CN106844924B - Method for optimizing PCB microstrip line structure based on response surface method and genetic algorithm - Google Patents
Method for optimizing PCB microstrip line structure based on response surface method and genetic algorithm Download PDFInfo
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Abstract
The invention discloses a method for optimizing PCB microstrip lines by adopting a response surface method-genetic algorithm, which comprises the following steps: the method comprises the steps of establishing an electromagnetic simulation model of the PCB microstrip line based on HFSS software, obtaining return loss and insertion loss of the microstrip line based on the model, designing 29 groups of test calculation simulation by taking the thickness of a substrate, the width of the microstrip line, the thickness of the microstrip line and a dielectric constant as design parameters and the return loss as a target value, fitting the relation between the return loss and an influence factor of the return loss under the condition of 5GHZ obtained by the test by adopting a response surface method, optimizing an obtained fitting function by utilizing the advantage of searching a global optimal solution of a genetic algorithm, and obtaining a combination parameter with the minimum return loss. And HFSS simulation verification is carried out, so that the accuracy of the optimization result is verified, and the method has a guiding effect on the optimization design of other interconnection structures.
Description
Technical Field
The invention relates to the technical field of microelectronic packaging signal integrity, in particular to a method for optimizing a PCB microstrip line structure based on a response surface method and a genetic algorithm.
Background
With the rapid development of large-scale integrated circuits toward high speed, high frequency and high density, the clock frequency can reach hundreds of MHz and even several GHz, the data rate can reach more than Gbps, and even more than tens of thousands of electronic components are integrated on a circuit board. The transmission of signals between devices and between chips cannot be separated from each other, but with the increase of the density of the devices, the density of the interconnection structure is changed to be more compact, and especially, the distance between microstrip lines reaches the um level. Under the conditions of increasing frequency, increasing interconnection structure density and decreasing structure size, the wavelength corresponding to the high-speed pulse signal transmitted by the interconnection structure at the high end of the frequency spectrum is in the same order of magnitude as the size of the interconnection structure, the signal pulse presents obvious fluctuation effect on the interconnection line, and the interconnection line is not a simple connection line and is treated as a multi-conductor transmission line with parasitic effect. Parasitics can cause noise and interference on the transmitted signal, making high speed interconnect signal integrity issues more and more pronounced. The microstrip line is used as a key part in the interconnection structure, and must ensure the correct transmission of current and signals, and under the condition of high speed and high frequency, if the correct transmission of signals in the transmission line cannot be ensured, the performance of the whole system is reduced, so that the analysis of the microstrip line spreading signal integrity problem is necessary.
Due to the complexity of engineering structures, the functions of the structures cannot be directly expressed by using random variables of structural design as functions, so that the functions cannot be directly calculated by using a first-order second moment method, and a BOX (BOX) and Wilson propose a response surface method. The response surface method is also called regression analysis, is a product of combination of a mathematical method and mathematical statistics, and is a fitting design method for expressing variables and targets by approximate functional relations. The method comprises the steps of firstly establishing a plurality of experimental combinations of factors by using experimental methods such as center complex, Box-Behnken design, uniform experimental design and uniform experimental method, obtaining corresponding target values for each experimental combination, then selecting a plurality of experimental combinations of the method establishing factors, then selecting a proper mathematical model to express the factors and target results, then obtaining unknown coefficients by using a least square principle, and finally obtaining a fitting function expression of variables and results. The RSM can accurately approximate the functional relation between the factors and the target value in a certain range through fewer experimental times, is displayed by a simple expression, can simulate a complex response relation in a certain range through selection of a regression model, has excellent robustness and is simple to calculate, and great convenience is brought to later parameter optimization design.
The genetic algorithm is a global optimization algorithm in computational mathematics, and is very suitable for solving the large-scale combinatorial optimization problem. The layout of electronic components belongs to the problem of Traveling Salesmen (TSP) in combinatorial optimization, and in recent years, scholars apply genetic algorithms to the research in the field, so that a better result can be obtained by adopting a standard genetic algorithm for optimization, and the optimization effect is easy to realize.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for optimizing a PCB microstrip line structure by a response surface method-genetic algorithm, which has excellent robustness and simpler calculation, brings great convenience to later parameter optimization design and has ideal calculation results after optimization.
