CN107590338B - Method for fitting mathematical model of transmission line impedance upward drift - Google Patents
Method for fitting mathematical model of transmission line impedance upward drift Download PDFInfo
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Abstract
The invention discloses a method for fitting a mathematical model of transmission line impedance upward drift in the field of circuit boards, which comprises the following steps: and obtaining curve fitting results of insertion loss, return loss and transmission line impedance by using ADS simulation software, respectively carrying out batch simulation on the line width W, the copper foil thickness T, the dielectric loss DF and the copper foil roughness R, importing the results of various groups of variables obtained by simulation into excel, and fitting out a relation formula of the impedance drift amount and the variables. The invention predicts the impedance drift amount in advance by fitting and utilizing the mathematical model and inputting each influence factor of the transmission line, and performs corresponding transmission line optimization in the design stage to improve the influence of the impedance drift on the link.
Description
Technical Field
The invention relates to the field of circuit boards, in particular to a method for fitting a mathematical model of transmission line impedance upward drift.
Background
A Printed Circuit Board (PCB), also called a PCB, is an important component for physical support and signal transmission of electronic products, wherein the most important component is a transmission line, and the test impedance of the transmission line has a significant floating phenomenon.
The upward drift amount is related to the length of a transmission line, the width of a routing line, the roughness of a copper foil, the thickness of the copper foil and the dielectric loss DF value of a plate, and the upward drift of impedance has obvious deteriorating influence on the impedance matching of a link. At present, the traditional method can only obtain specific upward drift amount from testing, and can only obtain the specific numerical value of the upward drift after the PCB is designed and processed, but can not obtain the value at the PCB design stage, and can not carry out certain optimization and improvement at the design stage.
Experiments prove that the upward drift of the TDR impedance is strongly related to 5 factors of line width, copper foil roughness, copper thickness, dielectric loss DF value and line length, wherein the line length is relatively independent from other 4 factors and is a linear relation of one time, but the line width, the copper foil roughness, the copper thickness and the dielectric loss DF value have a mutually dependent relation, so that the influence of each parameter on the upward drift of the impedance is difficult to obtain.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for fitting a mathematical model of the impedance upward-floating of a transmission line, the upward-floating amount of the impedance is predicted in advance by fitting and utilizing the mathematical model and various influence factors input into the transmission line, the corresponding transmission line optimization is carried out in the design stage, and the influence of the impedance upward-floating on a link is improved.
The technical scheme of the invention is as follows:
a method of fitting a mathematical model of the upward drift of the impedance of a transmission line, comprising the steps of:
and 4, respectively selecting X, Y areas in regression analysis, wherein the X area is simulation data of 8 variables, the Y area is simulation data of impedance upward drift D, fitting a mathematical model, and obtaining the impedance upward drift D of the Y area after the variables of the X areas are mutually operated, namely a relational formula of the impedance upward drift and the variables.
The invention according to the above aspect is characterized in that, in the step 2, the method specifically includes the steps of:
(1) obtaining the impedance drift through the result of single-group data variable obtained by the simulation of the laminated structure;
(2) respectively setting initial and cut-off ranges of variable line width W, copper foil thickness T, dielectric loss DF and copper foil roughness R, and setting the variables in the laminated and transmission line structure of ADS simulation software to obtain the simulation result of the variables;
(3) and recording all the variables according to the simulation result in a single-group variable recording mode.
Further, in the step (2):
the line width W is scanned from 4mil to 8mil, and the step length is 2 mil;
the thickness T of the copper foil is from 0.6mil to 1.2mil, and the step length is 0.3 mil;
dielectric loss DF is from 0.004 to 0.02, step length is 0.008;
the roughness R of the copper foil is from 0um to 1um, and the step length is 0.5 um.
The invention according to the above aspect is characterized in that in the step 3, variables, that is, the reciprocal of copper thickness T, the reciprocal of line width W, the reciprocal of the product of line width W and copper thickness T, and the reciprocal of dielectric loss DF are added in excel.
The invention according to the above scheme is characterized in that the mathematical formula of the impedance upward-floating model obtained in step 4 is as follows:
the invention according to the above scheme is characterized by further comprising a step 5 of adding a linear variable line length after obtaining the relationship between the impedance upward drift amount and each variable to obtain the impedance upward drift amount of the total link.
Further, the mathematical formula of the impedance upward-floating model obtained in step 5 is as follows:
wherein the amount of impedance rise drift DWHOLEThe units are ohm, the line width W unit is mil, the copper thickness T unit is mil, the roughness R unit is um, and the line length L unit is inch.
The method has the advantages that the mathematical model with high fitting precision with the test result is obtained through simulation test fitting, and then the upward drift of the impedance can be predicted in advance by inputting various influence factors of the transmission line through the mathematical model in the PCB design stage, so that corresponding processing improvement can be carried out in the design, and the aim of optimizing the link performance is fulfilled.
Drawings
Fig. 1 is a simulation test fitting graph of insertion loss of the present invention.
FIG. 2 is a fitting graph of a simulation test of return loss according to the present invention.
