CN113505480A - Method for improving transient simulation convergence of transmission line - Google Patents

Method for improving transient simulation convergence of transmission line Download PDF

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CN113505480A
CN113505480A CN202110771149.XA CN202110771149A CN113505480A CN 113505480 A CN113505480 A CN 113505480A CN 202110771149 A CN202110771149 A CN 202110771149A CN 113505480 A CN113505480 A CN 113505480A
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transmission line
convergence
transient simulation
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improving
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吴大可
周振亚
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Beijing Empyrean Technology Co Ltd
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Abstract

A method for improving transient simulation convergence of a transmission line comprises the following steps: 1) obtaining a data set to be fitted: (omega)i,yi) I is 1, …, N, where ω isiIs the ith frequency point, yiIs omegaiThe corresponding value of the physical quantity, N is the number of data points; 2) establishing a fitting object model: re (z)i)＝Re(yi)，Im(zi)＝αIm(yi)+(1‑α)Im(yi c) Wherein z isiRe (z) as a fitting objecti) To fit the real part of the object, Im (z)i) To fit the imaginary part of the object, α is the convergence factor, yi cCalculating a fitting value obtained by the pole and the residue after the last iteration at the ith frequency point; 3) given poles, the real part of a given physical quantity is fitted. The method greatly improves the convergence of W-element calculation without increasing the cost of original vector fitting calculation.