The technical scheme for realizing the purpose of the invention is as follows:
the method for optimizing the PCB microstrip line structure based on the response surface method and the genetic algorithm comprises the steps of firstly designing 29 groups of experimental combinations by using the response surface method, establishing corresponding 29 groups of simulation models according to the 29 groups of experimental parameters, obtaining a functional relation between return loss S11 and key factors under 5GHZ by using the response surface method, carrying out variance analysis on the obtained functional relation, and determining the effectiveness of a regression equation; optimizing the regression equation by using a genetic algorithm, sequentially executing initial population generation, crossing, variation and evolution reversion operation to obtain an optimal combination most beneficial to microstrip line signal transmission, and finally verifying by establishing an HFSS simulation model and manufacturing test sample measurement, wherein the method specifically comprises the following steps of:
step 1: establishing an HFSS microstrip line signal integrity analysis model;
step 2: acquiring return loss and insertion loss of the microstrip line;
and step 3: determining influence factors influencing return loss;
and 4, step 4: establishing a parameter level value of the influencing factor;
and 5: designing 29 groups of required experimental samples by adopting a BOX-Behnken central combined design model;
step 6: obtaining a functional relation between the influence factors and the return loss;
and 7: carrying out variance analysis on the obtained functional relation;
and 8: the correctness of the obtained functional relation is established;
and step 9: generating an initial population in a random mode;
step 10: obtaining a current evolution algebra gen and an optimal fitness value;
step 11: respectively carrying out cross operation on the populations;
step 12: respectively carrying out mutation operation on the populations;
step 13: respectively carrying out evolution reversion on the populations;
step 14: calculating a fitness function value by taking the population as a whole, and selecting the best individual by adopting an optimal storage strategy;
step 15: and judging again after the population is updated, and if the gen value is less than 50 and the num value is more than 0, performing local catastrophe on the population.
In the step 1, the size of the model is that the length of a PCB substrate is 15-20mm, the width is 5-15mm, the height is 5-15mm, the PCB substrate is made of FR4, and the dielectric constant is 4.4; the length of the microstrip line is 15-20mm, the width is 0.1-0.2mm, and the thickness is 0.03-0.04 mm; the reference layer has a thickness of 0.2-0.4 mm.
In the step 2, the frequency range of the return loss and the insertion loss is 1 GHz-5 GHz.
In the step 3, the influencing factors are the thickness of the substrate, the width of the microstrip line, the thickness of the microstrip line and the dielectric constant of the substrate.
In the step 4, the level number of the parameter level value is 3, and the factor number is 4.
In the step 5, 29 groups of experimental samples required by the design of a BOX-Behnken center combination design model are adopted, wherein 24 groups are analysis factors, 5 groups are zero factors, and the parameter level combinations are the same and are used for experimental error estimation.
In the step 6, the relationship between the influence factor and the return loss is analyzed under the condition that the signal frequency is 5 GHZ.
In the step 9, the population size is set to 40.
In the step 10, the genetic algebra is set to 50.
Has the advantages that: the method more accurately approximates the functional relationship between the factors and the target value in a certain range through fewer experimental times, is displayed by a simple expression, can simulate a complex response relationship in a certain range through selection of a regression model, has excellent robustness and simpler calculation, and brings great convenience for later parameter optimization design.
Drawings
FIG. 1 is a return loss plot obtained after simulation of a basic model of the present invention;
FIG. 2 is a return loss plot obtained after simulation of the basic model of the present invention;
FIG. 3 is a graph of mean change of a regression equation after neural network optimization;
FIG. 4 is a graph of the change of the optimal solution of the regression equation after neural network optimization;
FIG. 5 is a graph of the results of HFSS simulations for optimal combinations;
fig. 6 is a graph of experimental verification results of the optimal combination.
Detailed Description
The invention is further illustrated but not limited by the following figures and examples.