FIG. 3 is a simulated test fit of TDR (simulated line) impedance of the present invention.
FIG. 4 is a graph of the impedance drift-up simulation for one set of variables in accordance with the present invention.
FIG. 5 is a diagram of variables set in the overlay and transmission line structures provided by ADS simulation software according to the present invention.
FIG. 6 is a graph of the impedance drift-up simulation for all variables of the present invention.
FIG. 7 is a graph comparing the amount of overshoot for the present invention during simulation and testing.
Detailed Description
The invention is further described with reference to the following figures and embodiments:
a method of fitting a mathematical model of the upward drift of the impedance of a transmission line, comprising the steps of:
1. the existing test data is subjected to simulation model fitting, so that the model used in the following simulation is ensured to have very high consistency with the real test data, and the precision of the simulation test is ensured.
The selected test object is a PCB transmission line structure with 5inch, and a transmission line laminated structure model built in ADS simulation software is used for simulation test fitting.
As shown in fig. 1-3, the results of curve fitting of insertion loss, return loss and transmission line impedance are obtained, respectively. The three graphs can verify that the test result can be well fitted by using ADS simulation software, the accuracy is high, and the model is used for simulation scanning subsequently.
2. And carrying out batch simulation on the following 4 variables, wherein the variables are the line width W, the copper foil thickness T, the dielectric loss DF and the copper foil roughness R. The length of the line is 5 inches for clearer resolution. The results of the single set of data variables obtained by the simulation of the laminated structure provided by the software (the line width W is set to 4mil, the copper foil thickness T is set to 0.6mil, the dielectric loss DF is set to 0.004, the copper foil roughness R is set to 1um, and the line length is 5inch) are shown in fig. 4.
The time of recording the starting point m1 and the end point m2 of the impedance upward drift is 80ps and 1.45ns, the obtained impedance Z is 100.227 ohm and 105.976 ohm respectively, and further the impedance upward drift D is the difference of the two impedance values, namely 5.749 ohm.
Batch simulation can be carried out, the simulation results of various conditions are obtained by setting the initial and cut-off ranges of each variable, and the setting process is as follows:
the variables are 4 as explained above: the line width W, the copper foil thickness T, the dielectric loss DF, and the copper foil roughness R are set at the stack and transmission line structures provided by the ADS, respectively, as shown in fig. 5.
The range of 4 variables was scanned as follows:
line width W: scanning from 4mil to 8mil with the step length of 2 mil;
thickness T of copper foil: from 0.6mil to 1.2mil, the step length is 0.3 mil;
dielectric loss DF, from 0.004 to 0.02, step size 0.008;
the roughness R of the copper foil is 0um to 1um, and the step length is 0.5 um.
The batch simulation results of each set of variables obtained by simulation are shown in fig. 6.
All variables were recorded in the above-described recording method for a single set of variables, and part of the data is shown in the following table.
Table one: partial record table of impedance value Z and upward drift D of all variables starting point m1 and ending point m2
3. And importing the results of each group of variables obtained by simulation into excel, as shown in table two.
Table two: simulation results for each set of variables
According to the table, the initial judgment can be carried out, the amount of the upper drift is inversely proportional to the line width, the copper thickness and the dielectric loss and is directly proportional to the roughness of the copper foil, and for further accuracy of fitting, 4 variables are added, namely the reciprocal of the copper thickness T, the reciprocal of the line width W, the reciprocal of the product of the line width W and the copper thickness T and the reciprocal of the dielectric loss DF, which are shown in the third table. Because the upward drift of the impedance is in a contrast relation with the above variables according to the theory of the transmission line impedance, the fitting precision can be improved after the corresponding variables are added.
Table three: data record table with 4 groups of variables added
4. Regression analysis was performed on all 8 variables
Selecting an X area and a Y area, wherein the X area is simulation data of 8 variables, the Y area is simulation data of impedance upward drift D, and fitting a mathematical model with high precision to ensure that the impedance upward drift D of the Y area is accurately obtained after the variables of the X areas are mutually operated, namely finding out a relational formula of the impedance upward drift and the variables.
The linear coefficients for each variable are obtained as shown in the table below.
Table four: linear coefficient of each variable
The mathematical formula of the impedance upward-floating model can be obtained as follows:
the fitting error of the mathematical model is basically within 0.1, the fitting precision is very high, and the comparison of the upper drift amounts obtained in the test and simulation is shown in the fifth table and fig. 7.
Table five: the value obtained by testing (D) and the value obtained by fitting a formula (prediction D) and the difference value of the two
Since the data is the upward drift data of 5 inches, after the linear variable of the line length is added, the impedance upward drift amount of the total link is as follows:
wherein the amount of impedance rise drift DWHOLEThe units are ohm, the line width W unit is mil, the copper thickness T unit is mil, the roughness R unit is um, DF dimensionless, and the line length L unit is inch.
Example of computing
Example 1
When the line width W is 4mil, the copper thickness T is 0.6mil, the dielectric loss DF is 0.004, the copper foil roughness R is 1um, and the line length L is 5inch, the impedance rise D is 5.745 ohms.
