitting and simulation method based on the vector matching method as claimed in claim 1, wherein the pair K is 2, 4, …, K_maxFitting S by K order vector matching method_ijThe calculation formula of (2) is as follows:

3. The nport problem adaptive fitting and simulation method based on the vector matching method as claimed in claim 1, wherein the calculation formula for calculating the fitting error of the K-th order vector matching method is:

fitting error of K order vector matching method:

in the formula, S_ij,K(s_l) Expressing rational components fitted according to the vector matching method at s_lTo the calculated value, S_ij,lRepresenting the value of S parameter corresponding to the ith sample point, e_ij,KDenotes the fitting error of the K-order vector matching method, and Δ d denotes the maximum delay time d_maxDividing M times, and recording delta d as d_maxand/M, L represents the total number of sampling points in the S parameter.

4. The nport problem adaptive fitting and simulation method based on the vector matching method as claimed in claim 1, wherein the S parameter after the delay time is calculated and extracted

The calculation method comprises the following steps:

at port i, j and frequency s_lValue of (A)

In the formula, S_ij,lAnd expressing the S parameter value corresponding to the ith sampling point.

5. The nport problem adaptive fitting and simulation method based on the vector matching method as claimed in claim 1, wherein the step (2) is to apply the transfer function S in the frequency domain through inverse Laplace transform_ij(s) conversion to an excitation function s in the time domain_ij(t): let the transfer function S_ij(s) is fitted with

The excitation function s in the time domain_ij(t) is in the form of

Where δ (·) denotes a dirac function, d is the delay time of the extraction,

in the formula, r_ijIs a constant term, p_ij,kAnd q is_ij,kRespectively the pole and the residue, K_ijOrder of rational formula, p_ij,kAnd q is_ij,kBeing real numbers or respectively conjugate complex numbers occurring in pairs, d_ijAre non-negative real numbers.