Example (b):
the method for optimizing the PCB microstrip line structure based on the response surface method and the genetic algorithm specifically comprises the following steps:
(1) establishing a micro-strip line simulation analysis model of HFSS, wherein the size of a model substrate is shown in table 1;
(2) obtaining the return loss S11 and the insertion loss S21 at the frequency of 1 GHz-5 GHz, as shown in FIGS. 1 and 2;
(3) obtaining the influence factors influencing the microstrip line as follows: a substrate thickness H1, a microstrip line width t, a microstrip line thickness H2, and a substrate dielectric constant E; selecting 3 level values for each factor, wherein the factor level table is shown in table 2;
(4) adopting a BOX-Behnken central combination design model, wherein 29 groups of simulation model horizontal combinations are adopted, wherein 24 groups are analysis factors, and 5 groups are zero factors, namely, the parameter horizontal combinations are the same and are used for experimental error estimation;
(5) according to the calculus knowledge, any function can be approximately represented by a plurality of polynomials in a segmented mode, so in the practical problem, no matter how complex the relation between the variable and the result is, polynomial regression can be used for analyzing and calculating, since the design variable is 4 and the function relation between the variable and the target is nonlinear, and the second-order polynomial model based on the Taylor expansion is selected by combining the experimental sample numbers in the table 2:
(A) in which the constant term alpha is included0Linear term
Linear cross terms
Second order term
αiIs a linear term coefficient; alpha is alphaijIs a linear cross term coefficient; alpha is alphaiiIs a quadratic coefficient; epsilon is a random error; x is a design variable; y is a target value; n is the number of variables.
(6) Performing quadratic multiple regression fitting on the experimental factor combinations and the results in the table 2 to obtain the height (X) of the return loss (Y) to the substrate1) Microstrip line width (X)2) Microstrip line thickness (X)3) Dielectric constant (X)4) The second order polynomial regression equation is:
(7) in order to ensure the credibility of the regression equation, the data in the table 2 is subjected to variance analysis and model significance verification to obtain the relevant evaluation indexes of the regression equation, and the results are shown in the table 3;
(8) the model 'Preb > F' obtained by response surface analysis is less than 0.0001, generally less than 0.05, which means that the term is significant, namely the regression effect of the response surface model is particularly obvious; the coefficient R-Squared of the regression equation is 0.956, which shows that the fitting degree of the regression equation is high; the regression equation adjustment coefficient Adj R-Squared is 0.946, so that the fitting degree of the equation is accurately reflected to be high; the regression equation prediction coefficient Pred R-Squared is 0.912, which shows that the equation prediction accuracy is good; the result coefficients all show that the formula (B) can highly fit the experimental results in the table 2, so that the regression equation is accurate and credible;
(9) optimizing the regression equation by using a genetic algorithm, wherein the algorithm randomly determines a group of initial solutions from a definition domain at first, then searches for the optimal or optimal solution of the target function in the field range, and then searches for the optimal or suboptimal solution of the target function in the field range;
the genetic algorithm optimizes a regression equation and specifically comprises the following steps:
step a: generating an initial population in a random mode;
step b: obtaining a current evolution algebra gen and an optimal fitness value;
step c: respectively carrying out cross operation on the populations;
step d: respectively carrying out mutation operation on the populations;
step e: respectively carrying out evolution reversion on the populations;
step f: calculating a fitness function value by taking the population as a whole, and selecting the best individual by adopting an optimal storage strategy;
step g: judging again after the population is updated, if the gen value is less than 50 and the num value is greater than 0, implementing local catastrophe on the population, and then returning to the step b, otherwise, directly returning to the step b; the maximum genetic algebra of the algorithm is set as 50 generations, and the gen value exceeds 50, the evolution is stopped.
(10) Performing parameter optimization by using a MATLAB genetic algorithm toolbox with the lowest callback loss S11 as a target; the problem mean and the optimal solution change are shown in fig. 3 and 4.
(11) The value range of the influence factor is set according to the parameter table of the factor, the optimal combination is obtained that the PCB substrate H1 is 0.5mm, the microstrip line width is 0.4mm, the microstrip line thickness is 0.075mm, the dielectric constant E is 4.4, and the 5GHZ predicted return loss value is-13.006 dB.