Example 2
When the line width W was 5mil, the copper thickness T was 0.6mil, the dielectric loss DF was 0.02, the copper foil roughness R was 1um, and the line length L was 5inch, the impedance rise D was 3.142 ohm.
Example 3
When the line width W was 6mil, the copper thickness T was 1.2mil, the dielectric loss DF was 0.01, the copper foil roughness R was 0.5um, and the line length L was 10inch, the impedance rise D was 5.883 ohms.
Example 4
When the line width W was 10mil, the copper thickness T was 0.6mil, the dielectric loss DF was 0.015, the copper foil roughness R was 0.2um, and the line length L was 8inch, the impedance rise D was 1.864 ohms.
The difference between the up-drift amount obtained by the mathematical model and the up-drift amount obtained by the test is very small, the precision is high, the corresponding transmission line optimization can be carried out at the design stage, and the influence of the impedance up-drift on the link is improved.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
The invention is described above with reference to the accompanying drawings, which are illustrative, and it is obvious that the implementation of the invention is not limited in the above manner, and it is within the scope of the invention to adopt various modifications of the inventive method concept and technical solution, or to apply the inventive concept and technical solution to other fields without modification.
Claims (6)
1. A method of fitting a mathematical model of the upward drift of the impedance of a transmission line, comprising the steps of:
step 1, fitting an existing test data by using a transmission line laminated structure model built in ADS simulation software to obtain curve fitting results of insertion loss, return loss and transmission line impedance;
step 2, respectively carrying out batch simulation on the line width W, the copper foil thickness T, the dielectric loss DF and the copper foil roughness R by using ADS simulation software;
step 3, importing the results of each group of variables obtained by simulation into excel, and adding variables, namely the reciprocal of copper thickness T, the reciprocal of line width W, the reciprocal of the product of line width W and copper thickness T and the reciprocal of dielectric loss DF in the excel;
and 4, respectively selecting X, Y areas, wherein the X area is simulation data of 8 variables, the Y area is simulation data of impedance upward drift D, fitting a mathematical model, and obtaining the impedance upward drift D of the Y area after the variables of the X areas are mutually operated, namely a relational formula of the impedance upward drift and the variables.
2. The method of fitting a mathematical model of the upward shift in transmission line impedance as claimed in claim 1, characterized in that in said step 2, it comprises in particular the steps of:
(1) obtaining the impedance drift through the result of single-group data variable obtained by the simulation of the laminated structure;
(2) respectively setting initial and cut-off ranges of variable line width W, copper foil thickness T, dielectric loss DF and copper foil roughness R, and setting the variables in the laminated and transmission line structure of ADS simulation software to obtain the simulation result of the variables;
(3) and recording all the variables according to the simulation result in a single-group variable recording mode.
3. A method of fitting a mathematical model of the upward drift of the impedance of a transmission line according to claim 2, characterized in that in step (2):
the line width W is scanned from 4mil to 8mil, and the step length is 2 mil;
the thickness T of the copper foil is from 0.6mil to 1.2mil, and the step length is 0.3 mil;
dielectric loss DF is from 0.004 to 0.02, step length is 0.008;
the roughness R of the copper foil is from 0um to 1um, and the step length is 0.5 um.
4. The method of fitting a mathematical model of the transmission line impedance float of claim 1, wherein the mathematical formula of the impedance float model obtained in step 4 is:
5. the method of fitting a mathematical model of the impedance updrift of a transmission line according to claim 1, further comprising a step 5 of adding the linear variable line length after obtaining the relationship between the impedance updrift and each variable to obtain the impedance updrift of the total link.
6. The method of fitting a mathematical model of the transmission line impedance float of claim 5, wherein the mathematical formula of the impedance float model obtained in step 5 is:
wherein the amount of impedance rise drift DWHOLEThe units are ohm, the line width W unit is mil, the copper thickness T unit is mil, the roughness R unit is um, and the line length L unit is inch.
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| CN108595770B (en) * | 2018-03-28 | 2022-03-25 | 深圳市一博科技股份有限公司 | Mathematical model for accurately fitting plate parameters and fitting method thereof |
| CN108829937B (en) * | 2018-05-24 | 2022-02-18 | 郑州云海信息技术有限公司 | Method for optimizing PCB high-speed signal via hole |
| CN109086546B (en) * | 2018-08-22 | 2021-10-29 | 郑州云海信息技术有限公司 | Signal link signal quality evaluation method, device, equipment and readable storage medium |
| CN109299534B (en) * | 2018-09-20 | 2023-07-25 | 深圳市一博科技股份有限公司 | Modeling method and device for printed circuit board |
| CN110290637B (en) * | 2019-07-30 | 2021-02-02 | 广东浪潮大数据研究有限公司 | Method, system and related assembly for reducing signal crosstalk of PCB (printed circuit board) |
| CN113033140B (en) * | 2021-03-02 | 2023-12-29 | 深圳市一博科技股份有限公司 | Simulation method for accurately obtaining dielectric constant difference of upper and lower layers of PCB wiring |
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