Description

Method for improving transient simulation convergence of transmission line
Technical Field
The invention belongs to the field of transmission line transient simulation modeling, and particularly relates to a method for improving the transient simulation convergence of a transmission line.
Background
Transmission line simulation models are widely used in analog circuit simulation. In many models, the transmission line can be characterized by lumped parameter resistance, inductance, conductance and capacitance (RLGC), and the impulse response of the system can be calculated through specific calculation steps. The output signal can be determined very quickly once the input signal is given. This model is commonly referred to as the W-element transmission line model.
In the simulation of the W-element transmission line model, the RLGC parameters cannot be directly used for the calculation of impulse response. In brief, sampling is required to be performed in a certain frequency range, a transfer function and a characteristic admittance of a model are obtained through calculation at each frequency sampling point, and then a vector fitting method is adopted to model the transfer function and the characteristic admittance in the certain frequency range. The result of the vector fit is used in subsequent transient analysis.
Since the W-element transmission line model tends to introduce skin effect and dielectric loss effect, the causality of the RLGC model is destroyed. A common method for restoring causality of the RLGC model is to fit only the real part of a transfer function and a characteristic admittance in vector fitting, and the imaginary part is completely released and is not limited to the original imaginary part of a physical quantity. The vector fitting mode can well solve the causality problem brought by the skin effect and the dielectric loss effect. However, when the skin effect and the dielectric loss effect in the model are large, convergence problems are often caused in transient simulation. The adjustment can be carried out by changing the cut-off frequency, the point number and the mode of frequency sampling and the order of vector fitting.
In fact, vector fitting is only a modeling method that facilitates subsequent transient simulation, and it does not guarantee that the system is passivity. That is, the passivity of the system after the vector fitting may be destroyed, thereby causing the transient simulation to be non-converged.
There is a certain difficulty in solving the passivity problem in the W-element. The traditional method for correcting the S parameter and the Y parameter in an passivity way cannot be directly used in the W-element because the W-element transfer function and the characteristic admittance have quite complex relations with the S parameter and the Y parameter.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a method for improving the transient simulation convergence of a transmission line, which does not adopt special passivity correction and greatly improves the convergence of W-element under the condition that the calculation cost is the same as that of the traditional method.
In order to achieve the above object, the present invention provides a method for improving transient simulation convergence of a transmission line, comprising the following steps:
1) obtaining a data set to be fitted: (omega)i,yi) I is 1, …, N, where ω isiIs the ith frequency point, yiIs omegaiThe corresponding value of the physical quantity, N is the number of data points;
2) establishing a fitting object model:
Re(zi)＝Re(yi)，
Im(zi)＝αIm(yi)+(1-α)Im(yi c)；
wherein z isiRe (z) as a fitting objecti) To fit the real part of the object, Im (z)i) To fit the imaginary part of the object, α is the convergence factor, yi cCalculating a fitting value obtained by the pole and the residue after the last iteration at the ith frequency point;
3) given the poles, the real part of the physical quantity is fitted.
Further, the fitted value of the pole and the residue after the ith frequency point passes the last iteration is calculated according to the following formula:
Figure BDA0003153439640000021
wherein N iscEach pair of poles can be represented as a, as a logarithm of complex conjugate poleskAnd ak *，k＝1,…,Nc(ii) a M is the total number of poles, the real number of poles is M-2NcCorresponding to pole ak，k＝2Nc+1,…,M，c0Is a constant term independent of frequency; in the first summation term, ckAnd ckIs a complex pole a of mutual conjugatekAnd ak *Corresponding residue; in the second summation term, ckIs a real pole akThe residue of (2); omegaiIs the ith frequency point.
Further, the value range of alpha in the step 2) is more than or equal to 0 and less than or equal to 1.
Further, the step 3) of fitting the real part of the physical quantity further includes the steps of:
solving Ax ═ b, and calculating to obtain x, wherein A is an Nx (M +1) matrix, and b is an Nx 1 vector;
calculating the residue, wherein the corresponding relation between the residue and x is as follows:
ci＝xi+jxi+1,ci+1＝xi-jxi+1when 1 ≦ i ≦ 2NcAnd is odd;
ci＝xiwhen 2N is presentc+1≦i≦M；
c0＝xM+1；
Where M is the total number of poles.
In order to achieve the above object, the present invention further provides an electronic device, which includes a memory and a processor, where the memory stores a program running on the processor, and the processor executes the steps of the method for improving the transient simulation convergence of the transmission line when running the program.
To achieve the above object, the present invention further provides a computer readable storage medium, on which computer instructions are stored, and when the computer instructions are executed, the steps of the method for improving the transient simulation convergence of the transmission line are performed.
Compared with the prior art, the method for improving the transient simulation convergence of the transmission line has the following beneficial effects: the convergence of W-element calculation is greatly improved while the calculation cost of original vector fitting is not increased.
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 flow chart of a method for improving transmission line transient simulation convergence according to the present invention;
FIG. 2 shows a schematic diagram of feature admittance of a conventional method vector fit;
FIG. 3 shows a schematic of the output signal of a conventional method;
FIG. 4 shows a schematic diagram of feature admittance of a vector fit according to an embodiment of the invention;
fig. 5 shows a schematic diagram of an output signal according to an embodiment of the 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.
Example 1
Fig. 1 is a flowchart of a method for improving transient simulation convergence of a transmission line according to the present invention, and the method for improving transient simulation convergence of a transmission line according to the present invention will be described in detail with reference to fig. 1.
In step 101, a dataset to be fitted is obtained: (omega)i，yi) I is 1, …, N, where ω isiIs the ith frequency point, yiIs omegaiThe corresponding value of the physical quantity, which may be an S parameter, a Y parameter, etc., N is the number of data points.
At step 102, the iterative fitting object is modified and a new fitting object model is established.
In a conventional iteration of each vector fit, the subject of the fit is the experimental data yiI-1, …, N, and in the present embodiment, the fitting object for each iteration is modified to the fitting object model ziNew fitting object model z is establishediThe real and imaginary parts of (c) are as follows:
Re(zi)＝Re(yi)
Figure BDA0003153439640000041
wherein i is 1, 2, …, N, alpha is convergence factor, and the value range is 0 ≤Alpha is less than or equal to 1 and usually takes a value of 0.8, and if the convergence is not realized, the alpha can be slightly adjusted to be larger, such as 0.9;
Figure BDA0003153439640000042
is obtained by calculating the pole and the residue of vector fitting after the last iteration at the ith frequency point, which is equivalent to a fitting value,
Figure BDA0003153439640000043
the calculation formula of (a) is as follows:
Figure BDA0003153439640000044
in the formula, NcEach pair of poles can be represented as a, as a logarithm of complex conjugate poleskAnd ak *，k＝1，…，Nc. M is the total number of poles, the real number of poles is M-2NcCorresponding to pole ak，k＝2Nc+1，…，M，c0Is a constant term independent of frequency; when k is less than NcTime (first summation term), ckAnd ckIs a complex pole a of mutual conjugatekAnd ak *Corresponding residue; when k > 2Nc(second summation term), ckIs a real pole akThe residue of (2); omegaiIs the ith frequency point.
And 103, setting poles and acquiring the fitting residue.
In the embodiment of the present invention, the method for obtaining the residue is to solve the equation Ax ═ b, where a is an N × (M +1) matrix, and b is an N × 1 vector. The elements of A are calculated as follows:
when k is less than or equal to Nc
Figure BDA0003153439640000045
Figure BDA0003153439640000046
Here: a isk1And ak2Are respectively akThe real and imaginary parts of, i.e. ak＝ak1+jak2。
When 2N is presentc＜k≤M
Figure BDA0003153439640000051
When k is M +1
Ai，k＝1 (3)
Wherein i is 1, 2, …, N.
The component of the vector b is defined as
bi＝Re(yi) (4)
Wherein i is 1, 2, …, N.
After solving the equation Ax ═ b to obtain x, the corresponding relation between the residue number and x is as follows:
ci＝xi+jxi+1，ci+1＝xi-jxi+1when i is more than or equal to 1 and less than or equal to 2NcAnd is odd;
ci＝xiwhen 2N is presentc+1≤i≤M；
c0＝xM+1；
Where M is the total number of poles. (5)
Example 2
Steps 101-103 according to an embodiment of the present invention are fitted and compared with conventional simulation combinations. Fig. 2 shows a characteristic admittance diagram of a vector fitting of a conventional method, and it can be seen from fig. 2 that the imaginary part of the characteristic admittance increases rapidly when the frequency increases, thus destroying the system passivity, and causing the output signal of fig. 3 to fail to converge.
Fig. 4 shows a schematic diagram of the characteristic admittance of the vector fitting according to an embodiment of the invention, from fig. 4 it can be seen that the imaginary part of the characteristic admittance is always small, of the same order of magnitude as the imaginary part of the experimental values, so that the output signal may converge, as shown in fig. 5.
Example 3
The invention also provides an electronic device, which comprises a memory and a processor, wherein the memory is stored with a program running on the processor, and the processor executes the steps of the method for improving the transient simulation convergence of the transmission line when running the program.
Example 4
The invention further provides a computer-readable storage medium, on which computer instructions are stored, and when the computer instructions are executed, the steps of the method for improving the transient simulation convergence of the transmission line are performed, and the method for improving the transient simulation convergence of the transmission line is described in the foregoing description and is not described in detail again.
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 (6)