(12) And establishing a corresponding HFSS microstrip line simulation model according to the obtained final parameter combination, wherein a simulation result curve is shown in fig. 5, a return loss value S11 under the condition of 5GHZ is-12.8 dB and is very close to a predicted value of a genetic algorithm, and the effectiveness of the genetic algorithm in optimizing the microstrip line structure is proved.
(13) According to the obtained optimal parameter combination, a test sample of the optimal parameter combination is manufactured, the approximate trend of the measured curve graph and the return loss value S11 which are obtained through measurement are relatively close, and as shown in fig. 6, the accuracy of the HFSS-based microstrip line simulation model is verified to be based on the accuracy of the response surface-genetic algorithm.
TABLE 1 model dimension chart
TABLE 2 factor level table
Table 329 set of parameter combination results
TABLE 4 results of response surface analysis
Claims (3)
1. The method for optimizing the PCB microstrip line structure based on the response surface method and the genetic algorithm is characterized in that 29 groups of experimental combinations are designed by using the response surface method, corresponding 29 groups of simulation models are established according to the 29 groups of experimental parameters, a functional relation between return loss S11 and key factors under 5GHZ is obtained by using the response surface method, variance analysis is carried out on the obtained functional relation, and the effectiveness of a regression equation is determined; optimizing the regression equation by using a genetic algorithm, sequentially executing initial population generation, crossing, variation and evolution reversion operation to obtain an optimal combination most beneficial to microstrip line signal transmission, and finally verifying by establishing an HFSS simulation model and manufacturing test sample measurement, wherein the method specifically comprises the following steps of:
step 1: establishing an HFSS microstrip line signal integrity analysis model;
step 2: acquiring return loss and insertion loss of the microstrip line;
and step 3: determining influence factors influencing return loss;
and 4, step 4: establishing a parameter level value of the influencing factor;
and 5: designing 29 groups of required experimental samples by adopting a BOX-Behnken central combined design model;
step 6: obtaining a functional relation between the influence factors and the return loss;
and 7: carrying out variance analysis on the obtained functional relation;
and 8: the correctness of the obtained functional relation is established;
and step 9: generating an initial population in a random mode;
step 10: obtaining a current evolutionary algebragenAnd an optimal fitness value;
step 11: respectively carrying out cross operation on the populations;
step 12: respectively carrying out mutation operation on the populations;
step 13: respectively carrying out evolution reversion on the populations;
step 14: calculating a fitness function value by taking the population as a whole, and selecting the best individual by adopting an optimal storage strategy;
step 15: judging again after the population is updated, if sogenA value of less than 50 andnumif the value is greater than 0, local catastrophe is carried out on the population;
the size of the model is that the length of the PCB substrate is 15-20mm, the width is 5-15mm, the height is 5-15mm, the PCB substrate material is FR4, and the dielectric constant is 4.4; the length of the microstrip line is 15-20mm, the width is 0.1-0.2mm, and the thickness is 0.03-0.04 mm; the thickness of the reference layer is 0.2-0.4 mm;
in the step 3, the influencing factors are the thickness of the substrate, the width of the microstrip line, the thickness of the microstrip line and the dielectric constant of the substrate;
in the step 5, 29 groups of experimental samples required by the design of a BOX-Behnken central combination design model are adopted, wherein 24 groups are analysis factors, and 5 groups are zero point factors, namely, the parameter level combinations are the same and are used for experimental error estimation;
in the step 2, the frequency ranges of return loss and insertion loss are 1 GHz-5 GHz;
in the step 4, the level number of the parameter level value is 3, and the factor number is 4;
in the step 6, the relationship between the influence factor and the return loss is analyzed under the condition that the signal frequency is 5 GHZ.
2. The method of claim 1, wherein in step 9, the population size is set to 40.
3. The method of claim 1, wherein in step 10, the genetic algebra is set to 50.
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Application publication date: 20170613 Assignee: Guilin Gaopu Electronic Technology Co.,Ltd. Assignor: GUILIN University OF ELECTRONIC TECHNOLOGY Contract record no.: X2022450000412 Denomination of invention: Optimization of PCB Microstrip Line Structure Based on Response Surface Methodology and Genetic Algorithm Granted publication date: 20210223 License type: Common License Record date: 20221227 |
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