1. A method for improving transient simulation convergence of a transmission line is characterized by comprising the following steps:
1) obtaining a data set to be fitted: (omega)i,yi) I is 1, …, N, where ω isiIs the ith frequency point, yiIs omegaiThe corresponding value of the physical quantity, N is the number of data points;
2) establishing a fitting object model:
Re(zi)＝Re(yi)，
Im(zi)＝αIm(yi)+(1-α)Im(yi c)；
wherein z isiRe (z) as a fitting objecti) To fit the real part of the object, Im (z)i) To fit the imaginary part of the object, α is the convergence factor, yi cFor passing the previous step stack at the ith frequency pointCalculating a fitting value obtained by the pole and the residue after the generation;
3) given the poles, the real part of the physical quantity is fitted.
2. The method for improving the transient simulation convergence of the transmission line according to claim 1, wherein the fitting value obtained by calculating the pole and the residue after the previous iteration at the ith frequency point is calculated by the following formula:
Figure FDA0003153439630000011
wherein N iscEach pair of poles can be represented as a, as a logarithm of complex conjugate poleskAnd ak *，k＝1,…,Nc(ii) a M is the total number of poles, the real number of poles is M-2NcCorresponding to pole ak，k＝2Nc+1,…,M，c0In the first summation term for a constant term independent of frequency, ckAnd ckIs a complex pole a of mutual conjugatekAnd ak *Corresponding residue; in the second summation term, ckIs a real pole akThe residue of (2); omegaiIs the ith frequency point.
3. The method for improving the transient simulation convergence of the transmission line according to claim 1, wherein α in the step 2) is in a range of 0 ≦ α ≦ 1.
4. The method for improving the convergence of the transient simulation of the transmission line according to claim 1, wherein the step 3) of fitting the real part of the physical quantity further comprises the steps of:
solving Ax ═ b, and calculating to obtain x, wherein A is an Nx (M +1) matrix, and b is an Nx 1 vector;
calculating the residue, wherein the corresponding relation between the residue and x is as follows:
ci＝xi+jxi+1,ci+1＝xi-jxi+1when 1 ≦ i ≦ 2NcAnd is thatOdd number;
ci＝xiwhen 2N is presentc+1≦i≦M；
c0＝xM+1；
Where M is the total number of poles.
5. An apparatus for improving transmission line transient simulation convergence, comprising a memory and a processor, wherein the memory stores a program running on the processor, and the processor executes the program to perform the steps of the method for improving transmission line transient simulation convergence according to any one of claims 1 to 4.
6. A computer readable storage medium having stored thereon computer instructions, wherein the computer instructions when executed perform the steps of the method of improving transmission line transient simulation convergence according to any one of claims 1 to 4.
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